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:
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