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

[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).

 

[PAllen]

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).

No, it simply means that pure LC and pure time dilation are frame dependent phenomena. Also, you can't have one without the other unless you choose to believe there is a universally preferred frame (you need a theory of the atmosphere in the muon frame unless you reject it as an inferior frame). What your can verify are observable consequences - muons reach the ground; muon half life in a ring is energy dependent in the expected way.

 

[universal_101]

No, it simply means that pure LC and pure time dilation are frame dependent phenomena.

O..K.

Also, you can't have one without the other unless you choose to believe there is a universally preferred frame (you need a theory of the atmosphere in the muon frame unless you reject it as an inferior frame). What your can verify are observable consequences - muons reach the ground; muon half life in a ring is energy dependent in the expected way.

Right, but ofcourse it would be easy to use only TD part in the preferred frame.

 

[Dale]

This thread has certainly run amok.

Length contraction is a direct consequence of the Lorentz transform. Therefore all evidence confirming the Lorentz transform is evidence supporting length contraction as well. As such, the experimental evidence is overwhelming and it is not in the least bit disputed in current professional debate.

As to its "reality" or not, that is a philosophical/semantic question which hinges critically on the definition of "real". It is a measurable but frame-variant effect, call it "real" or not as you will.