Is Lorentz Contraction Indistinguishable from Standard Relativity?

[matheinste]

In the case of the article in question

http://arxiv.org/abs/0906.1919 shows the article has been submitted to the European Journal of Physics

http://www.iop.org/EJ/journal/-page=forthart/0143-0807 shows it has been accepted for publication and is "provisionally scheduled for October 2009"(!)

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.

 

[JesseM]

Neither I nor anyone else on this thread has disputed the claim that the distance will remain constant in the launch frame if both ships have the same coordinate acceleration in this frame. Again, the point is that the stress in the string will be continually increasing even though its length in the launch frame is remaining constant.

This peer reviewed paper proves the string contracts and that is the reason for the string to break. See theorem 3.
http://arxiv.org/PS_cache/arxiv/pdf/0902/0902.2032v2.pdf

I don't know what you mean by "theorem 3"--what page are you looking at? In any case, looking over the paper, in equation 3.12 at the bottom of p. 11 they explicitly show that the length of the string does not change in the frame where the ships have identical coordinate accelerations (and started accelerating simultaneously). I'm sure you won't find any physicists who dispute this very obvious and trivial point.

Here is a peer reviewed paper just published Oct 18, 2009

Bell’s paradox was that his intuition told him the cable would break, yet there was no change in the distance between the ships in system S. He suggested resolving the paradox by stating that a cable between the ships would shorten due to the contraction of a physical object proposed by Fitzgerald and Lorentz, while the distance between the ships would not change. This resolution however contradicts special relativity which allows no such difference in any measurement of these two equal lengths.

Conclusion:
For two spaceships having equal accelerations, as in Bell’s spaceship example, the distance between the moving ships appears to be constant, but the rest frame distance between
them continually increases.

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

This paper does not dispute Bell's claim that the cable would break! Instead it calls for a rethinking of the reason the cable breaks...the author's argument seems to be that the only physical way of defining an object's length is by looking at its own rest frame, so that treating "length contraction" as a change in length is overly confusing...from p. 3:

This suggests the need for a definition of “length” that is the same for any state of uniform motion. This would correspond to the use in relativity of “proper time” and “invariant mass” for time and mass, but the terms “proper length” and “invariant length” have already been used in the literature with other meanings. The term we recommend for length is “rest frame length”, which we define as the length a moving object has after a Lorentz transformation to its rest system. If length is to be considered a physical attribute of an object, then this physical attribute should be the rest frame length. This length, of course, would not be changed by uniform motion.

The author then points out that the "rest frame length" of the cable or string does grow as the ships accelerate, even though the distance between them in the observer's frame does not change, and that this should be seen as the true reason a cable or string would break, not length contraction:

Although the spaceships are accelerating, the system S′ is a Lorentz system moving at constant velocity. Since each ship is instantaneously at rest in this system, the length d′ = gamma*d is the rest frame distance between the ships. As such, it is the physical distance between the ships. If there were an inextensible cable between the ships, it would snap at the start of motion of the ships. An elastic cable would stretch until it reached its maximum possible length d_Max, at which point it would snap.

 

[DrGreg]

I have a question.

From what I have seen, all calculations agree the launch frame observer believes there is no distance differential between the two ships.

Is this correct as far as you know?

Yes.

There is no doubt about this. In the launch frame the distance between the ships is constant. You gave a valid explanation at the end of post #18.

If the string was attached to the front ship only, trailing behind it, it would initially be touching the back ship, but as soon as the acceleration begins, the length of the string contracts as measured in the launch frame (assuming its "rest length" remains constant i.e. its length in any frame in which it is momentarily at rest).

Therefore if you had attached the string to the back ship, if the string was elastic it would stretch and if it couldn't stretch it would break.

I think this agrees with what everyone else has been saying in this thread and what the quoted paper says.

There is certainly no disagreement amongst experts that the string will break (despite the fact that long ago some experts initially got it wrong when they heard of the problem for the first time; even experts can make mistakes occasionally but now there is consensus as to what the correct answer is).

 

[cfrogue]

Yes.

There is no doubt about this. In the launch frame the distance between the ships is constant. You gave a valid explanation at the end of post #18.

If the string was attached to the front ship only, trailing behind it, it would initially be touching the back ship, but as soon as the acceleration begins, the length of the string contracts as measured in the launch frame (assuming its "rest length" remains constant i.e. its length in any frame in which it is momentarily at rest).

Therefore if you had attached the string to the back ship, if the string was elastic it would stretch and if it couldn't stretch it would break.

I think this agrees with what everyone else has been saying in this thread and what the quoted paper says.

There is certainly no disagreement amongst experts that the string will break (despite the fact that long ago some experts initially got it wrong when they heard of the problem for the first time; even experts can make mistakes occasionally but now there is consensus as to what the correct answer is).

OK, would the rest frame/launch frame conclude the string will break given the distance does not change between the ships from the POV of the rest frame?

In other words, does the launch frame conclude the distance does not change yet the string contracts?

 

[JesseM]

OK, would the rest frame/launch frame conclude the string will break given the distance does not change between the ships from the POV of the rest frame?

In other words, does the launch frame conclude the distance does not change yet the string contracts?

In the launch frame the string won't experience any change in length until it snaps. As I've said, the stress in the string will increase though. I think when people cite "Lorentz contraction" as an explanation for the string breaking, what they're getting at is that the string "wants" to contract but can't because it's attached to the ships...it may be easier to make sense of this if we think of a spring rather than a string, since you may remember from classical mechanics that springs have a "rest length" that they naturally assume when nothing is pulling or pushing on them (the rest length minimizing the stress in the spring), and that when they are pulled to a greater length than the rest length they pull back with greater and greater force, as if they are "trying" to return to that length (and obviously if you pull a spring far enough past its rest length, it'll snap). If you had two identical springs traveling alongside each other, one attached to the two ships and one with its ends free whose length was equal to its rest length, then the length of the free spring would grow shorter and shorter as seen by the launch frame as its velocity increased, which implies that the spring attached to the ships, whose length does not change in this frame, is being extended farther and farther past its own natural rest length.

 

[cfrogue]

In the launch frame the string won't experience any change in length until it snaps. As I've said, the stress in the string will increase though. I think when people cite "Lorentz contraction" as an explanation for the string breaking, what they're getting at is that the string "wants" to contract but can't because it's attached to the ships...it may be easier to make sense of this if we think of a spring rather than a string, since you may remember from classical mechanics that springs have a "rest length" that they naturally assume when nothing is pulling or pushing on them (the rest length minimizing the stress in the spring), and that when they are pulled to a greater length than the rest length they pull back with greater and greater force, as if they are "trying" to return to that length (and obviously if you pull a spring far enough past its rest length, it'll snap). If you had two identical springs traveling alongside each other, one attached to the two ships and one with its ends free whose length was equal to its rest length, then the length of the free spring would grow shorter and shorter as seen by the launch frame as its velocity increased, which implies that the spring attached to the ships, whose length does not change in this frame, is being extended farther and farther past its own natural rest length.

Well, the SR acceleration equations indicate the distance between ther ships will not change.

From the POV of the rest observer, what is the math to indicate the space remains constant but a rod will contract if allowed between the two ships.

All these links show what happens from the POV of the accelerating ships.

I want to concentrate on the math from the rest/launch frame's POV.

Also, this paper seems to say something different.

4 Conclusion
We have seen that the physical length of an object is the rest frame length as
measured in the instantaneous rest frame of the object. For two spaceships
having equal accelerations, as in Bell’s spaceship example, the distance between
the moving ships appears to be constant, but the rest frame distance between
them continually increases. This means that a cable between the two ships must
eventually break if the acceleration continues.

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

 

[JesseM]

Well, the SR acceleration equations indicate the distance between ther ships will not change.

From the POV of the rest observer, what is the math to indicate the space remains constant but a rod will contract if allowed between the two ships.

If the ends of the rod are connected to the ships then it can't contract, although it will eventually break. If it's not connected, then the math to indicate it contracts is just the fact that we expect the length of a free rod to stay constant in its own rest frame (assuming it behaves like a spring and has a natural 'rest length' it will return to after a small deformation due to acceleration), which means in the observer's frame it should contract according to the length contraction equation (if you want to calculate things without even referring to the rod's rest frame, I'm sure you could show why it contracts with a detailed analysis of the intermolecular forces in the rod at different velocities as defined in the observer's frame).

Also, this paper seems to say something different.

4 Conclusion
We have seen that the physical length of an object is the rest frame length as
measured in the instantaneous rest frame of the object. For two spaceships
having equal accelerations, as in Bell’s spaceship example, the distance between
the moving ships appears to be constant, but the rest frame distance between
them continually increases. This means that a cable between the two ships must
eventually break if the acceleration continues.

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

I already addressed this paper (and pointed out that it definitely says that string will snap) in post #32, did you read that one? The paper certainly doesn't dispute the idea that in the frame of the observer the length of the string will be constant until it snaps, it just argues that defining "length" in terms of the coordinates of an outside observer is not very physical, and that it's better to use a quantity called "rest frame length" which is defined solely in the string's own rest frame.

 

[DrGreg]

I think it is perhaps worth pointing out that some people have a false impression about what Lorentz contraction is. They may think that "when something accelerates it gets shorter". Or to be a bit more precise, if Alice measures (=x) something at rest (relative to Alice) and then later measures (=y) the same thing in motion, the length contracts. There may then be some debate over whether or not the "things" this applies to are just solid objects, or gaps between objects, or "space itself".

The above description of Lorentz contraction is wrong.

In many circumstances, what I said above is true, but reason it is true is not simply Lorentz contraction alone; it is Lorentz contraction plus some other reason combined.

A more accurate description of Lorentz contraction is that when inertial observer Bob measures the length z between two things both at rest relative to Bob, and another inertial observer Alice in relative motion measures the length y between the same two things at the same time, Alice measures a shorter distance than Bob.

So, the situation I described in the first paragraph will arise if there is a reason why Alice's initial "rest distance" x between the two things beforehand is the same as the Bob's final "rest distance" z. For example if the the two things are the two ends of a rigid object that doesn't break into pieces as a result of the acceleration.

The attached illustration emphasises my point. The transformation of x to y is not Lorentz contraction. The transformation of z to y is Lorentz contraction. If there is a reason why x = z, then the transformation of x to y will be a contraction. But if there's no reason, then contraction need not occur.

 

[A.T.]

I want to concentrate on the math from the rest/launch frame's POV.

The string is made up of atoms held together by electromagnetic forces. In the launch frame all these atoms and their electromagnetic fields are contracting and cannot fill the constant distance between the rockets anymore.

 

[cfrogue]

If the ends of the rod are connected to the ships then it can't contract, although it will eventually break. If it's not connected, then the math to indicate it contracts is just the fact that we expect the length of a free rod to stay constant in its own rest frame (assuming it behaves like a spring and has a natural 'rest length' it will return to after a small deformation due to acceleration), which means in the observer's frame it should contract according to the length contraction equation (if you want to calculate things without even referring to the rod's rest frame, I'm sure you could show why it contracts with a detailed analysis of the intermolecular forces in the rod at different velocities as defined in the observer's frame).

There are three frames, the launch frame, a theoretical instantaneous at rest frame and the accelerating frame.

In the theoretical instantaneous at rest frame, this is where the various papers prove one way or another the string snaps.

But, I want to focus on the launch frame. This frame is not seeing the distance change between the ships..

Question, does the launch frame conclude based on observations that the string breaks?

If so, what is the math from the launch frame to show this.

I already addressed this paper (and pointed out that it definitely says that string will snap) in post #32, did you read that one? The paper certainly doesn't dispute the idea that in the frame of the observer the length of the string will be constant until it snaps, it just argues that defining "length" in terms of the coordinates of an outside observer is not very physical, and that it's better to use a quantity called "rest frame length" which is defined solely in the string's own rest frame.

Yea, I am OK with that but, this author says the distance between them increases whereas before you mentioned the string wants to contract. Is this not a difference or am I misunderstanding you?

 

[A.T.]

Question, does the launch frame conclude based on observations that the string breaks?

Yes, see post #39

If so, what is the math from the launch frame to show this.

It is the same math that shows that the string breaks in its rest frame: The distances between the string atoms/molecules are to great for the bonding forces to hold them together. The only difference is:

- In the string rest frame the distances between the atoms/molecules are increased by stretching the string.
- In the launch frame the range of the bonding interactions is decreased as the atoms/molecules are contracted

 

[JesseM]

Question, does the launch frame conclude based on observations that the string breaks?

Yes.

If so, what is the math from the launch frame to show this.

As I've said before, if you wanted to do the calculation solely from the perspective of the launch frame I think you would need to actually do some detailed calculation of the inter-atomic forces in this frame. Even though the average distance between atoms wouldn't change in the launch frame until the string snaps (since the length of the string and the total number of atoms remains constant in this frame), as A.T. said the way the electromagnetic field between atoms varies as a function of distance would change, and from this you could presumably show that the stress in the string was increasing. The details of such a calculation are beyond me though.

Yea, I am OK with that but, this author says the distance between them increases whereas before you mentioned the string wants to contract. Is this not a difference or am I misunderstanding you?

You're misunderstanding. The author is talking about the actual length in the string's instantaneous rest frame, which does increase, while I was talking about the idea of a spring's "rest length" from classical mechanics (google 'spring' and 'rest length' to see that this is a common term) which has nothing to do with the spring's actual length in its rest frame, it just means the length the spring would naturally assume if it were relaxed and no forces were being applied to either end, which can of course be different from the spring's actual length if it is being stretched or compressed by outside forces.

 

[cfrogue]

Yes, see post #39

It is the same math that shows that the string breaks in its rest frame: The distances between the string atoms/molecules are to great for the bonding forces to hold them together. The only difference is:

- In the string rest frame the distances between the atoms/molecules are increased by stretching the string.
- In the launch frame the range of the interactions is decreased as the atoms/molecules are contracted

The integral for all of the solutions is calculated vs a theoretical instantaneous at rest frame not the launch frame.

Is this not correct?

 

[cfrogue]

Yes.

As I've said before, if you wanted to do the calculation solely from the perspective of the launch frame I think you would need to actually do some detailed calculation of the inter-atomic forces in this frame. Even though the average distance between atoms wouldn't change in the launch frame until the string snaps (since the length of the string and the total number of atoms remains constant in this frame), as A.T. said the way the electromagnetic field between atoms varies as a function of distance would change, and from this you could presumably show that the stress in the string was increasing. The details of such a calculation are beyond me though.

You're misunderstanding. The author is talking about the actual length in the string's instantaneous rest frame, which does increase, while I was talking about the idea of a spring's "rest length" from classical mechanics (google 'spring' and 'rest length' to see that this is a common term) which has nothing to do with the spring's actual length in its rest frame, it just means the length the spring would naturally assume if it were relaxed and no forces were being applied to either end, which can of course be different from the spring's actual length if it is being stretched or compressed by outside forces.

OK, I have not seen any mainstream articles that calculate the integral and prove the string breaks from strictly the POV of the launch frame. All I have seen use an instantaneous at rest frame within the context of the accelerating frame.

Do you have such calculations or mainstream articles strictly from the launch frame?

 

[A.T.]

The integral for all of the solutions is calculated vs a theoretical instantaneous at rest frame not the launch frame.

Is this not correct?

Not sure what you mean here. You can use both frames, but I guess the rest frame of the string is easier.

EDIT: Oh I see what you mean. No you are not correct. You don't need the rest frame of the string to conclude that the string will snap. In the launch frame you observe constant atom distances, but decreasing range of bonding forces.

 

[JesseM]

OK, I have not seen any mainstream articles that calculate the integral and prove the string breaks from strictly the POV of the launch frame. All I have seen use an instantaneous at rest frame within the context of the accelerating frame.

Do you have such calculations or mainstream articles strictly from the launch frame?

No, I don't know of any. It seems like it'd be a needlessly complicated approach, since it's easier to understand why it breaks by looking at the string's rest frame, and we know that in relativity all frames always agree about the answers to local physical questions like whether a string breaks.

 

[cfrogue]

No, I don't know of any. It seems like it'd be a needlessly complicated approach, since it's easier to understand why it breaks by looking at the string's rest frame, and we know that in relativity all frames always agree about the answers to local physical questions like whether a string breaks.

I have not seen any either, but that does not mean they do no exist.

Let me ask you this.

If you have two rockets at a distance d with a string of length d between them and the rockets at in the same frame moving relative v to a stationary observer, would the string break?

 

[JesseM]

Let me ask you this.

If you have two rockets at a distance d with a string of length d between them and the rockets at in the same frame moving relative v to a stationary observer, would the string break?

Are the distance d between rockets and the length d of the string measured in the rocket/string rest frame or the observer's frame? And all questions about whether a string would break depend on the elasticity of the string...if an identical string were placed at rest relative to the observer and gradually both ends were pulled apart, at what length would the string stretch to in the observer's frame before it snapped?

 

[cfrogue]

Are the distance d between rockets and the length d of the string measured in the rocket/string rest frame or the observer's frame? And all questions about whether a string would break depend on the elasticity of the string...if an identical string were placed at rest relative to the observer and gradually both ends were pulled apart, at what length would the string stretch to in the observer's frame before it snapped?

Oh, the d's are measured in the moving frame and are initially known in the rest frame.

Say that the string is very weak and brittle.

 

[yuiop]

OK, would the rest frame/launch frame conclude the string will break given the distance does not change between the ships from the POV of the rest frame?

In other words, does the launch frame conclude the distance does not change yet the string contracts?

Here is another way of looking at it. The two ships accelerate as per Bells's paradox, but this time the string is only connected to the front ship. The gap between the two ships stays constant according to the launch frame, but the string is length contracting. When the sting has contracted to say one hundredth of its original length, any attempt to force the string to connect the two ships, without bringing the two ships closer together (as measured in the launch frame) will snap the string. Of course, if the string is very flexible and stretching one hundred times is not sufficient to snap it, then we only have to run the experiment for a little longer until a point is reached where the string does snap, assuming that is impossible to have a string with infinite elasticity.

[EDIT] I have just noticed noticed that what I said is basically what Dr Greg said in post #33. Sorry about that. The posts in this thread are coming so fast, I missed a few.

 

[cfrogue]

Here is another way of looking at it. The two ships accelerate as per Bells's paradox, but this time the string is only connected to the front ship. The gap between the two ships stays constant according to the launch frame, but the string is length contracting. When the sting has contracted to say one hundredth of its original length, any attempt to force the string to connect the two ships, without bringing the two ships closer together (as measured in the launch frame) will snap the string. Of course, if the string is very lexible and stretching one hundred times is not sufficient to snap it, then we only have to run the experiment for a little longer until a point is reached where the string does snap, assuming that is impossible to have a string with infinite elasticity.

OK, does this imply space does not contract only rods?

Next, at any instant t in the two rocket and string frame, all three are at rest?

 

[JesseM]

Oh, the d's are measured in the moving frame and are initially known in the rest frame.

Say that the string is very weak and brittle.

Yes, but even a brittle string might have a relaxed length much greater than d...do you want to say that if we had laid out the string at rest relative to the observer with nothing pulling on either end, the distance in the observer's frame would be d? In that case, if the two ships are moving relative to the observer and the distance between them in the observer's frame is d, then since the distance between the ships in their own rest frame is greater than d, you couldn't stretch the string between the ships without breaking it.

 

[matheinste]

OK, does this imply space does not contract only rods?

Next, at any instant t in the two rocket and string frame, all three are at rest?

I think a direct answer to this in the context of standard SR would help to clarify the explanations.

Matheinste.

 

[yuiop]

Next, at any instant t in the two rocket and string frame, all three are at rest?

Nope, to one of the rocket observers the gap between the rockets is getting larger and the other rocket is getting further away, so the two rockets do not regard themselves as being at rest with respect to each other.

 

[cfrogue]

Nope, to one of the rocket observers the gap between the rockets is getting larger and the other rocket is getting further away, so the two rockets do not regard themselves as being at rest with respect to each other.

OK, so the rockets see themselves as getting further apart.

Yet, the launch frame does not see it this way. It sees the distance as constant.

How is this so?

 

[yuiop]

OK, so the rockets see themselves as getting further apart.

Yet, the launch frame does not see it this way. It sees the distance as constant.

How is this so?

The launch frame is using rulers that are not length contracted, while the rocket observers are measuring the gap using rulers that are gettting progressively shorter so to them the gap appears to be expanding.

 

[cfrogue]

The launch frame is using rulers that are not length contracted, while the rocket observers are measuring the gap using rulers that are gettting progressively shorter so to them the gap appears to be expanding.

Is there evidence that length actually contracts within a frame, I mean within the internals of a frame?

Isn't length contraction a phenomena of the "at rest" frame when viewing the moving frame?

 

[yuiop]

OK, does this imply space does not contract only rods?

Let's try a slightly modified experiment, to try and shed light on your question.

We have four rockets all with identical solid fuel propellants that burn at a fixed rate for a fixed length of time. Rocket A and B are joined by a tough cable of length d and rockets C and D are separated by a distance of d but not physically connected. All 4 rockets launch simultaneously in the launch frame. When they have exhausted their fuel rockets C and D are still a distance d apart, but rockets A and B are less than d apart. Rockets A and B have been physically pulled closer together by the length contraction of the cable.

If a fifth rocket and observer was introduced and this time only the fifth observer accelerated, then distances between the unconnected and connected rocket pairs would appear to length contract equally, but the apparent length contraction of the gap between the unconnected rockets is not physical. The changes in the clock rates and ruler lengths of the fifth observer makes the gap appear to contract.

 

[yuiop]

Is there evidence that length actually contracts within a frame, I mean within the internals of a frame?

Isn't length contraction a phenomena of the "at rest" frame when viewing the moving frame?

You can not actually observe length contraction if you are in the frame moving with the object. In the case of Bell's rocket observers they do not see the string as shrinking, but rather see it being stretched across a larger gap.

 

[cfrogue]

You can not actually observe length contraction if you are in the frame moving with the object. In the case of Bell's rocket observers they do not see the string as shrinking, but rather see it being stretched across a larger gap.

But why?

The rest frame does not see the gap getting wider.