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
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