Is Lorentz Contraction Indistinguishable from Standard Relativity?

[cfrogue]

If the rod is rigid, and a and b are firmly glued to the rod and not glued to anything else, the rod contracts and the points become less than d apart, relative to the original frame.

If the rod is rigid, and a and b are not glued to the rod and are firmly glued to something else, the rod contracts and the points will do whatever the "something elses" do.

If the rod is rigid, and a and b are firmly glued to the rod and are firmly glued to something else, the rod contracts and either the "something elses" will be pulled together by the force of the rod, or something will fall to pieces.

Wow, this is very specific.

But, then you agree the points and rod contract together.

What about the perspective of the launch frame now?

 

[JesseM]

But these publications don't rely purely on SR either--they have to make at least some implicit qualitative assumptions about the behavior of materials to conclude the string snaps, like the idea that if you keep increasing the length of a string in its rest frame it will eventually snap. There's no way to answer a question about a string snapping without at least some basic assumptions about materials science that go beyond the basic axioms of SR; it just so happens that your assumptions about materials science need to be a bit more detailed if you want to analyze things purely in the launch frame.

Yes, but none of these things apply to the launch frame do they?

None of what things? I just said that you have to take into account assumptions about materials science in the string's rest frame, and the same is true in the launch frame.

In particular, one paper says the string continues to contact as the acceleration continues.

I don't think any of the papers say the string itself contracts, although they may say that the atoms and electromagnetic fields around them contract, or that the equilibrium length that the string would be if it weren't attached to the ship contracts.

Another says the distance between the ships increases as the acceleration continues.

It doesn't say the distance increases in the launch frame.

Eventually, breakage will occur in both cases.

But, the launch frame has no such limitations. In the launch frame, at least all of us agree, has no reason for the string to break without imposing standards from some other source of logic outside SR.

And exactly the same is true in every other frame, you always need at least some basic assumptions about materials that go beyond the basic axioms of SR! That was the whole point of my last post!

 

[Al68]

cfrogue

(a) Do you accept that a loose, straight piece of string, which is free at both ends, gets shorter when accelerated along its length, as measured in the launch frame? If yes, does that satisfy your stipulation that you must work things out in the launch frame only?

(b) Everyone agrees the distance between the ships remains constant in the launch frame.

Now repeat the experiment with the string attached between the ships. (a) says the string contracts. (b) says it doesn't. There's only one way to resolve this apparent contradiction. The string must break.

I never mentioned any frame except the launch frame.

Your second statement about (b) is false. In the launch frame, the string's length is contracted, and the distance between the ships is also contracted but stays constant, and the string's relaxed length becomes increasingly shorter than the distance between the ships.

Again, the word "contracted" in this context does not mean "shorter than before", it means shorter than its length in the co-moving frame of the string.

 

[matheinste]

Your second statement about (b) is false. In the launch frame, the string's length is contracted, and the distance between the ships is also contracted but stays constant, and the string's relaxed length becomes increasingly shorter than the distance between the ships.

Again, the word "contracted" in this context does not mean "shorter than before", it means shorter than its length in the co-moving frame of the string.

Yes, I am getting confused because sometimes the term contracted seems to be used in this discussion to mean Lorentz contraction and sometimes to mean the result of a Lorentz trnaformation withiut making it explicit which is meant. The context is not always clear.

Matheinste.

 

[A.T.]

I agree SR is not material science.

Good

Why do we need to go outside the theory to conclude the string will break from the launch frame perspective?

You need some material science in every frame to show that the string brakes. And applying SR to material science is not "going outside SR", but the opposite: it is using SR consistently on every level.

Why can't this be concluded from within SR?
...
I must have missed the argument from SR.
...
Please only use SR.

You sound like a broken record. See above.

 

[Fredrik]

If the rod is rigid, and a and b are firmly glued to the rod and not glued to anything else, the rod contracts and the points become less than d apart, relative to the original frame.

If the rod is rigid, and a and b are not glued to the rod and are firmly glued to something else, the rod contracts and the points will do whatever the "something elses" do.

If the rod is rigid, and a and b are firmly glued to the rod and are firmly glued to something else, the rod contracts and either the "something elses" will be pulled together by the force of the rod, or something will fall to pieces.

Wow, this is very specific.

But, then you agree the points and rod contract together.

What about the perspective of the launch frame now?

Why do you think that DrGreg's reply didn't completely answer all your concerns? It does. In the Bell's spaceship scenario, you're supposed to assume that the effect of the string on the spaceships is negligible, and that both rockets move in exactly the same way (except for their starting position). That last requirement implies that they stay a constant distance d apart in the launch frame. The Lorentz contraction of the string implies that its natural length in the launch frame at speed v is d/\gamma<d, so it must break. Note that the string can't change the motion of the rockets, because it's been specified in the problem that it doesn't.

 

[matheinste]

Why do you think that DrGreg's reply didn't completely answer all your concerns? It does. In the Bell's spaceship scenario, you're supposed to assume that the effect of the string on the spaceships is negligible, and that both rockets move in exactly the same way (except for their starting position). That last requirement implies that they stay a constant distance d apart in the launch frame. The Lorentz contraction of the string implies that its natural length in the launch frame at speed v is d/\gamma<d, so it must break. Note that the string can't change the motion of the rockets, because it's been specified in the problem that it doesn't.

So can we say by reasoning using SR and not LET and so avoiding Lorentz contraction, that to an observer in the launch frame, by the way the problem is posed, despite acceleration and thus change in relative velocity, the distance between the ships remains the same. As we would expect the result of aLorentz transformation into the launch frame from the ships frame(s) to result in smaller distances/lengths, this constant separation after Lorentz transformation, implies that the ships are actually moving apart in their own frame(s) as time progresses, thus breaking the string.

Matheinste

 

[Fredrik]

So can we say by reasoning using SR and not LET and so avoiding Lorentz contraction,

Huh?

...to an observer in the launch frame, by the way the problem is posed, despite acceleration and thus change in relative velocity, the distance between the ships remains the same.

Yes, that's what I said.

As we would expect the result of aLorentz transformation into the launch frame from the ships frame(s) to result in smaller distances/lengths,

I'm a bit uncomfortable with this argument since the two world lines aren't straight and parallel. You would need to supply more information to be convincing.

...the ships are actually moving apart in their own frame(s) as time progresses, thus breaking the string.

That's the reason an observer at rest in one of the co-moving inertial frames (or in one of the accelerating frames) would use to explain why the string breaks.

 

[matheinste]

My words-----As we would expect the result of a Lorentz transformation into the launch frame from the ships frame(s) to result in smaller distances/lengths,-----

Your reply----I'm a bit uncomfortable with this argument since the two world lines aren't straight and parallel. You would need to supply more information to be convincing.---


I will have to give this more thought. I am quite happy to accept that my reasoning may be wrong. If you can see a specific problem with the quoted passage please let me know.

Part of my motivation is, as I said earlier, to remove references such as "the string contracts", or "Lorentz contraction" which I have found used ambiguously in the past. I would be happier viewing the problem purely in an SR context although I understand that the formulations always lead to the same results.

Matheinste.

 

[Fredrik]

I will have to give this more thought. I am quite happy to accept that my reasoning may be wrong. If you can see a specific problem with the quoted passage please let me know.

For starters, you didn't even say which event(s) you're applying the Lorentz transformation to.

Part of my motivation is, as I said earlier, to remove references such as "the string contracts", or "Lorentz contraction" which I have found used ambiguously in the past. I would be happier viewing the problem purely in an SR context although I understand that the formulations always lead to the same results.

What I said in #126 is a pure SR solution of this problem. (Hence the "Huh?" in my previous post).

 

[matheinste]

For starters, you didn't even say which event(s) you're applying the Lorentz transformation to.


What I said in #126 is a pure SR solution of this problem. (Hence the "Huh?" in my previous post).

I accept your reasonings completely. I am not here to argue, just to learn thoroughly off people who know more than me. I am afraid the term Lorentz contraction as far as I can see sometimes seems to be used as the physical contraction of the LET and sometimes as the result of a coordinate transformation in SR. Perhaps its a problem other people don't have so I'll just have to live it.

I will continue watching with interest.

Matheinste.

 

[Fredrik]

You need some material science in every frame to show that the string brakes.

It depends on what we consider the axioms of SR to be. One axiom must tell us how to measure lengths, and if we choose to say that length is measured using solid objects (i.e. objects that are doing Born rigid motion when they're accelerated gently), then it follows immediately from the axioms that the string must break.

Now that I think about it, I realize that that's the axiom we should use when we intend to add matter "manually" to the model (by simply associating properties like mass and charge with certain world lines). When we intend to introduce matter using a Lagrangian, we should use radar instead. Then it should be possible to prove the Born rigidity of a solid that's accelerated gently.

1. Physical events are represented by points in Minkowski space. (Note that this implies that the motion of a classical object can be represented by a set of curves in Minkowski space, and that this suggests that we define a classical particle to be "a physical system whose motion can be represented by exactly one such curve").

2. A clock measures the proper time of the curve in Minkowski space that represents its motion.

It's clear that we also need to postulate something about measurements of length, but this is more difficult because of Lorentz contraction. There might be more than one OK way to do it, and one of them seems to be to postulate that lengths are measured by rulers, and that a solid object (like a ruler) that's accelerated gently undergoes Born rigid motion (which guarantees that if we slowly change its velocity, its measurements before and after the acceleration will be consistent with the Lorentz contraction formula).

Unfortunately, this postulate is inappropriate when we formulate theories of matter in this framework (as described in my previous post). It must be possible to possible to use those theories to prove the Born rigidity of an accelerating solid. However, that result isn't going to be a testable prediction of the theory unless we use something other than solid objects to perform length measurements.

If we can't use solids, it seems natural to use light instead. We can use radar to define distance. If we emit a signal at time t₁ (as measured by a clock attached to the radar device) and detect the signal coming back at time t₂, then the distance to the reflection event can be defined as (t₂-t₁)/2. But of course this only works as well as we'd like if the radar isn't accelerating. So we can take the third postulate to be that "lengths are measured by radar devices that move on geodesics", or that "infinitesimal lengths are measured by radar devices".

Hey, I learned something. Some of these things weren't perfectly clear to me before, in particular the reason why the postulate about length measurements should use radar instead of rulers.

 

[matheinste]

Fredrik may I offer this as a paraphrase of your description in #126, the SR resolution.

In the launch frame the distance between the ships is constant whereas it should be continually contracting in the launch frame due to increasing velocity of the ships relative to the launch frame . The thread occupies the distance between the ships and so too should appear contracted in the launch frame. It does not appear so and therefore must be increasingly stressed. Simple as that?

Matheinste

 

[atyy]

Fredrik may I offer this as a paraphrase of your description in #126, the SR resolution.

In the launch frame the distance between the ships is constant whereas it should be continually contracting in the launch frame due to increasing velocity of the ships relative to the launch frame . The thread occupies the distance between the ships and so too should appear contracted in the launch frame. It does not appear so and therefore must be increasingly stressed. Simple as that?

Matheinste

I guess this is what you meant by the confusing usage of "Lorentz contraction" you objected to above? If the distance should be continually contracting but remains constant, at this point we should say we have obtained a contradiction and the theory is wrong.

 

[yuiop]

I guess this is what you meant by the confusing usage of "Lorentz contraction" you objected to above? If the distance should be continually contracting but remains constant, at this point we should say we have obtained a contradiction and the theory is wrong.

Oh nooo.. we shouldn,t say that!

If we had a theory that a cooled metal rod contracts, and then anchored the two ends of the rod so they could not move and then cooled the rod, would that prove that the theory that a cooled rod contracts is wrong?

 

[atyy]

Oh nooo.. we shouldn,t say that!

If we had a theory that a cooled metal rod contracts, and then anchored the two ends of the rod so they could not move and then cooled the rod, would that prove that the theory that a cooled rod contracts is wrong?

Yes.

 

[yuiop]

Oh nooo.. we shouldn,t say that!

If we had a theory that a cooled metal rod contracts, and then anchored the two ends of the rod so they could not move and then cooled the rod, would that prove that the theory that a cooled rod contracts is wrong?

Yes.

LOL

OK, to satisfy you I would have to reformulate the cooled rod contracts to something like " An unstressed rod contracts when cooled if it remains unstressed" or maybe "A cooled rod contracts if it is allowed to do so". Similarly we could say something like"an accelerated unstressed rod/string length contracts if it remains unstressed". The fact that the string in the Bell's rocket paradox does not length contract when accelerated is proof that it does not remain unstressed.

 

[atyy]

LOL

OK, to satisfy you I would have to reformulate the cooled rod contracts to something like " An unstressed rod contracts when cooled if it remains unstressed" or maybe "A cooled rod contracts if it is allowed to do so". Similarly we could say something like"an accelerated unstressed rod/string length contracts if it remains unstressed". The fact that the string in the Bell's rocket paradox does not length contract when accelerated is proof that it does not remain unstressed.

Yes, something like that

 

[A.T.]

You need some material science in every frame to show that the string brakes.

It depends on what we consider the axioms of SR to be...

What I meant is: Even aside of SR, defining the condition for a material to break is already a form of material science.

The relevant part was: Combining SR & material science is just using SR consistently on every level. This is what cfrogue fails to acknowledge, by asking to use "only SR". SR as such doesn't tell you anything about breaking of some materials in any frame.

 

[cfrogue]

The relevant part was: Combining SR & material science is just using SR consistently on every level. This is what cfrogue fails to acknowledge, by asking to use "only SR". SR as such doesn't tell you anything about breaking of some materials in any frame.

OK, let's do this.

Let us abandon the logic of breakage.

One solution from the accelerating ships concludes a rod within the space will contract.

One solution from the accelerating ships concludes the ships get further apart.

Now, from the launch frame, the distance between the ships does not change and there is no prevision for rod contraction under the acceleration equations unless space and the rod length diverge and even with that there are no mainstream papers to support that either.

So, the theory concludes the rod experiences change from the accelerating frame and from the launch frame, no such conclusion can be drawn.

Is this a problem?

 

[yuiop]

One solution from the accelerating ships concludes a rod within the space will contract.

I do not think that would be a correct solution. If the rod is attached to just one ship the observers on that ship will not consider the rod to be contracting. If the rod is connected to both ships they will consider the rod as being stretched.

One solution from the accelerating ships concludes the ships get further apart.

That's an OK solution. The ships are getting further apart and anything connecting them is being stretched from the POV of the ship observers.

In the lauch frame the observers calculate the relaxed length of the accelerating rod to be d' which is less than the relaxed length of the rod when it was at rest in the launch frame. Since they observe the rod is still spanning a distance of d when it moving relative to them the launch frame observers consider the rod to stretched or under stress and will probably break if the stress continues to increase unless the rod has infinite strength which is unlikely.

 

[cfrogue]

I do not think that would be a correct solution. If the rod is attached to just one ship the observers on that ship will not consider the rod to be contracting. If the rod is connected to both ships they will consider the rod as being stretched.

This is the latest mainstream paper.

Although Bell’s name has been attached to the paradox, the
thought experiment involved was first considered by Dewan and Beran[5] as
a demonstration “that relativistic contraction can introduce stress effects in a
moving body.” We have disputed this contention in the previous section.

http://arxiv.org/PS_cache/arxiv/pdf/0906/0906.1919v2.pdf

That's an OK solution. The ships are getting further apart and anything connecting them is being stretched from the POV of the ship observers.

Yes, but what about the launch frame?

 

[Al68]

Now, from the launch frame, the distance between the ships does not change and there is no prevision for rod contraction under the acceleration equations unless space and the rod length diverge and even with that there are no mainstream papers to support that either.

So, the theory concludes the rod experiences change from the accelerating frame and from the launch frame, no such conclusion can be drawn.

Is this a problem?

Still not correct. The rod is contracted by the lorentz factor.

In the launch frame, the rod is contracted because it is in relative motion. That's just basic SR. It is length contracted in the launch frame regardless of whether it stretches and stays the same length, or breaks and gets shorter. Either way its length in the launch frame is less than its proper length.

In the launch frame, there is an increasing difference between the relaxed length of the string (or rod) and the distance between the ships.

 

[yuiop]

This is the latest mainstream paper.
http://arxiv.org/PS_cache/arxiv/pdf/0906/0906.1919v2.pdf

The person that wrote that paper seems a bit confused. He seems to think that in the accelerating frame there is a series of instantaneous rest frames, but how can one ship consider itself to be in the same rest frame as the other ship fs it observes the other ship to be moving with respect to his own ship?

Also, the author seems to think there is only one possible physical explanation for an observation. In fact observers with different relative velocities will have different physical explanations for the same outcome.

Explanation 1)

From the POV of the accelerated observer the gap is increasing and the string is being stretched.

Explanation 2)

From the POV of the launch frame observers the gap remains constant and the string is length contracting.

Explantion 3)

From the POV of an observer moving with constant velocity relative to the launch frame in the same direction as the intended path of the rockets, the front rocket takes off before the rear rocket and it is the difference in synchronicity that causes the string to break.

All the explanations are equally valid and all reach the same conclusion that the string will snap. Every observer must have an explanation for why the string snaps from their point of view even if that explanation differs from the explanation of other observers in different reference frames. The author of the paper claims that only the accelerating observers can provide a physical explanation for why the string snaps and leaves observers in other frames without an explanation.

 

[matheinste]

These comments referred to the cited paper.

On page 3 the author seems to be using the fact that Lorentz transforms (coordinate transforms) do not induce stress in an object as proof that Lorentz contraction, in the original Lorentzian use of the term, do not either.-----"-One other point to be considered is whether strains and stresses can be induced by Lorentz contraction, as is contended in Refs. [1,2,4,5]. Our answer to this is clear from the previous discussion. Just as a 3D rotation of an object does not induce strain, a 4D rotation (Lorentz transformation) will not induce strain and consequent stress."--------

Also the fact that he describes the apparent relativistic contraction of length as illusory is a bit unusual.-------"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."----------

I have not read the rest of the article closely yet but the above points disturb me a little.
Of course it may just be my reading of the text that is in error.

Matheinste.

So I am not alone in finding it a bit unusual.

 

[cfrogue]

The person that wrote that paper seems a bit confused. He seems to think that in the accelerating frame there is a series of instantaneous rest frames but how can one ship consider itself to be the same rest frame as the other ship is it observes the other ship to be moving with respect to his own ship?

Also, the author seems to think there is only one possible physical explanation for an observation. In fact observers with different relative velocities will have different physical explanations for the same outcome.

Explanation 1)

From the POV of the accelerated observer the gap is increasing and the string is being stretched.

Explanation 2)

From the POV of the launch frame observers the gap remains constant and the string is length contracting.

Explantion 3)

From the POV of an observer moving with constant velocity relative to the launch frame in the same direction as the intended path of the rockets, the front rocket takes off before the rear rocket and it is the difference in synchronicity that causes the string to break.

All the explanations are equally valid and all reach the same conclusion that the string will snap. Every observer must have an explanation for why the string snaps from their point of view even if that explanation differs from the explanation of other observers in different reference frames. The author of the paper claims that the only the accelerating observers can provide a physical explanation for why the string snaps and leaves observers in other frames without an explanation.

You did not specifify the launch frame.

How about that?

The person that wrote that paper seems a bit confused. He seems to think that in the accelerating frame there is a series of instantaneous rest frames but how can one ship consider itself to be the same rest frame as the other ship is it observes the other ship to be moving with respect to his own ship?

This is the way all of them look at the problem.

They all consider an artificial at rest frame for an infinitesimally small segment of the "string" vs the accelerating frame.

Here is another analysis using the same "at rest frame" with a different conclusion.

http://www.mathpages.com/home/kmath422/kmath422.htm


Please read it again.

 

[JesseM]

You did not specifify the launch frame.

How about that?

Yes he did:

Explanation 2)

From the POV of the launch frame observers the gap remains constant and the string is length contracting.

This is the way all of them look at the problem.

They all consider an artificial at rest frame for an infinitesimally small segment of the "string" vs the accelerating frame.

Yes, but I think kev's point was that in the instantaneous rest frame of one of the ships, the other ship is moving--there is no common rest frame for the entire ship/string combo. The paper seems to say otherwise on p. 4 when the author writes "If, at a time when each spaceship has a velocity v, we make a Lorentz transformation with velocity v, each spaceship will be at rest".

Here is another analysis using the same "at rest frame" with a different conclusion.

http://www.mathpages.com/home/kmath422/kmath422.htm

This page isn't talking about the type of acceleration seen in Bell's spaceship paradox, it's talking about Born rigid acceleration, where the two ships would not have the same acceleration in the launch frame (nor would they have the same proper acceleration), instead the acceleration of the ship in the rear would be greater than that of the ship in front. Born rigid acceleration is specifically designed so that if you pick the instantaneous inertial rest frame of one point on the accelerating object (like the front ship), at that moment in that frame every other part of the object (like the back ship) is at rest too.

 

[cfrogue]

Yes he did:

How?

This page isn't talking about the type of acceleration seen in Bell's spaceship paradox, it's talking about Born rigid acceleration, where the two ships would not have the same acceleration in the launch frame (nor would they have the same proper acceleration), instead the acceleration of the ship in the rear would be less than that of the ship in front. Born rigid acceleration is specifically designed so that if you pick the instantaneous inertial rest frame of one point on the accelerating object (like the front ship), at that moment in that frame every other part of the object (like the back ship) is at rest too.

It is talking about how to reduce the acceleration of the front ship to equate the effect of the string's length contraction.

On the other hand, with respect to the original inertial coordinates x,t, the two branch families represent two widely separate clusters of particles, initially both approaching the pivot event at near light speed and highly contracted spatially. As they approach, each cluster slows down and expands, until finally the two clusters both come to rest at time t = 0, just as they touch each other and achieve their maximum lengths. Then they separate again, each accelerating away and contracting.
http://www.mathpages.com/home/kmath422/kmath422.htm

Am I wrong?

 

[yuiop]

Here is another analysis using the same "at rest frame" with a different conclusion.

http://www.mathpages.com/home/kmath422/kmath422.htm

As Jesse mentioned, the author of that webpage (Kevin Brown) is talking about a different kind of acceleration that keeps the gap between the rockets constant from the point of view of the rocket observers, but now observers in the launch frame see the gap as length contracting at the same rate as anything connecting the two rockets. In that context an instantaneous rest frame for the accelerating rockets makes sense.

As an aside, I like this interesting quote from Kevin Brown in the linked webpage:

More fundamentally, it's worth recognizing that, even in circumstances when Born rigid motion of a configuration of particles is feasible, it does not actually represent perfectly "stressless" motion, because although the proper distances with respect to the instantaneously co-moving reference frames remain constant, the proper times of the different parts of the object do not remain coherent. In other words, if we contrive to hold the spatial relations fixed during an acceleration, a phase shift is introduced between different parts of the object, just as, if the phase is held constant, there is spatial stretching. (This is even more obvious in the case of angular acceleration, because in that case both spatial and temporal distortions are unavoidable.) This raises the question of whether material particles and their associated fields resist changes in their temporal as well as their spatial relationships. Typically we regard the equilibrium conditions as dependent only on the latter, and ignore differences in elapsed proper time, probably because such differences are extremely slight for the motions of ordinary macroscopic objects. Also, once a phase shift has been introduced, the assumed memorylessness of elementary entities ensures that the new equilibrium configuration will have the same spatial relations as the old. Nevertheless, it may still be the case that entities resist changes in their proper phase relations.

This leads to the intriguing idea that inertia, i.e., the resistance of objects to acceleration, may be partly or totally due to self-stresses of extended configurations. When we push on an object, it seeks to maintain not only the pre-existing spatial relations between its parts, but also the temporal phase relations. As we've seen, a direct consequence of the Minkowskian structure of spacetime is that if all these relations are held constant, the object cannot be accelerated. In order for the object to be accelerated, it is necessary to overcome the object's intrinsic resistance to changes in these relations (spatial, temporal, or both), and this resistance might be identified with the resistance of inertial bodies to acceleration. The only truly stressless "acceleration" would be of objects in a perfectly uniform gravitational field, in which case the intrinsic curvature of spacetime conforms identically to the skewed spatio-temporal relations usually associated with acceleration, so that in a local sense the object is actually moving inertially.

 

[matheinste]

cfrogue,

Try thinking of what happens in the launch frame as a sort of inverse of what happens in the ship frame.

In the ships frame(s) the gap is increasing but the length of the thread is not. In the launch frame the gap is constant but the length of the thread is not. Both cases lead to stress in the thread and eventually breaksge.

Matheinste.