Quick question - has length contraction actually been experimentally confirmed?

[jeebs]

Hi,
I am aware that time dilation has been observed experimentally with atomic clocks on satellites etc. but after a few google searches I have not found anything about experimental confirmation of length contraction. Has this been observed at all? If so, how was it tested?
thanks.

 

[Dale]

I would say that the bunch length has been demonstrated to contract in particle accelerators (otherwise they would not work as expected). But I know that is not universally accepted as a demonstration of length contraction.

 

[Austin0]

I would say that the bunch length has been demonstrated to contract in particle accelerators (otherwise they would not work as expected). But I know that is not universally accepted as a demonstration of length contraction.

Hi DaleSpam Could you provide a simple conceptual explanation of bunch length and how it demonstrates contraction. I have sought this before and researched the web but find myself still unsure of the concepts. If what I remember is correct it relates to implse timing for acceleration but I couldn't really grasp the connection to contraction.
Thanks

 

[Dale]

In a particle accelerator you don't accelerate an individual particle, you accelerate a whole bunch of particles. Each of the particles in the bunch has the same charge, so they repel electromagnetically quite strongly, and one of the things that you have to do in designing an accelerator experiment is figure out how densely you can pack them given the limitations of your equipment. This is often done in the rest frame of the bunch where the repulsive interactions are easier to calculate. If you do not consider length contraction then you get the wrong answer about how many particles you can pack into the bunch.

 

[Austin0]

In a particle accelerator you don't accelerate an individual particle, you accelerate a whole bunch of particles. Each of the particles in the bunch has the same charge, so they repel electromagnetically quite strongly, and one of the things that you have to do in designing an accelerator experiment is figure out how densely you can pack them given the limitations of your equipment. This is often done in the rest frame of the bunch where the repulsive interactions are easier to calculate. If you do not consider length contraction then you get the wrong answer about how many particles you can pack into the bunch.

Does this then mean what is being contracted is the electrostatic field associated with the electron
so they can acutally bunch closer together than would be possible at low velocities?
Thanks for keeping it simple :-)

 

[Dale]

Yes. Similarly (in principle) with a solid material, the intermolecular EM fields contract so the rod is shorter.

 

[Austin0]

Yes. Similarly (in principle) with a solid material, the intermolecular EM fields contract so the rod is shorter.

Hold on there pardner , what happened to "contraction is purely kinematic , it does not make sense to talk obout real or not ...or to look for causality or physical implications with the Lorentz effects" QUotes here being generic, not referring to you specifically [at least maybe not]? :-)

Thanks

 

[DaveC426913]

There's a frame that is moving relativistically relative to us. Everything in that frame is length-contracted, yes, even the electrostatic field.

 

[Austin0]

There's a frame that is moving relativistically relative to us. Everything in that frame is length-contracted, yes, even the electrostatic field.

I wasn't making any distinction between electrostatic fields and other contraction , only making a comment, partially a joke , related to the fact that DaleSpam made contraction sound pretty darn physical and causal. I.e. Things contract because the EM fields contract.

 

[Dale]

I don't understand the point you are trying to make. What is surprising to you here? All lengths contract, regardless of whether the length is the length of a rod or some characteristic EM field.

 

[yuiop]

I wasn't making any distinction between electrostatic fields and other contraction , only making a comment, partially a joke , related to the fact that DaleSpam made contraction sound pretty darn physical and causal. I.e. Things contract because the EM fields contract.

What if we had some sort of accelerator device in a lab of radius r meters, and some rods with rest lengths of Pi meters each and what if we could comfortably fit more than 2*r rods around the perimeter if they were moving at high enough velocity. Would that be physically real enough for you?

 

[dpeagler]

I'm relatively new to relativity at this depth, but I was wondering why the EM fields contract due to relativistic effects. Obviously it's not because the values of [\mu]₀ or [\epsilon]₀ have varied, otherwise the frame wouldn't be a reference frame, correct?

Thanks for any information.

 

[Austin0]

I wasn't making any distinction between electrostatic fields and other contraction , only making a comment, partially a joke , related to the fact that DaleSpam made contraction sound pretty darn physical and causal. I.e. Things contract because the EM fields contract.

I don't understand the point you are trying to make. What is surprising to you here? All lengths contract, regardless of whether the length is the length of a rod or some characteristic EM field.

Sorry DaleSpam I should probably not indulge in my ideosyncratic humor.
There was absoutely nothing I found surprising and I appreciated your clear and direct explication which made perfect sense to me.

The basis of my comment , not exactly a point, was the inconsistency between two interpretations of the Lorentz effects.
There are many threads where people ask about the causal mechanism of these effects and whether they are to be taken as real or not and whether motion is real or not.
There are many responces to these questions that go: Well this is not really a meaningful question
because there is no causality involved , that these effects are purely kinmatic effects diue to measurements in relative frames. That motion itself is purely relative with no physical implications whatever.
Well this position may wel be true but is not neccessarily consistent with interpretations that attribute real physicallity to contraction i.e. creating internal tension if occurring within constraints for eg. or in this context seeming to imply actual EM field changes resulting in lattice contraction. You may not actually maintain that view but it could be interpreted from your choice of words.
Once again I have no problem at all with this interprtation and tend to assume the reality of these effects and was basically kidding you on the assumption that you were well aware of all of the above, from many previous threads.
Thanks again for your clear responce

 

[starthaus]

What if we had some sort of accelerator device in a lab of radius r meters, and some rods with rest lengths of Pi meters each and what if we could comfortably fit more than 2*r rods around the perimeter if they were moving at high enough velocity. Would that be physically real enough for you?

Once you start accelerating the rods around the perimeter they expand since they are not Born rigid, so you could not fit in more than 2*r rods. This is not a valid thought experiment for demonstrating length contraction. The above is a variant of the Ehrenfest paradox and the resolution is the same. Direct experimental verification of length contraction (as opposed to the direct experimental verification of time dilation) is not possible with today's technology. Indirect verification , including the calculation for the length of particle beams and the explanation of the Michelson Morley experiment as viewed from a frame external to the moving Earth (like the Sun) are the only things we have available today.

 

[Dale]

There are many threads where people ask about the causal mechanism of these effects and whether they are to be taken as real or not and whether motion is real or not.
There are many responces to these questions that go: Well this is not really a meaningful question
because there is no causality involved , that these effects are purely kinmatic effects diue to measurements in relative frames. That motion itself is purely relative with no physical implications whatever.
Well this position may wel be true but is not neccessarily consistent with interpretations that attribute real physicallity to contraction i.e. creating internal tension if occurring within constraints for eg. or in this context seeming to imply actual EM field changes resulting in lattice contraction. You may not actually maintain that view but it could be interpreted from your choice of words.
Once again I have no problem at all with this interprtation and tend to assume the reality of these effects and was basically kidding you on the assumption that you were well aware of all of the above, from many previous threads.

I see what you are saying. I am always very leery of such discussions. I think that they hinge critically on the various persons' definitions of the words "real" and "physical", which nobody seems to be able to define unambiguously but everybody has a kind of gut feeling that their impression is right and obvious.

Length contraction (and all other relativistic effects) is a coordinate-dependent measurable effect. Some people think that it is measurable so it must be "real" and others think that it is coordinate-dependent so it must not be "real". So I try to avoid ambiguous words like "real" and use well-defined ones like "coordinate dependent" instead.

IMO, the question of the "reality" of length contraction is a purely semantic one which I don't take too seriously.

 

[matheinste]

I see what you are saying. I am always very leery of such discussions. I think that they hinge critically on the various persons' definitions of the words "real" and "physical", which nobody seems to be able to define unambiguously but everybody has a kind of gut feeling that their impression is right and obvious.

Length contraction (and all other relativistic effects) is a coordinate-dependent measurable effect. Some people think that it is measurable so it must be "real" and others think that it is coordinate-dependent so it must not be "real". So I try to avoid ambiguous words like "real" and use well-defined ones like "coordinate dependent" instead.

IMO, the question of the "reality" of length contraction is a purely semantic one which I don't take too seriously.

Yes it is a problem. When I was first introduced to SR I was, wisely, very much influenced by Rindler who in a couple of his earlier books says that length contraction is "real in every sense of the word" which is not very helpful. My sense of the word real may be very different from that of other people. Since learning a little more on the subject I would prefer to say that it is measurable, and that its effect is coordinate dependent because in its own rest frame nothing is happening to length, we are laying our coordinate system on the rest length and coming up with a smaller value.

On the other hand it is theoretically possible (if of course it exists) to demonstrate contraction, by a comparison using three "identical" rods alongside each other. This is probably nearer to most peoples idea of reality

But if we understand the mechanism and can make use of it in our physics then our idea of its "reality" is of no importance except from a philosophical viewpoint.

Matheinste.

 

[Dale]

Yes it is a problem. ... My sense of the word real may be very different from that of other people. Since learning a little more on the subject I would prefer to say that it is measurable, and that its effect is coordinate dependent ...

But if we understand the mechanism and can make use of it in our physics then our idea of its "reality" is of no importance except from a philosophical viewpoint.

I agree strongly!

 

[Austin0]

I see what you are saying. I am always very leery of such discussions. I think that they hinge critically on the various persons' definitions of the words "real" and "physical", which nobody seems to be able to define unambiguously but everybody has a kind of gut feeling that their impression is right and obvious.

Length contraction (and all other relativistic effects) is a coordinate-dependent measurable effect. Some people think that it is measurable so it must be "real" and others think that it is coordinate-dependent so it must not be "real". So I try to avoid ambiguous words like "real" and use well-defined ones like "coordinate dependent" instead.IMO, the question of the "reality" of length contraction is a purely semantic one which I don't take too seriously.

I just want to say that I think your summation above is a masterpeice of rational equivocation and I mean that in a positive complimentary way. it doesn't directly contradict anyone and it neatly and succinctly removes you from the question.

But,,,,, although I don't have an answer, I do think there is a "real" question to be explored and and I don't think it is just semantic Just MHO

 

[Dale]

I do think there is a "real" question to be explored and and I don't think it is just semantic Just MHO

Well, if you can ever formulate the "real" question in a non-semantic way then I think that I would greatly enjoy the resulting discussion.

 

[Cleonis]

I am always very leery of such discussions. I think that they hinge critically on the various persons' definitions of the words "real" and "physical", which nobody seems to be able to define unambiguously but everybody has a kind of gut feeling that their impression is right and obvious.

Length contraction (and all other relativistic effects) is a coordinate-dependent measurable effect. Some people think that it is measurable so it must be "real" and others think that it is coordinate-dependent so it must not be "real". So I try to avoid ambiguous words like "real" and use well-defined ones like "coordinate dependent" instead.

IMO, the question of the "reality" of length contraction is a purely semantic one which I don't take too seriously.

I do think the question can and should be taken seriously.

There is the thought demonstation, first presented by Dewan and Beran, later retold by John Stewart Bell, usually referred to as 'Bell's spaceship paradox'. Two spaceships, connected by an unstretchable tether of length L, tether fully extended, are initially comoving. They synchronize their clocks. At an agreed point in time they commence acceleration, parallel to the tether, both accelerating at exactly the same G-count. For the tether to not break it would have to decrease the separation between the spaceships. However, since the spaceships meticulously maintain the same G-count the tether will snap.

There is only one physical factor that the breaking of the tether can be attributed to: length contraction.
Hence we have that the principles of SR imply that in specific circumstances length contraction leads to an irreversible result: a tether breaks.

With an irreversible consequence on the table I don't see a way of maintaining that the issue is purely semantic.

 

[Passionflower]

I do think the question can and should be taken seriously.

There is the thought demonstation, first presented by Dewan and Beran, later retold by John Stewart Bell, usually referred to as 'Bell's spaceship paradox'. Two spaceships, connected by an unstretchable tether of length L, tether fully extended, are initially comoving. They synchronize their clocks. At an agreed point in time they commence acceleration, parallel to the tether, both accelerating at exactly the same G-count. For the tether to not break it would have to decrease the separation between the spaceships. However, since the spaceships meticulously maintain the same G-count the tether will snap.

There is only one physical factor that the breaking of the tether can be attributed to: length contraction.

This is an inaccurate conclusion about the Bell spaceship paradox. The rope gets stretched or breaks because the trailing spaceship does not accelerate hard enough to keep up with the front spaceship.

 

[Cleonis]

This is an inaccurate conclusion about the Bell spaceship paradox. The rope gets stretched or breaks because the trailing spaceship does not accelerate hard enough to keep up with the front spaceship.

We're touching here on the very principle of relativity.

The principle of relativity entails the demand that our explanations of what is taking place must be frame invariant.

For example, prior to relativistic physics the physics of magnet and coil with relative velocity was accounted for differently, depending on whether the magnet was moving with respect to the luminiferous ether, or the coil. Depending on which one is moving (with respect to the ether) a particuler magnetic field(component) is present or not. To the relativist this is an unacceptable state of affairs.

In the case of Bell's spaceship paradox it is not particularly informative to take one particular frame as providing the 'real explanation'. It is not particularly informative to take as point of view the frame instantaneously co-moving with, say, the leading spaceship. Of course, as mapped in the frame instantaneously co-moving with the leading spaceship the trailing spaceship has less velocity. But essentially you're then committing the explanation to one particular point of view, which goes squarely against relativity.

You need to focus on what is common to all inertial frames. The factors that are invariant across the equivalence class of inertial frames are the factors that count.

 

[Passionflower]

All what you write is not relevant to my comment and it does not support your statement that the string breaks due to Lorentz contraction.

The Bell Spaceship Paradox is not irrelevant to this topic so I think there is already enough said about it. If you feel an urge to support your statement that the string breaks due to Lorentz contraction I suggest you open a new topic.

 

[Dale]

There is only one physical factor that the breaking of the tether can be attributed to: length contraction.

That is certainly not the case. In the launch frame it is attributed to length contraction. In the accelerating frame it is essentially attributed to time dilation (which leads to different acceleration profiles as mentioned by Passionflower). And in an inertial frame other than the launch frame it can be attributed to relativity of simultaneity.

With an irreversible consequence on the table I don't see a way of maintaining that the issue is purely semantic.

Length contraction itself is not semantic, but the question of whether or not length contraction is "real" is purely semantic. As I said before, it is a coordinate-dependent measurable effect. Whether or not such effects are "real" depends on your definition of "real".

 

[Cleonis]

All what you write is not relevant to my comment and it does not support your statement that the string breaks due to Lorentz contraction.

The Bell Spaceship Paradox is not irrelevant to this topic so I think there is already enough said about it. If you feel an urge to support your statement that the string breaks due to Lorentz contraction I suggest you open a new topic.

OK. You prefer to not enter a discussion about this subject.

His this thread drifted too far from the original entry?
The starting question was whether length contraction has been experimentally confirmed, and around post #10 the talk shifted to wondering whether length contraction should be regarded as physically real; Bell's spaceship paradox bears on the question of what level of physical reality we must attribute.

 

[Cleonis]

In the launch frame it is attributed to length contraction. In the accelerating frame it is essentially attributed to time dilation (which leads to different acceleration profiles as mentioned by Passionflower). And in an inertial frame other than the launch frame it can be attributed to relativity of simultaneity.

Just to make sure: you have read my comment in https://www.physicsforums.com/showpost.php?p=2866583&postcount=22" of this thread?

 

[Dale]

Just to make sure: you have read my comment in https://www.physicsforums.com/showpost.php?p=2866583&postcount=22" of this thread?

Yes. But not until after I posted.

Then it seemed that you were directly contradicting yourself since this:

The factors that are invariant across the equivalence class of inertial frames are the factors that count.

Disagrees with this:

There is only one physical factor that the breaking of the tether can be attributed to: length contraction.

Length contraction is not frame invariant so in one post you say it is a factor that doesn't count and in another post you say it is the only factor that it can be attributed to. I don't really want to argue with you until you are done arguing with yourself.

 

[Cleonis]

Length contraction is not frame invariant

Amount of length contraction is frame dependent, yes. The very occurrence of length contraction effects is the common factor. If there is a force gage at the tether mount then for all frames the prediction for the reading of the force gage will be the same.

Part of this point of view is that loss-of-simultaneity and length-contraction are regarded as one and the same thing. That is, if someone asks, 'is loss of simultaneity real' then I would equally refer to Bell's spaceship paradox as bearing on that question. As we know, during the acceleration phase the two spaceships are out of simultaneity. (Or more precisely, during acceleration no consistent synchronisation procedure exists.)

We have these different expressions for talking about relativistic phenomena: 'relativity of simultaneity' , 'length contraction'. If those are treated as different phenomena then there's room for the view that questioning level of physical reality is semantic.

So I have learned something about my own point of view: I regard loss-of-simultaneity-effect and 'length-contraction-effect as one and the same thing.

 

[jtbell]

Part of this point of view is that loss-of-simultaneity and length-contraction are regarded as one and the same thing.

I'd expand this to include time dilation as well. All three of (1) length contraction, (2) time dilation, and (3) relativity of simultaneity are consequences of the Lorentz transformation of x and t; going the other way, the three taken together imply the Lorentz transformation for x and t.

 

[Cleonis]

Part of this point of view is that loss-of-simultaneity and length-contraction are regarded as one and the same thing.

I'd expand this to include time dilation as well. All three of (1) length contraction, (2) time dilation, and (3) relativity of simultaneity are consequences of the Lorentz transformation of x and t; going the other way, the three taken together imply the Lorentz transformation for x and t.

Of course, the threesome is one.

We have that unlike moving around in space we cannot make a U-turn in time. Hence the twin scenario can seemingly isolate time dilation from relativity of simultaneity and length contraction.

At the end of the twin scenario the twins are close together again, so their clocks run at the same rate again. By contrast, in Bell's spaceship scenario extension over a large stretch of space is the very subject. You cannot get the appearance of isolation of length contraction the way appearance of isolating time dilation can be achieved.

 

[starthaus]

That is certainly not the case. In the launch frame it is attributed to length contraction. In the accelerating frame it is essentially attributed to time dilation (which leads to different acceleration profiles as mentioned by Passionflower). And in an inertial frame other than the launch frame it can be attributed to relativity of simultaneity.

Definitely, see here

Length contraction itself is not semantic, but the question of whether or not length contraction is "real" is purely semantic. As I said before, it is a coordinate-dependent measurable effect. Whether or not such effects are "real" depends on your definition of "real".

The main point is that the thought experiment put forward by Bell cannot be considered an experimental verification of length contraction since, amongst other issues, is not physically implementable.

 

[Dale]

Amount of length contraction is frame dependent, yes.

Exactly. At the event of the string breaking there exists a reference frame where the length contraction is 0, therefore it cannot possibly be a frame-invariant explanation for why the string breaks.

If there is a force gage at the tether mount then for all frames the prediction for the reading of the force gage will be the same.

Yes, the reading of the force gauge is an invariant scalar. Force gauges do not measure length contraction.

Part of this point of view is that loss-of-simultaneity and length-contraction are regarded as one and the same thing. ...

We have these different expressions for talking about relativistic phenomena: 'relativity of simultaneity' , 'length contraction'. If those are treated as different phenomena then there's room for the view that questioning level of physical reality is semantic.

So I have learned something about my own point of view: I regard loss-of-simultaneity-effect and 'length-contraction-effect as one and the same thing.

It is a non-standard point of view, certainly. Length contraction, time dilation, and relativity of simultaneity each refer to a different feature of the Lorentz transform. I think that you can say that a ball is red and a ball is bouncy without saying that bouncy is red. To me that is what it seems like you are doing with the above statement.

 

[Cleonis]

If there is a force gage at the tether mount then for all frames the prediction for the reading of the force gage will be the same.

Yes, the reading of the force gauge is an invariant scalar.

This emphasizes the point that only invariant properties qualify to figure in the physical explanation.
The amount of length contraction is frame dependent; the very occurrence of length contraction effects is the common factor.

So I have learned something about my own point of view: I regard loss-of-simultaneity-effect and 'length-contraction-effect as one and the same thing.

[...] Length contraction, time dilation, and relativity of simultaneity each refer to a different feature of the Lorentz transform. I think that you can say that a ball is red and a ball is bouncy without saying that bouncy is red.

We have that time dilation, relativity of simultaneity and length contraction are inseparable.

The difference with elasticity and color of a ball is clear; elasticity and color are independent. But there is no such thing as time dilation, and/or relativity of simultaneity, and/or length contraction occurring independently.

For example, we can refer to the temperature of a gas, or to the internal kinetic energy of a gas. While those are different units, they are inseparable properties.

 

[Dale]

the very occurrence of length contraction effects is the common factor.

As I already said, at the event of the breaking there is always a frame where the string is not length contracted. So length contraction is not a common factor in all frames.

 

[Cleonis]

[...] at the event of the breaking there is always a frame where the string is not length contracted. So length contraction is not a common factor in all frames.

This raises the question: is Bell's spaceship scenario about a process or about a single state? If it would be about a single state then presenting the scenario would involve only single slice of time. But of course Bell's spaceship scenario is about a process, it's about a development over time.

So let's examine the perspective of a frame that at the beginning has such a velocity relative to the spaceships that it's co-moving with the tether at the point in time that it breaks. In that frame the tether length is initially length contracted. As its velocity relative to the chosen frame decreases its length contraction decreases. As mapped in the chosen frame the two spaceships do not start accelerating simultaneously. Does the length contraction decrease fast enough to make up for the non-simultaneous start of acceleration? No it doesn't, the tether breaks.

Depending on what inertial frame of reference is chosen the narrative comes out differently, in how length contraction and shift of simultaneity proceed over time.
My underlying assumption is that SR is by nature a causal theory; a theory in which there is a one-on-one relation between cause and effect. Having multiple narratives means a deeper interpretation must exist, of a more abstract nature.

Then again, others may prefer a philosophy where our narratives are regarded as heuristic devices only. In such a philosophy what counts is whether machines that have been constructed are operating as designed (Do we get the density of particle bunches that we predicted to be achievable?), and no deeper interpretation is expected.

 

[Passionflower]

So let's examine the perspective of a frame that at the beginning has such a velocity relative to the spaceships that it's co-moving with the tether at the point in time that it breaks. In that frame the tether length is initially length contracted. As its velocity relative to the chosen frame decreases its length contraction decreases. As mapped in the chosen frame the two spaceships do not start accelerating simultaneously. Does the length contraction decrease fast enough to make up for the non-simultaneous start of acceleration? No it doesn't, the tether breaks.

Depending on what inertial frame of reference is chosen the narrative comes out differently, in how length contraction and shift of simultaneity proceed over time.
My underlying assumption is that SR is by nature a causal theory; a theory in which there is a one-on-one relation between cause and effect.

Reality knows of no frames, frames are human constructs and not physical at all.

Having multiple narratives means a deeper interpretation must exist, of a more abstract nature.

You got it exactly backwards. The creation of frames creates the false contradictions the reality is simple and unambiguous.

 

[Cleonis]

You got it exactly backwards.

Your disagreement is not with me. You are attributing a point of view to me that isn't mine.

Just to make sure: you have read my comment in https://www.physicsforums.com/showpost.php?p=2866583&postcount=22" of this thread?

 

[Passionflower]

Your disagreement is not with me. You are attributing a point of view to me that isn't mine.

The words I quoted are yours aren't they?

 

[Dale]

I'm with you on this Passionflower. I can't tell what position Cleonis is trying to take. Everything else that he says seems to contradict his post 22, but he keeps referring to it. Very confusing.

 

[Austin0]

Once you start accelerating the rods around the perimeter they expand since they are not Born rigid, so you could not fit in more than 2*r rods. This is not a valid thought experiment for demonstrating length contraction. The above is a variant of the Ehrenfest paradox and the resolution is the same. Direct experimental verification of length contraction (as opposed to the direct experimental verification of time dilation) is not possible with today's technology. Indirect verification , including the calculation for the length of particle beams and the explanation of the Michelson Morley experiment as viewed from a frame external to the moving Earth (like the Sun) are the only things we have available today.

Does this mean that in the Ehrenfest scenario that the length contraction would be completely negated by the inertial forces resulting from rotation?

SInce you have a regard for realistic physics in hypothetical scenarios do you consider it realistic that any material could maintain structural integrity in the face of the outward inertial forces inherent in relativistic angular velocities??

 

[William Nelso]

Length contraction is real. You can compute the length of a moving ruler using E&M and Quantum Mechanics, without ever using Relativity or the Lorentz Transformation. Relativity comes from the physics, not the other way around.

 

[yuiop]

Once you start accelerating the rods around the perimeter they expand since they are not Born rigid, so you could not fit in more than 2*r rods. This is not a valid thought experiment for demonstrating length contraction. The above is a variant of the Ehrenfest paradox and the resolution is the same.

This is just nonsense. The rods do not expand because they are not linked to each other. In the Ehrenfest paradox the train carriages are more rigid than the elastic links between the carriages and so the links have to expand to take up the extra space between the carriages at higher velocities. In the rod thought experiment, it is the gaps between the rods that expands as the rods contract and so you can fit additional rods in the gaps. I don't think Born rigidity is even relevant here. Born rigidity is a method of acceleration, rather than a property of a material. It does not matter how the rods are accelerated as long as they get to a final velocity and are allowed to stabilize to their length contracted length. It is only when we are considering methods of spinning up solid discs to relativistic speeds that applying Born rigid acceleration becomes a problem. For rods that are not connected to each other, it is not a problem.

If you wanted to make the Ehrenfest paradox a bit more like the rod thought experiment, you could remove one link so that the train is not connected all the way around, but occupies all the track and is is just touching at the point where the link has been removed. When the train gets to high enough velocity it will have length contracted sufficiently that you could (in principle but with considerable technical difficulty) slip another (high speed) carriage onto the track into the expanded gap.

 

[Passionflower]

I think this topic is not the place to discuss the Erhenfest paradox, but one comment: how can a rod remain Born rigid if it rotates? I thought only rods that accelerate in one direction can remain Born rigid? It seems to me that because the rod is spatially separated there will be some form of Thomas precession which will make Born rigidity impossible.

Am I wrong?

 

[Dale]

how can a rod remain Born rigid if it rotates? I thought only rods that accelerate in one direction can remain Born rigid? It seems to me that because the rod is spatially separated there will be some form of Thomas precession which will make Born rigidity impossible.

Am I wrong?

You are correct. Linear acceleration can be done without material strain (Born rigid), but there is no way to have angular acceleration without mechanical strain. Something must stretch.

 

[Austin0]

Length contraction is real. You can compute the length of a moving ruler using E&M and Quantum Mechanics, without ever using Relativity or the Lorentz Transformation. Relativity comes from the physics, not the other way around.

Does relative simultaneity enter into these calculations?
Or does anything comparable to relative simultaneity fall out of the calculatiosn??
Thanks

 

[yuiop]

I think this topic is not the place to discuss the Erhenfest paradox, ...

You are right that it is getting off topic, so I have started a new thread here https://www.physicsforums.com/showthread.php?p=2876211#post2876211 to discuss the issues raised by yourself, Dalespam and Starthaus.

 

[starthaus]

This is just nonsense. The rods do not expand because they are not linked to each other.

Err, you are talking about a "ring" of rods, how do you get them to move together as a whole?

In the Ehrenfest paradox the train carriages are more rigid than the elastic links between the carriages and so the links have to expand to take up the extra space between the carriages at higher velocities.

The Ehrenfest paradox I was referring to is the case of a disc, exactly as your attempt at the ring of rods.

In the rod thought experiment, it is the gaps between the rods that expands as the rods contract and so you can fit additional rods in the gaps.

The gaps expand?

I don't think Born rigidity is even relevant here.

You would, if you paid attention to the underlying physics. How do you plan to ramp up the speed of your "ring"?

 

[Meir Achuz]

Hi,
I am aware that time dilation has been observed experimentally with atomic clocks on satellites etc. but after a few google searches I have not found anything about experimental confirmation of length contraction. Has this been observed at all? If so, how was it tested?
thanks.

I came across this thread late in the game.
The quick answer is that length contraction has NOT "been observed at all".

Some of the controversy in this thread might be resolved by reading the first section of <http://arxiv.org/abs/0906.1919>.

 

[yuiop]

I came across this thread late in the game.
The quick answer is that length contraction has NOT "been observed at all".

Some of the controversy in this thread might be resolved by reading the first section of <http://arxiv.org/abs/0906.1919>.[/QUOTE]

I believe there are some misleading statements in that paper. One is their claim that Lorentz contraction would predict a positive result for the MM experiment. The other is this statement:

It should also be pointed out that another classically reasonable method of
measuring the length is to take a photograph of a moving object and compare
it with a photograph of the same object at rest. As Terrell[3] showed some time
ago, the photograph would show an object that is somewhat rotated, but of
the same shape and dimensions as it had at rest. Indeed, the photograph of a
moving sphere would show a sphere of the same size.

Although they mention a sphere at the end, they neglect to mention that the claim "the photograph would show an object that is somewhat rotated, but of the same shape and dimensions as it had at rest." is true if and only if the moving object is a sphere. It is not true for a rod for example and this shows the biased view of the authors.

There is another way to "photograph" length contraction. Set up an array of inject jet nozzles on one side of a narrow passage. Have the moving object pass through the passage and set off the ink jets nozzles simultaneously and briefly. The silhouette of the object left on the opposite side of the passage will be length contracted.

As for ... length contraction has NOT "been observed at all"... an example was given earlier in this thread of the observed length contraction in bunches of particles moving around a particle accelerator ring. Do you disagree with that?

 

[GiftOfPlasma]

I always thought that the most common form of length contraction was the distance between two charged particles. It's demonstrated by calculating out the electrodynamic forces on one charged particle wrt another. The distance changes depending on the frame of reference.