Is Lorentz Contraction Indistinguishable from Standard Relativity?

[atyy]

In that chapter he does discuss how the electromagnetic field of a moving atom is altered by its velocity, but from skimming it, it doesn't look like he actually goes so far as to apply that to the case of the accelerating string to show how the stress increases until the electromagnetic forces between atoms are no longer strong enough to hold the string together and thereby show at what point it will snap.

Some crucial pages are missing to me on Google, but I think he goes far enough to show that the equilibrium state of a moving rod will be shorter - wouldn't that be enough?

 

[JesseM]

Some crucial pages are missing to me on Google, but I think he goes far enough to show that the equilibrium state of a moving rod will be shorter - wouldn't that be enough?

Ah, I didn't think of calculating the equilibrium length in the launch frame (which will get increasingly short relative to the actual length of the rod in this frame) rather than calculating the stress in the launch frame...that seems like a good approach.

 

[atyy]

Ah, I didn't think of calculating the equilibrium length in the launch frame (which will get increasingly short relative to the actual length of the rod in this frame) rather than calculating the stress in the launch frame...that seems like a good approach.

Yes, exactly the same approach you suggested earlier in the thread - but just without switching frames.

 

[yuiop]

I am surprised this thread is still going. Is there anyone here who still has any shadow of a doubt that the string connecting the rockets WILL break??

Where did you prove the string would snap from the POV of the launch frame?

Dr Greg demonstrated that the string would snap from the POV of the launch frame way back in post #33 of this thread here: https://www.physicsforums.com/showpost.php?p=2443127&postcount=33

I am confused.

Where did you prove the string would snap from the POV of the launch frame?

I mean, where is the math? It is certainly not in the SR acceleration equations or is it?

It is not in the SR equations because SR is specifically about reference frame that are NOT accelerating. However, SR does tell us that if an object is moving relative to an observer (accelerating or not) then that object should be length contracted. If the moving object is not length contracted then it MUST be under stress.

 

[yuiop]

There is a way to demonstrate that the string will break without invoking electromagnetic forces or even length contraction. Imagine rockets A and B are moving to the right with constant velocity v relative to observer C. The rockets are separated by a distance (d) and joined by an unstressed string. Rockets A and B are instructed to launch simultaneously according to the clocks in their inertial frame and thereafter accelerate to the left with constant acceleration until they come to rest in C's frame. In this scenario they are slowing down according to observer C and so length contraction of the string is not a factor according to observer C. (if anything he expects the string to expand.) When the rockets take off, C notices that the rear rocket takes of first because the clocks of A and B are not synchronised from C's point of view and the string snaps because the rear rocket slows down to a stop while the front rocket is still going to the right. In this case it is the relativity of simultaneity that snaps the string rather than length contraction, but the end result is still the same - the string snaps.

 

[matheinste]

It is not in the SR equations because SR is specifically about reference frame that are NOT accelerating. However, SR does tell us that if an object is moving relative to an observer (accelerating or not) then that object should be length contracted. If the moving object is not length contracted then it MUST be under stress.

Would it be OK to say that if an object whose unstressed rest length is known, appears to have, at a later time, the same length viewed from a frame moving relative to the one at which it is at rest, then it must at this later time be stressed.

Whatever its rest length, stressed or unstressed, it must in, real time, appear contracted when viewed from a relatively moving frame.

Matheinste.

 

[A.T.]

There is no distance differential in the launch frame for the ships.

So? Where is your problem? The condition for the string to snap is that the distance between the rockets is greater than the maximal length of the string. In the launch frame the distance between the rockets is constant, but the maximum length of the string reduces, because all elements the string is made of (fibers, chain links, down to individual atoms) are contracting as they accelerate.

 

[JesseM]

So? Where is your problem? The condition for the string to snap is that the distance between the rockets is greater than the maximal length of the string. In the launch frame the distance between the rockets is constant, but the maximum length of the string reduces, because all elements the string is made of (fibers, chain links, down to individual atoms) are contracting as they accelerate.

Well, the individual atoms contract, as do the electromagnetic fields surrounding them, but since the average distance between atoms remains constant until the string snaps in the launch frame, the fibers or chain links can't actually contract. The equilibrium length of the string (that is, the length it would be if its ends were free) does contract though, and the maximum length the string can reach without snapping is just some multiple of the equilibrium length.

 

[yuiop]

Would it be OK to say that if an object whose unstressed rest length is known, appears to have, at a later time, the same length viewed from a frame moving relative to the one at which it is at rest, then it must at this later time be stressed.

Whatever its rest length, stressed or unstressed, it must in, real time, appear contracted when viewed from a relatively moving frame.

Matheinste.

I agree. In the launch frame the (stressed) string between the accelerating rockets has length (d') and in an frame instantaneously co-moving with the average velocity of the accelerating rockets, the length of the string by their measurements (d) is greater than d' by aproximately the average gamma factor. (In the frame of one rocket the other rocket is moving so a sort of average velocity has to be used to estimate what is going on.)

 

[A.T.]

but since the average distance between atoms remains constant until the string snaps in the launch frame, the fibers or chain links can't actually contract.

If a stationary chain is already under maximal stress, then the chain links don't contract on acceleration, but simply break. But since atoms and bonding forces a difficult to grasp, it might be helpful consider a chain that still has some play when stationary, yet brakes at a certain speed, despite keeping a constant length:

 

[cfrogue]

Well, the individual atoms contract, as do the electromagnetic fields surrounding them, but since the average distance between atoms remains constant until the string snaps in the launch frame, the fibers or chain links can't actually contract. The equilibrium length of the string (that is, the length it would be if its ends were free) does contract though, and the maximum length the string can reach without snapping is just some multiple of the equilibrium length.

Yes, but the math from the launch frame should somehow make the string snap while the distance between the two ship remains constant.


Do you know how to do this from the launch frame only?

 

[yuiop]

Yes, but the math from the launch frame should somehow make the string snap while the distance between the two ship remains constant.


Do you know how to do this from the launch frame only?

Say we have string of length d and we know that if we stretch the string to twice its relaxed length that it will snap. If the string is connected to two rockets and its average velocity is such that we calculate its relaxed length to be d/2 and it is spanning a distance of d then it is about to snap, right?

 

[JesseM]

Yes, but the math from the launch frame should somehow make the string snap while the distance between the two ship remains constant.


Do you know how to do this from the launch frame only?

Why do you keep asking the same questions and not paying any attention to my answers? I already told you I didn't have the specific math in post #88, but that I'm confident the approach of calculating the changing electromagnetic force between atoms in the launch frame would show that it snaps.

Also, if you read posts 89-93 you'll see that atyy gave the alternate approach of using the electromagnetic force between atoms in the launch frame to calculate the relaxed length at different velocities in the launch frame, which shows that the relaxed length is shorter and shorter at higher velocities, implying that if the string is at constant length as its velocity increases in the launch frame, it is getting farther and farther past its relaxed length, so without actually calculating the stresses we can conclude it should eventually snap for this reason. The math for calculating the relaxed length as a function of velocity seems to be given in the book that atyy linked to.

 

[cfrogue]

I am surprised this thread is still going. Is there anyone here who still has any shadow of a doubt that the string connecting the rockets WILL break??



Dr Greg demonstrated that the string would snap from the POV of the launch frame way back in post #33 of this thread here: https://www.physicsforums.com/showpost.php?p=2443127&postcount=33





It is not in the SR equations because SR is specifically about reference frame that are NOT accelerating. However, SR does tell us that if an object is moving relative to an observer (accelerating or not) then that object should be length contracted. If the moving object is not length contracted then it MUST be under stress.

It appears the launch frame is having a problem WITHIN SR at proving the string will break.

The launch frame believes the distance between the two ships does not change and this is not disputed.

Thus, the accelerating frames believe the string will break within SR and the launch frame believes they will not under SR only.

It is this correct or do you have a proof or paper that shows the launch frame decides the string will break completely from the theory of SR.

 

[cfrogue]

Why do you keep asking the same questions and not paying any attention to my answers? I already told you I didn't have the specific math in post #88, but that I'm confident the approach of calculating the changing electromagnetic force between atoms in the launch frame would show that it snaps.

Also, if you read posts 89-93 you'll see that atyy gave the alternate approach of using the electromagnetic force between atoms in the launch frame to calculate the relaxed length at different velocities in the launch frame, which shows that the relaxed length is shorter and shorter at higher velocities, implying that if the string is at constant length as its velocity increases in the launch frame, it is getting farther and farther past its relaxed length, so without actually calculating the stresses we can conclude it should eventually snap for this reason. The math for calculating the relaxed length as a function of velocity seems to be given in the book that atyy linked to.

Does this argument appeal to QT to solve a problem in SR?

Should this be decidable in SR from the POV of the launch frame?

 

[yuiop]

Let's say we had a thin rod that expands significantly when heated and correspondingly shrinks significantly when cooled. I am sure you will agree such a thing exists. Now if the rod is heated to a high temperature and welded the rod in its hot state in-between two very strong pillars and then cooled the rod down rapidly, there could come a point when the rod would snap. Right up to the point before the rod snaps as it cools the length of the rod remains constant. Would you take that to mean that we had no theory to predict that the rod would snap in this case? If you agree that we can predict the rod will snap then can you agree that we can in principle predict things about stress, even when we can not measure a change in length?

 

[cfrogue]

Let's say we had a thin rod that expands significantly when heated and correspondingly shrinks significantly when cooled. I am sure you will agree such a thing exists. Now if the rod is heated to a high temperature and welded the rod in its hot state in-between two very strong pillars and then cooled the rod down rapidly, there could come a point when the rod would snap. Right up to the point before the rod snaps as it cools the length of the rod remains constant. Would you take that to mean that we had no theory to predict that the rod would snap in this case? If you agree that we can predict the rod will snap then can you agree that we can in principle predict things about stress, even when we can not measure a change in length?

I agree with all of you that the accelerating ships conclude the string will break.


The launch frame has available to it a collection of acceleration equations from SR.

These equations predict the distance between the ships does not change.

Should we ignore this scientific evidence of the launch frame?

 

[JesseM]

Does this argument appeal to QT to solve a problem in SR?

The argument about the equilibrium length of the string seems to have involved only classical electromagnetism, although of course we know that this is only an approximation for a more accurate quantum theory of electromagnetic bonds between atoms.

Should this be decidable in SR from the POV of the launch frame?

"SR" is not a theory of how materials behave under stress, it's just a general statement that all possible laws of physics (including whatever laws govern the behavior of materials) should be Lorentz-symmetric. So regardless of whether you use classical electromagnetism or a relativistic quantum theory of atomic bonds, you need to go outside the bare axioms of SR to say anything about how materials will behave, but whatever additional theory you use will still be consistent with SR as long as it's Lorentz-symmetric.

 

[atyy]

Does this argument appeal to QT to solve a problem in SR?

Should this be decidable in SR from the POV of the launch frame?

The full argument must appeal to quantum mechanics, because classical physics cannot give a microscopic explanation for the existence of rigid bodies, and this is precisely what is needed here.

However, I do believe Bell brings in enough classical arguments to show that the string will break when considered wholly from the point of view of the launch frame.

First he notes the electric field of a moving charge is not the same as that of a stationary charge. Thus the equilibrium state of a moving rod cannot be the same, and if the rod is stressed to start with, then the stress must either increase or decrease. It is not obvious (to me) which happens, but certainly the stress cannot stay the same.

To argue that the stress increases, Bell calculates (strictly wrongly, but I think correctly enough, and he discusses this in the text) the equilibrium radius of a negative charge orbiting a positive charge, and shows the equilibrium radius is smaller, which argues that the stress on the moving rod increases.

Bell, "How to teach special relativity" in http://books.google.com/books?id=FG...eakable+and+unspeakable&source=gbs_navlinks_s

Also useful is Fitzpatrick's "Fields due to a moving charge" http://farside.ph.utexas.edu/teaching/em/lectures/node125.html

 

[yuiop]

The launch frame has available to it a collection of acceleration equations from SR.

These equations predict the distance between the ships does not change.

Should we ignore this scientific evidence of the launch frame?

Did I not just demonstrate that I could snap a rod without changing the distance between the ends of the rod?

 

[cfrogue]

The argument about the equilibrium length of the string seems to have involved only classical electromagnetism, although of course we know that this is only an approximation for a more accurate quantum theory of bonds between atoms.

"SR" is not a theory of how materials behave under stress, it's just a general statement that all possible laws of physics (including whatever laws govern the behavior of materials) should be Lorentz-symmetric. So regardless of whether you use classical electromagnetism or a relativistic quantum theory of atomic bonds, you need to go outside the bare axioms of SR to say anything about how materials will behave, but whatever additional theory you use will still be consistent with SR as long as it's Lorentz-symmetric.

I agree SR is not material science.

However, we have seen articles posted here that concluded the string contracts as the reason it will break.

Also, the latest mainstream publication shows the ships drift further apart and the string will break.

But, this is all from integrating within the context of the accelerating frames.

So, it is natural to ask what does the launch frame think. The accelerating frames did not have to appeal to an outside authority to decide the string will break. These papers concluded from the POV of the accelerating frame, the string will break strictly within SR.

Why do we need to go outside the theory to conclude the string will break from the launch frame perspective? Why can't this be concluded from within SR? Because all we have right now is undisputed evidence the distance between the ships does not change.

 

[cfrogue]

Did I not just demonstrate that I could snap a rod without changing the distance between the ends of the rod?

You did.

So, are you going to heat up the rod and cool it to make SR solve this problem?

Is this correct?

 

[matheinste]

I am OK with the fact that the string breaks.

I think that the problem gets sidetracked if it is necesary to explain the physics of the actual breaking. Couldn't we just propose an element between the ships that will break under any stress and then,if stress is the reason for the breaking, demonstrate that there is stress. After all, whether it breaks or it doesn't is the point, not the physics of the detailed behaviour of the molecular structure of the string under stress, interesting though that may be.

Matheinste.

 

[JesseM]

I agree SR is not material science.

However, we have seen articles posted here that concluded the string contracts as the reason it will break.

Also, the latest mainstream publication shows the ships drift further apart and the string will break.

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.

 

[yuiop]

You did.

So, are you going to heat up the rod and cool it to make SR solve this problem?

Is this correct?

I was making the point that you can induce stress in the rod (by cooling OR length contraction) and snap the rod, without changing the length of the rod. It follows that demonstrating that the length of the string does not change according to the launch frame does not prove that no stresses are induced. Now I am sure you will agree that calculating the intermolecular forces of the string is no easy matter, but myself, Jesse, Dr Greg and others have shown you many ways to logically deduce that the string will snap, even from the point of view of the launch frame.

 

[cfrogue]

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?

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

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

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.

I wish someone had a mainstream paper on this.

 

[cfrogue]

I was making the point that you can induce stress in the rod (by cooling OR length contraction) and snap the rod, without changing the length of the rod. It follows that demonstrating that the length of the string does not change according to the launch frame does not prove that no stresses are induced. Now I am sure you will agree that calculating the intermolecular forces of the string is no easy matter, but myself, Jesse, Dr Greg and others have shown you many ways to logically deduce that the string will snap, even from the point of view of the launch frame.

I must have missed the argument from SR.

Could you explain it?

Please only use SR.

 

[DrGreg]

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.

 

[cfrogue]

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.

(a) Two questions

1) Let a and b be two points at a distance d. Join them with a rod.

Now, move the unit in relative motion to another observer. Do the two points remain at a distance d and the rod contracts?

2) Do you have the integral from the launch frame to prove the rod contracts? We already know a and b remain at a distance d for the acceleration.

 

[DrGreg]

1) Let a and b be two points at a distance d. Join them with a rod.

Now, move the unit in relative motion to another observer. Do the two points remain at a distance d and the rod contracts?

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.