Does Bell's Paradox Suggest String Shouldn't Break Due to Length Contraction?

[yuiop]

Just to check we are all on the same page, please consider the following. We have a pair of rockets A1 and A2 on the ground connected by a resilient, elastic and tough 1km rod. Alongside them is another identical pair of rockets, B1 and B2 also connected by 1Km rod like so:

A2--------------------A1
B2--------------------B1

It is assumed the connecting rods are initially under negligible stress. All the rocket engines are identical with identical fuel loads and burn rates etc. Just before take off we disconnect the end of the rod that was attached to rocket A2. The rockets all take off simultaneously in the ground frame and set to burn at an equal and constant rate. When all the rockets have depleted their fuel at a velocity of around 0.9c relative to the ground and everything has stabilised, the situation as seen from the ground should be something like this:

A2...----------A1
...B2----------B1

The length contraction of the resilient rod has physically dragged the B1/B2 rockets closer together (about 1/2 Km apart) than the disconnected A1/A2 rockets that are still about 1 Km apart. Everyone agree?

P.S. The small white dots are just spacers and should be ignored in the diagram.

 

[harrylin]

[..] So would you say the relative contraction of ship A was the result of physical EM forces?
Or would you agree that purely kinematic changes due to the increasing relative velocity effected an equivalent contraction indistinguishable from the contraction of B as observed in A?

Starting with a re-take in part of my post #183:

Many different "because" answers on a single question can be correct. In particular, SR is based on the assumption that Maxwell's laws are valid. According to those laws the EM fields that hold the matter together contract (and that was the basis for Fitzgerald's assumption of length contraction).

SR is not magic, every physical principle must relate to physical means by which it works.
For example, it was found that the gas laws relate to how molecules interact; and conservation of energy is achieved by means of forces.

And I don't know what you mean with "purely kinematic" in this context of physical description, as being different from "physical".

However, I mentioned how physical cause-and-effect considerations help us to correctly pinpoint the asymmetry of Bell's "paradox" in posts #15 and #47, and perhaps this relates to what you really meant with "kinematic". Retake:

Lorentz contraction should not be understood as a magical "space contraction" between unconnected objects. It should be treated as a physical effect, as both Lorentz and Einstein described it.

A physical contraction of bodies cannot affect the distance between accelerating rockets. However, in combination with a different synchronization of clocks, the result is that for a reference system that accelerated from rest to a certain speed, after re-synchronization all space in the stationary system appears to be contracted.

Even the distance between stars will appear to be contracted, as the physical cause is fully ascribed to changes of measurement by the accelerating system - nothing happens to the stationary system.

[comment moved up:]

[..] Momentum and KE are both inherently kinematic evaluations. Applying to interactions with external entities. Completely relative values that say nothing about the internal conditions of the particle in question.
As far as the contraction , as I stated previously; viewed kinematically there is no problem with the ship contracting relative to one frame and expanding relative to another.

I perceive here the same problem with the meaning of "kinematic", and the discussion here is about physical causes and not about "internal conditions" - sorry I don't know what you mean with it. What is the "internal condition" of a state of motion? I don't want to get to such a philosophical discussion (and it may go beyond what this forum is meant for).

I would say that any quantitative evaluation of the speed of light relative to an atom depends on the chosen frame. [..] I simply talked about a change in velocity with no implication that it was even determinable whether it was an increase or decrease.

OK - then I still don't know why you think that there is something "problematic" with Bell's explanation...

When I said invariant wrt light I was not not talking about the frame invariance of measured speed but the independent isotropic constancy that we assume. [..]

Ah, here's another point that could be bugging you; those two things are strongly related. Only when the astronauts do a new clock synchronization in flight, will they make light isotropic "in" (= according to) their newly set up reference system.
By the way, that is another illustration to show that SR is physics, relating to physical changes.

In your opinion does this or does this not imply some indeterminate, but actual, change in velocity relative to light resulting from a change of velocity through acceleration ??

Evidently! That is the case according to measurements with all inertial reference frames and it explains the reason for the need to re-synchronize the clocks.

Obviously the change can be either way according to relative frames but do you think it could be both increasing and decreasing relative to light /
Do you think that the fact that we can not determine the reality means that there is no definite condition?

That's very philosophical, but IMHO at most only one perspective of contradictory ones can be true. And of course indeterminable is not the same as non-existing!

I think there may be a bit of a typo in case 2. I assume you meant to write "is" expanded and "has" less kinetic energy.

Ah yes, sorry for that (your following comments moved up).

Well I think if you look that is exactly what I did say (the bolded text without the reference to KE)

There is a subtle but important difference: you wrote it as a self contradiction. "Ship B is both contracting and expanding." In mathematics: B<X ^ B>X. The solution is empty, just as in the example you give next:

I was [..] looking at the implications of the purely physical interpretation of contraction as applied to both frames at once.

Consider the fictitious paradox of contraction.
Length A is smaller than length B AND length B is smaller than length A
Obviously the correct application of the L transformation resolves this in a completely logically consistent way.
But that resolution is a kinematic one. It includes the relativity of simultaneity. [...]

Obviously we don't speak the same language! A self contradiction cannot be solved by applying a system transformation or by invoking "kinematic factors", it needs the correction of a wrong statement.

Yes of course.But to my understanding the relevant physics in this case is the maths of the Lorentz transformation. This is a kinematic description that predicts the expected measurements of relative frames .

From what you wrote next ("But the maths do not per se, directly describe or entail any physics interpretation"), I understand that you meant that the relevant physics in this case follows from the maths of the Lorentz transformation. Yes of course.

As I said I assume this to be a totally accurate description of reality. [...]

I had not seen that remark by you, and I don't know what you mean with it. If you mean that you assume that the Lorentz transformations accurately describe how observations with different inertial frames compare in a single reality, then I am like-minded.

 

[Austin0]

Just to check we are all on the same page, please consider the following. We have a pair of rockets A1 and A2 on the ground connected by a resilient, elastic and tough 1km rod. Alongside them is another identical pair of rockets, B1 and B2 also connected by 1Km rod like so:

A2--------------------A1
B2--------------------B1

It is assumed the connecting rods are initially under negligible stress. All the rocket engines are identical with identical fuel loads and burn rates etc. Just before take off we disconnect the end of the rod that was attached to rocket A2. The rockets all take off simultaneously in the ground frame and set to burn at an equal and constant rate. When all the rockets have depleted their fuel at a velocity of around 0.9c relative to the ground and everything has stabilised, the situation as seen from the ground should be something like this:

A2...----------A1
...B2----------B1

The length contraction of the resilient rod has physically dragged the B1/B2 rockets closer together (about 1/2 Km apart) than the disconnected A1/A2 rockets that are still about 1 Km apart. Everyone agree?

P.S. The small white dots are just spacers and should be ignored in the diagram.

I don't know about everyone else But I totally agree. That is exactly my analysis.
The assumption that a rigidly connected system would have equal coordinate acceleration and maintain a constant separation in the launch frame simply because of equal thrust,is in my opinion, not founded in realistic physics.
Also in the case of the independent systems there is a physical basis for an assumption of increasing separation wrt other frames moving in the same direction.
For instance a frame at 0.8c In this frame the earlier ignition of the lead ship would result in in a velocity differential that would actually increase over time because the coordinate acceleration in that frame would be increasing by a factor of 1/\gamma³ and the lead ship would be infinitesimally ahead on the acceleration curve.
This would not be the case with the connected system. The prior ignition of the lead ship would not lead to significant actual coordinate motion relative to the back of the system while the momentum was propagating back through the system. With any kind of realistic acceleration ,for simplicity say 1 g, the system would begin actual motion as a whole with any infinitesimal differential between the front and back equalizing as full acceleration was achieved and internal tensile forces realized a stable stress gradient.
To me it appears to be a simple situation: There are the tensile forces of L contraction acting inward toward the center of mass and the forces of thrust directed forward. So from the middle to the front the two forces are in oppositon which would result in a minute retardation of the acceleration of the front (in launch frame). From the center backward the forces are aligned ,so would result in a comparable increase in the coordinate acceleration of the rear.
The end result being the expected contraction in the launch frame with a coordinate differential of acceleration and velocity between the front and the back without a necessary precise scaling of distributed acceleration with a larger acceleration appllied to the rear as proposed by the Born hypothesis.
I agree with the premise that if a constant separation could be maintained in the launch frame that this would result in physical disruption of the system. But my feeling is that not only would this be impossible but to even attempt it would require massive thrust with some degree of actual reverse thrust being applied to the rear . IMHO

 

[yuiop]

I don't know about everyone else But I totally agree. That is exactly my analysis.

Thanks for the agreement. I cannot think of a clearer demonstration of the physical nature of length contraction in SR.

I agree with the premise that if a constant separation could be maintained in the launch frame that this would result in physical disruption of the system. But my feeling is that not only would this be impossible but to even attempt it would require massive thrust with some degree of actual reverse thrust being applied to the rear . IMHO

Surely that woud depend on the power of the rockets and the tensile strength/ elasticity of the connecting tether. For example if the connector was a bungee cord then a pair of powerful rockets would have no trouble maintaining constant separation in the launch frame and the elasticity of the bungee can take a lot of stress without breaking, but of course with indefinite acceleration, it would have to eventually snap.

 

[Austin0]

First you say your question is not related to the string scenario and then you proceed to exactly describe the string scenario, except that it is replaced by a rigid rod, and then you agree that obviously there is going to be stress. So I'm not sure what you are looking for.

Nevertheless, even though this issue has been dealt with countless times in this and other threads, I will say succinctly that if you accelerate the two ships identically then they will maintain the same distance apart in their initial rest frame. But the connecting rod between them will be subject to length contraction in the same initial rest frame. Therefore, if it is rigid, it will break, if it is not rigid, it will stretch.

Yes this topic has come up before. A long time ago I had a prolonged discussion just like this, with someone who maintained the same basic view that you hold. Unfortunately that discussion got derailed midstream into a side argument about whether conservation of momentum could be applied absolutely in the real world. In any case the main question was never resolved so I welcome this opportunity to explore it.

Originally Posted by ghwellsjr

Yes, if we move a rod by accelerating it at one point then we won't squeeze or pull on it but if we accelerate one end of rod separately from accelerating the other end of the rod, we can end up squeezing it or pulling it apart. Isn't that obvious?

I am sorry but it is not obvious to me. You say that acceleration from one end does not cause a problem or disruption. (SO in this case that would mean only firing up the lead ship). But application at two points would result in disruption.
If the force is applied only at the front, that creates the maximum expansive stress possible without applying reverse thrust to the rear. SO adding a forward thrust at the rear actually reduces the overall expansive stress, so I am confused as to why you think this would lead to expansive disruption where the single thrust would not.

The basic premise of Born rigid acceleration; that stressless acceleration would necessitate a scaled and distributed acceleration scheme is certainly reasonable.
But aside from the fact that it is unrealistic in application , until we develop some totally new science that negates inertia and momentum,(gravity drive or?) stress is an inevitable consequence of acceleration, and stress, per se, is not a big problem. We live every day under a constant stress of 1 g. The relevant concern is if that stress is constant or dynamically increasing. So why do you think it would be increasing to the point of disruption?
You also did not provide any basis for your assumption that equal thrust at the front and rear would necessarily result in equal coordinate acceleration at those points and a constant separation in the launch frame.

 

[Austin0]

Thanks for the agreement. I cannot think of a clearer demonstration of the physical nature of length contraction in SR.
Surely that woud depend on the power of the rockets and the tensile strength/ elasticity of the connecting tether. For example if the connector was a bungee cord then a pair of powerful rockets would have no trouble maintaining constant separation in the launch frame and the elasticity of the bungee can take a lot of stress without breaking, but of course with indefinite acceleration, it would have to eventually snap.

i was talking within the context of this discussion; assuming a realistically strong rigid connecting structure and reasonable acceleration. Certainly the actual stresses and results would be affected by the magnitude of acceleration. I would imagine that given a sufficiently long structure and high enough magnitude of acceleration, that serious deformation ,even to the point of disruption could occur in the front section before the momentum reached the middle and motion began at that point. But what if it was a dynamically increasing acceleration, starting from 0 and slowly increasing to the desired final magnitude??

 

[phyti]

austinO post 191

I myself find the, physical contraction as a consequence of EM and atomic light speed interactions hypothesis very convincing. But as you have shown here it is somewhat problematic in application to specific scenarios.

This seems to be the same problem I was working on recently. Maybe it will help you.
U is the universal rest frame. A and B space ships pass U at t=0, moving at v = .6c.
Both experience equal length contraction to .8L in the x direction. If length contraction
is a result of em deformation in response to acceleration, then length expansion should
be the response to deceleration. If the A ship returns to U and stops, it should recover
its original length.
According to SR, if A moves away from B, B should measure a length contraction of A.
At first it seems A would have to expand and contract simultaneously to satisfy both
requirements, but not so. The confusion occurs because there are two different length
contractions, the first due to absolute motion relative to light speed, the second due
to perception. Since U is the absolute rest frame, the A & B contraction is the result of
em phenomena. After deceleration of A to v=0, it expands to 1L. Now consider B as
passing A at rest in the U frame. Time dilation for B is .8t, thus B arrives early at
locations on the Ux axis. Since everything in the B frame slows B trusts his clock and
interprets the effects as length contraction of the U frame, thus A is contracted to
.8L, and both requirements are met.

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