What is the proof/validity of Born rigidity in Special relativity?

[Trojan666ru]

Relativity theory always find some ridiculous explanations like "born rigidity or relativity of simultaneity" when in face paradoxes
What is the experimental validity of such predictions?

 

[Dale]

So far SR has withstood every experimental test within its domain of validity.

Perhaps you should spend some time reading through the sticky on experimental evidence for relativity before using words like "ridiculous", it just makes you look like an uninformed crackpot.

 

[Trojan666ru]

Sorry I've already red most of the experimental evidences that support relativity, but that doesn't prove "born rigidity" happen in SR. What if "the experimental evidences that support relativity has some other kind of explanations? "

 

[Nugatory]

What if "the experimental evidences that support relativity has some other kind of explanations? "

That would be a more interesting question if someone were to find a reasonable alternative explanation to consider, or a significant hole in the way that relativity explains the experimental evidence. So far, no one has found either... And it's not for want of looking.

 

[universal_101]

Sorry I've already red most of the experimental evidences that support relativity, but that doesn't prove "born rigidity" happen in SR. What if "the experimental evidences that support relativity has some other kind of explanations? "

Born rigidity was introduced in SR, so that the objects can go under Length Contraction (due to inertial relative motion w.r.t an observer, i.e. Lorentz contraction) without breaking the objects in the process(i.e. no permanent damage done) and at the same time maintaining the rigidity(i.e. born rigidity).

The bitter part of this introduction is that we don't have any experimental proof of Length contraction(directly implied), nor of the increase in the density due to length contraction.

The above definition of born rigidity does not include accelerating objects, i.e. every non-point object undergoes permanent deformation along the line of motion when accelerated(i.e. according to theory, the born rigidity breaks every time any real object accelerates).

And same as the inertial Lorentz contraction mentioned before, there is again, NO Experimental evidence (direct or implied).

 

[ZapperZ]

Born rigidity was introduced in SR, so that the objects can go under Length Contraction (due to inertial relative motion w.r.t an observer, i.e. Lorentz contraction) without breaking the objects in the process(i.e. no permanent damage done) and at the same time maintaining the rigidity(i.e. born rigidity).

The bitter part of this introduction is that we don't have any experimental proof of Length contraction(directly implied), nor of the increase in the density due to length contraction.

The above definition of born rigidity does not include accelerating objects, i.e. every non-point object undergoes permanent deformation along the line of motion when accelerated(i.e. according to theory, the born rigidity breaks every time any real object accelerates).

And same as the inertial Lorentz contraction mentioned before, there is again, NO Experimental evidence (direct or implied).

Try designing particle accelerator structures without incorporating such effects in the design! For example in FELs, from the electron bunch frame, the spacing of the undulator/wiggler is severely contracted. Without taking into such account, the description in that frame and lab frame will be completely off! It works when you use it, it doesn't work when you don't. To me, as an experimentalist, that is a darn strong evidence for its validity.

Furthermore, this appears to be a common misunderstanding of what this effect. It isn't the object that is contracting. It is the spatial dimension!

http://arxiv.org/abs/0906.1919

Zz.

 

[stevendaryl]

Sorry I've already red most of the experimental evidences that support relativity, but that doesn't prove "born rigidity" happen in SR. What if "the experimental evidences that support relativity has some other kind of explanations? "

Born rigidity is not something that can be proved or disproved--it's a definition: An object is "Born rigid" if it always has the same length, as measured in its own instantaneous rest frame. Real objects are not perfectly Born rigid. If you push on one end of a long rod, it will compress a little. If you pull on the other end, it will stretch a little. Rigidity is an idealization.

 

[Dale]

that doesn't prove "born rigidity" happen in SR

Born rigidity is a definition. I don't know what kind of experiment you are talking about.

 

[universal_101]

Try designing particle accelerator structures without incorporating such effects in the design! For example in FELs, from the electron bunch frame, the spacing of the undulator/wiggler is severely contracted. Without taking into such account, the description in that frame and lab frame will be completely off! It works when you use it, it doesn't work when you don't. To me, as an experimentalist, that is a darn strong evidence for its validity.

Theoretical Explanation of FELs, comes under the category of 'suit yourself', the so called rigorous derivation of {λ_w}/{γ^2} from Maxwell's Equations, is based on jumping frames(it is because of this theoretical inconsistency that most texts do not include the derivation) to get the square of the gamma. That is, the only reason the case is studied by jumping frames, so as to make theory(Length contraction) compatible with experimental results.

Furthermore, this appears to be a common misunderstanding of what this effect. It isn't the object that is contracting. It is the spatial dimension!

http://arxiv.org/abs/0906.1919

According to the linked paper, the inertial Length contraction is nothing but illusion, i.e. its an apparent measured effect which we should not worry much about. In other words the length has meaning only in the proper frames.

And, just as the ‘shortening’ of a stick that is rotated in three dimensions is an illusion, we now can see that the ‘shortening’ of a stick that is rotated in four dimensions by a Lorentz transformation is also illusory.

Now, intuitively/logically the definition of inertial length contraction(according to the paper) does not match very well with the explanation of FELs using the inertial Length contraction(frames jumping), because the former is a measured/apparent effect(illusion), whereas later is used to explain non illusory effects(radiation).

 

[yuiop]

...
And same as the inertial Lorentz contraction mentioned before, there is again, NO Experimental evidence (direct or implied).

I think length contraction is implied by observations of the number of muons that make it from the top of the atmosphere to sea level. The average lifetime of a muon is very short and they would decay before they reached sea level, if the thickness of the atmosphere was not length contracted from their point of view.

Length contraction is also implied by the MMX experiment. If the arm parallel to the motion was not length contracted by the right amount, the famous "null result" would not have been obtained.

 

[bcrowell]

Born rigidity was introduced in SR, so that the objects can go under Length Contraction (due to inertial relative motion w.r.t an observer, i.e. Lorentz contraction) without breaking the objects in the process(i.e. no permanent damage done) and at the same time maintaining the rigidity(i.e. born rigidity).

No, this is a complete misunderstanding of Born rigidity. Born rigidity is a definition, not a prediction of SR. Born rigidity does not exist in reality. It's of no interest for an object moving inertially and without rotation. It is not a property of an object (even a hypothetical, idealized object) but rather a theoretically possible motion of an object on which external forces are exerted according to a plan that has to have been constructed before the motion even began.

The bitter part of this introduction is that we don't have any experimental proof of Length contraction(directly implied), nor of the increase in the density due to length contraction.

This is total nonsense. Length contraction is part of the Lorentz transformation, and Lorentz invariance is one of the most accurately tested theories in the history of science. See, e.g., http://relativity.livingreviews.org/Articles/lrr-2005-5/

The above definition of born rigidity does not include accelerating objects, i.e. every non-point object undergoes permanent deformation along the line of motion when accelerated(i.e. according to theory, the born rigidity breaks every time any real object accelerates).

More nonsense.

And same as the inertial Lorentz contraction mentioned before, there is again, NO Experimental evidence (direct or implied).

More nonsense.

Furthermore, this appears to be a common misunderstanding of what this effect. It isn't the object that is contracting. It is the spatial dimension!

http://arxiv.org/abs/0906.1919

This is an interesting and subtle point that is not going to get the discussion it deserves in a thread as contaminated with nonsense as this one. Franklin's interpretation is fine, but it's not the only correct one. Bell's interpretation differs markedly from Franklin's, and Bell isn't betraying his "misunderstanding" of SR. Everybody agrees on the mathematics and the experimental validation of the mathematics, but the interpretation is a matter of philosophy, not science.

 

[stevendaryl]

According to the linked paper, the inertial Length contraction is nothing but illusion, i.e. its an apparent measured effect which we should not worry much about. In other words the length has meaning only in the proper frames.

I don't quite agree with the use of the word "illusion". Length has a very precise (if frame-dependent) definition: the length of an object at time t is the spatial distance between the locations of the two endpoints at time t. It's not an illusion that a moving object has a shorter length than the same object when at rest, it's true. (Assuming relativity is correct.)

I would reserve the word "illusion" to apply in a case where someone is given misleading information that leads him to make an incorrect conclusion. For example, someone holding his hand up in such a way that an elephant seems to be sitting in his hand--in actuality, the elephant is far away, and seems smaller by perspective. For a more physics-relevant illusion, moving objects appear rotated, because of the Terrell rotation.

 

[PAllen]

According to the linked paper, the inertial Length contraction is nothing but illusion, i.e. its an apparent measured effect which we should not worry much about. In other words the length has meaning only in the proper frames.


Now, intuitively/logically the definition of inertial length contraction(according to the paper) does not match very well with the explanation of FELs using the inertial Length contraction(frames jumping), because the former is a measured/apparent effect(illusion), whereas later is used to explain non illusory effects(radiation).

This is one of the few weak points of a pretty good paper. A simple counter argument is there is nothing illusory about rotating an object in 3-space. You can fit long, thin, objects through small openings because of the ability to rotate them. Similarly, the reality of spacetime rotation (=length contraction) produces phenomena that would not otherwise be possible. For example, the muon reaching the ground, in the muon's frame.

 

[Meir Achuz]

Bell does 'misunderstand' SR, because he wants to use both Lorentz's (and Fitzgeralds0 notion that there is a real contraction of the object AND Einstein's contraction due the transformation between frames. You can argue for one or the other, but they can't be combined.

 

[stevendaryl]

This is total nonsense. Length contraction is part of the Lorentz transformation, and Lorentz invariance is one of the most accurately tested theories in the history of science.

I think that it is correct to say that Lorentz contraction has not been directly observed in the way that time dilation has been. I mean, we don't have any objects of accurately known rest length that have been accelerated to high enough speed to measure their contraction. Not that there is very much doubt about the reality of Lorentz contraction (There is, as far as I know, no alternative to relativity that agrees with all known experiments but does not predict length contraction.)

 

[universal_101]

I think length contraction is implied by observations of the number of muons that make it from the top of the atmosphere to sea level. The average lifetime of a muon is very short and they would decay before they reached sea level, if the thickness of the atmosphere was not length contracted from their point of view.

Length contraction is also implied by the MMX experiment. If the arm parallel to the motion was not length contracted by the right amount, the famous "null result" would not have been obtained.

I didn't say one cannot imply inertial length contraction, instead I said it cannot be directly implied. (For example, I can also think of different theories that implies something else or may be nothing). The quote that you used from my post is about the length contraction due to acceleration for non-point objects(i.e. real effects)

 

[Meir Achuz]

The Lorentz contraction of SR has not been tested experimentally, and probably can't be, but it is implied by all the other experimental successes of SR. SR would have to be radically changed (destroyed) if Lorentz contraction (in the SR sense) were dropped. Many things in physics have that kind of 'evidence'.

 

[stevendaryl]

Bell does 'misunderstand' SR, because he wants to use both Lorentz's (and Fitzgeralds0 notion that there is a real contraction of the object AND Einstein's contraction due the transformation between frames. You can argue for one or the other, but they can't be combined.

I don't think that Bell misunderstands it. I'm not exactly sure what you mean by those two alternatives (1) contraction is real, and (2) contraction is due to transformation between frames, but they don't seem incompatible to me.

 

[Meir Achuz]

Another reference that shows how accelerating a rigid body leads to the SR shortening is
http://link.springer.com/article/10.1007/s10701-013-9757-x

 

[PAllen]

Another reference that shows how accelerating a rigid body leads to the SR shortening is
http://link.springer.com/article/10.1007/s10701-013-9757-x

Here is the non-paywall version of that paper, a companion to the one Zapper linked (same author):

http://arxiv.org/abs/1105.3899

 

[nitsuj]

I think that it is correct to say that Lorentz contraction has not been directly observed in the way that time dilation has been. I mean, we don't have any objects of accurately known rest length that have been accelerated to high enough speed to measure their contraction. Not that there is very much doubt about the reality of Lorentz contraction (There is, as far as I know, no alternative to relativity that agrees with all known experiments but does not predict length contraction.)

I think it is correct to say that the "observed" time dilation is the reciprocal? of length contraction. (SR)Time dilation doesn't somehow exist on it's own.

I presume by time dilation has been "observed" you are referring to differential aging, which itself isn't time dilation. Has time dilation even been observed, or is it merely calculated...just like length contraction?

 

[universal_101]

No, this is a complete misunderstanding of Born rigidity. Born rigidity is a definition, not a prediction of SR. Born rigidity does not exist in reality. It's of no interest for an object moving inertially and without rotation. It is not a property of an object (even a hypothetical, idealized object) but rather a theoretically possible motion of an object on which external forces are exerted according to a plan that has to have been constructed before the motion even began.

I didn't say born rigidity is a prediction of SR, ofcourse it is an idealized condition of an object so that the effects of acceleration on real objects can be ignored, and so only the geometrical effects are left to be analysed.

This is total nonsense. Length contraction is part of the Lorentz transformation, and Lorentz invariance is one of the most accurately tested theories in the history of science. See, e.g., http://relativity.livingreviews.org/Articles/lrr-2005-5/


More nonsense.


More nonsense.

Lorentz transformation is based on Lorentz in-variance of Electromagnetic phenomenon(Maxwell's equations) under relative motion. This implies being a transformation, LT is a set of transformation equations which give the same absolute result(For ex.- acceleration etc.) irrespective of the frame we choose to see the effects from. In other words, just as under the rotation of a stick in 3-D gives us different spatial co-ordinates (without changing the actual length), LT gives us different co-ordinates (spatial, temporal) for a same absolute property.

My point being co-ordinates does not mean anything, I can always choose a different co-ordinate system and get the same results. That is the length of the stick never changes.

This is an interesting and subtle point that is not going to get the discussion it deserves in a thread as contaminated with nonsense as this one. Franklin's interpretation is fine, but it's not the only correct one. Bell's interpretation differs markedly from Franklin's, and Bell isn't betraying his "misunderstanding" of SR. Everybody agrees on the mathematics and the experimental validation of the mathematics, but the interpretation is a matter of philosophy, not science.

Labeling is easy!, the more important point is not betraying the one's 'understanding'.

 

[universal_101]

I don't quite agree with the use of the word "illusion". Length has a very precise (if frame-dependent) definition: the length of an object at time t is the spatial distance between the locations of the two endpoints at time t. It's not an illusion that a moving object has a shorter length than the same object when at rest, it's true. (Assuming relativity is correct.)

I would reserve the word "illusion" to apply in a case where someone is given misleading information that leads him to make an incorrect conclusion. For example, someone holding his hand up in such a way that an elephant seems to be sitting in his hand--in actuality, the elephant is far away, and seems smaller by perspective. For a more physics-relevant illusion, moving objects appear rotated, because of the Terrell rotation.

You are in direct contradiction with the author if you suggest that Inertial Length Contraction is true. Since it is an (just like simultaneity)measured effect and it does not imply the length of an object actually contracted {i.e. it produced strain or stress).

 

[stevendaryl]

I presume by time dilation has been "observed" you are referring to differential aging, which itself isn't time dilation.

I was using those two synonymously. What do you mean by "time dilation"?

 

[stevendaryl]

You are in direct contradiction with the author if you suggest that Inertial Length Contraction is true.

Then I think the author is wrong. As I said, "length" has a definition, and according to that definition, a moving object is contracted compared with a similarly constructed object at rest.

Since it is an (just like simultaneity)measured effect and it does not imply the length of an object actually contracted {i.e. it produced strain or stress).

Somebody made the analogy between Lorentz transformations and rotations. I think that's a very good analogy. If you have a two-dimensional object lying on the ground, you can characterize it by giving its East/West extent, and by giving its North/South extent. A rotated version of the same object will in general have a different East/West extent, and a different North/South extent. That doesn't mean that there are any additional stresses on the rotated version of the object. That's because the forces keeping the object together are rotationally invariant; they don't have a preferred direction in space. But it's not an ILLUSION that the rotated object has a different East/West extent.

 

[nitsuj]

I was using those two synonymously. What do you mean by "time dilation"?

Proper to coordinate comparative, you know the frame dependent one.

 

[universal_101]

Bell does 'misunderstand' SR, because he wants to use both Lorentz's (and Fitzgeralds0 notion that there is a real contraction of the object AND Einstein's contraction due the transformation between frames. You can argue for one or the other, but they can't be combined.

Correct. Atleast we can agree on that much.

 

[universal_101]

This is one of the few weak points of a pretty good paper. A simple counter argument is there is nothing illusory about rotating an object in 3-space. You can fit long, thin, objects through small openings because of the ability to rotate them. Similarly, the reality of spacetime rotation (=length contraction) produces phenomena that would not otherwise be possible. For example, the muon reaching the ground, in the muon's frame.

Nobody said there is something illusory about the rotation of the stick. The point is change in Length of the stick due to rotation is illusory.

 

[WannabeNewton]

This has devolved into an argument over semantics. If we model an extended body by a time-like congruence $u$ then Born rigidity is defined as $\mathcal{L}_u h = 0$ where $h$ is the spatial metric relative to $u$ and $\mathcal{L}_u$ is the Lie derivative along $u$. If $\mathcal{L}_u h \neq 0$ then the extended body has a non-vanishing expansion tensor (e.g. because $\nabla \cdot u \neq 0$) which means that the spatial distances (i.e. $h$) between neighboring constituent particles making up the body changes over time (relative to clocks carried along integral curves of the congruence). This is a very real effect in the obvious sense of the word.

 

[Meir Achuz]

Then I think the author is wrong. As I said, "length" has a definition, and according to that definition, a moving object is contracted compared with a similarly constructed object at rest.

"the length of an object at time t is the spatial distance between the locations of the two endpoints at time t" is your definition, but there are others. Good definitions like 'age' and 'mass' are invariants in SR. The invariant definition of 'length' is also invariant.

 

[stevendaryl]

Proper to coordinate comparative, you know the frame dependent one.

Hmm. To me, that's what differential aging is all about. We have a formula relating proper time to coordinate time:

\tau = \int \sqrt{1-\frac{v^2}{c^2}} dt

We can test that formula by having an object (a clock, or an elementary particle) travel in a circle that ends up back where it started, and comparing its elapsed time (or half-life, in the case of a particle) to one that didn't make the trip.

 

[stevendaryl]

"the length of an object at time t is the spatial distance between the locations of the two endpoints at time t" is your definition

I'm sure it's not original with me.

 

[universal_101]

Then I think the author is wrong. As I said, "length" has a definition, and according to that definition, a moving object is contracted compared with a similarly constructed object at rest.

It barely matters what the definition of the length is, what matters is whether the inertial relative motion causes strain in the moving objects(it actually does not and it is indisputable). Now try to reconcile this with whatever the definition of the length you think is correct.

Somebody made the analogy between Lorentz transformations and rotations. I think that's a very good analogy. If you have a two-dimensional object lying on the ground, you can characterize it by giving its East/West extent, and by giving its North/South extent. A rotated version of the same object will in general have a different East/West extent, and a different North/South extent. That doesn't mean that there are any additional stresses on the rotated version of the object. That's because the forces keeping the object together are rotationally invariant; they don't have a preferred direction in space. But it's not an ILLUSION that the rotated object has a different East/West extent.

See my reply to PAllen.

 

[PAllen]

Hmm. To me, that's what differential aging is all about. We have a formula relating proper time to coordinate time:

\tau = \int \sqrt{1-\frac{v^2}{c^2}} dt

We can test that formula by having an object (a clock, or an elementary particle) travel in a circle that ends up back where it started, and comparing its elapsed time (or half-life, in the case of a particle) to one that didn't make the trip.

Well, you can use non-inertial coordinates for the circular traveler such that along his path tau/t = 1, and it is the non-traveler suffering time expansion that explains the result. I generally distinguish between time dilation being a coordinate or frame dependent effect (which doesn't mean, IMO, it isn't 'real'), while differential aging is an invariant effect existing independently of any frame or coordinates.

 

[universal_101]

I think it is correct to say that the "observed" time dilation is the reciprocal? of length contraction. (SR)Time dilation doesn't somehow exist on it's own.

Observed Time Dilation is a net effect, which being reciprocal to length contraction should produce a net effect(not observed).

 

[stevendaryl]

It barely matters what the definition of the length is, what matters is whether the inertial relative motion causes strain in the moving objects(it actually does not and it is indisputable). Now try to reconcile this with whatever the definition of the length you think is correct.

Clearly, by the normal definition of "length", the moving object is contracted. We can also say that the moving object has no stresses, which follows from the Lorentz invariance of the forces at work on the object. Those are two different issues.

 

[stevendaryl]

Nobody said there is something illusory about the rotation of the stick. The point is change in Length of the stick due to rotation is illusory.

Right, but for a stick parallel to the ground, the north/south extent of the stick changes, and the east/west extent of the stick changes when you rotate it.

So length in Minkowsky spacetime is analogous to north/south extent in Euclidean geometry. It really does change when you set the stick in motion (in the first case) or when you rotate a stick (in the second case).

 

[Histspec]

Bell does 'misunderstand' SR, because he wants to use both Lorentz's (and Fitzgeralds0 notion that there is a real contraction of the object AND Einstein's contraction due the transformation between frames. You can argue for one or the other, but they can't be combined.

Einstein didn't believe that there is any observational difference ("physical facts") between his or Lorentz's interpretation of length contraction. See http://en.wikipedia.org/wiki/Length_contraction#Reality_of_length_contraction

In 1911 Vladimir Varićak asserted that length contraction is "real" according to Lorentz, while it is "apparent or subjective" according to Einstein.[17] Einstein replied:

The author unjustifiably stated a difference of Lorentz's view and that of mine concerning the physical facts. The question as to whether length contraction really exists or not is misleading. It doesn't "really" exist, in so far as it doesn't exist for a comoving observer; though it "really" exists, i.e. in such a way that it could be demonstrated in principle by physical means by a non-comoving observer.[18] —Albert Einstein, 1911

Einstein, Albert (1911). "Zum Ehrenfestschen Paradoxon. Eine Bemerkung zu V. Variĉaks Aufsatz". Physikalische Zeitschrift 12: 509–510.

 

[PAllen]

Nobody said there is something illusory about the rotation of the stick. The point is change in Length of the stick due to rotation is illusory.

Well you need some explanatory term to describe the muon reaching the ground in the muon frame. That it does, is not illusory. The explanation is frame dependent, but the fact is not. No one complains about saying time dilation is the cause in the Earth frame. Clearly, time dilation is irrelevant in the muon frame. If you prefer to say 'the atmosphere is rotated in time' instead of 'the atmosphere is length contracted', I don't much care. I do care that the muon frame is equally valid, and that the explanation from the muon frame is fully as valid as from the Earth frame.

 

[nitsuj]

We can test that formula by having an object (a clock, or an elementary particle) travel in a circle that ends up back where it started, and comparing its elapsed time (or half-life, in the case of a particle) to one that didn't make the trip.

Which would be a comparative of proper time(s), and is differential aging. the "hard" evidence time dilation and length contraction have occurred, as opposed to the mere calculations.

 

[universal_101]

Clearly, by the normal definition of "length", the moving object is contracted. We can also say that the moving object has no stresses, which follows from the Lorentz invariance of the forces at work on the object. Those are two different issues.

You cannot draw curtains on other facets of the physical theory(SR), the only way you can reach the conclusion that there are NO stresses in presence of Length Contraction, is if the contraction is not real-true, non-physical in the sense that it is illusory/apparent.

Which is in direct contradiction with the supposedly true contraction in the case of FELs.

 

[yuiop]

There seems to a problem with Fig 3 in the Franklin paper http://arxiv.org/pdf/1105.3899v3.pdf posted by PAllen.

It shows the rear of the rod reacting to a collision at a time T₁ that is before the collision actually occurs at the front of the rod at t=0. I am not sure if they have made a mistake or they are trying to demonstrate that bodies cannot remain rigid during a collision. Are they suggesting that the rear of the rod is accelerated backwards artificially in anticipation of the collision? The situation they show certainly cannot occur naturally.

 

[PAllen]

You cannot draw curtains on other facets of the physical theory(SR), the only way you can reach the conclusion that there are NO stresses in presence of Length Contraction, is if the contraction is not real-true, non-physical in the sense that it is illusory/apparent.

Who says no stresses = not real? Stress can be defined in an invariant way such maintaining it as zero is a definition of Born rigid motion. Then length contraction of an inertially moving object would have no stress.

 

[PAllen]

There seems to a problem with Fig 3 in the Franklin paper http://arxiv.org/pdf/1105.3899v3.pdf posted by PAllen.

It shows the rear of the rod reacting to a collision at a time T₁ that is before the collision actually occurs at the front of the rod at t=0. I am not sure if they have made a mistake or they are trying to demonstrate that that bodies cannot remain rigid during a collision. Are they suggesting that the rear of the rod is accelerated backwards artificially in anticipation of the collision? The situation they show certainly cannot occur naturally.

They explain that a little later in the paper. Remember, non-inertial rigid motion is all about 'conspiracy' to move right way. The temporal inversion is for spacelike separated events, thus is frame dependent. In a different frame there is no inversion.

 

[Meir Achuz]

"Viewers in system S may be
surprised to see the back end of the rod start to decelerate before the front end
hits the wall. However, in the rest system of the rod, the onset of deceleration
occurs at the same time for each end. Because the invariant separation of the
front and back ends is space-like, the relative time order can be different in other
Lorentz frames, but this has no physical significance. The early deceleration of
the back end seen by viewers in system S is illusory."

 

[PAllen]

Which is in direct contradiction with the supposedly true contraction in the case of FELs.

I see no difference between this and other cases. You can do a complete derivation in the lab frame, the electron bunch frame, or part in each. The explanation is frame dependent (just like the simple muon case), however the observation is invariant (wavelength of emittted radiation; muon reaches the ground).

 

[universal_101]

Well you need some explanatory term to describe the muon reaching the ground in the muon frame. That it does, is not illusory. The explanation is frame dependent, but the fact is not. No one complains about saying time dilation is the cause in the Earth frame. Clearly, time dilation is irrelevant in the muon frame. If you prefer to say 'the atmosphere is rotated in time' instead of 'the atmosphere is length contracted', I don't much care. I do care that the muon frame is equally valid, and that the explanation from the muon frame is fully as valid as from the Earth frame.

This is a good post and I completely agree with it. But I think its implications are far reaching.

As long as it is just an explanatory term nobody cares much, but the moment you choose to use or refuse to use, the physical meaning of the explanatory term(i.e. true/illusory), in other similar physical situations, the physical meaning itself is doomed to fail(observed facts), because of the nature a transformation has. That is, a transformation's job is not to provide physical results, it's job is to provide the co-ordinates(spatial, temporal) so that the absolute properties(like acceleration) remains same(so called Lorentz invariant), when viewed from the either frames. BTW, I can write another transformation like LT where I would use the different co-ordinates and the same time keeping the absolute properties invariant.(Actually there can be infinitely many such transformations).

 

[universal_101]

Who says no stresses = not real? Stress can be defined in an invariant way such maintaining it as zero is a definition of Born rigid motion. Then length contraction of an inertially moving object would have no stress.

My first post in this thread was about this, the only reason Born rigidity was introduced in SR formalism, so as to make the stresses invariant under length contraction(i.e. to keep the LC real at the same time when there is NO stress). This was exactly the point of OP, the problem is we are introducing new definitions in favor of SR to keep the Length Contraction for which we don't have any evidence of being there at the first place.

 

[PAllen]

My first post in this thread was about this, the only reason Born rigidity was introduced in SR formalism, so as to make the stresses invariant under length contraction. This was exactly the point of OP, the problem is we are introducing new definitions in favor of SR to keep the Length Contraction for which we don't have any evidence of being there at the first place.

There is perfectly good physical justification for the expansion tensor independent of any purpose related to Born rigidity. It says that stress is defined by invariant operations on a congruence of world lines describing an object, and the latter is the most natural way to capture than an object is built out of microscopic components. Having realized that physical theories need to be Lorentz invariant, this was a necessary path to take.

 

[universal_101]

There is perfectly good physical justification for the expansion tensor independent of any purpose related to Born rigidity. It says that stress is defined by invariant operations on a congruence of world lines describing an object, and the latter is the most natural way to capture than an object is built out of microscopic components. Having realized that physical theories need to be Lorentz invariant, this was a necessary path to take.

Does it mean, that you realize, that there can never be any experimental verification of length contraction, because physical theories need to be Lorentz Invariant, and it means you are never going to find any variant property in order to prove that LC is real.

Because then there is NO point debating the nature of LC(or any name of your liking).