Einstein’s special relativity is sometimes popularized with statements like: “moving clocks run slower than stationary clocks and moving rods are length contracted relative to stationary rods”. The problem is that special relativity also states that there can be no absolute motion; so how can one define “moving” and “being stationary”?
The usual answer is that all motion is relative and you can take any inertial frame and declare it the “reference frame” against which all other motions can be measured. This however cannot mean that all other inertial frames, moving relative to this one, must now have slower clocks and contracted rods.
To illustrate this, consider two flashes happening at the same spot, one after the other, say with a ten seconds interval as timed in the reference frame. Two identical vehicles happen to pass in opposite directions, just as the first flash occurs. Assume that the vehicles maintain identical (but opposite) speeds and the occupants measure the distance traveled and the time it took before the second flash was observed (seen). Because light travels at the same speed in all directions in every inertial frame, the observers in the vehicles must get the exact same results.
Now the dilemma: The two vehicles were moving relative to each other and special relativity predicts that their clocks and rods must behave differently due to their relative speed. However, if the vehicles would stop and the occupants compare results, they will find that, within experimental error, they recorded the same distances and the same times.
At ordinary road speeds, this is probably an impractical experiment – the errors will be larger than the effect being looked for. Put the same experiment in space, with ultra fast spacecraft and ultra sensitive equipment, and the results must be identical.
For the scientists out there: how do you explain this apparent paradox in special relativity?
SL: Your Aerospace Watchdog
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David:
Thank you for this.
As you note, there is a wide variety of ways of thinking about such matters.
Christopher
Christopher:
Unfortunately it appears that you are using the terms “sensation” and “perception” in essentially the opposite way to the way I tend to think of them. So I looked them up.
Since we are talking about light and color, here, I chose the “Lighting Design Knowledgebase”. Sensation: (Term of physiology) The immediate result of the stimulation of the sense organs; as distinguished from perception which involves the combination of incoming sensations with contextual information and past experience so that the objects or events from which the stimuli arise are recognised and assigned meaning.
Perception: (Term of psychology) A meaningful impression obtained through the senses and apprehended by the mind. Perception goes beyond plain sensation in that it includes the results of further processing of the sensed stimuli, either conceously or inconceously.
These are actually more closely aligned with my concepts that what I understand your definitions to be, judging by context within your post. Of course I may simply be misunderstanding what you were saying.
To me there are at least three levels, involving increasing amounts of processing within the brain, with increasing degrees of consciousness, or the extent to which the conscious mind is engaged: Sensual stimulus, to sensation, and on to perception.
Just so we may understand each-other’s use of terms.
David
P.S. I looked up sensation and perception in other dictionaries as well, and found nothing to contradict what I have expressed, though most didn’t do it as directly as what I quoted above. However, I certainly found definitions that muddy the waters, even to the point of stating that these two terms are synonyms of each-other.
David: Thank you for this. Christopher
Christopher:
Congratulations on recognizing that the “color space” solids* are three dimensional manifolds, apparently without anyone telling you such. :-)
If you are saying that, conceptually, at least, the color perception space, at the perception level (as opposed to our assigning coordinate like labels to the individual colors, for our own convenience/thinking) is not some “numerically coordinated set”, I may be inclined to agree. However, there is the apparent “fact” that the firing of neurons is equivalent to “numbers”, at least at some level. Really, how are we to distinguish them?
However, the physical space in which we dwell is certainly not any kind of “numerically coordinated set”, until we humans assign such labels to points within it. This is one of the features of the general coordinate system approach used by General Relativity that strongly appeals to me.
The feature being that the phenomena of nature care absolutely nothing for what coordinates we may assign to the points of space and time. They will “merrily” go about “doing their thing”, completely independent of our choice for any such labeling.
Therefore, until the coordinate independent nature of natural phenomena is somehow shown to disagree with nature I consider that any and all theories of natural phenomena must be independent of the assignment of coordinates. In other words, all must be invariant to general coordinate transformations, without having anything other than (unchanging) constants and “dynamical” quantities in their equations.
Incidentally, on the subject of the manifold nature of human color perception, I ran into an article, a while back, that purported to have found that the human perception of shades of gray, in terms of light/dark, was not one dimensional, as one would expect (since we generally consider light/dark, shades of gray, to be able to be characterized by a single parameter). Instead they purported to have found evidence that it is two dimensional. (This makes me wonder whether human perceived color space may be six dimensional, or maybe even more.)
Certainly it is known that our perception of colors does depend upon what other colors are around.
Of course if all we have are “distances” we can get into trouble by assuming a metric relation, when it is possible there is only a norm relation. I’m not sure what the “angle” or “inner product” relations would be, let alone mean, for colors. However, we do know that linear combinations of colors do create other perceived colors for all non-negative linear combinations (meaning linear combinations where the coefficients are all non-negative).
Of course we know that physically realized colors actually lie in a function space (the color spectrum of the pigment/filter/light/whatever), however, our color sense is not so sophisticated as to be able to distinguish this space. What we see is some kind of projection into a space of smaller dimension (almost certainly of finite dimension, but I’m not completely certain that even this can be taken as a given, though I find it highly likely).
Recognizing the possibility that things may not be as simple as we may believe is important to keep in mind as one investigates a given phenomena. However, the nature of science is the continual cycle of: Theory/hypothesis/supposition/idea -> experiment/observation -> analysis/fitting/pondering -> back to theory/hypothesis/supposition/idea. And, as humans, our thinking is usually facilitated by starting with simpler models first. (Besides, Newton’s first “Rule of Reasoning in Philosophy” and Occam’s razor are designed to favor the simpler models.) So, as evidence accumulates, and as investigators actually look outside the present models to see if things are as simple as we expect/assume, then the science advances.
David
* They are solids only because they are three dimensional (in a “filled figure” sense), not because they are solid objects within our physical space, except when someone makes a physical representation of one.
David:
The idea just came to me as I was writing. I have no idea where it came from. I do not recall reading it, but that is perhaps just testimony to my poor memory. I think I can safely say I did not get it from Spivak, nor from Riemann, because I have read them only recently. When I looked it up for you, I seem to recall a Wikipedia article that mentions the difference between Euclidean and Riemannian geometry and may perhaps lead you to a useful reference, but looking again just now I did not find it again.
Yes, I find it helpful as an example of a manifold that conceptually does not start out as a numerically coordinatised set, but only becomes one as a consequence of its “distance”, considered as a function of point pairs. I would be interested to hear of other examples.
Christopher
Christopher:
I’m not so interested in “who first thought of the colour solid as a manifold.” What I was asking was whether the ideas was your own, or if you read it somewhere? If it was your own, then I congratulate you, even if others have thought of it first. If you read it somewhere, then I simply would like a reference. (If I really care to know “who first thought” of it, I’ll try and pursue it through the reference you provide.)
Simply read what I originally asked
And my secondary question
These are the questions I’m seeking answers to.
David
David:
A little grammatical carelessness there, sorry. I meant that the distance in just-noticeable-differences is a metric, within experimental approximation.
I have no idea who first thought of the colour solid as a manifold.
Christopher
All:
Did anyone besides Christopher know that when he was talking about a “colour solid” in previous posts (Re: Re: A different theory of Gravity; considerably edited now, Re3: A different theory of Gravity; considerably edited now, and first introduced in Re: A different theory of Gravity; considerably edited now) he was actually referring to the visual perception “color space” “solid” given in the referenced post Colour space (namely the links http://en.wikipedia.org/wiki/Color_solid, and
http://en.wikipedia.org/wiki/Munsell_color_system)?
If any of you (besides Christopher, of course) recognized this before the referenced Colour space post, I’ll feel exceedingly sheepish at not having recognized this. :-) I was picturing something more like a solid with six, or so, colored sides, like maybe a rounded colored cube (maybe like one of the frames of the Windows “3D FlowerBox” screen saver).
I don’t know, maybe I just, somehow, got on the wrong track, but I don’t see how I was supposed to guess/know that he was referring to something altogether different.
Talk about miscommunication. :-)
David
Christopher:
This is not at all what I meant when I asked
I was referring to the idea of using a “color space” manifold as an example of a manifold. I was most certainly not asking about whose idea it was to map perceived colors into a “color solid”. (I know essentially all that you have expressed in your latest post.)
Incidentally, it would make absolutely no sense to talk about “distance” between colors using some human physical length scale: The units are not compatible (unless someone finds a “fundamental conversion constant” of some kind). Now, while this “color space” manifold is not related to physical space (like spacetime, or some such) that doesn’t preclude it from being some “natural space” (like some “perception space”, or some part of some “cognitive space”). And just because it doesn’t have to do with some physical space in which objects we can touch dwell doesn’t make it “metaphorical”. (Though its mapping into a solid object within our three dimensional [approximately] Euclidean space most certainly is metaphorical [baring some “fundamental conversion constant” of some kind].)
By the way, did you simply stumble over terminology, or do you not quite recognize the distinction between a manifold (even one with a metric) and a metric itself? You say (emphasis added)
It certainly is a manifold (there is an essentially continuous neighborhood of points, and the set is open). It can, possibly, be considered to be a manifold with a norm, and possibly even a metric (one would have to determine whether there is an “angle” or “inner product” measure, even though there certainly does appear to be a “distance” measure). However, it most certainly is not a metric, itself, by any stretch of my imagination, at least. :-)
Of course, if “This [the ‘metaphorical’ nature of a “color space” manifold] is the basis of my story that some geometries are naturally geometrical and others are only metaphorically so”, then why have I been getting the impression that you lump all non-uniformly curved manifolds, including “physical space” type manifolds into this “metaphorical” (as opposed to “geometrical”) classification? I have no problem considering some manifolds as non-physical, even “metaphorical”. I can even handle presenting (or even believing, or allowing others that option) that the four dimensional spacetime is simply a construct (call it “metaphorical” if you want, but I would not present it with this bias, at least not to students), it helps avoid the push-back from those that simply must believe there is three-space that changes over some separate thing called “time”. (It appears, at least, to help smooth the transition.)
However, I do believe one should keep in mind that whatever constructs we as humans may employ, they may have little to do with how nature actually works. The best we can ever do is find no conflict between the workings of nature and our constructs. :-) (Again, this is in spite of the fact that I am, at heart, an ontologist: I want to know more than just “the appearances”; I want to know “what’s really going on under the hood”.)
This is why I always return to the need for experimental/observational correspondence with nature.* Anything that is more or less than this is not science, in my opinion.
David
* Any construct that succeeds at the correspondence test is perfectly viable. Furthermore, if more than one such theory exist that never differ in their predictions of observations or the results of experiments, then the only difference is “interpretation”. In which case the choice is simply a matter of preference, though it is usually informed by both Newton’s first “Rule of Reasoning in Philosophy” and Occam’s razor.
David:
I am no expert on the colour solid. The Wikipedia tells me that it was invented by http://en.wikipedia.org/wiki/Philipp_Otto_Runge, who died in 1810, after long correspondence with Goethe. Riemann was born in 1826.
Colour is not as simple as one might assume, not as simple as I have an idea that Newton assumed? At the risk of being mistaken, and emphasising that I am no expert, I recall that the sensorium continuously constructs a temporary “reference white” as a kind of average of the whole visual field, and then takes ratios of patches of colour to the reference. A sort of projective geometry? This was partly understood by Goethe, a quite remarkable fact of history, I seem to recall. Even today it is not quite readily known perhaps.
The sensation of colour comes from light stimulation of patches of the retina, which has cells which respectively contain just one of four genetically determined visual pigments, white, red, blue, and green. It seems that various linear operations are performed by the network of nerve cells of the retina to produce colour signals for propagation to the brain. The normal four pigment responses are reduced to a three dimensional manifold by the ratio business, I think. Colour-blind people have defects of pigment production, and so they have radically abnormal colour solids, not just minor variations.
The sensations of colour exemplify the subjective qualia of experience in the mode of presentational immediacy. For example, one usually would not say that the note A above middle C is at a higher or lower pitch than yellow. “Secondary quality” was recognised in this sense by Galileo, and discussed further by Locke. According to one view, that I am rather inclined to accept, perception is a thing different from sensation, which is always consciously experienced. Perception is about behavioural response, is in a sense quite objective, is not necessarily immediate, and can be consciously or unconsciously experienced. But the sensation of colour is purely subjective and immediately conscious. (This is just one of the senses of the word conscious, that is relevant to the present context.) In general, one cannot talk or think oneself into seeing something as having a certain colour; it is just immediately present to one. Nevertheless one can make behavioural responses when presented with comparisons, and many repetitions lead to fairly good accuracy. The results have many practical industrial applications. I would not slight animal perception without some careful evidence; different species have different powers of colour perception; of course we do not know what sensations non-human animals have. I think the industrial usefulness of the colour solid depends on its being rather well reproducible and the nearly the same for all colour-perception-normal people.
That there are four pigments places very strict constraints on what can be sensed and what can be perceived, of course. The colours are subjective, and can only be made objective by way of repeated comparisons and so forth. Of course one can easily assign number coordinates to mixtures of monochromatic light beams; by themselves light beams do not have colour in the strict sense of the word. But there is no proper way to assign number coordinates to subjective colours apart from various methods of comparison, which in effect have to presented as a kind of metric.
It seems to me that the notion of distance between colours is therefore not naturally geometrical in the sense of being a measurement of a natural space. For example, I don’t know what it might mean to say that red is four inches to the left of green. The notion of distance between colours is metaphorically geometrical in the sense of being a measurement of a metaphorical space. But I think it comes, within the range of experimental approximation, as you say, to be a metric in the sense that Riemann meant.
This is the basis of my story that some geometries are naturally geometrical and others are only metaphorically so. I think it is a distinction worth making.
Christopher
Christopher:
Ah! Why didn’t you say so when I first mentioned that I wasn’t sure what you were referring to?!?
Yes, I have often thought that one should be able to determine an approximation to a “color metric” based upon “just-noticeable-differences” in color within such color spaces! So, yes, this is, indeed, an example of a manifold, though trying to get down to anything like an “exact” “differential” “color metric” form is probably nigh unto impossible, due to the crudity of human perception. (Actually, really good attempts at such fine level distinctions will probably tell us more about variations between humans, than any “intrinsic” “color manifold”.)
Your the first person (besides myself) that I have experienced that has had such an idea. Was the idea yours, or did you read about this idea in one of Spivak’s volumes? Was the idea Spivak’s, or Riemann’s, or someone-else’s?
So, yes, I take it back! :-) The color solids are examples of different coordinatizations of a “color space” manifold.
However, if this idea wasn’t your own, did you find this idea helpful in understanding manifolds? Based upon the way you rail against curved spaces as “not being ‘spaces'” (as you consider ‘spaces’) and not being “geometries”, either—even though their “inventor”, Riemann, considered them so to be—I have to wonder whether you’ve “got it”.
So many questions now that I finally have a picture of what you’ve been talking about! See how easy it is to have misunderstandings when terms are not properly defined, and how easy it is to clear such misunderstandings up?!?
I only wish you had expressed this long ago, instead of, apparently, assuming that I “knew what you meant”! Now we can talk on the same page, instead of “passed” each-other!
Whew!
David
David:
When I wrote of the colour solid, I had in mind things such as you will see at http://en.wikipedia.org/wiki/Color_solid, and at
http://en.wikipedia.org/wiki/Munsell_color_system.
Christopher
Christopher:
(In what follows, and from now on, generally, I will simply use the terms metric, inner product, Riemannian, etc. to include both the strictly positive definite forms that mathematicians restrict such to and to the indefinite non-degenerate forms we physicists apply such to. So I hope this will not lead to any confusion. However, since you are so very fond of Minkowski space, I don’t think you’ll object.)
On the “colour[sic] solid”, sou said
Actually, the oriented volume element has nothing to do with a manifold, and is even independent of a metric (though if one has a metric one can use it to “normalize” the volume element). Furthermore, since I guessed (apparently correctly, judging by this paragraph) that you were thinking of the “colour[sic] solid” as an infinitesimal object, I was thinking of the infinitesimal oriented volume element. (A finite oriented volume element is not well defined in any finite sense, since it can be highly deformed without changing its fundamental properties. In addition, if the space is curved, there are even worse ambiguities, and even, potentially, inconsistencies in trying to define a finite oriented volume element.)
In terms of an infinitesimal “space” (your “just-noticeable-differences”, though even smaller) the infinitesimal oriented volume element with metric (what you apparently refer to as the “colour[sic] solid”) is most closely related to the tangent space associated with a single point of the manifold.* It is a vector space (actually a metric space, when we have a metric), and is an infinite open flat manifold (if you wish). So it is just as much “geometrical” as any other infinite open flat space (especially any such that have a metric of similar character). (Incidentally, you do recognize that a metric provides far more than just “distances”, but inner products and thus angles as well?)
In this vector space reside things like velocities, momentum, etc. Hardly just “infinitesimal” quantities. In fact the whole set of tensors, like the curvature tensor, and the mass-energy-momentum-stress tensor reside in this tangent space (or, perhaps more properly, within product spaces of such). Again, not just infinitesimal quantities.
It should be quite obvious that this tangent space is just as “geometrical” as any other vector space (with or without a metric). (Of course there are also the dual spaces of these tangent spaces. These dual spaces are also vector spaces. However, if one has a metric one can map the dual space right back one-to-one and onto the tangent space.)
However, though this tangent space contains arbitrarily large vector and tensor quantities, in general (unless one can identify the manifold with its tangent space[s]) the tangent space can only contain infinitesimal translation (“distance”) vectors, since finite translations cary a point within the manifold to a point associated with a different tangent space. (One is permitted to map all the individual tangent spaces into a single vector space of the same character. However, this will involve transforming all the individual metrics into a single metric [which, in general, requires a non-coordinate transformation]. Besides, one really gains nothing, and one must be careful not to fall prey to the temptation to directly compare vectors associated with different points on the manifold, since such can only be compared via “parallel transport” along a path between the points.)
If you have read Riemann’s treatise on geometry within Spovak’s book, I would hope that he would have been able to help you understand that there is at least as much “geometry” about curved manifolds as there are with (flat) vector spaces. After all, the latter are simply special cases of the former.
On the other hand, if one is insistent that translations be contained within the transformation group of the points (and even other objects) within a manifold, then one will be greatly restricting the possible manifolds. (As the “Relativity without tears” paper points out, constant curvature manifolds are certainly allowed.)
I could go on (and on) about how such a restriction is not called for by nature/observation**, and even how particle physicists are questioning the physicality of the Poincaré group. In fact, some are questioning whether there is any way to incorporate gravity using such. (And even when the Poincaré group is used, now days, it is “gauged”, so it is no longer the global symmetry involved in the previous paragraph, but only a local form, quite analogous to the tangent spaces of curved manifolds.)
However, getting back to my comment that lead to our discussion of the appropriateness (or not) of using a “colour[sic] solid” as an illustration of “manifolds”. While the “colour[sic] solid” may be illustrative of the tangent space associated with a point on a manifold (though the fact that you apparently thought it was restricted to “just-noticeable-differences” suggests it’s even rather poor at that), I would rather use some nice topological surface, or even the surface of an apple (as Misner, Throrne, and Wheeler did—which actually is even more clever when one considers the association between apples and Newton’s theory of universal gravitation).
Oh, there’s so much more here, but I’m sure this is plenty for now.
David
* Actually, the infinitesimal oriented volume element (with or without a metric) can be said to generate the tangent space.
** After all, why should we conflate the concept of position with that of vectors? How many students get confused at how position “vectors” “must” be anchored at an “origin”, while other vectors are free to be unanchored? Or other such issues?
David:
Thank you for this.
Christopher
Christopher:
On the matter of
First, refer to what I quoted from Feynman about always doubting.
Second, I hope you recognize that there can be no such thing as “Oh, look, I have found the way to check this theory once and for all!” At least not in the affirmative, since there is simply no way to “prove” a theory, unlike proving theorems in mathematics*: One can only “prove” a theory incorrect (inconsistent with reality/nature); one can only invalidate (falsify) a theory.
Third, there’s absolutely nothing to keep anyone from testing anything, via observations and/or experiments, concerning any theory any human being has or ever will come up with. Yes, there are some things within General Relativity (GR) for which “the results are assumed by the formalism”. However, such does not make any “desirable empirical checks logically meaningless”. After all, the experiments are not governed by the theory, only by nature, and the ingenuity of the experimenter/observer.
For instance, GR “assumes” the equivalence of inertial and gravitational mass**, but that hasn’t prevented experiments from being run to test this assumption.
Now, as I understand the Whitehead/Logunov concept, at least, they suggest, at least, that there is some underlying Minkowski space (flat spacetime) underlying the “observable” (“effective”) “metric-field” that GR want’s to call the actual “metric”. Fair enough. The only question is whether there is some experiment and/or observation that can distinguish between the predictions of such a theory and those of GR. It’s as simple and as complicated as that! :-)
If the underlying Minkowski space is unobservable, as is the case with the self consistent spin-2 (tensor) “particle”/”field” theory of Feynman (and I think Steven Weinberg as well***), then even if one considers such to differ from GR at some “gut”/”fundamental”/conceptual/ontological level, it is completely equivalent in the only area that truly matters: observationally and experimentally. (And I say this as an unabashed ontologist!) Anything else is a matter of interpretation/preference. (Though both Newton’s first “Rule of Reasoning in Philosophy” and Occam’s razor will argue that if one cannot observe something, or any consequence thereof [such as the presence of some unobservable Minkowski space/metric] then one really shouldn’t keep it around.)
As for the charge of “precariousness” you apparently lay upon GR, to which you say you are referring to its “reliance on things that are not easily checked”. I say “guilty as charged”. (Even more so with regard to how little wiggle room the theory gives itself.) Of course all human theories have had this “issue”. We as humans have to start somewhere, after all.
One of the “biggies”, in my opinion, is the “assumption” that spacetime is a continuum. How can we check that it’s not simply some discreet “space” that’s just too finely divided for us to tell the difference?
Ah, but that’s another one of those things I said can, at least in principle, be tested by any sufficiently ingenious experimenter/observer! True, at this point we can only say that any lack of continuity has to be below some threshold, that any discreetness must be below some size. This is no different than bounds upon how massive the photon or the “graviton” can be! (Incidentally, last time I checked, the constraint on the graviton’s mass was tighter than that of the photon.)
If the theory is “precarious” in that it depends on something that’s not absolutely “nailed down solid”, then that’s an opportunity for an ingenious experimentalist and/or observer! Have at it! (See what Feynman has to say about the potential for excitement physicists can look forward to if any of our great theories are falsified! What fun!)
As for the “ambiguous and so untestable” charge that is apparently lain down by Logunov, I’ll have to check into what he is actually accusing GR of before I make a judgement.
David
* Even theorems in mathematics are only “if … then …” statements (with the best, in my opinion, being “if and only if … then …” statements, which are really only two coupled “if … then …” statements). So if their proposition is not satisfied that you have no guarantee that the result will hold. (Of course the “if and only if … then …” cases go further to guarantee that the result does not hold, in such case.)
** Actually it only “requires” the constant ratio of what one could measure of such, but that’s beside the point.
*** I have found this theory expressed with Misner, Thorne, and Wheeler’s Gravitation, with references to a number of Feynman’s papers/writings. It only makes sense that two great particle physicists would come up with a particle/field theoretical explanation for gravity. What’s really interesting is that when they try to make it completely self consistent they find that the original Minkowski metric of the theory is no longer present in any of the equations, including the equations of motion of the matter. So the Minkowski metric/space is no longer observable! And what they are left with are equations that are exactly equivalent to GR! There is nothing that is observationally different. Hence their statements that it is “the same as GR” (even though, at a conceptual level, at an ontological level, it does differ from GR).
I am new,I hope it is ok to reply.This intense reflexion make me do some introspection and it will not end,now.I was honestly mad about some part and also strongly happy about other.This bring to my rigid undiplomatic hard head,a question?I love when it is good for me.I say love.I hate what could be wrong for my believe.It is to early for anwser my self,and may be I am not directly to the topic it self,surely I grasp the depth.beautiful ,and thank you ,phil
David.
Thank you for this.
Christopher
Christopher:
You ended with
Actually, read Feynman:
(1979 Omni magazine interview with Feynman. I have it in “The Smartest Man in the World” chapter of Feynman’s “The Pleasure of Finding Things Out.”)
Another good quote pertains to the question “What is Science?” (the “What is Science?” chapter of Feynman’s “The Pleasure of Finding Things Out.”)
Of course this is not to say that one should neglect the accumulated “race experience from the past.” It’s that one should always be questioning and reproducing, hopefully with ever increasing precision, the experiments and observations of the past. In addition, one should always be coming up with new additional observations and experiments in order to better test “the way things really are.” And, a fortiori, one should not simply accept the explanations handed down, but should always be looking for ways to test such.
So, I really don’t see your accusations concerning “the orthodoxy”, etc. Perhaps you are a victim of the The Galileo Complex (see Renaisauce’s blog), at least in a vicarious sense. (It would probably do you well to read that post, along with the accompanying comments.) Such is not science in any way that I know of such. (Of course that’s not to say that you, and others, may not have experienced small minded pseudo-science types. However, I would be very surprised if they were “good scientists”. [Of course one could use such as a measure of “good scientist”.])
However, regarding the last sentence of your comment
I would say that honing/educating/informing/developing our physical intuition will play a huge part in this: Namely careful observations and experiments. Remember the ultimate arbiter is Nature. As to whether the relevant explanation (theory) to be attached to such will jibe with “common sense”, in almost any sense of the term, is a completely open question. (Again see Feynman’s Omni interview. I think he has some very good insight into whether or not such may ever be the case: In short, he suggests he really has no idea one way or the other, based upon his experience.)
Wasn’t it Einstein that said something to the effect that “it’s amazing that the Universe is even comprehensible by the human mind.” So why should we insist that it make “common sense”? It’s really up to us to change our thinking to conform with “the way things really are,” whatever that might be. To hone/educate/inform/develop our physical intuition.
David
Christopher:
Within the context of blogs such as this I will always be using “technical terminology”. We are, after all, presumably, talking about technical subjects (science and mathematics). We are, after all, on a science blog. I can play wonderful word games, but I do not engage in such in contexts such as this because it gets in the way of understanding, and I thought, after all, that understanding was the intent of such exchanges within this context.
On the matter of “common sense”: Yes, we are using slightly divergent definitions. (However, the difference is probably more in the connotational sense.)
First, “common sense”, as it is commonly used in “common language” is usually not so common. Of course, the common use of the term has much less to do with anything more than a passing glance at Aristotle’s original intent.
Second, the Aristotelean, more physical, sense of the term, is now more closely expressed with the term “physical intuition”, at least within the realm of science, especially physics (which is what I had thought we were discussing).
Third, almost anyone with a good understanding of Newtonian physics (along with the likes of Galilean relativity), let alone with anything beyond, will tend to consider Aristotle’s physical intuition to be rather lacking. This is not to say that he didn’t think deeply on such matters, or wasn’t a great philosopher, or anything like that. The problem is that he didn’t even do some of the simplest experiments that he could certainly have done in order to test his ideas—to hone/inform/develop his physical intuition!
Aristotle appears to have acted as if human thought “trumped” all. Science very early on placed the power of ultimate arbitration in the “hands” of Nature. As I’ve said many times before, Nature is the ultimate arbiter: The correspondence with experimental results and observations is what ultimately determines whether a theory is consistent with Nature. It has nothing at all to do with how beautiful we, as humans, may think a given idea is, or how much “common sense” we think the idea makes. If it disagrees with observations and/or experiments then it doesn’t pertain to the real world.
So, yes, in terms of the common usage, I will agree that “to depart radically from common sense is to be crazy.” Furthermore, if you substitute the term “physical intuition” in place of “common sense” in statements like
I, and probably all scientists, will agree with you whole heartedly!
On the other hand, within the realm of science, especially physics, as I’ve said time and time again, it doesn’t matter much at all whether we think a given theory makes “common sense”. What matters is whether it matches Nature, via observation and experiment. (Once you have that, with more than one competing theory, all else is primarily a matter of preference. Of course this is usually tempered by Newton’s first “Rule of Reasoning in Philosophy”: “We are to admit no more causes of natural things than such as are both true and sufficient to explain their appearances.” This is in correspondence with Occam’s razor: “entities should not be multiplied beyond necessity”. )
If you will keep these things in mind in our discussions, then we should be productive. Forget them, and misunderstanding will almost certainly ensue.
Furthermore, on the matter of the insistence “upon very definite definitions”. Philosophers and lawyers often spend a very large portion of their writing to creating “very definite definitions” for the terms (words and phrases) they use. The only difference between this and the use of “very definite definitions” within mathematics and science is that writers within these fields are usually building upon a vast body of work, and can, therefore, attain such “very definite definitions” by way of reference.
Unfortunately, until I know exactly what body of such “very definite definitions” you are intimately familiar with, I can most certainly make mistakes about such. So, please, if you suspect I’m using a “technical term” in a way that appears to conflict with a “very definite definition” that you may have, then just ask what my definition is. OK? And I’ll try to do the same.
But no “word games” or intentional conflation of technical vs. “ordinary” language. Such will most certainly not serve the intent of blogs such as this.
David
Hi, Miguel AF Sanjuan.
Thank you for this.
As I said, it will take me some time to digest your paper.
Christopher
The problem with “common sense” in physics is that our common experiences do not include relative velocities that are significant compared to light.
They also do not include regimes where particles and waves are indistinguishable.
To me, common sense includes accepting that our intuitions are shaped by our experiences, which means that we need to be prepared to re-tune our intuitions based on observations in unfamiliar regimes.
Time-dilation and length contraction would be everyday observations and thus fit with our notion of common sense if we lived in a world where cars moved at a significant fraction of the speed of light.
Tunneling would fit our common sense notions if trains could appear on the opposite sides of mountains rather than electrons on opposite sides of potential barriers.
The issue here may be that some people prefer phenomenological explanations while others prefer mathematical ones.
I think that we haven’t achieved a full physical understanding until we have both phenomenological and mathematical explanations.
For instance, Feynman diagrams are a more phenomenological approach to quantum electrodynamics, while Schwinger (and Tomonaga, independently) produced the same theory from equations. Dyson had the genius to see how the two approaches were equivalent, but didn’t share the Nobel Prize because of the three-person limit.
This is described in some detail in my book Physics: Decade by Decade (Twentieth Century Science).
Fred Bortz — Science and technology books for young readers (www.fredbortz.com) and Science book reviews (www.scienceshelf.com)
Hi Christopher,
I am delighted to read your comment:
“My interest here is to develop my common sense to better understand the basic principles of physics.”
Many times I have also experienced your sentence:
“For me, to depart radically from common sense is to be crazy.”
This is precisely one of the guiding principles I also keep. It is true that “common sense” uses to be not well understood by certain people, but I would say I share basically the way you describe it.
Miguel AF Sanjuan
David:
Perhaps I may reply with relevance to the present blog.
I am mostly not joking here, but of course I make jokes from time to time. For me, in this rather philosophical vein, all use of language is playing word games; for me, this is a technical term of philosophy. So by not putting quotation marks on it, perhaps I have committed the very error that I am complaining about: using language in a way that does not make it clear whether I am using ordinary language or technical terminology.
You write:
“Of course we don’t use “common sense” to attach meaning (again see any of a number of coglanglab’s blog posts). However, we do use context (both locally, within the message, whether spoken or written, and more globally, like what is the audience, branch of “knowledge”, overall subjects, etc.), and past experience/history/culture/upbringing/etc. (of course this can be considered to be an even larger “context”, but it differs more from individual to individual).”
To me it seems we are using the term ‘common sense’ differently. For me, to depart radically from common sense is to be crazy. That is obviously not the usage you mean here. For me, the various guides you mention (“context … experience”) are guides to common sense, not opposed to it. For me, common sense is the psychological faculty that uses the guides you mention, with experience as the ultimate criterion.
You seem, however, at least to some extent, to oppose or slight the use of common sense: “Of course we don’t use “common sense” to attach meaning”, as if you see common sense as some kind of limited or even perhaps slightly stupid way of thinking. You write: “science and mathematics insist upon very definite definitions, rather than “common language” with some expectation that meaning will be derived via “common sense”.”
The term arose, I recall, as a technical term in the writings of Aristotle, in Greek (in the De Anima), and then was used in translation in Latin, and is now used also in English. For him, it was a faculty of experience that combined the raw senses, sight, hearing, touch, smell, taste, a basic engine of perception and consciousness, in a sense a physiological conception. For us today, the term has drifted to mean a general psychological power of deliberation and speculation, and Aristotle’s reference to raw sensation is usually forgotten. For me, common sense is on the lookout for various ways of attaching meaning, checking out when ordinary language or technical terminology is intended, on guard against muddles that can arise when the different senses of words are conflated, and when allegory and category are confounded. Common sense is not rigid nor stupid, but evolves adaptively, as the boundaries of knowledge are extended.
My interest here is to develop my common sense to better understand the basic principles of physics.
I am uncomfortable when common sense is slighted. It is part of my worry about the “general theory of relativity” that its keenest advocates sometimes seem to have no such discomfort.
I think we have a long way to go before we understand the extremities of nature, the grand scheme of cosmology. Some scientists argue that we need to think of important contributions from the effects of “dark matter” and “dark energy”. This seems to me to require us to have a very keen sense of doubt about all our theories of nature on a grand scale. I think common sense has a part to play here.
Christopher
Hi, Michael AF Sanjuan.
Thank you for the useful guidance to the Yaglom translation. I will try to get hold of a copy.
Also for the the reference to your own paper, which I have now downloaded from the internet. It will take me some time to understand it.
I have read the Bacry and Lévy-Leblond paper and am looking for ways to improve my understanding of it. I expect these references will be some of them.
Regards,
Christopher
Christopher:
You are the one that started arguing linguistics, particularly the use and definition of words, and whether “common senses/usage” should be the determiner, as opposed to the scientific and mathematical necessity of creating and adhering to finer distinctions.
You know that misunderstanding thing? That’s why mathematics and science define finer distinctions, so all can understand together.
David
Concerning the nine Cayley-Klein geometries and the table you refer to, it appears in the book by Yaglom I.M., A simple non-Euclidean geometry and its physical basis: an elementary account of Galilean geometry and the Galilean principle of relativity, Heidelberg Science Library, translated from the Russian by A. Shenitzer, with the editorial assistance of B. Gordon, Springer-Verlag, New York – Heidelberg, 1979.
The idea of the possible kinematics is due to Bacry H., Lévy-Leblond J., Possible kinematics, J. Math. Phys. 9 (1968), 1605-1614.
And the connection of the kinematic groups and the Cayley-Klein geometries was done by Sanjuan M.A.F., Group contraction and the nine Cayley-Klein geometries, Internat. J. Theoret. Phys. 23 (1984), 1-14.
Miguel AF Sanjuan
David:
This is perhaps getting too far off the track.
Christopher
David:
I think you are charging me with inconsistency? Surely you will have guessed by now that I would lay both charges, ambiguity and precariousness, against the “general theory of relativity”? I will claim that it is in some respects ambiguous and so untestable, and that it makes some desirable empirical checks logically meaningless because the results are assumed by the formalism. By precariousness I mean reliance on things that are not easily checked. One likes to be free to check a theory in diverse ways that one does not at first anticipate, and one (at least those of us who are not perfect) cannot be sure that one’s logic is so perfect that one can say “Oh, look, I have found the way to check this theory once and for all!”
Really I am criticising extremism in minimalist operationalist localist ideology in general.
But let’s not get distracted by the question of what is my position, because I am bit of a dill, and my position doesn’t matter. What matters here is what Logunov argues, I think.
Christopher
David:
Spivak gives translations of original papers and lectures by Gauss and Riemann. I haven’t read all five volumes. Other suitably helpful texts on Cartan geometry not readily found by me.
I don’t see why the colour solid would not pass muster as a manifold with boundary, mapped into an oriented volume element if you like? The oriented volume element is geometrical, I would say. The colour solid in abstracto has, as I understand it, a nice non-geometrical metric, namely the “distance” in just-noticeable-differences; I think that is pretty close to being a metric, at least for smallish “distances”?
Christopher
Christopher:
By the way, when you say “I have been reading Spivak on Riemann” are you referring to Spivak’s five volume epic “A Comprehensive Introduction to Differential Geometry”. If so, my hat’s off to you. :-) (Actually, I hadn’t heard of it, let alone seen it, so I don’t really know how large it is in reality, only by reputation as I tried to find out what you were referring to.)
Additionally, I don’t know what “space” your “colour solid” is trying to illustrate. I know that I wouldn’t use a “colour solid” as an illustration of a manifold, though I might us it as an illustration of an oriented volume element.
David
Christopher:
I most certainly wasn’t at all trying to suggest that the PPN formalism in any way “remove[s] the ambiguity of the GTR.” (I’m assuming GTR stands for General Theory of Relativity, also often referred to simply as General Relativity.) Other than the necessary (in my mind, at least) ambiguity of general coordinate transformations (and, hence, coordinate systems), and the often neglected cosmological term, I have never suggested that there was/is any ambiguity in GTR.
In fact, I used the absence of unfixed parameters in the PPN formalism when applied to GTR as an illustration of the lack of ambiguity.
As a point of fact, it appears that you understand the extent to which GTR has little if any “wiggle room” (ambiguity, the ability “to make suitable arbitrary supplementary assumptions”, etc.) when you posted
Absolutely, the GTR is like “walking on a tightrope without a net” because if “some assumption is wrong” there are no tweak-able parameters that can be used to fit observations, no ability “to make suitable arbitrary supplementary assumptions” that may solve a resultant disagreement with experiment.
Actually, I notice that you made the “precarious” position statement after you made to “ambiguity” accusation. So what actually is your position?
It’s hard to tell for certain from the very short snippets you provided in your “chapter and verse” post of Logunov’s “ambiguity” accusations aimed at the GTR, but it appears that he, at least, thinks there’s a true “ambiguity”. Then why is the “orthodoxy’s” “minimalist approach” with the GTR so “precarious”?
I just have to wonder. :-)
David
Christopher:
Thanks for the “chapter and verse”. :-)
I’ll have to see what I can do about obtaining copies of at least some of these in order to better ascertain what “ambiguity” Logunov is referring to.
David
Christopher:
You say
Of course we don’t use “common sense” to attach meaning (again see any of a number of coglanglab’s blog posts). However, we do use context (both locally, within the message, whether spoken or written, and more globally, like what is the audience, branch of “knowledge”, overall subjects, etc.), and past experience/history/culture/upbringing/etc. (of course this can be considered to be an even larger “context”, but it differs more from individual to individual).
You are correct that “word games can confuse.” However, I’m most certainly not trying to play any word games. Are you? Then who?
You then state
Am I “playing” with multiple meanings of the word “rigidity”? No. I’m only using it in terms of the extent to which an object is or is not deformable (not rigid, in an absolute sense; as opposed to some relative sense like saying a solid is essentially rigid, or can be fairly well approximated as such, while a liquid is far from rigid, at least the kinds of liquids people are commonly familiar with). Of course if this is not the use of the term you meant by your assertion I quoted, to wit
Then who’s playing “word games”?
Yes, when appropriate distinctions are “inappropriately forgotten, then inappropriate confusion arises.” Of course this is another reason why science and mathematics insist upon very definite definitions, rather than “common language” with some expectation that meaning will be derived via “common sense”.
Unfortunately, unless you were making a joke, in which case I apologize for not getting it, this post appears to be a case of talking around a point in order to avoid such.
David
David:
When we speak we don’t immediately define each word of our utterance. We use common sense to attach meaning to it. But word games can confuse. You make it clear that you know this by writing “… the relationship between ‘rigidity’ and …”. You are making it clear that several senses of the word rigidity are in play, and that the distinction matters. When it is inappropriately forgotten, then inappropriate confusion arises.
Christopher
Christopher:
Unfortunately, I, and most scientists, don’t find “the viewpoint of common language” to be a great guide toward understanding—especially deep understanding. The problem is that “common language” is so imprecise (“fuzzy”). (See, for instance, a number of linguistic posts by coglanglab.) At best, “common language” provides a very general guide and stepping off point.
Yes, “the mathematical generalisations are metaphoric technical extensions of but not the same as the common language usage.” However, the specificity required by mathematics and science requires such. I, and I’m sure other scientists, apologize for the potential for confusion this can cause for those that don’t take the time to actually determine the definitions being used. (I usually try to make any assumptions I use as explicit as possible, but I’m sure I’m not perfect at that, and I certainly do take shortcuts in internet communication, since I’m not taking the time and space to write an entire dissertation.) So yes, “this distinction” most certainly “matters”—scientific and mathematical languages are far more precise than “common language usage”, and, of necessity, make far finer distinctions.
I agree that
However, this is only true provided 1) the elastic limit of the object has not been exceeded, and 2) the forces acting on the “rigid” object are identical when at rest in both its original and ending positions (not just net “force”, since this is of necessity zero since the object is specified to be at rest in both locations, but things like tidal “forces”).
On the other hand, if you truly believe
Then your physical intuition most certainly needs some refinement. :-) Are you unaware of the relationship between “rigidity” and the speed of sound within a material? Are you aware of iceberg ringing? What do you think is the speed of sound within ice? What do you think is the maximum speed of sound?
Thank you David.
Chapter and verse:
1.
A. Logunov’s Lectures in Relativity and Gravitation: A Modern Look; Chapter 3, Relativistic Theory of Gravitation; section 3.5 On ambiguity of GTR [“general theory of relativity”] Predictions for Gravitational Effects and Fundamentals of RTG [Relativistic Theory of Gravitation], pages 232-240.
At page 232: “… ambiguity is inherent in GTR and concerns all gravitational effects. We will illustrate this by the example of the effect of gravitational delay of a radio signal in the field of a static centrally symmetrical body of mass M.”
2.
A.A. Logunov’s The Theory of Gravity; Chapter 12, Gravitational effects in the Solar system; at page 159: “This is actually the essence of the ambiguity in predictions of gravitational effects in GRT. [Logunov’s bold type]”
3.
A. Logunov and M. Mestvirishvili’s The Relativistic Theory of Gravitation; Chapter 18, RTG and Solar-System Gravitational Experiments. Ambiguities in the Predictions of GR; section 18.9, GR and Gravitational Effects in the Solar System. Conclusion. At page 165: “Summing up, we can say the GR is incapable, no matter what the advocates of this ideology may say, of making definite predictions concerning the geometry of the Riemann space-time and gravitational effects.”
I didn’t find this question about empirical checks examined in A.A. Logunov’s Relativistic Theory of Gravity.
Christopher
David:
I didn’t mean that the PPN formalism is ambiguous. I meant that its use doesn’t remove the ambiguity of the GTR.
Christopher
Thank you David.
I find the “Possible Kinematics” article very interesting and physically clarifying. I am concerned to avoid not abstraction in general, but inappropriate abstraction.
Christopher
David:
Thank you for this.
My concern is that it should be without tears for a schoolboy when well presented. The tears come not so much from the intrinsic difficulties, but more from the obscurantist habits of presentation. Aristotle could have hit on the principle that causal agency must propagate at a finite maximum speed for some observer. Using Euclid, Alfred the Great with his timers could have deduced that it was a universally constant maximum speed, and he would have had “special” relativity to bequeath to Galileo and Newton. No tears.
Yes. The word space is diversely used. You are looking in the direction of most general mathematically rational usage. I am looking from the viewpoint of common language. For me, the mathematical generalisations are metaphoric technical extensions of but not the same as the common language usage. For me, this distinction matters. It is like the distinction between category and allegory, which is one of the most fundamentally important distinctions of clear thinking.
A space with angle measure but not necessarily length measure has a conformal geometry, which I think you well know. Inversive geometry is an example of a flat conformal geometry. According to my textbook, it is a subgeometry of projective geometry. It makes all generalised circles congruent.
Rigid objects can be moved to a new place and then let rest. If they are elastic, their before and after resting forms are congruent. The speed of motion and distortion of acceleration have been forgotten. The “non-existence” of rigid objects is a typical piece of obscurantist mystification. Not even Albert Einstein could dissuade me that the oceans are liquid and icebergs rigid.
Christopher
Christopher:
By the way, thanks for the reference to “Relativity without tears”, by Z.K. Silagadze. Of course this work would certainly not be “without tears” for an undergraduate or High School audience. :-)
I’ll only touch on the issue with “space” right now.
Unfortunately, the term has been used in a very large number of ways in a myriad of contexts. However, in almost all cases one can disentangle these by applying appropriate modifiers (limiters) to the term.
The most general concept of “space” I’m aware of comes from mathematics, where we are talking about a set of “points” in an open neighborhood. If these points can be considered to be tuples of elements from various Fields (like real or complex numbers, etc.) then the “space” can be viewed as a product space. This definition has no concept of distance, angle, metric, or a whole lot else. All other “spaces” are specializations of this, such as vector spaces (where one has the ability to obtain points as linear combinations of some basis set), norm spaces (where we have a length measure), metric spaces (where we have a metric, or as generalized by physicists, pseudo-metric, that allows for both length and angle measures), etc. (I don’t know what a space is called that has an angle measure without a length measure.)
Metric spaces that are vector spaces certainly have a “rigid motion” available. Also, as pointed out in the “Relativity without tears” paper, so do metric spaces with constant curvature (like motion on the surface of a ball). However, as Einstein pointed out with Special Relativity, wile one may (or may not) have “rigid motion” available, one cannot have “rigid objects” since there is no propagation of “information” (like the fact that part of the object has moved) that is faster than c (the special “speed” of Minkowski spacetime, whether or not it is that of “light”). So I would say that the availability of “rigid motion” is not a physical necessity. In fact, we see how tidal effects (“forces”) distort objects (like the Earth’s oceans), so this appears to be a “good thing”. :-)
Anyway, there is more, but I have to go, again.
David
Christopher:
First I’ll ignore the “fighting words” you apply in your message:
(The “customary slight” you then present is certainly heard, but, as I would have hoped you would have noticed, at least from Burt, this “customary slight” is totally discounted by those that have a true understanding of special relativity, and even more so if they understand general relativity.)
As to the “Possible Kinematics” J. Math. Phys. article. This is simply a group theoretic consideration, so it has limited applicability, especially for curved spacetimes. Besides, I would expect someone like yourself to actually have some difficulty with such abstractions: They are far more abstract than GR, in my opinion.
Furthermore, you appear to have some trouble in your understanding and/or application of the term “space”. Unfortunately, I have to go right now so I’ll address this issue later.
David
Christopher:
If the “proposal that the ‘general theory of relativity’ needs arbitrary supplementary assumptions to make it empirically testable is indeed from Logunov” then we need to see specific references! So, please, as I said before, please provide the references. (I certainly don’t have the time to just read a bunch of books in the hope that I way find what you believe you have found in this regard.)
As to your comment that “As far as I can work out, the use of the PPN formalism falls within the ambit of this proposal.” Are you trying to suggest that the mere use of the PPN formalism is within the purview of the “proposal that the ‘general theory of relativity’ needs arbitrary supplementary assumptions to make it empirically testable”? How do you justify this? While it is true that the PPN formalism cannot be applied to all possible gravitational theories, this has no bearing on whether “the ‘general theory of relativity’ needs arbitrary supplementary assumptions to make it empirically testable.”
You have opened up a can of worms with this “proposal”. Now it is up to you to put up. Either it is indeed a stance taken by Logunov, in which case we need references, or you are putting words in his mouth, in which case you could have trouble with him. (Just saying that it can be found somewhere in “some of the four books” you have previously listed, or somewhere in the references “listed in the Gerstein-led paper that we have looked at” is not sufficient: We must have “chapter and verse”, at least of a specific statement made by Logunov where he makes the claim you attribute to him.)
David
David:
My proposal that the “general theory of relativity” needs arbitrary supplementary assumptions to make it empirically testable is indeed from Logunov; I assumed that the reader would expect that. Logunov and his colleague Mestvirishvili in their books are the best source for the extensive details. I have already listed some of the four books and they are also listed in the Gerstein-led paper that we have looked at.
As far as I can work out, the use of the PPN formalism falls within the ambit of this proposal.
Christopher
David:
I see the “unsettled” state of “special” relativity as caused by muddying of the waters, by the pushers of the “general theory of relativity”, or should I call it a snow-job?
For example, it is customary to slight the powers of the Minkowski approach by saying quite early on “Oh, this cannot be done in Minkowski geometry because it involves acceleration, and we will have to use the ‘general theory of relativity’ “, when the problem could easily be solved in the Minkowski framework.
The result is that many books don’t bother to set out the rules and powers of Minkowski geometry, and the simple things are left unsaid, and people are left unnecessarily mystified and baffled.
H. Bacry and J.-M. Lévy-Leblond in “Possible Kinematics”, J. Math. Phys. 9(10): 1605-1614 (1968) tell us about various geometries some of which might support the notion of the movement of a rigid object. This is a very fundamental notion for physics, I think. And some of these geometries also have a notion of causality that makes sense. Some geometries don’t allow such things. It is helpful to understanding such physical notions to have these various geometries set out for the student. Bacry and Lévy-Leblond display 11 enlightening kinematical theories along these lines. For example, they write of the (Lewis) Carroll (Alice Through the Looking Glass) kinematics, in which “it takes all the running you can do to to keep in the same place. If you want to get somewhere else, you must run at least twice as fast as that!”
Some of this is set out in “Relativity without tears” http://arxiv.org/abs/0708.0929 by Z.K. Silagadze, who gives several relevant references, sadly for me mostly in Russian which I don’t know. Silagadze gives a nice little 3 x 3 table of the nine two-dimensional Cayley-Klein geometries, tabulated by how angles and lengths are measured: hyperbolic, parabolic, elliptic measurements. Minkowski geometry appears as the entry for hyperbolic angle measurement, parabolic length measurement. Euclidean appears for elliptic angle measurement, parabolic length measurement. And so on.
I have a nice geometry textbook with a Kleinian slant that tells me how affine geometry is a subgeometry of projective geometry, and how euclidean geometry is a subgeometry of affine geometry, and also a subgeometry of Lobachevsky geometry, which is also a subgeometry of projective geometry. I think inversive geometry is also a subgeometry of projective geometry, and I am sure that spherical geometry(Reimann geometry I think it is also called in this context) is a subgeometry of inversive geometry. Sad to say the book doesn’t go as far as the ninefold table of Cayley-Klein geometries, and doesn’t mention Minkowski geometry.
I have not found a book in English that sets out the Bacry-Lévy-Leblond story in more detail at a suitable level for me. I have the impression that some of the Russian ones cited by Silagadze might do that?
I would have been grateful, I think, to have known sooner and more easily of these things. They provide a context that makes it easier to see what is really meant by various physical concepts. The more extreme generality of Gaussian geometry then Riemannian (manifold) geometry and then Cartan geometry would be further steps.
Just a little point. For me, I think, a space properly so called allows the movement of rigid objects, which is in general not possible in manifolds. There is a sense in which this is the essence of the physical concept of space. I think this might be how I would define the difference between space properly so called and “space” metaphorically so called, for example the colour solid.
Of course the theory of gravity is more complicated than the theory of dynamics of things of small weight in places far from heavy things, where gravity can be neglected for many problems. But I think it would be easier if it were customarily done on the simple basis of Minkowski geometry. It seems Feynman and Weinberg think so too.
Logunov presents a far more extensive and advanced treatment than does Whitehead, who is mainly concerned only at a rather general level of principle. The details and developments of the Logunov theory are best presented by him and his colleagues in their books. They are not restricted to weak field approximations.
Christopher
David:
The quote is from Feynman Lectures on Gravitation, by Richard P. Feynman, Fernando B. Morinigo, and William G. Wagner, edited by Brian Hatfield, Addison-Wesley, Reading Mass. etc, 1995. I did not detail this because I seemed to recall (subject to my imperfect memory) that I had previously done so in this blog.
Christopher
Christopher:
In what book is the Richard Feynman quote you say is on page 202. (Of course I’m only assuming it is a book.)
This is not to say that I have any problem with the quote or with him having “reservations” about the Schwartzchild solution, or even reservations about General Relativity (or at least singularities therein).
David
Christopher :
You state
How can you possibly believe that when you see how “unsettled” things are even in the much simpler Special theory of Relativity (SR), as evidenced by discussions within this and related threads? :-)
If even those that purport to agree with SR have such a hard time agreeing on various points thereof, then how in the world is any sort of “settl[ing] these things in a transparent way” going to have occurred in a far more complex theory? :-)
In addition, while I’m familiar with at least two classes of vierbein (or tetrad) approaches to GR*, that I believe are, at least, very similar to what I believe is the “Minkowski geometry” type formulation of GR (or even just the Hilbert-Einstein equation) I suspect Logunov and Whitehead espouse (though I cannot be certain, at this time, especially since the Gershtein-Logunov-Mestvirishvili paper used the tensor like formulation), I see no way for any of them to make things simpler to the point of approaching “settl[ing] these things in a[ny] transparent way” in anything like a similar timeframe.
The only other “Minkowski geometry” type formulation of GR that I can think of is the one often used for weak field approximations, where the “metric field”, g, is a sum of the Minkowski metric and another set of fields. This one can really get messy. Especially when the fields get large. :-)
Or is the Logunov and Whitehead “Minkowski geometry” type formulation of GR something else entirely. Does it include additional equations beyond the Hilbert-Einstein equation? Like equation #2 in the Gershtein-Logunov-Mestvirishvili paper?
David
* I believe the Weinberg and Feynman’s Minkowski geometry based prescription(s) for gravity/GR are vierbein based formulations.
Incidentally, since these vierbein approaches are so closely coupled to the Dirac equation, there are certainly those in the Quantum Mechanics “camp” that tend toward this formulation of GR. Also incidentally, my dissertation pertained to a generalization of the Dirac equation, and in the process I discovered a generalization of the vierbein that have a number of benefits for applications of the Dirac equation, though I believe they have little if any benefit for GR.
Christopher:
In my last reply to this post I mostly addressed the first statement
In that response, I most certainly wasn’t comparing General Relativity (GR) to Newtonian Mechanics (NM) because I, in any way, thought you were espousing NM, but as a juxtaposition that, I hoped, would help in illustrating the extent to which GR is “complete”, even though I also pointed out how it (and any similarly placed competitor) is “incomplete”.
Now I would like to address the later statements/assertions within the post. Namely
As you say, “This seems like a knockdown argument …, not a mere matter of preference of interpretation.”
Now since you state that “These are very technical questions, and need a very good understanding to criticise properly”, I assume that these claims of “specious appearance of testing” and “unfalsifiability” are claims laid down by Logunov and not yourself. Is that true? If so, I believe you should provide the reference, because these do sound like very strong claims.
In point of fact, I don’t see how they can possibly be supportable, since the tests to which GR has been subjected to, to date, most certainly have no “arbitrary supplementary assumptions” that are available in order “to make suitable” adjustments “so that it is always [or even ever] possible to give a specious appearance of testing it.” I’m sure the experimentalists would vehemently object to any assertion “that the ‘general theory of relativity’ has passed every empirical test with flying colours, because no such test really exists.” (They like nothing more than falsifying theories, and the more famous the theory the better, in their view.)
Without the cosmological term, GR had but one parameter: The constant of proportionality between the source term (the energy-momentum-stress of matter and non-gravitational fields) and the “curvature” field (via the Einstein tensor, made from the Ricci tensor and scalar). But in order to pass the first test any new theory must pass—matching all previous observations and experiments (pertaining to the purported realm of applicability of said theory)—this parameter became fixed. (Even once the cosmological term was added, it became constrained to be very close to zero, which even today is rather troubling to Quantum Field theory.) So GR can be viewed as a theory with but one “tweak-able” parameter, and even that parameter is constrained to be close to zero.
GR has been, and continues to be tested against competing theories with far more “tweak-able” parameters (“arbitrary supplementary assumptions”), and the only ones that have thus-far survived have been those that contain the ability for their parameters to take on values such that they are indistinguishable from GR. So far, there have been no tests that require any of the additional terms/field/etc. that pertain to such parameters. (The methodology that codifies this procedure is the Parameterized Post Newtonian formulation [or is it formalism?].)
All that is available in any such tests is the distribution and nature (in terms of the energy-momentum-stress tensor) of the matter and/or non-gravitational fields involved. Such tests include laboratory, planetary, Solar system, galactic, and all the way to cosmological scale tests. While it is true that as one moves to the larger scales, one has decreasing certainty with regard to the distribution and nature of the matter and/or non-gravitational fields involved, the important thing is that that is all that is available for “tweaking”, while the theory must remain unchanged at all such scales (including the cosmological term).
So, like I said, I don’t see how they, or anyone, can support a claim of “specious appearance of testing” and “unfalsifiability” with regard to GR. So maybe a reference will help?
David
David,
Thank you for this. Boy, oh, boy, are we going at it! We can hardly keep up with it!
It is now apparent that we are looking at seriously technical questions that need very deep understanding to resolve. Moreover, reputations and careers might be relevant. You speak of a “fix” using Sobolev spaces, and I think you would agree that that is rather technical. I am not saying that technical is wrong, just that it needs good understanding to assess. My feeling is that if the very abstract approach of the “general theory of relativity” were the best way, it should have settled these things in a transparent way by the end of the last century. The authoritative orthodoxy says it has done that well and truly, and that quibblers are cranks. On the other hand, according to Richard Feynman, on page 202 “The many discussions we have had on the Schwartzchild solutions are a symptom of the fact that we have a theory which is not fully investigated.” Silly old Feynman, silly old Whitehead, silly old Einstein. As I have mentioned, I do not yet feel my physical intuition is likely to be as good as Feymnan’s. Perhaps tomorrow I will become more enlightened.
I think that the Minkowski way is more transparent than the “general theory” way. I think it seems a fair bet that if the orthodoxy had chosen it, as you say they might validly have done, we would not be having these quibbles after so long. Perhaps because I am ignorant, it seems to me that the orthodoxy mostly replies to this kind of thinking: “Trust me, I am from the government.”
An example is that recently there has been a controversy about the fact that one of the arguments for dark matter has previously rested on the Newtonian approximation for the angular momentum of galaxies because it is near enough to the “general theory” for this purpose. The proposal went that the non-linearity of the proper theory, counting also the weight of gravitational waves, meant that dark matter was not needed to account for the speed of rotation of galaxies. But then the argument got bogged down in questions of what was the meaning of singularities in coordinate systems as opposed to singularities in physical processes.
At this level, the use of fancy coordinate systems is not quite a royal road, and the minimalist operationalist localist doctrine of the orthodoxy seems precarious. What if some assumption is wrong? The minimalist approach is like walking on a tightrope without a net. Very brave, but not for the average man.
All of the above is just waffle and handwaving, of course. It is not rigorous argument.
But, if I am to believe it, I would like to see a more consistent and transparent way of presenting the orthodox approach than I have seen so far. Perhaps I have not yet read the right book. These problems are so important that I think a very good presentation is worth its weight, and should have been available long ago.
The “simple minded” approach that I canvassed some time ago, and myself “dismissed” on the spot because the “trained physicist” knew it was “nonsense”, is in fact not nonsense, but is perfectly reasonable, as attested by the proposition that we are just looking at a preference for interpretations, supported by Weyl amongst others. But no peep of defence came for it on this blog. Not a peep. It was entirely accepted, at least by lack of response, that the “trained physicist” was right to dismiss it as nonsense. I think it fair to say that if it was orthodox to accept that we are just looking at “preference”, and the orthodoxy were widely taught, then defence of the other “preference” as physically equivalent would have been automatically forthcoming on the blog. The “preference” for orthodoxy is suspiciously strong. Perhaps I am just a paranoid crank? I cannot safely dismiss that possibility. That is why I am pursuing this line of thinking. On the other hand, I find myself unable to swallow instructions to “believe only, and thou shalt be saved”, believe in the sense of accepting doctrine that seems to lead to unshakeable “preference”. All the presentations that I have so far encountered stop me at this point. I cannot bring myself to dive into a sea of pure acceptance of what seems like a muddle. My fear of being bluffed into acceptance of apparent nonsense is much stronger than my fear that I am a paranoid crank. Perhaps that proves that I am one? Or just a dill?
A glance at your next reply. I am not pushing Newton’s theory of gravity. As you have noted, even Newton knew it couldn’t be right, and I think for the right reason. He was relying on Aristotle’s intuition, that causal agency must propagate at a finite speed. The idea of infinitely fast propagation is fundamentally contrary to the notion of causal agency. That is why the “special” theory of relativity can be worked out to require Minkowski geometry without any mention of the speed of light. I think this latter fact was first published by von Ignatowski in 1910, long before Whitehead’s book of 1922.
I think I am likely to be getting into too narrow a frame of argument, and I should take a little break for reflection, and do some more reading before wasting too many more electron orbits.
Christopher
Christopher:
I would say that the “general theory of relativity” (GR) is more a complete theory than is Newtonian Mechanics (NM) or Newton’s theory of gravity. The reason I say this is that it only has boundary (and topological, in general) conditions that need to be specified (at least when the cosmological term is not used, which was most common until Dark Energy came into play), while Newtonian mechanics (and thus also Newton’s theory of gravity) can always accommodate someone coming in with a pool cue and knocking a ball or something. In actual point of fact, GR is what I term hyper-deterministic, since, other than the necessary arbitrariness of coordinate systems in order to allow for general coordinate transformations, the equations are actually overdetermined!
Actually, there is of course the issue of the dynamics of whatever matter/fields/etc. (outside of gravity/spacetime itself, of course) that must be accommodated by both NM and any full dynamics using GR. However, GR puts more constraints on such than does NM. (And yes, GR has full conservation of energy. Unlike what I have seen you lament. The only thing it’s missing, in such things, is a separation of gravitational energy into localizable, separable terms, such a “gravitational potential energy”. After all, unlike Newton’s gravity, there’s also something like “gravitational dynamic/kinetic energy”. It’s just that these appear to be inseparably entangled into the nonlinear dynamics of gravity/spacetime. [It’s a bit difficult to talk about the energy of gravity/spacetime traveling/changing/localizing in spacetime when gravity and spacetime are so intimately tied together. We can do it for cases of small perturbations, but its very much like trying to separate the surface of the ocean from ocean waves—what gets put in which category is rather arbitrary.])
Are there arbitrary parameters involved with cosmology? Yes. There are questions of boundary/initial conditions, topology, particle and non-gravitational field dynamics (this is where things like Dark Matter get placed, it’s another, possible, matter constituent), and the possible cosmological term (this is where Dark Energy is usually placed, but it can also go into non-gravitational field dynamics). Are these non-gravitational parameters (other than the possible cosmological term) GR’s fault? Aren’t they there, at least as potential players, in any competing theory?
Now, the fact that the dynamics of matter and other non-gravitational fields are not determined by GR was actually a lament of Einstein. I fully understand his lament. It sure would have been nice to have it all packaged up! So, yes, as a Theory of Everything (TOE) GR most certainly is incomplete! What should one expect? :-)
There have been those that have tried to specify matter and other fields in such a way that GR can account for everything, but this hasn’t worked in over 50 years! (This is the GR camp trying to “include” all of what Quantum Mechanics [QM] has explained so well over this time frame. Of course the QM camp has tried the reverse also with as little success.) Of course, even beyond this, there are good reasons to believe that neither GR nor QM are “the answer”, but that we need something that incorporates both, or at least contains both as appropriate approximations.
So “incompleteness” is a claim that needs clarification, and, depending on the nature of the claim, you may find all are in agreement. :-)
David
In my edit of last night I forgot to add that according to Logunov, the orthodox “general theory of relativity” is not a completely specific theory, and requires supplementary arbitrary assumptions to make it testable. It is always possible to make suitable arbitrary supplementary assumptions, so that it is always possible to give a specious appearance of testing it. But strictly in its own terms it is unfalsifiable, in this light. Consequently one can safely say that the “general theory of relativity” has passed every empirical test with flying colours, because no such test really exists. This seems like a knockdown argument to me, not a mere matter of preference of interpretation. These are very technical questions, and need a very good understanding to criticise properly. I am still learning.
Christopher
Christopher:
In reading the “Black holes: a prediction of theory or phantasy?” paper by Logunov, Mestvirishvili, and Kiselev that you linked to (and thank you, by the way), even ignoring the apparent typo where they talk of v2 < or = to "1" (unity), rather than the unit correct (according to their own units) c2, there is a potential logical straw-man being espoused (essentially identical to the “violates physics” argument of any system of singularities within GR because it violates the C-infinity [continuous to all orders of derivatives] manifold assumption of the original derivation of GR). Basically, in their argument, “physical” means v2 < c2 everywhere (without the slightest exception, in any coordinate system).
(Incidentally, they appear to ignore, until after the fact, that there are nice coordinate systems such that v2 < c2 for all time-like curves even for the Schwarzschild black hole, since the “singularity” at the event horizon is only a coordinate singularity. But using their straw-man argument they then proceed to assert that the only “physical” portion of the solution must be outside the event horizon. [They discount the “nice” coordinate system as involving “singular” coordinate transformations, and rail against it because “it {the velocity violation} appears at another point”. They then proceed with other “singular” transformations and contradict their own velocities at infinity. Of course part of the problem is they keep obtaining their solutions by transforming their original solution, instead of obtaining solutions in their new coordinate system: This methodology is almost guaranteed to have problems when dealing with singular transformations.])
Of course I have no problem with Albert Einstein having trouble accepting the singularities predicted by his own theory. After all, he also had trouble accepting the expanding cosmological solutions, and, hence, created the cosmological constant in order to avoid this. (Of course he later considered this to be his biggest blunder. :-) )
The problem I have is with straw-man arguments that then lead to a presupposed conclusion such as their conclusion:
(Now if they had been referring to the “physical” singularity, here, rather than the coordinate singularity [the event horizon] I would still not necessarily agree with them, but at least I would respect them more, since the “physical” singularity does, indeed, violate the C-infinity assumption at the basis of pseudo–Riemannian geometry [even though there is a “fix” by using appropriate Sobolev spaces in the Lagrangian formulation].)
David
P.S. I don’t like how the new formatting creates so little space between paragraphs that one can hardly see the breaks, at least on the browsers I’ve used to view this. But, again, se l’vie.
Let a neutral observer judge the times elapsed. No need to compare different clock rates. Let us use conventional two dimensional Minkowski geometry. The outward and homeward legs are symmetrical and continuous. The timing can be taken from just one of the legs, because of symmetry. The home-clock is privileged in being inertial for the whole adventure. The other clocks are inertial only within each leg.
Below is a diagram of the outward leg. The broken lines are world lines (dashed) and lines-of-simultaneity (dotted) for the home-clock (blue), the away-clock (red), and the neutral clock halfway between them (green), plotted in the frame of reference of the home clock. The full lines are for the same, plotted in the frame of reference of the neutral clock. The diagram shows a tranformation of reference frames that takes the broken lines into the full lines; it takes the turning point T into T’; it takes the “midpoint” of the home-clock M into M’; and it takes the “halfway point” of the outward leg of the home clock, H, as judged in the reference frame of the neutral observer, into H’. c and -c mark the light cone of the origin O. The transformation of reference frames is done with elementary geometry, using ruler and compass, according to the rules of Minkowski geometry; no numerical calculations here.
The neutral observer in his reference frame considers both test clocks to be working equally at the same rate until the away-clock reaches the turning point and thus completes its outward leg. Then there is no more time to be recorded in the outward leg for the away-clock, but the home-clock has not yet reached the midpoint of its entire adventures, that is to say, it has not completed its outward leg.
The neutral observer watches and waits from NH’ to NM’ on his time axis, for the home-clock to complete its outward leg. In his frame the home and away clocks run at the same rates, but the home clock has longer to run to reach the end of the leg.
This presentation shows that the rates of the clocks are not quite the heart of the difference: they are not different in the neutral observer’s frame. The home-clock simply has more time to record, at a common clock rate. This is comforting for the clock maker, who made the clocks identical, and for simple souls who aren’t comfortable with identical clocks under identical conditions running at different rates.
The diagram can be downloaded for monitor display or printing, as a .pdf file from http://www.bellstheorem.com/docs/neutralobserver.pdf, in case it does not display very clearly on the blog page. It is important that one have a very clear display to make sense of the diagram.
Christopher
David,
Thank you for this.
Yes, the new paper with Gerstein as lead author seems to give a different theory from that of Logunov’s Lectures. The latter has at page 217: “If we put into correspondence to this field some particles, they must have a zero rest mass.” This seems discrepant from the Gerstein-led paper that says “the non-zero graviton mass is mandatory”. I am learning here that the Lectures are only a stepping stone. Logunov’s “The Theory of Gravity”, translated by G. Pontecorvo, Nauka, Mosocw, 2001, states on page 122: “We shall especially note that within the framework of RTG [relativistic theory of gravity] a homogeneous and isotropic universe can exist only if the graviton mass differs from zero.” Logunov and Mestvirishvili’s “The Relativistic Theory of Gravitation”, translated by E. Yankowsky, Mir, 1989, also discusses non-zero rest mass for gravitons. Besides these two books, and “Relativistic Theory of Gravity”, Nova, New Yourk 2001, there are several papers at http://front.math.ucdavis.edu/author/A.Logunov that seem to help to clarify this. It seems to be a question of what kind of universe we really live in, is it homogenous, isotropic, etc., a question that we cannot answer, indeed that I suspect we are very very far from answering.
As far as I can see, the non-zero graviton mass is so small that it will never be detected as a particle by a particle detector. What is at stake will be the speed of propagation of gravitational causal agency. For a non-zero mass particle it has to be less than the universal maximum speed, which is attained only by “particles” of zero rest mass, such as “photons”. For my instinct, I find it hard to believe in gravity propagating at a speed less than the maximum, and so I find it hard to believe in massive gravitons, however finitely light. But my instinct is no more than that. In the orthodoxy, there is, so far as I can work out, no physical meaning to the notion of the speed of propagation of gravity, and no logical possibility of measuring it.
The rest mass of the graviton seems a very technical issue. I do not think it seems to affect the basic point that concerns me, that Minkowski spacetime is the fundamental physical one, and the curvilinear coordinates are secondary mathematical conveniences.
You suspect that the difference that worries me is only interpretation subject to mere preference. I think that the fundamentally curved spacetime dogma is said to predict black holes’ having cores of singular accumulations of infinite mass density. This is contrary to both the Logunov Lectures theory and to the present Gerstein-led theory. I don’t think this is just a matter of preferential interpretation, but perhaps I am mistaken about that. As far as I can work out, we will never receive a report of a local observation from the near neighbourhood of such a singularity, and in that sense such a singularity is locally unobservable to us. As I noted in my comment, I think atomic clocks would not work reliably there because they would have too large a size, being finite. On the other hand, perhaps they just get smaller and smaller as necessary? Another problem for them would be if the singularity were surrounded by dense matter, not a vacuum.
On the other hand, at http://uk.arxiv.org/PS_cache/gr-qc/pdf/0412/0412058v1.pdf, Logunov, Mestvirishvili, and Kiselev argue that Einstein presented good but neglected arguments within his “general theory of relativity” that singularities of density will not occur in nature. If Einstein and they are right about that, then perhaps after all it may be that the black hole density singularity issue will not be the one that shows that we are not looking only at preferences of interpretation. Perhaps, even, it is only a matter of preference that I like to use the crutch of the law of the conservation of energy.
According to Logunov and Whitehead, there is nothing wrong with using the curvilinear coordinates when they help to solve problems; and they often are the best way to do that. It is just that they by themselves do not tell the full physical story, namely, when taken by themselves, they do not account for the spatial distribution of gravitational potential energy, and so do not support the principle of conservation of energy. The tough guys of the orthodoxy say real men don’t need that crutch of the feeble.
I have been reading Spivak on Riemann. It is very helpful, but still not quite clear. As far as I can see, we can distinguish between (1) a “space” such as the colour solid, where the “metric” is something like a function with values that are numbers of just-noticeable-differences, and (2) a space such as we use to think about the motion of ponderable matter, where the metric is geometrical in a sense that I find natural. I would think of the colour solid as a manifold with boundary, not as a space in the more geometrical sense; this is “geometry” only by metaphor, I think. So far as I can see, the orthodoxy likes us to think of physical geometrical space in the more abstract way, as a manifold in the more abstract sense. Very sophisticated, very locally operationally minimalist, very much for the cognoscenti and the afficionados.
One of the references in the Gerstein-led paper is to the Russian original of one of Logunov’s books, but I have the English translation (by Eugene Yankowsky) of that in my library at home, and I think you could find it in your local library. The other references to books by Logunov are in English, as is the Lectures that I have referred to. I bought them on the web a few years ago, and likely many local libraries will also hold them.
Christopher
Christopher:
I was glad to see the link to the “IMPOSSIBILITY of UNLIMITED GRAVITATIONAL COLLAPSE” paper in your post. Is this theory what you have been alluding to in previous posts, or something a bit different?
It certainly has a different equation for the relationship between the Ricci tensor and the energy-momentum-stress tensor of matter and other (non-gravitational) fields. It will even have different vacuum solutions, due to the extra term (provided the graviton has a non-zero rest mass, as the paper makes claim to).
Of course I don’t believe that any scientist would claim that the equations should be the same as General Relativity (GR) if the graviton were to have a nonzero rest mass. (In fact, this leads to a Newtonian limit that deviates from the inverse square law of Newtonian gravity.)
Since this theory appears to have only a single parameter that causes a difference in its equations vs. General Relativity (that being the graviton rest mass), it can be viewed as a viable, parameterized alternative to GR, so long as the graviton rest mass is not required to be non-zero. I don’t have my copy of Misner, Thorne, and Wheeler with me, here, but I wouldn’t be surprised if there is already a graviton rest mass term available in the Parameterized Post Newtonian formulation. If so (and even if such is not already there), the question is simply how far off from zero may such a term be without violating any known experiments/observations.
The next question, then, pertains to what experiments can be devised to further constrain this term and/or find that a zero value is inconsistent with said experiment. This is the nature of the falsification process so fundamental to the scientific endeavor.
I have no doubt that such a theory with a non-zero graviton rest mass will have predictions that deviate from those of General Relativity. However, until there is some experiment that falsifies it or GR any “preference” for one or the other is just that, a “preference“.
As to whether Weinberg’s and Feynman’s Minkowski geometry based prescription(s) for gravity is(are) equivalent to the “orthodox” curved spacetime of GR, I suspect the only issue is in interpretation. As I understand their results, there are no observational differences (up to potential topological differences, but we haven’t observed anything that would take us outside of a flat topology [which, personally, I think is disappointing, but so it goes]). This means that a preference for one interpretation vs. the other is, again, just that, a preference, until such time as one may, possibly, find a theory that incorporates both GR and Quantum Mechanics that requires one formulation as opposed to the other.
So it stands, as far as I can tell thus far. But I do thank you for the paper. (I just wish the other references to Logunov’s work weren’t in Russian, since I can’t read Russian.)
David
Christopher:
I thought that earlier post sounded an lot like you. :-)
Unfortunately, even your edit doesn’t correct things. The point at which the stay-at-home clock reaches “half way”, and the point at which both “away” ships turn back is only simultaneous in the stay-at-home reference frame. However, you are right to correct the lack of simultaneity of the “neutral observer’s” reception of the stay-at-home clock’s “half way” signal with the “turning point” signal of the “traveling clock”. (Of course if the “neutral observer” had simply stopped, relative to the stay-at-home clock, at his designated turn around point, then he would have observed a simultaneous receipt of these signals.)
David
Hi Christopher, you wrote:
“P.S. Hi, Burt. If I am not mistaken, you would do well to make a slight edit on your just posted comment.”
No, nothing missing there, but I have edited it to make it a bit clearer. Thanks for pointing it out. :)
Regards,
Burt Jordaan (www.Relativity-4-Engineers.com)
“The neutral observer, in his time system, will see a light pulse sent from travelling clock at its turning point at the same instant that he sees a light pulse sent from the stay-at-home clock at its halftime instant.”
This is not quite what needs to be said, because the neutral observer does not stay in that outgoing time system long enough to see that light pulse while he is in it. It should read:
For the neutral observer in his outgoing time system, the light pulse from the turn-around instant of the travelling clock will start simultaneously with the the halftime event of the stay-at-home clock. But the neutral observer has an impulsive change of velocity at that midtime, and, by the time the light pulses reach him in his trip home, he will be moving with respect to his position in his outgoing reference system at that point of simultaneity. In his homeward-bound time system, he will see the halftime light pulse from the stay-at-home clock before he sees the turn-around light pulse from the travelling clock. If he had stayed in his outgoing trajectory and time system, he would have seen the two pulses simultaneously, some time after the moment of their (to him in his outgoing time system) simultaneous emissions. These relations in the homeward bound time system are not mirrored in the analysis of the homeward leg, because time runs backward for a mirror analysis.
Christopher (I did not use the login facility when posting my comment, so I cannot use the edit facility for this correction.)
P.S. Hi, Burt. If I am not mistaken, you would do well to make a slight edit on your just posted comment. “The away-twin’s outbound synchronized clocks read 6.25 years after 5 years of his own time passed. He cannot know about the away-twin’s turnaround other than that the observers at each of her clocks abrubtly set their clocks back by a predetermined amount, in accordance with her new simultaneity.” This does not make grammatical sense to me. Perhaps you have accidentally cut out a clause or two while working on it. I think you will be able to edit it more quickly than I can work out exactly what fix is needed. Regards, Christopher.
Since it is really at the heart of the matter that “twins ‘see’ aging rates by looking at clocks”, it is odd, even irrelevant or a red herring, to call it a “twin aging paradox”, when it seems more natural to call it a “clock rate paradox”. The scientific measurement of aging as such is not as easy as the reading of clocks, of course. Aging is likely affected by gravity, and is not, I think, the real focus of interest in this discussion. A aging twin on the rotating and orbiting earth is moving quite fast relative to a neutral observer, such as one who is in a space ship that stays halfway between the aging twins all the time. In this case the precise acceleration of the travelling twin should be stated, and of course the gravitational and orbiting acceleration of the stay-on-earth twin should be taken into account. (At first, here, we ignore the empirical fact that some important kinds of atomic clocks do actually age, in the sense that they slightly change their rate of running as time passes. This presents a serious, and so far as I know unacknowledged, problem for someone wanting to define time in terms of such an “operational” atomic clock.)
But I think the use of the label “twin aging paradox” is more about motivating audience interest in the question than about scientific principle.
The natural way to look at the clock paradox, which is, I think, the real focus of the present discussion, is to compare instantaneous clock rates for two clocks, and to compare measurements of a certain prescribed finite duration by the two clocks.
One scientific way of doing a comparison is to set up a neutral observer who observes both test clocks. The neutral observer will move so as to stay halfway between the two paradoxical clocks, and so will be present at the start and end points of the comparison of durations.
The neutral observer sees both clocks running at the same rate because each is travelling at the same speed with respect to him, one “forward”, the other “backward”.
For the simple case of an outward-return-symmetrical trip for the travelling clock, the observation period can be split into two halves, the first leg and the second leg of the round trip. Analysis of one half will be enough to settle the question.
We can arrange for the neutral observer to start his clock at the same time as the starts of the two travelling clocks at the same place. The stay-at-home clock is inertially unmoving at that fixed place throughout the trial.
The question then remains, how to compare the neutral observer’s estimate of the times of the two clocks’ ends of the first leg of the round trip, the inertially judged turning point for the travelling clock but no special inertially judged event for the stay-at-home clock.
To the neutral observer, it will seem that the travelling clock reaches its turning point, and turns back, before the halftime mark for the stay-at-home clock. The neutral observer will therefore say that for the first leg (and by symmetry for the second leg, and so for the whole trip) the travelling clock will register less time.
The duration comparison can be visualised by looking at the Minkowski diagram for the three trips. Start with a diagram in which time is reckoned by the stay-at-home clock, and draw straight lines for the three clocks. The neutral observer will move a distance, say x, from home, the travelling clock will move 2x from home. Now rotate the axes, to put the neutral observer’s clock on the time axis. The respective lines of simultaneity for the three clocks will be rotated according to the rules for Minkowski geometry. The result is then visible.
In the coordinate system of the stay-at-home clock, the turning point of the travelling clock will occur simultaneously with the midtime point of the stay-at-home clock. Therefore the stay-at-home clock will see a light pulse, sent from the turning point by the travelling clock, some time after the midpoint of the time on the stay-at-home system, because light travels no faster than the universal finite maximum speed of propagation of causal agency. The travelling clock’s turning point is thus “elsewhere” and not “here” for the stay-at-home clock. The neutral observer, in his time system, will see a light pulse sent from travelling clock at its the turning point at the same instant that he sees a light pulse sent from the stay-at-home clock at its halftime instant.
How to make sense of what seems like a paradox to average persons like myself who usually, intuitively perhaps, think in terms of Newtonian absolute time, but are open to improvng their intuition?
The total duration comparison is going to be with respect to a fixed place in the time system of the stay-at-home clock. The stay-at-home clock has more “experience” of that place than does the travelling clock. For part of the trip around the turning point, that place is “elsewhere” for the travelling clock. Likewise, the turning point, and a finite duration of events surrounding it, of the travelling clock, are spatially separated from the mid-time mark of the stay-at-home clock. That duration cannot be present for the stay-at-home clock, it cannot “experience” that duration. For the stay-at-home clock, that that duration, experienced as “here or nearby” by the travelling clock, is “elsewhere”. The stay-at-home clock lacks some “experience” that the travelling clock has.
But the problem was set for a comparison in the frame of the stay-at-home clock. That frame is a special frame, indeed not a “neutral” reference frame, not neutral with respect to the two clocks.
The difference in “experience” of the two clocks is explained by the special selection of that special reference frame for the comparison of their performances.
It is not explained by a real physical difference in clock rates; the clocks are the same. Nor is it explained by the “speeds of motion” of the clocks; the speeds are relative. Nor is it explained by the different accelerations of the two clocks, which are not affected by acceleration.
What the stay-at-home clock has in intensity of local experience “at home”, the travelling clock makes up for by breadth of experience “elsewhere”. This is not quite so paradoxical.
This special selection of reference frame is an assumption built into quantum mechanics in a way that is not generally recognised. Quantum mechanics refers always to specific experiments, with timelike separation between the start and the end of a specific experimental run of collection of counts from specific particle detectors. The actual specific occasion of experience here is an experimental run, not the adventures of a single physical particle, which is subject to random effects when viewed from this perspective.
For this discussion, we have assumed the “clock hypothesis”, that “ideal” clocks are not affected by acceleration, nor by the empirically known aging of physically feasible clocks (see e.g. Physics Today, November 2007, 60: 33-39, article by James Camparo).
This is theoretically true by definition for “ideal” clocks, but not for any feasible physical clock. An example of a candidate for an ideal clock would be Fokker’s spherical light clock (A.D. Fokker, Accelerated spherical light wave clocks in chronogeometry,” Nederl. Akad. Wetensch. Proc. Ser. B 59, 451-454 (1956)). For conditions of acceleration, it is “ideal” only when its diameter tends to zero, and then it is “infinitesimal”. This strict standard of ideality is of course not reached even by the best possible atomic clocks, because of the finite diameter of atoms.
It is also approximately (near enough but not exactly) true for feasible atomic clocks in situations of mild acceleration such as we might envisage for practical conduct of a “clock paradox experiment”.
On the other hand, of course, it means that atomic clocks, or indeed any physically feasible clock, could not provide reliable local physical measurements under the extreme conditions very near a supposed or putative singularity of density of ponderable matter, a hypothetical “black hole singularity of density”. Therefore such a hypothetical singularity is in principle unobservable by reliable local measurements. If it existed in nature, it could be reliably observed in principle only by a remote observer.
The remote observer is always free to use a Euclidean inertial reference frame to describe his observations of objects remote to him (Hermann Weyl, Philosophy of Mathematics and Natural Science, Princeton, 1949, page 118). This fact allows a consistent consideration of what a remote observer will see. All real observers who can report their results will be remote from the hypothetical singularity in this sense. It shows that such hypothetical singularities will not form in any finite time (S.S. Gershtein, A.A. Logunov, M.A.Mestvirishvili, at http://uk.arxiv.org/PS_cache/gr-qc/pdf/0612/0612177v1.pdf).
This presents a choice for a rational person: believe in a finite age of the universe, or else believe in “black hole singularities” being formed for us in our infinitely remote past, but not both. We can’t have a “big bang” universe with “black hole singularities of density” in it. The seeds of this are in the “clock paradox”: the two clocks experience the world differently. We have no local observational reports from “black hole singularities of density”.
Time is not to be defined “operationally” by local use of feasible physical clocks, as desired by devotees of the “general theory of relativity”. It has to be defined geometrically, by use of many finite, that is to say, partly remote, observations in Minkowski space. Feasible physical clocks can then be assessed for accuracy against the definition. Remote pulsars are useful for this purpose, even though they do not keep constant time. An “operational” definition, in terms of a supposedly ideal clock, would not be checkable for accuracy; there would be no standard against which to check it. Accuracy is a requirement for a scientific instrument.
The clock parodox shows for us that instantaneous clock rates do not have to match measurements of finite durations. Think of differential equations. They need boundary conditions to make their solutions definite. Boundary conditions refer to finitely separated point events, and are in principle distinct and different from local differential conditions. In the clock paradox, the boundary conditions are set to make one clock stationary and the other to move, though the clocks must in a differential, local, sense run at the same rate throughout the experiment, because they are built and run in the same way.
The clock rate is just a differential condition, leaving the boundary conditions unspecified. The same applies to the “equivalence principle” that compares a gravitational field with an accelerated coordinate system. This is why the theory of gravity cannot be constructed by use of the “equivalence principle” alone. The theory of gravity needs boundary conditions, not supplied by the “equivalence principle”, as well as differential conditions, supplied by it. The “equivalence principle”, as far as it goes, is a consequence of gravity theory, not a sufficient axiom for it. The root of this is in the principle of conservation of energy. The equivalence principle does not tell how to assess or aqccount for the local density of gravitational potential energy, which nevertheless appears in the equations for the gravitational field. This local density is what makes the theory of gravity non-linear. This is why the theory of gravity must be based on Minkowski geometry, as it is in the textbooks of Steven Weinberg and Richard Feynman, as well as in the writings of some others. WEinberg and Feynman thought that their Minkowski geometry presentations were equivalent to the orthodox curved spacetime “equivalence-principle”-based story. But they were mistaken in this. The two approaches are different. The natural physical intuitions of those two authors, Weinberg and Feynman, was the cause of their choice of their Minkowski geometry approaches. At present I am not quite sure that my physical intuition is better than Feynman’s.
The ideology of operationalism, embodied in the use of the clock hypothesis, assumed to work for physically feasible clocks for all possible phenomena, to define time, is not enough for these problems. The view of Vladimir Fock (The Theory of Space, Time, and Gravitation, translated by N. Kemmer, 2nd revised edition, Pergamon, 1964, page 224) is relevant here: “What is decisive in a definition is not immediate observability, but a correspondence with Nature, even if this correspondence has to be established by indirect reasoning.” His sentence refers to a global correspondence with Nature, as against merely locally immediate observability. As it happens, Fock did not take this insight far enough to reach an entirely satisfactory theory, but it is still a good principle.
Sorry to disturb you.
you will find an interesting presentation of the accelerated objects on arXiv:gr-qc/0206082v1 27 Jun 2002. This is pdf file from Bahram Mashhoon and Uwe Muench
Department of Physics & Astronomy, University of Missouri–Columbia, Columbia, Missouri
65211, USA
I found it by chance searching for information about measurements of distance from accelerated observators on accelerated objects. (exactly as I found your discussion.)
Note: at my understanding, the string will decrease because of the Lorentz contraction effect, but the observators on the spaceship will be unable to notice it, because all their measurement devices will decrease too.
Best regards.
Michel De Landtsheer
Hi David, you wrote on our “falling through Earth” thought experiment:
“… incidentally, in terms of the Post Newtonian formulation, it appears that the Gravitational time dilation formula you have been using is at the “Newtonian” level (first order) of the approximation—the level at which Newtonian Gravity is recovered, … ”
You are right, but I did check the higher order effects for magnitude. The effects of redshift and the time dilation due to velocity, reaching ~7800 m/s at the center (in vacuum), add up to some 1 microsecond (about 50:50) on the 43 minutes duration; utterly negligible.
“I know, it seems odd to say that first order Gravitational time effects are “Newtonian”, but so it goes.”
Yes, but when one approximates time dilation dtau/dt = sqrt(1-2GM/(rc^2)-v^2/c^2) by using dtau/dt ~ 1-GM/(rc^2) – v^2/(2c^2), it is still not Newtonian. It is just a weak field relativistic approximation, I suppose, not quite the weak field limit.
Regards,
Burt Jordaan (www.Relativity-4-Engineers.com)
Oops! Thanks David, I can’t edit that post any longer, so here is the picture in a more accessible place.
I suggest copying text without picture and then also the picture into one word file for ease of reading. Sorry for the inconvenience.
Regards,
Burt Jordaan (www.Relativity-4-Engineers.com)
Burt:
I don’t think it was intentional, but it appears that we need to be logged into Physics Forums in order to view your image.
David
Hi David.
First, thanks for entering the discussion and bringing your valuable insights! :)
I’ve done the full relativistic calculations for the Bell-spaceship-string scenario and the results are plotted below. I’ve used low accelerations (~1g), but a very long time of acceleration (2 years) of a very long Born-rigid string (0.5 ly) to make the effect as visible as possible. I assumed the spaceships to have negligible own length and initially separated by 0.5 ly.
The salient points of the spacetime diagram are:
From the spaceships’ frame of reference (after the acceleration stops), the proper length of the string is obviously just 0.5 ly, while the proper separation between the two ships goes to 1.116 ly (not directly visible on this diagram).
I’ve used the algorithm I gave before and also the hyperbolic motion equations found in the literature, and both yielded the same results. The hyperbolic equations demand that x^2 – t^2 = 1/a^2, where x represents the spatial coordinate of an object at time t, starting at the origin (x=t=0), accelerating at constant proper acceleration a, making it very simple to calculate and plot.
I hope this converges the discussion with “rockinggoose” now. The only thing we seemed to disagree on was the fact that the identically accelerated spaceships would remain at a constant coordinate separation, while the unattached string would contract from a coordinate point of view. This analysis is in line with what MTW, Nikolic, Mallinckrodt and others wrote, meaning an attached string would break!
Regards,
Burt Jordaan (www.Relativity-4-Engineers.com)
PS: I’ll respond separately to our previous “fall through earth” scenario.
rockinggoose:
You appear to have a few misconceptions, particularly about what Burt has been trying to tell you, and help you understand.
When Burt, and others, are talking about two spaceships accelerating, the “constant separation” is in the initial inertial reference frame (we can keep a “stationary” observer in this reference frame, if that will help you).
What we have are two spaceships (let’s simplify them down into two individual points, so we don’t have to address issues of rigidity and/or contraction of the spaceships themselves) that undergo the same acceleration profile (in one spacial dimension, to keep things simple), both starting at rest in some initial inertial reference frame (let’s set observer A as always stationary with respect to this inertial reference frame, with B and C designating the two spaceships). Actually, since the initial velocities are the same (zero, in this case) we actually have a case where the velocity profiles are the same for the two spaceships. Integrating once, if you will, we have positions with respect to time (as measured in A’s reference frame) of
xB(t)=x(t)
and
xC(t)=x(t)+Δx
where Δx is constant, in A’s reference frame. Furthermore, since we are restricting ourselves to motion in one dimension, to make things simple, this is in the same direction as will be all the travel.
(Of course one may transform into the respective non-inertial “reference” frames of the two spaceships, where one will find that since the only difference in the two spacetime paths is a spacial translation of the initial locations the velocity and acceleration profiles, as seen by whatever instrumentation the two spaceships wish to employ, will be identical. So we could suppose that this experiment may be accomplished using identical preprogrammed robotic spaceships.)
Let’s suppose that somewhere along these identical velocity profiles we have an extended period of constant velocity (coasting), so we may carry out simple Special Relativistic measurements. To make this interesting, let’s simply look at a case where the velocity of this coasting period is non-zero with respect to A’s reference frame.
During such a period, A sees the two spaceships as traveling with a constant non-zero velocity with respect to his/her reference frame, with a constant separation of Δx (this is by definition of the velocity/acceleration profiles). However, we know that in order to appear to have such a separation in A’s reference frame, the spaceships must have a larger separation in their new rest frame. This is simply an inverse application of the “space contraction” relationship.
(Furthermore, while A must be very careful to measure the separation of the spaceships by simultaneously measuring their positions in his/her reference frame, any observers onboard the two spaceships [such as nano-robots, since they are points, after all :-) ] may measure the relative separation at their leisure, employing any [and all] measurement techniques they may desire, since the two spaceships are both stationary with respect to their common inertial reference frame [during this coasting phase of their journey].)
So we see that if we have two spaceships (at least if they are infinitesimally small, so we don’t have any rigidity complications) undergo identical acceleration/velocity profiles, with an initial separation along the direction of travel, then the apparent separation will always be a time independent Δx in A’s inertial reference frame, but will be greater than Δx as seen by observers onboard the spaceships, at least during any coasting periods (where they don’t have to deal with complications associated with taking measurements under non-inertial conditions) during which the spaceships are in motion relative to their initial positions.
rockinggoose, you are not completely incorrect in saying that the situation of Special Relativity is similar to “perspective”: In both cases it all has to do with what one observes and/or how one makes measurements. Additionally, the Lorentz transformations are to Minkowski space(time) (the spacetime of Special Relativity) what rotations are to Euclidean space. So, yes, it’s about the nature of observations/measurements (and the nature of the spacetime in which we exist).
The problem you appear to have is that you haven’t properly applied your “perspective” analogy to this situation. The way one should apply “perspective” in an analogous way would be to have the two objects move away from the observer in such a way as to always appear, to the observer, to have the same apparent separation. Of course, I would expect that you would then recognize that the actual separation between the objects will increase: Thus breaking the string. :-)
I hope this has been helpful.
David
P.S. Burt, I haven’t, yet, been able to carry out the “falling through the Earth” calculations, but I have exposed a few of my own “blind spots” in the process of looking things up.
Also, incidentally, in terms of the Post Newtonian formulation, it appears that the Gravitational time dilation formula you have been using is at the “Newtonian” level (first order) of the approximation—the level at which Newtonian Gravity is recovered, since the zeroth order is just Special Relativity. (The “Einsteinian” level [second and higher order], which is “required” to see General Relativistic effects, has additional terms, both in the time and space parts of the metric.)
I know, it seems odd to say that first order Gravitational time effects are “Newtonian”, but so it goes. (It’s really an issue of terminology. I don’t think anyone, in their right mind [ :-) ], would try to use such as an argument that Newtonian Gravity predicts gravitational time dilation.)
Rockinggoose, I’m ducking into this discussion to say the contraction is measurable. That makes it physically real by my definition.
Now it is true that contraction is not perceived/measured in the frame of reference of the rod, which is why we need to discuss what we mean by a “rigid” body.
It seems to me that you and Burt are using the same, or nearly the same, terminology, but have different understandings of the terms. That’s a sure recipe for a circular argument.
And circular arguments quickly become tiresome, so I am now ducking out again.
Fred Bortz — Science and technology books for young readers (www.fredbortz.com) and Science book reviews (www.scienceshelf.com)
Hi Burt
Born rigidity and so on are not relevant. All this stuff about pressure waves etc. is just a red herring. It is an assumed part of the problem that purely inertial effects are exempted, just like acceleration can and should be excluded in the “twins” paradox. When Bell refers to the (by then 17 year old problem) he makes it explicitly clear that acceleration is sufficiently “gentle” that only kinematical effects of SR are under consideration.
Like I keep on saying, you are hopelessly “stuck” in constantly thinking of the contraction as a “physical shrinkage”. Of course if you can’t escape from that paradigm you are constantly going to run into paradoxes and problems like (as I keep asking) ‘how do you distinguish an accelerated rod from the one in constant uniform motion ?’ If there’s no difference (and SR allows none) then acceleration has no contributes no special “extra” qualities to standard SR.
If you adopt the view in Taylor and Wheeler of the effect being purely an apparent one resulting from and restricted to the particular Einsteinian procedure of clock synchronisation and “simultaneous” measurement, there are no problems or paradoxes.
Your description of the rocket trajectories holding constant distance is identical to that describing the string ends and confirms the constancy of the “proper” physical length of the string. Thus the rockets do stay at constant “proper” distance and it is only when their separation is subjected to the same “simultaneous” marking of positions as the string ends that obviously we would get the same “contracted” measurement whether the string was there or not !
Remember that there is no atomic or molecular mechanism for “contraction” and there is not expected to be one because the effect is purely kinematical, that is it comes about from the relationship between time and space in simultaneity, due to the assumed constancy of the speed of light.
The string doesn’t “really” contract any more than a rod does, which is why the “proper” length, which is the true physical length, always remains constant.
This is precisely what Einstein’s reasoning in the 1905 paper says [available on the web]. In particular it also does not claim that of two specific clocks, each goes slower than the other (when in relative motion). That would be ridiculous. No, it merely shows that the natural synchronisation procedure for spatially separated clocks in each frame leads to a symmetrical situation where each observer finds that although all clocks run at the same rate, the “other” frame’s clocks appear to be mis-set so that oncoming clocks appear to be set progressively ahead by equal increments (if they are equally spaced). [Also receding clocks seem incrementally “behind”, of course.](This is spelled out in detail in Rindler and various other sources.)
What would be simplest is if you supplied or referenced a proof of length contraction that you are satisfied with and if in doing so it is not already obvious how it applies equally to two rockets, I can the indicate what small adjustments may be necessary to make it obvious that it does so.
After all, how could any proof of “contraction” of a rod proceed other than by using simply the coordinates of its ends ?
Those “ends” must be assumed to be travelling at the same velocity ( for we have to start in Newtonian terms in order to “derive” relativistic effects).
Any such proof therefore shows how two points (the “ends”) travelling at the same velocity, must yield relativistically “contracted” seperation measurements. This must obviously and trivially apply equally to two seperated “rockets”.
Hi SL, you asked:
“How is that taken into account in this argument? Is it pulled or is it pushed, or both?”
Yep, this is an issue in reality and initially, a semi-rigid rod will be pulled from the one end and pushed from the other end, with the center remaining static. The forces on the two ends will propagate up and down the rod at the speed of sound in the rod and when the two pressure waves meet at the center of the rod, funny things like ‘length ringing’ should indeed happen.
However, after a while, the ringing should dissipate and the rod will be ‘pulled’ from both ends and stretched, provided the rockets are heavy and powerful enough to maintain their constant, identical accelerations. The reason for this is that the rod will attempt to length contract relative to the inertial frame, meaning its front end accelerates less than its rear end. The rockets will resist that, because they maintain constant accelerations relative to the reference frame; hence the proper length of the rod must increase.
If have ‘specified’ Born-rigid acceleration in my last reply to ‘rockinggoose’. This is the relativistic equivalent to the Newtonian concept of a “perfectly rigid” rod, which is impossible. A rod being accelerated Born-rigidly has no internal stresses, but it means forces must be applied all along the length of the rod and what’s more, the forces must follow a specific pattern – larger at the rear than at the front, a quite tricky concept.
Regards,
Burt Jordaan (www.Relativity-4-Engineers.com)
I’ve looked at Burt’s “process” for determining the spatial separation between two identically accelerating rockets, line astern, and cannot find any obvious errors. It seems pretty inevitable that if accelerations are identical and start at the same time in the inertial frame, speeds and distance apart must remain constant.
The moment a string or rod is attached between the rockets, funny things can happen, I guess. Any string/rod that is accelerated by being pulled will necessarily stretch and if it is pushed, it will compress.
How is that taken into account in this argument? Is it pulled or is it pushed, or both?
SL: Your Aerospace Watchdog
Hi rockinggoose, you wrote:
“I can’t help noticing you’re strategy of constantly ignoring everything except one small point you wish to challenge, …”
The point I’m challenging is the crux of Bell’s ‘paradox’ – not a small point at all – and what’s more, I think you are totally wrong about it. You can settle it by giving us the equations to support your position, not hand-waving arguments, which you may think “… have pointed out quite clearly that in SR there is no difference in the relativistic measurement shortening to be expected of the distance between two objects (whether at constant or varying velocity) as that between two points on a given object“, but many will not agree with you.
The difference that you apparently fail to recognize (or accept) is that two identically accelerated objects will stay a constant distance apart in the reference frame, while the accelerations on the two ends of a lengthwise accelerated (Born-) rigid object are different due to its Lorentz contraction. The rear end always accelerates faster than the front end (Misner, Thorne and Wheeler’s Gravitation, section 6.6, figure 6.4 – now that’s authority!) Can you please tell us how two ends of a rod that have different accelerations can remain at the same spatial positions as two points that have identical accelerations.
Your arguments about the ‘realness’ of the contraction and differences in simultaneity are not relevant to the Bell spaceship problem. In the reference frame, the measurements can all be done according to reference frame simultaneity and the string will be measured as length contracted while the two spaceships will be measured to remain at their initial distance apart. Bell himself used this situation to teach special relativity!
My challenge still stands: I’ll concede the point if you can show us a rigorous calculation for identically accelerating (line astern) spaceships where the distance between them Lorentz contracts, i.e., that their spacetime worldlines do not stay parallel at all coordinate times. I have done the integrations for constant, identical proper accelerations separately for each spaceship and got a constant distance between the COMs of the ships, up to highly relativistic speeds.
The process is fully relativistic: define an inertial frame comoving with the spaceship and then let the ship accelerate by an arbitrarily small dv = a dt, which is added relativistically to the speed of the comoving frame to obtain the new coordinate velocity of the ship at time t + dt. Choose a new comoving frame and repeat. Integrate this over the desired time interval, say 0 to t1, and you have the relativistic velocity of the ship in the reference frame at time t1. Simultaneously integrate the changing velocity and you have the x-position of the ship in the reference frame at time t1.
Now do the same for the second ship, just start the integration with an initial spatial separation, say dx = x_front – x_rear. It is immediately obvious this separation will not change if x_front and x_rear are measured at the same (later) reference frame time t1, provided that the ships accelerate identically. However, the measured length of a rigid string, attached to the front ship only, will decrease if the x-coordinates of its two ends are measured at that same reference frame time t1.
If you do not agree with this process, show me the flaw, so that we can zoom in on that and at least show some progress.
Regards,
Burt Jordaan (www.Relativity-4-Engineers.com)
Hi Burt
I can’t help noticing you’re strategy of constantly ignoring everything except one small point you wish to challenge, whilst making no attempt to address the other parts of the consistent explanations I provide.
You seem to be just quibbling for the sake of argument whilst your position is untenable.
I have pointed out quite clearly that in SR there is no difference in the relativistic measurement shortening to be expected of the distance between two objects (whether at constant or varying velocity) as that between two points on a given object.
This is consistent with the standard view among the most authoritative names in the field that the measured “contraction” is only apparent, is due to the relatively different simultaneity and can be likened to the effect of perspective.
You’re problem is that you are unable to escape the idea that what is measured must be what is actually physically “really” happening. That this cannot be the case is demonstrated by the reciprocity of the effect. Attempts to claim that there is a “different” kind of contraction for constant motion and acceleration fail because they are not part of SR, not acknowledged by experts and lead to nonsense like trying to distinguish an accelerated rod from one already in constant motion (that I’ve already asked you twice, without response).
Your delusion that the string must break in the two rockets scenario is, as I have shown in detail in my previous, due to applying two different methods of determining distance for each case.
For the string you are happy to take the relativistic simultaneity measurement that yields a shorter result [whilst of course the “proper” length remains constant] but….
Contrariwise, for the inter-rocket distance, you conveniently discard relativity and “simultaneous” locations and argue from a Newtonian perspective that because they start at a given distance, they must remain so.
How about using the same argument for a string or rod ? The ends are a certain distance apart and since each end has at all times identical velocity and identical acceleration, then the ends must stay at the same distance ??
Now I expect you would want to try and wriggle out of that by arguing the rear end of the rod must accelerate faster (and have different velocities) to “catch up” ? Unfortunately that leads straight into non-SR Lorentz theory, where the reciprocity is lost and an absolutely stationary frame exists.
Let’s distinguish what’s going on. The “proper” length of the string corresponds to the distance between rockets as “parallel” trajectories as you would have it. This doesn’t involve relativistic measurement and means proper string length stays equal to “expected” rocket distance.
The “contracting” string length is the result of a specific type of “simultaneous” position marking measurement and if the same procedure is applied to the two rockets each travelling (like the string ends) at the same velocity, then the same shortened result will be obtained for exactly the same reasons.
The proper length of the string is not measured but “by definition” remains constant, just as the rocket distance that “by definition” remains constant, is also not measured. When the appropriate measurement procedure is followed SR predicts exactly the same result because the “mechanism” creating an apparent shortening applies irrespective of whether the moving length is between two point on a body, or points on two seperate bodies in identical motion.
Hi SL, you wrote:
“Observe” would be the better term, in which case there is no such thing as the “stay-home twin aging much more rapidly during the turn-around period”
I suppose Fred can argue that the away-twin can measure the changing redshift of a signal that her brother sends out and hence is observing his clock speeding up during her turn-around acceleration.
I would say that the sister knows her velocity and acceleration status by means of on-board Doppler devices and accelerometers and should compensate for that. Her observation of the age of her brother comes from the data after the compensation and would agree with SL’s synchronized clocks.
This is just like compensating for light travel time when observing the time of a distant event.
Regards,
Burt Jordaan (www.Relativity-4-Engineers.com)
Methinks you’re getting a little too picky, SL. Not your usual style.
When recapitulating an old argument, I used a less precise verb, to see, than in my original statement, where I talked about the measurement of time.
How do they see time? They look at clocks, of course. In other words, they measure it. As I pointed out early in this thread, there’s no other reality, scientifically speaking, than that which can be observed or measured.
Fred Bortz — Science and technology books for young readers (www.fredbortz.com) and Science book reviews (www.scienceshelf.com)
Fred wrote:
It is exactly this sort of statement (using the vague term “sees”) that causes a lot of confusion. “Observe” would be the better term, in which case there is no such thing as the “stay-home twin aging much more rapidly during the turn-around period”.
The easiest way to do such observation is for the stay-home twin to have laid out a set of equidistant clocks, all synchronized to his own clock. Sister can then read off twin-brother’s aging directly from these clocks as she passes them and she will observe him to age gradually and always faster then herself, for as long as she is moving relative to his frame.
Like Fred, I’ll stay out of the debate between Burt and the ‘rockinggoose’.
SL: Your Aerospace Watchdog
Scruffy writes:
That probably needs a little clarification.
Burt and Christopher led me to rethink the situation in circumstances where acceleration effects are so low that the gravitational redshift is negligible, and we only need to consider the effects of special relativity–especially the degree of mis-synchronization of the clocks as the twins get farther apart.
That is why the adjective “direct” is important in Scruffy’s statement.
But the fact that only one twin experiences acceleration is, of course, a crucial distinction. So the fact of acceleration plays a role even if the value of the acceleration is so small that we can neglect it in comparing clock rates.
At the close of a long comment above, I write why the explanation described in that comment satisfied me:
My reference in that statement is to the fact that I was trying to analyze the way the age difference accumulates as viewed by each twin.
The stay-home twin sees the age difference increasing monotonically, while the traveling twin sees the stay-home twin aging more slowly during the periods of coasting, but aging much more rapidly during the turn-around period. When they finally meet again and are at rest with respect to each other, they compare wristwatches. Each measures the same net difference in age for the period of separation, and neither is surprised at the other’s result.
Fred Bortz — Science and technology books for young readers (www.fredbortz.com) and Science book reviews (www.scienceshelf.com)
Hi rockinggoose, you wrote:
“I’m afraid Burt’s version of the rockets & string scenario in which Scruffy can find no flaw, is hopelessly flawed. I also notice that the notion of the rockets staying at fixed distance “by definition” [ what definition ?, from where ? ]”
OK, let’s stop beating around the bush and show us the relativistic math that proves that the centers of mass of two identical (line astern) rockets with identical accelerations relative to the original inertial frame (hereinafter the ‘reference frame’), starting simultaneously in the reference frame, do not stay at a fixed distance apart in the reference frame. I’ll bet on it that you can’t give rigorous prove for that, but prove me wrong.
By mathematical definition, identical accelerations (dv/dt), starting simultaneously, result in identical velocities at any reference frame time. Identical velocities mean zero relative velocity, yielding unchanging separation in the reference frame. This is true for Newtonian as well as relativistic dynamics.
You must remember that the two rockets do not comprise a single object that Lorentz contracts – they are forcefully held at the same acceleration in the reference frame. In fact, if your position is that the separation (distance in reference frame) between the nose of the trailing rocket and the tail of the leading rocket contracts, it is doubly flawed – the rockets themselves Lorentz contract, so the coordinate distance between the two mentioned points increases, but for simplicity, let’s leave that out of the equations that you are to supply to convince us. (Edit: i.e., assume that the rod/string is attached to the center of mass of each rocket.)
This coordinate distance issue is the crux of our disagreement, so it is fruitless to continue if we can’t resolve it.
Regards,
Burt Jordaan (www.Relativity-4-Engineers.com)
Hi Burt & Scruffy
I’m afraid Burt’s version of the rockets & string scenario in which Scruffy can find no flaw, is hopelessly flawed. I also notice that the notion of the rockets staying at fixed distance “by definition” [ what definition ?, from where ? ] seems to come from Wikipedia ! [The reason Wikipedia is dismissed by academia is because there is zero quality control & anyone whatever their misconceptions can replace the previous content so that the prevailing entries reflect more dogged persistence than enlightened contribution.]
Firstly let’s take a cue from W.Rindler and consider the perspective analogy. If you look down a set of railroad tracks running off into the distance, the sleepers (string) appear to contract with distance (velocity) but the tracks themselves (rockets) “by definition” stay at the same distance. Spot the error in reasoning.
Secondly, contraction is only apparent as clearly stated by Wheeler, Bohm etc. because it is the result of differing simultaneity causing the front to be registered before the rear, from point of view of “moving” frame whilst seeming simultaneous from “stationary” frame. This is the same process as during acceleration, where the objects are smoothly passing through a range of velocities.
That it is certainly not physically real is further shown by using instead the simultaneity of the “moving” frame, where we would obtain increased lengths with increasing velocity so that the moving length gets longer as it accelerates. It just depends on what procedure is used for measurement.
Now let’s consider a statement about relativistic length contraction:
The [rod] appears to be shorter because relativity of simultaneity causes the position of the front [end of the rod] to be marked before the position of the rear [end of the rod].
Now when we replace [rod] by [distance between rockets] and [end of rod] by [rocket] we have a simple and correct statement that the rocket distance also “contracts” when it is measured by the same means as the rod. The last statement is important because Einstein’s theory lays down specific means for synchronising spatially separated clocks and using such synchronised clocks for measuring moving lengths.
Burt’s mistake is to think that there is some other abstract way of determining length during acceleration without measuring it. In effect he’s claiming that the rockets stay at the same distance in Newtonian terms whilst reserving relativistic effects for the string.
If one were to say that “by definition” the proper length of the string remains constant (as is the case), we can see that the “argument” tacitly allows relativistic measurement shortening to act on the string, while for no rational reason witholding it from the inter-rocket distance, for which the same “relative simultaneity” would in fact shorten the measured distance.
Also Scruffy is under a common misconception that the “Twin Paradox” requires acceleration for its resolution. It has been pointed out many times that this is not so. It has got nothing to do with acceleration.
Not only can the period of travel be indefinitely extended before turnaround to render the effect negligable, but also if clocks are used instead ( and more accurately !) a third identical clock can be supposed to be incoming from a distance and be synchronised with the outgoing clock at the moment they pass, thus carrying the time back without any acceleration being involved.
Hi SL, good to hear from you again.
You wrote: “How do you reconcile the two perspectives? As rockinggoose said, you can’t have it both ways! :p”
What both ways? There is no difference between the “realness” from a measurement point of view – time dilation and length contraction are ‘real and measurable’ effects in both cases. The acceleration is just a “crutch”, so to speak, in order to be able to measure time dilation and length contraction more or less independently from simultaneity.
In the ‘rockets and rod’ case, we replace the conventional synchronized clocks and standard meter sticks with directly measurable identical accelerations (of arbitrary magnitude), lasting for identical times in the reference frame. So, the acceleration is not the issue, it is velocity time dilation and length contraction that count, ‘real and measurable’.
Just as real and measurable as the fact that “Bell’s string” would break!
Regards,
Burt Jordaan (www.Relativity-4-Engineers.com)
Burt, I can find no flaw in your “rockets and rod” conclusion, but it brings up an interesting issue:
Just like the in the ‘twin paradox’ where the age difference only becomes ‘real and measurable’ when acceleration enter the scene, it appears that length contraction also only becomes ‘real and measurable’ when acceleration is present.
When acceleration is absent, it seems to me that both effects are due to simultaneity definitions that differ. As you noted, there is no simultaneity issue in the “rockets and rod” from the perspective of the reference frame. Neither is there any simultaneity issue when the traveling twin comes back to her brother – they can both read each other’s clocks directly.
However, you seemed to have convinced Fred above that acceleration does not play a direct role in the aging (or not) of either twin. How do you reconcile the two perspectives? As rockinggoose said, you can’t have it both ways! :p
SL: Your Aerospace Watchdog
Hi rockinggoose, you wrote:
“Why have you avoided answering my obvious question about what difference you surmise to exist between the constant velocity metre rod “contracted” to 90% and one I accelerate up to the same velocity where it will also appear as 90cm ?”
Hmm…, maybe this offers a way to finally settle the Bell ‘paradox’ issue. Do you agree with the following variant, based on your question:
The relativity of simultaneity does not enter into this argument because the simultaneity definition of the reference frame has not changed. What observers in the reference frame measure is ‘real’, as T&W and Thorne argued. For those observers, the rod had to be stretched by the rockets in order to stay attached to both.
I’m prepared to continue with this discussion only if we can concentrate and hopefully agree on the outcome of the above scenario, one way or the other.
Regards,
Burt Jordaan (www.Relativity-4-Engineers.com)
Hi Burt
You couldn’t be more wrong ! I’ve already pointed out that acceleration makes no difference to the reciprocal nature of contraction, and therefore its physical reality. The next two sentences you omitted in the extract you used from my quote state explicitly that the contraction is only “apparent” [their word] and purely a result of relative simultaneity affecting the process of measurement.
Why have you avoided answering my obvious question about what difference you surmise to exist between the constant velocity metre rod “contracted” to 90% and one I accelerate up to the same velocity where it will also appear as 90cm ?
The apparent contraction is in SR simply the result of relativity of simultaneity causing the front end to be registered slightly before the rear end as judged by an observer riding on the rod, whilst they may be “simultaneous” in the different frame of the “stationary” observer.
You seem to forget that if simultaneity in the “moving” frame is used instead, as in the train carriage with a firecracker at each end detonated from the centre leaving soot marks further apart than the original[ proper, normal, or stationary ] carriage length. They would also get further apart as the train accelerated.
As far as the Lorentz transformations go, acceleration is merely change in velocity and at each instant the “contraction” relating to that velocity is reciprocal and apparent.
As David Bohm says: Instead of assuming they are real ie. structural changes in length and duration owing to motion, Einstein’s theory involves only apparent changes, and these are independant of the microscopic constitution….Unlike real changes, these apparent phenomena are reciprocal.”
Or Wolfgang Rindler:
“Relativistic effects are comparable to perspective effects….Moving lengths are reduced, a kind of perspective effect. But of course nothing has happened to the rod itself…” and Rindler goes on by saying that the effect is real – thus showing that the use of the word “real” [by him and others] is not meant to be thought “physically real” but just that the apparent shortening is a real measurable effect.
It’s no good trying to claim that acceleration is “different”. Do you really suppose that Wheeler, Bohm, Rindler and others simply forget to mention such a striking fact ? Have they overlooked mentioning it ? Where, in any book, have found such a phrase as “Oh, by the way, this constant motion contraction is not to be confused with that resulting from acceleration which is no longer reciprocal etc.” ?
I think the opinion of world acknowledged authorities like Wheeler, Thorne etc. is rather more reliable than that of relative unknowns from obscure institutions. The absence of formal refutations is not confirmation of veracity, and I’m surprised that you should suggest this. Physicists have got better things to do, ie. have neither the time nor inclination to search the internet for half-baked articles of which to write formal rebuttals. There’s just way too much dross out there. [I notice Nicolic has also written proposing black holes do not evaporate, but I doubt if black hole theorists are rushing to submit formal refutations.]
You also say Mallinckrodt and Nicolic are “essentially saying the same thing”.
Have you actually read them ? Nicolic is proposing a pulled rod contracts faster than a pushed rod, which has got nothing whatever to do with Mallinckrodt’s slides proposing (among other things) an event horizon related to acceleration. [He also consigns himself to a tiny minority with his title – What ? do you mean to say hardly anyone else realised these things in only a hundred years !]
Hi rockinggoose, you wrote:
“I think you’ll find that what I said does indeed follow from the quotes I gave. ”
I don’t think so! Those quotes have nothing to do with accelerated systems.
“Although it’s true that acceleration can always be distinguished from inertial motion, that does not mean that there must be two types of contraction – one absolute involving mysterious forces somehow “pulling the object together” along its motional direction; and another relative type that is perfectly reciprocal. I know of no text that makes such a claim. ”
Who said anything about “mysterious forces somehow pulling the object together” apart from yourself? In accelerated systems it is the original inertial frame of reference that observes the length contraction of the accelerated rod. In the rod-frame, its length remains constant (if assumed to be perfectly rigid).
However, in the Bell spaceship ‘paradox’, the two identically accelerating ships remain at constant separation in the inertial reference frame (by definition, i.e., identical coordinate accelerations and speeds at all times). If the string was only attached to the leading ship, the inertial reference frame will observe it to Lorentz contract. To remain attached to both ships, it must be physically stretched to a longer proper length.
If we analyze the situation from the rod-frame’s point of view, the leading ship pulls away from the trailing ship. Although their coordinate accelerations are the same, their proper accelerations differ (see Prof. John Mallinckrodt’s presentation: “Simple, Interesting, and Unappreciated Facts about Relativistic Acceleration”). The unattached string remains at constant proper length, but the moment it is attached to both ships, it is stretched. No paradox. And nothing shrinks in absolute terms; something is however stretched in absolute terms in Bell’s scenario.
If we cannot agree on these standard relativistic interpretations of accelerated frames (including Nikolic’s paper), it is a waste of time to argue in circles around it.
Regards,
Burt Jordaan (www.Relativity-4-Engineers.com)
PS: any luck in finding a formal debunking of Nikolic’s paper? (and Mallinckrodt’s presentation, for that matter, because they are essentially saying the same thing).
Hi Burt
I think you’ll find that what I said does indeed follow from the quotes I gave. Although it’s true that acceleration can always be distinguished from inertial motion, that does not mean that there must be two types of contraction – one absolute involving mysterious forces somehow “pulling the object together” along its motional direction; and another relative type that is perfectly reciprocal. I know of no text that makes such a claim.
That the contraction “is not due to any forces” supports the perspective analogy and rules out the appearance of tension in the string scenario. Since T&W make it clear that contraction is of the measurements due to relative motion affecting simultaneity of the measuring process, it follows that two identically accelerating rockets will exhibit a contracting distance just like any object.
Your use of Michelson-Morley is incorrect. The Lorentz-Fitzgerald contraction hypothesis was to explain the M-M null result when the wave theory of light would predict back and forth time should exceed side-to-side and cause a fringe shift. Einstein introduced the constant to-and-fro speed of light instead as a starting hypothesis so that “real” contraction (of the interferometer) was no longer necessary – indeed to include it as well would reintroduce a fringe shift prediction.
The “proper” length of a rod is its real physical length and this does not change regardless of whether the rod increases in speed or the observer does so. The reciprocation of the contraction in SR is independant of which accelerates.
Consider an an inertially moving metre rod that measures say, 90cm according to us. If we now take our metre rod and accelerate it up to same speed it will also measure 90cm, but what you are suggesting is that there will be some difference in the moving frame between the two rods because one was “accelerated” and the other not !
Although measurements give the appearance of contraction in SR, the proper length remains unchanged and therefore the acceleration and the “inertial” force associated with it must be constant along the length.
Furthermore, in SR the contraction is independant of whether the rod is pushed from the back, pulled from the front or propelled from any other point along its length.
If “real” physical contraction is assumed (departing from SR) then you immediately have problems deciding for instance for a non-uniform rod where most mass is in the front or back half, whether contraction takes place around the geometric centre or the cenre of mass ! Without any “dynamical” theory of contraction, such questions are insurmountable.
What Nicolic does is define an acceleration for the point x at the front or at the rear, from which it seems the rod will “contract” forwards or backwards respectively towards the point of propulsion. Thus the bulk of the rod when back propelled will have slightly lower instantaneous velocity than when front propelled, and thus have a slightly lesser “contraction”. To put it another way the length will seem to contract “quicker” when pulled than when pushed.
All this is wrong, however, for two reasons:-
First the “real physical” contraction is outside SR so it’s misconceived from the outset, and
Secondly his assumption that contraction happens toward the propulsion point is not justified. Imagine a typical NASA type rocket undergoing “real physical” contraction – it is not realistic to suppose all the rest of the rocket contracts towards the engine unless you define it so. The only reasonable assumption for such a non-SR scenario would be contraction about the centre of mass, otherwise you run into problems with conservation of energy.
Hi rockinggoose, you wrote:
Note that he effectively says the contraction is “real” as far as can be measured and caused by “the peculiar nature of space and time. ” How else would the Michelson-Morley null result be interpreted? Also note that Thorne did not speak of accelerated frames here…
You quoted Taylor & Wheeler:
To which you commented: “It follows from their description that proper acceleration does not change linearly along the length of an accelerated rod. ”
I would like to learn how you find what you wrote to follow from the T&W quotation. I’m pretty sure that Wheeler will not agree with you! Your example using perspective ‘contraction’ also has nothing to do with accelerated rods. Perspective may be similar to inertial frames in relative motion, meaning it is a reciprocal ‘contraction’ effect as viewed by either observer. An accelerated frame cannot be exchanged for the inertial frame to obtain reciprocal effects, because (proper) acceleration is absolutely measurable. One frame accelerates and the other one not.
On Nikolic’s paper, you wote:
Whose authoritative opinion is that? Did you find a proper debunking anywhere? You were quoting the authorities Thorne and Wheeler, although the quotes were somewhat irrelevant to the accelerated rod problem. H. Nikolic is also a highly regarded physicist, with lots of publications in respected journals.
The accelerated rod is not contracting in its own frame of reference, but rather as measured in the inertial frame. At the same time, the two rockets are accelerating identically relative to the inertial frame and stay a constant distance apart, while the rod (string) contracts in that frame, so how can it not be stretched? Contraction may not be ‘real’, but that stretch is a real physical effect, applying a force to the string, just like tidal gravity stretching is a real physical effect.
With all that said, SL’s thread does not deal with accelerated frames, but only inertial frames. There, the contraction effects are more slippery and hard to understand. However, there is always the Michelson-Morley type of interferometer test that says something about the ‘realness’ of the contraction – how can there be no difference in the two-way times along the two orthogonal arms if the one arm does not contract?
Regards,
Burt Jordaan (www.Relativity-4-Engineers.com)
May I suggest that close attention is paid to the quotes I included from Kip Thorne and Taylor & Wheeler ( that’s John Archibald Wheeler ) that make it quite clear that the contraction in Einstein’s SR ( as contrasted with Lorentz-Fitzgerald ) is not a physical contraction but an aspect of measurement between relatively moving frames connected with the different simultaneity with which endpoints are recorded.
I particularly chose those quotes among others because J.A.Wheeler is about the most respected authority in the field of relativity and Kip Thorne is another as well respected as any I could think of.
It follows from their description that proper acceleration does not change linearly along the length of an accelerated rod. I included the D’Inverno quote to highlight the fact that misleading and incorrect information did not arrive only with the internet but was always present here and there in published material.
Nicolic’s paper is a not uncommon example (especially on the internet) of erroneous work produced by somebody who has either not properly understood SR, and/or has failed to appreciate the important difference between it and Lorentz’s theory.
To show the kind of error of reasoning involved, let me use the analogous perspective “contraction” due to distance.
If I have a horizontal line on the ground, then objects will “contract” in dimension as they move away perpendicular to the line, in propertion to distance. The effect is reciprocal.
Suppose two people 20 yards apart along the line, hold a cotton thread taut between them and each marches perpendicular to the line in the same direction.
Since I “know” that the thread will contract, and I also reason that the two people are moving parallel and therefore maintaining the same distance, then it follows that the thread will be stretched until it breaks, right ?
If we use the right hand end as a reference, an object seems to contract from the left, and vice versa, with the LH end as reference, contraction happens from the right.
So with an accelerating rod, if we use the forward end as our reference, it could seem that contraction is in the direction of motion from the back end, which we could (wrongly) deduce will have a slightly higher acceleration than the front.
Similarly if we use the back end as reference point, contraction “seems” to occur against the direction of motion from the front end.
Thus if we persist (contra to Wheeler & Thorne) in regarding the contraction as real physical shrinkage we not only are misled into thinking that acceleration changes along the rod, but that pushing a rod from the back is in some way manifestly different from pulling it from the front. This may be an interesting aspect of the old Lorentz theory but it has no place in Special Relativity.
rockinggoose wrote:
“Also far from being “undisputed”, the Nicolic paper is simply wrong, as you can easily verify yourself.”
I would be interested to know of any formal paper disputing (debunking) the Nikolic paper. I have in mind something more technical than the (technically flawed) reasoning that you supplied. You seem to have missed the meanings of those equations (21 and 23). They give different results, which represent the length contraction profiles as viewed in the original inertial frame. As shown in figure 1, they are for the cases where the constant acceleration is applied to the back end and front end of a rod respectively. If SR is right, then those results are perfectly correct.
“Therefore the main “result” of the paper is a trivial co-ordinate change !”
Proper acceleration changes linearly along the length of a rod accelerated lengthwise. This explains why the result has the appearance of a simple coordinate change, while it is not. When the rear end is accelerated at a, the front end accelerates at a_f a. This is stock-standard SR. One cannot dispute it without disputing SR.
Burt Jordaan (www.Relativity-4-Engineers.com)
I think it should be made clear that there are two distinctly different theories: Lorentz’s and Einstein’s. In the former, contraction is due to velocity with respect to an absolute space and is a real physical shrinkage that could cause mechanical tensions that could for instance break strings etc.
In the latter, contraction is an effect of the measurement process itself and thus has no physical effect on the object itself.
It is not consistent or acceptable to use a “pick’n’mix” combination of the two theories whereby you have two different types of contraction, one for constant motion and another for acceleration. Within each theory there is just one process of contraction and it arises differently in the two theories.
For the “standard” SR view, let’s hear from Kip Thorne:
“This was the contraction inferred by Fitzgerald, but now put on a firm foundation: The contraction is caused by the peculiar nature of space and time, and not by any physical forces that act on moving matter.”
And in Taylor and Wheeler we find:
“Is the contraction real or apparent ? We might answer this question by posing a similar question. Is the frequency, or wavelength, shift in the Doppler effect real or apparent ?…..When the source and observer are in relative motion, the observer definitely measures a frequency (wavelength) shift….The effects are real in the same sense that the measurements are real. We do not claim that the proper frequency has changed because of our measured shift….The effects are apparent (that is, caused by the motion) in the same sense that proper quantities have not changed.”
“We do not speak about theories of matter to explain the contraction but, instead, we invoke the measurement process itself.”
“Since length measurements involve the comparison of two lengths….we can see that the Lorentz length contraction is really not a property of a single rod by itself but instead is a relation between two such rods in relative motion.”
Nevertheless some authors seem to be confused, like Ray D’Inverno, author of a well known book on relativity, who writes (on page 33):
“In an attempt to explain the null result of the Michelson-Morley experiment, Fitzgerald had suggested the apparent shortening of a body in motion relative to the ether. This is rather different from the length contraction of special relativity, which is not to be regarded as illusory, but is a very real effect.”
Whatever view one takes of the “reality” of the measured contraction in SR, D’Inverno’s statement is quite wrong in regarding Fitzgerald’s contraction as less real than SR when it was in fact an absolute physical shrinkage of the interferometer that was hypothesized to explain The M-M null result.
No, this is wrong. If we are dealing strictly with standard SR then the whole concept of relativistic contraction is an effect of the measurement and therefore, not being physically real, cannot break strings etc. That acceleration is a vector has got nothing to do with it. There is no reason to suppose that the rockets will “pull away from each other”. This is merely a fanciful “reversing” of the “real Lorentz contraction” following the dubious “parallel trajectory” assumption I mentioned.
Now I realise that we would all like to believe that our views are “mainstream” views but I’m afraid that in this case there is plenty of divergent opinion. The originators of the problem were contradicted at the time, Bell (remember he disdained Einstein’s SR in favour of Poincare-Lorentz ) had all the CERN theorists against his view, and a recent resurrection of the problem in a Japanese journal was strongly opposed within the academic community.
Also far from being “undisputed”, the Nicolic paper is simply wrong, as you can easily verify yourself.
Look at the crucial equations (21) and (23) which represent the distinct scenarios. In fact they are the same equation ! All that has happened is that in one the rod is represented as from x-L to x whereas in the other it is represented as from x to x+L as you can easily check by substitution. Therefore the main “result” of the paper is a trivial co-ordinate change !
Hi Rockinggoose, you wrote:
“Some people favour one side, some the other and some withhold commitment, but there isn’t necessarily a “modern” view – and furthermore, even if a “modern view” were to adhere to string breaking, such would be to assert the absolute physical reality of the contraction and hence reject the reciprocal nature of SR.â€
The accelerating rocket problem is obviously not reciprocal. The standard SR interpretation says that the string will break, because the leading rocket will pull away from the trailing one. Acceleration is a vector and has an absolute direction, so there is never any doubt as to which one is leading.
You later wrote:
“In the rocket and string problem the crucial assumption in deducing string breaking is that since the trajectories must be parallel then any later distance must be the same as the starting distance. But we must distinguish between measurement and deduction here. â€
In this particular case, with constant and equal proper acceleration for both rockets, the separation in the inertial reference frame remains the same, but the proper distance between the rockets increase and hence the string breaks. I do not know of any mainstream relativist that disputes that analysis.
“ As I said before, the issue of string breaking depends on the very issue of this blog, ie, the “reality” of relativistic contraction; and opinion on that is as divided as it ever has been. â€
I think SL had the non-accelerated case in mind, where simultaneity plays a big role in the analyses. The accelerated case is not quite a GR scenario, as Fred seems to hold, but can be totally solved within SR. However, simultaneity becomes a thorny issue in accelerated frames of reference.
Apart form the reference that SL quoted, another accessible treatment of the (rigid) accelerating rod is H Nicolic: http://arxiv.org/abs/physics?papernum=9810017. Many analyses of the Bell spaceship paradox are based on this undisputed paper.
Burt Jordaan (www.Relativity-4-Engineers.com)
Rockinggoose honks, “In the same way if the contraction in relativity is not physically real but a measurement effect,…”
That gets us back to the beginning of this thread when we struggled to define the term “physically real.”
What is reality other than what we measure?
The reality is that A measures B’s meter sticks to be foreshortened and B measures A’s meter sticks to be foreshortened. Likewise, each measures the other’s clocks to run slowly and to be out of synchronization.
Though that reality boggles the mind of one whose instincts are forged in a non-relativistic environment, it is completely consistent with the laws of physics that both observers agree upon.
When you start to discuss the rocket and string problem, you introduce both the properties of materials and relative acceleration. The latter moves us out of the realm of special relativity and requires a general relativistic analysis.
In any case, it’s clear that whether the string breaks or not, both observers will agree about that fact, and it will be consistent with the laws of physics and the properties of the materials involved. If we assume that each observer is a good physicist and applies the properties of materials and the laws of mechanics properly, then each should predict the result correctly.
With that, I’ll hop back to the sidelines.
Fred Bortz — Science and technology books for young readers (www.fredbortz.com) and Science book reviews (www.scienceshelf.com)
In the rocket and string problem the crucial assumption in deducing string breaking is that since the trajectories must be parallel then any later distance must be the same as the starting distance. But we must distinguish between measurement and deduction here.
Let’s take the common analogy of “perspective” for the contraction whereby objects shrink as they get further away rather than getting faster.
If I’m on a platform and a distant railway carraige looks or measures shorter than a nearby one I can project a perpendicular at the rear of the near carraige that will graze the rear of the distant one. I can also move to the front and construct another perpendicular that grazes the front of both. I can thus deduce that the end-to-end distance has not “really” reduced for the far carraige.
But my direct measurements with say, a tape measure held in front of me will still show the contraction of perspective.
In the same way if the contraction in relativity is not physically real but a measurement effect, it will apply to the rockets as well, and a “deduction” based on “parallel” trajectories will not change the situation, just like the deduction from perpendiculars does not affect the measured perspective.
As I said before, the issue of string breaking depends on the very issue of this blog, ie. the “reality” of relativistic contraction; and opinion on that is as divided as it ever has been.
The header of this thread is “Is Einstein’s time dilation and length contraction real ?” Leaving aside the grammatical error I would like to point out that this debate has continued for over a century.
The positions are that the Fitzgerald-Lorentz contraction first hypothesized to account for the Michaelson-Morley expt. has always been regarded as an absolutely real physical shrinkage, whereas the SR contraction, because among other things of its reciprocal nature, has generally been regarded as “apparent” or an effect of measurement. This is because it is obviously impossible, not to say absurd, to suggest that:
length A < length B whilst length B < length A, whereas of course, to say that A's measurement of length B < length A is perfectly compatible with the condition with A & B reversed.
Now in the rocket string problem it is clearly the case that:
"Real" Lorentz-Fitzgerald contraction means the string breaks but…
If "measured" SR contraction is not physically real it means the string does not break.
Some people favour one side, some the other and some withhold commitment, but there isn't necessarily a "modern" view – and furthermore, even if a "modern view" were to adhere to string breaking, such would be to assert the absolute physical reality of the contraction and hence reject the reciprocal nature of SR.
Rockinggoose wrote:
The modern view can easily be derived from this easy-read presentation by dr. John Mallinckrodt of Pomona university. It deals with the acceleration of a rigid rod, but it is easy to deduce from it that if the rockets accelerate identically, then according to standard special relativity, the string must stretch.
For the string not to stretch, the front rocket must accelerate less than the rear rocket, just like the case of the two ends of the rigid rod.
Either you accept special relativity and conclude that the string must stretch, or you are effectively rejecting special relativity.
http://www.csupomona.edu/~ajm/professional/talks/relacc.ppt
SL: Your Aerospace Watchdog
Scruffy wrote “I thought I had made it quite clear that SR predicts…etc” but no, you have only made it clear what you believe will happen. Opinions vary.
As I indicated in my previous, those ( like John Bell ) who prefer the Lorentz – Poincare reality and disdain Einstein’s version with its unrealistic reciprocity etc. tend to expect the string to break, but those who closely follow the detail of Einstein’s SR with its geometrical kinematic structure expect no breakage. ( In Bell’s case he felt the observer dependancy could violate causality in EPR type experiments, but all his colleagues disagreed with him.)
As for Wikipedia, apart from its main reputation for notorious unreliability, I would point out that there are references that support either side and some of those listed are irrelevant to the problem.
Also look at “Lorentz Contraction” in Wiki, where you will find a classic presentation of the geometric argument, where the various contracted lengths are different “simultaneity slices” through the “world tube” of the object – which would obviously predict no string breaking but rather that the inter-rocket distance shortens exactly as the string-ends.
If you do any survey of textbooks on or including SR, you will find that the rocket/string problem is hardly ever mentioned and that the rotating disc paradox never is. There is a good reason why these are avoided in favour of “easy” explanations of the twin paradox & pole and barn problem etc. It is because they lead into deep and dark waters at the foundations of relativity and have no widely accepted resolution.
Con, your post does not address the issue of simultaneity or the synchronization of clocks that are separated in space. Michelson, Morley, LIGO and light clocks use interferometers and/or two-way measurements, which are not under dispute.
The issue is that the one-way speed of light depends on synchronization of clocks, which are conventional, not absolute. Also, synchronization does not concern the rate of the clocks, but how they are set to read the same time (the definition of simultaneity in an inertial reference frame).
The question is, does length contraction also depend on clock synchronization. If so, then Lorentz contraction is a convention. Looking at solutions to the “ladder paradox”, it seems to be the case.
SL: Your Aerospace Watchdog
rockinggoose wrote:
I thought I made it quite clear that SR predicts that the string would break, but as many others, I’ve got some reservations! This is in line with your view, except for your original statement that SR cannot solve this. I suppose it depends on what you mean by “solve”, but SR makes a definite prediction.
SL: Your Aerospace Watchdog
Con Morton wrote about inertial frames and light clocks (i.e. the standard SR stuff), but does not address the issue at hand: synchronization of clocks and hence simultaneity are conventional and may make length contraction just a convention as well.
Actually I thought the clocks were well synchronized in that the each recorded the same time duration when in the same reference frame. The first paragraph really just sets the table and is an reiteration of time dilation and mass increase that is proven almost daily in particle accelerators around the world. The crux is in the second part when one of the traveling clocks is rotated so that its axis is parallel to the direction of motion. In this case the question becomes. Does the clock read the same time in the same frame independent of the pointing direction of the clock? The fist cut without the Lorentz contraction results in the clock not agreeing with itself which is contrary to logic and numerous tests, Michelson, Morely and LIGO for example. The second cut invoking contraction results in the clock not knowing which direction it is pointing and agreeing with itself. In this case the moving clock in question is synchronized with itself being the same clock and the observers clock is only required to measure the same duration between ticks as only ratios are being observed.
There were a few word drawings with the origonal post that did not come through.
Incidentally the string breaks and if the ships are long enough it breaks befor the pilot of the trailing ship knows he is moving, providing the pilots are in the noses of the ships.
Thanks…..Con
I think your answer is somewhat self-contradictory ! If you are not clear as to whether the analyses represent reality or not then you cannot be sure the string will break, for such a breakage would definitely be physically real.
The problem is that the earlier views in this thread suggest that the Lorentz contraction is not a physical shrinkage but an artifact of measurement – which would accord with the “impossible” reciprocity whereby length A < length B and length B < length A.
Also with the multitude of different lengths for arbitrary observers and with Einstein's kinematic (ie. non-dynamic) derivation.
All of which suggest that the string would not break but that the whole assembly would behave like an irregularly shaped rod – and therefore the rockets would be measured as getting closer as the string gets shorter.
Unfortunately this conflicts with translational symmetry in that the rocket trajectories should be able to be translationally superimposed.
To claim that the string breaks is also to revert to Lorentian relativity that pre-dated Einstein, where the contraction is regarded as physically real as thermal expansion or contraction.
There is definitely a deep contradiction in this problem that (Wikipedia notwithstanding !) divides opinion about equally. Which is why I said the issue was still as yet unresolved.
[Another even worse paradox is the Ehrenfest problem of the rotating disc, on which conflicting papers are still being published on an almost monthly basis]
Con Morton wrote about inertial frames and light clocks (i.e. the standard SR stuff), but does not address the issue at hand: synchronization of clocks and hence simultaneity are conventional and may make length contraction just a convention as well.
SL: Your Aerospace Watchdog
Anonymous wrote:
“Surely the really awkward problem for Special Relativity is the Bell spaceship problem … SR cannot solve this question !”
I disagree with your statement, but I agree that the way scientists solve it may be suspect due to the clock synchronization issue.
If the two rockets are identical and have the exact same acceleration profiles, special relativity predicts that the string will break, without a doubt. Read the various Wikipedia analyses and references in there. To me the fuzzy thing is still the conventionality of simultaneity and my mind is nor clear as to whether the analyses represent reality or not.
SL: Your Aerospace Watchdog
Surely the really awkward problem for Special Relativity is the Bell spaceship problem (originally by Dewan & Beran 1959) where two identical rockets are connected nose to tail by a thin string and accelerate identically. Does the thread eventually break due to Lorentz contraction ? SR cannot solve this question !
Posted by Con
This goes back to your first post.
If I consider my frame my reference frame then any object that has a relative motion to me is in a different frame. Any object that is without relative motion to me is in my reference frame. The relative motion that I can measure is either towards me or away from me, inertial motion only as we are talking about SR.
Your moving vehicles are moving in relation to the light source, point A which is the reference frame. Let them be B and C. Also lets place identical light clocks at A and in B and C and positioned such that the light paths in each clock is at 90 degrees to the track of B and C. Note that the Acme Light Clock Co. specifies that the maximum deviation between any two clocks is less than one pico second per year when measured under their standard conditions at their laboratory location. Now suppose that B is moving from right to left at 0.86603c (Vab) with respect to A and C is moving from left to right at 0.86603c (Vac) with respect to A and that they have both passed A. I have chosen velocities so that Y (gamma) equals 2 for this example. Now an observer at A notes the clock in C ticks one time for every two ticks of the reference clock at A, looking at the clock in B also ticks one time for every two ticks of the reference clock at A. As far as A is concerned the clocks in B and C agree with each other and they are running at half the rate of the clock at A. Of course B and C do not agree. First the relative velocity of B with respect to C or C with respect to B must be determined. As these are relativistic velocities they do not simply add. Then Vr = (Vba+Vac)/( 1+ Vba*Vac) which equals 0.98797441c and Y equals 49 so B sees C’s clock ticking once for every 49 ticks of his and C sees B’s clock ticking once for every 49 ticks of his. However if B and C return to A’s reference frame, in the same manor then their clocks will agree tick for tick and show the same time, they will agree tick for tick for A’s clock but will only show one half the elapsed time from the original time they passed A.
Light clocks.
Transverse stationary Moving at 0.86603c
The stationary light clock counts seconds, one second each time the light pulse travels from one mirror to the other, the vertical distance between mirrors is 3*10^8 meters (L). The stationary observer sees the moving clock a bit differently. After one second the clock has moved horizontally 0.86603c and the light pulse has traveled a distance of c but has only traveled a vertical distance of H. As this forms a right triangle H is easily found as (1-0.86603^2)^0.5 = 0.5c or 0.5 seconds of the moving clocks time. Thusly the observers clock measures one second for every 0.5 seconds for the moving clock, Y = 2.
Rotating the clock so the length is parallel to the velocity vector not only shows the time dilation but the length contraction.
When stationary the results are the same as the vertical clock. When the clock is moving the results are similar to any race. The clock moves at 0.86603 c, a light pulse bounces off mirror 1 and travels towards mirror 2 at a velocity of c as seen by the stationary observer. The difference in velocity as seen by the observer is c – 0.86603c = 0.13397c. The time it take for the light pulse to reach mirror 2 is then L/0.13397 = 7.464357 seconds and the return time is L/(c+0.86603c) = 0.535897 for a total of 8.000 seconds as seen by the stationary observer. This is obviously wrong for several reasons. Reason says that the two clocks are moving at the same rate relative to the observer and should read the same as does SR. Experiment also says that they read the same, Michelson and Morley performed this experiment several time in the 1980s and much to their frustration the clocks always read the same. With L unchanged the moving clock runs to slow, if L is shortened so that L’ = L/Y = L/2 then the two clocks agree as the do in experiment. Lorentz determined the math required to reconcile this shortly after the Michelson/Morley experiments which formed the underpinnings of SR. This effect is also used in the ring laser gyros, three of which are used in thousands of inertial navigation systems used in military and commercial aircraft and missile systems world wide. This only leaves one more SR effect to comment on, the increase of mass with relative velocity. There are several ways to calculate and measure this effect. One is to use the Lorentz transform to determine Y and then multiply rest mass by Y, this is the easiest. Another is to determine the energy required to accelerate the rest mass to some velocity and then convert the energy to mass via e=mc^2, tedious when working at relativistic velocities but is results in the same answer as using Y. Note that at velocities approaching c the energy gain is immense. It is a good thing the pilots of the vehicles mentioned above were very good, if they had crashed head on at point A instead of passing for every kg of rest mass on one of the vehicles the resulting crash would release the equivalent of 49 kg of mass converted to energy. Interestingly this aspect of SR is a cornerstone of high energy physics and is tested and verified everytime a particle accelerator is used.
Thanks…..Con Morton
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Thanks, Burt.
I need to retune my instincts on clocks in gravitational fields. My terminology was indeed off, as I should have realized if I had used an electric field analog.
I also should have thought of the bottom of the well as the point at which the object would come to rest with a little friction included. Then that clearly is the center of the Earth.
So are you saying that the falling person both ages more slowly and has more fun doing it? :)
Fred Bortz — Science and technology books for young readers (www.fredbortz.com) and Science book reviews (www.scienceshelf.com)
Hi Fred, you wrote: “Inside a uniform density Earth, the field (GM/r2) increases linearly from zero.”
GM/r^2 is not the field, but the gradient of the gravitational potential (field). The Newtonian potential outside of a spherical, homogeneous body is just -GM/r. On the inside it is -0.5*GM/R * (1+r^2/R^2), where R is the radius of the body and r the coordinate from the center. It gets more negative as r goes to zero (a deeper ‘gravitational well’ than at the surface). The gradient on the outside is the familiar -GM/r^2 and on the inside it is -GM*r/R^3.
Clock rates (dtau/dt) are determined by the potential, not the gradient. It comes from GR, where static clocks in Schwarzschild coordinates run at a fraction sqrt[1-2GM/(rc^2)] (approx. 1-GM/(rc^2) in the low field limit) of clocks at ‘infinity’.
For David’s “twin falling through the Earth”, the low field approximation of the instantaneous clock rate is:
dtau/dt = 1-0.5GM/(Rc^2)*(1+r^2/R^2)-0.5*v^2/c^2, where dt refers to the clock at ‘infinity’.
The gravitational time dilation term has the same sign as the velocity time dilation term, indicating an error in your rationale.
Regards,
Burt Jordaan (www.Relativity-4-Engineers.com)
I’m not sure it’s a blunder, Burt.
It’s not a gravitational well in the sense that you are experiencing an inverse square field going outward from the surface of Earth.
Inside a uniform density Earth, the field (GM/r2) increases linearly from zero. That’s because the mass outside radius r produces a net zero field, and M, the mass inside r, is directly proportional to r3.
[Note added in edit]: In other words, the surface of the Earth is at the bottom/meeting point of two gravitational wells, since the field decreases in both directions from there.
Fred Bortz — Science and technology books for young readers (www.fredbortz.com) and Science book reviews (www.scienceshelf.com)
Hi Fred, you wrote: “Burt, “feeling” the acceleration is not a very precise term. ”
On the contrary: if I strap an accelerometer to my butt, I’m sure myself and that piece of technology will agree to a very large extent.
The acceleration that is important here is not relative to any specific reference frame, but relative to a ‘free-fall’ spacetime geodesic (‘proper acceleration’). Without worrying about the effect of gravity on ageing, let’s modify David’s ‘experiment’ slightly.
If you sit on a tower that reaches all the way up to orbital altitude and I’m in a circular orbit at the same altitude, who will age slower? Me, of course, who is ‘weightless’ and in a spacetime geodesic.
If I stay in orbit and you stay on the tower (given the proper life support), I’m sure you will live longer than me, purely due to ‘weightless illness’ or whatever. Nevertheless, you feel the acceleration and I don’t.
Huh? Fred, I just noticed that you blundered seriously in this paragraph:
“This time, the main contribution to age difference is that the traveler spends most of the trip in lower gravity (proportional to the distance from the center, assuming a uniform density planet). That means his/her clocks and biological processes run faster, so s/he ages more than the surface bound person“.
Clocks below Earth’s surface always tick slower than clocks on the surface. At the center of Earth, gravitational acceleration is zero, but the ‘depth of the gravitational well’ is greatest, meaning the slowest lapse of time.
Don’t worry, we all blunder now and then…
Regards,
Burt Jordaan (www.Relativity-4-Engineers.com)
The question of twin paradox is seen constantly on physics, relativity and science bolgs and books. Common explanations is that travelling twin experiences acceleration while stay home twin does not. Other explanation is similiar to explanation of accleration seen in rotating bodies that one is rotating in relation to the whole universe while other is at rest. The problem of twin paradox should be considered similiar to Mach’s principle. Both lack proper explanation.
The reason is basically movement against the background of space is not accepted by physicists because of ether problem. If we thought that one object or twin is moving through space and other is not then the problem is partially solved. Actually looking at Lorentz equation acceleration does not come into picture at all. Time dilation is calculated on velocity alone. Moreover acceleration deceleration of travelling twin could be made instantaneous so that the travel time is based mostly at high constant velocity. Acceleration of particles in linear accelerators cannot be used to calculate their time dilation but velocity can. Acceleration story does not solve twin paradox.
According to physicists space can be curved warped made into black holes however we still do not accept travel simply against background fixed space. There another major reason for that…the constancy of speed of light in all reference frames. So to all of those giving these unsatisfactory explanations for twin paradox by drawing space time diagrams etc good luck you will not have a solution till you have answered questions like:
1 What is Time?
2. What causes Time?
3. Why Time slows in gravity and with motion?
5. Why time is not really a dimension?
6. How gravity works?
7. Why gravity is only attractive?
8. Acceleration and Twin paradox
9 The mechanism of length contraction?
10 What is inertia?
11. Why speed of light remains constant?
12. Why black holes cannot have singularity?
13. Is the universal accelerating or time is slowing down?
14. Arrow of time
Look for answers at:
http://www.timephysics.com
Hi Burt.
I now see that:
The space traveller in the g accelerated rocket with a global warming engine (patent pending) after 30 years will reach the edge of the universe, but he will do so some time later than the hardy research assistant I have just despatched on a light beam (method so secret that I am not even patenting it). The latter will feel himself to have made the trip in no time at all, and will have plenty of time to examine and reflect on the nature of the edge of the universe while he awaits the arrival of the g accelerated rocket. Their respective arrivals are not at the same event, only at the same place.
Sincerely,
Christopher
Hi, Burt.
Thank you for this kind and careful reply. Do you never sleep?
I need to reflect on these very puzzling things.
Sincerely,
Christopher
Hi Christopher, you asked:
“… reply about particles in centrifuges. Is it convenient for you to give me the references for this?”
My source is the book “Gravitation”, by Misner, Thorne and Wheeler, with the specific case discussed on p. 1055. There are unfortunately no authoritative web based articles (that I know of) freely available on these tests.
On your previous post, where you wrote:
“I think the answer is to describe things from the viewpoint of a particular observer, in terms of what is physical for him.”
Of course, for a traveler (be it particle or human) it’s proper time that counts. The continuously accelerated observer (at 1g) can circumnavigate the present observable universe about 300 times in 30 years of his time, not the time of us Earthlings! This sort of space travel is pure SciFi, because there will most probably never exist an engine that can do that.
Back to your latest post. Your ‘man in the white hat’ should rather be located in inter-galactic space. Then I have told you that for the sibling on Earth’s equator, the umpire will observe her to lose some 10 second in every billion of his seconds. The sibling in geostationary orbit will lose about the same amount.
On the other hand, the umpire will observe the fly-away sibling to lose an average of over half a second every second, depending on his instantaneous relative speed. It will be small initially and become more severe, like losing 0.8 second for every second of inter-galactic time after 5 years (at the maximum speed of ~0.98c). Overall, the fly-away sibling will age ~2.3 years for every 5 years of the umpire’s time (which is for all practical purposes Earth time, within 1 part in 10^8).
I hope this eases the headache! You will be able to do all these sums when you have studied your “Relativity 4 Engineers” ;-)
Regards,
Burt Jordaan (www.Relativity-4-Engineers.com)
Hi Burt.
Thank you for your kind and very unexpectedly quick reply about particles in centrifuges. Is it convenient for you to give me the references for this? I would be grateful.
It is not altogether easy to translate from experiments on particles in centrifuges to scenarios of adventures of astronauts. The problem is in keeping a clear head about who is observing what. The interpretations of the observations on particle decay in centrifuges do not compare the effects of speed and acceleration in quite the terms that are needed to make clear what is really affecting what. They are interpreted in terms of verbalistic but not really physical ideas. The authors of these experiments and reports are happy to confirm certain orthodoxies, but they are in fact just repeating the muddled and verbalistic thinking that gives rise to those orthodoxies, instead of giving scientific accounts of the physical observations.
You note that the laboratory workers recorded longer lives for the more rapidly moving particles. Longer lives as recorded between certain events in the laboratory. But these particles were moving at the time. I am asking about the case when the triplets start and finish sitting stationary together drinking tea. Yes I agree that the effect of gravity will be small in comparison with the hypothetically potential effects of speed. But that doesn’t yet deal with the problem that I have stated. So far your comments haven’t indicated that gravity might have any relevant effect at all, yet it obviously does affect the problem at least as to osteoporosis.
The problem is to compare apples with apples, and blueberries with blueberries. This needs a careful statement of what the umpire in the white hat will observe in terms of what is physical for him. I think you have not made that careful statement.
Your reply implies or says that acceleration will not matter while speed will have a big effect, but you haven’t shown that by a proper comparison such as is needed for a scientific answer. This is partly because you have not explicitly compared the experiences of the three triplets as the man in the white hat would see them. Yes, your reply correctly echoes the orthodox views about this, but they also fail to make the comparisons that scientific method demands. That is why so much is written in this blog, with so many different opinions, some of them rather rancorous at times, I note. They think that basic scientific method can be abandoned because they have a superior mathematical understanding. But it is not safe to abandon basic scientific method, no matter how clever one might be. I think you will agree with me about this.
Sincerely,
Christopher
Hi Christopher. You wrote:
“But I think for natural understanding we do need to have a clear view of the “effects” of speed and acceleration separately, and I think we need triplets for that.”
It has been shown in centrifuge experiment with decaying particles that the half-life of the particles are only influenced by the rotational speed and not by the centripetal acceleration. It was done by simply rotating the particles in two centrifuges with different radii, spun so that the particles experienced the same speed, but different accelerations. The different accelerations made no difference to the decay times. However, when spun so that the centripetal accelerations were the same and the speeds different, the particles with the higher speed decayed slower, as predicted by SR.
Back to your ‘triplets scenario’. Wherever you “park” the two stay-at-home siblings, the gravitational time dilation working on them will be very, very small. At the surface of the Sun, it is ~50 seconds per million seconds and on the surface of Earth it is ~10 seconds per billion seconds. This is how much slower our clocks tick compared to a clock somewhere in inter-galactic space and at rest relative to the solar system. For Earth, it makes very little difference being on the surface or up in geostationary orbit – it is the depth of the Sun’s gravitational well that determines the rate of the clocks, because it overwhelms Earth’s own gravity well depth by about 14 to 1.
So how much correction must on make for an Earth observer in 20 years? At 10 parts per billion, I get ~6 seconds in 20 years. Hardly worth the bother if you consider the velocity induced effect is more than 10 years in 20 years!
Regards,
Burt Jordaan (www.Relativity-4-Engineers.com)