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

[Eli Botkin]

harrylin (162):
This hypothesis (which turned out to be a good guess) of a Lorentz contraction to explain the Michelson-Morley experimental result was overshadowed by SR’s explanation that this same contraction could be derived from the hypothesis of an invariant speed of light. SR is what leads us more firmly to understanding the reason for length contraction, and SR does not say that it is “because the EM fields that hold the matter together contract…”

 

[Eli Botkin]

Nugatory (172):
Yes, I know how en “event” is defined in SR. Forgive me for my awkward attempt at levity.

 

[Eli Botkin]

DaleSpam (173 & 174):
You really needn’t have spent so much of your time enlightening me about those “core concepts.” But thanks for your concern. PS, my degree in physics is 61 years old, undilated ;-)

 

[Eli Botkin]

Yuiop (175):
Be assured that I was careful in assuring that the string (or rod, if you like) was not heated or cooled ;-)

You add: I will state my belief as "The proper length of a rod that remains unstressed… does not change, regardless of its acceleration history...”

This is a worthy belief if you can show it on a Minkowski diagram (or through SR transformation equations).

 

[yuiop]

Hi Eli,
I would like to try a different approach and see what you think. Let us say we have two rockets, A and B, with the same proper length L that are at rest alongside each other. Rocket B accelerates off in the x direction, until it reaches a velocity of 0.8c relative to rocket A and then switches off the drive. The observers onboard rocket B measure the coordinate length of rocket A to be 0.6L. The observers on board rocket A report the proper length of rocket A to still be L. There is no reason for the proper length of rocket A be anything other than L because we have not done anything to rocket A. If we had stress gauges on the rockets, then they would indicate that rocket A is unstressed. If you agree with all the above then you should agree that in order for rocket A to be unstressed when it has a velocity relative to rocket B, then the rocket B observers must measure the coordinate length of rocket A to less than L. For the length of rocket A to still be L when it has motion relative to B then rocket A would have to be physically stretched and probably break. Agree?

You might argue that it would be different if we accelerated rocket A instead of rocket B, but once the rockets engines are switched off and the stresses are allowed to settle down, then SR tells us that the proper length of both rockets is still L and they each measure the coordinate length of the other ship to less than L, so it makes no difference which rocket actually accelerates.

If you agree with the above, then you should conclude that if you accelerate an object while maintaining its coordinate length in the initial reference frame, then its proper length must be increasing (which I think you have already figured out) AND it must be under increasing stress and eventually break.

 

[yuiop]

You add: I will state my belief as "The proper length of a rod that remains unstressed… does not change, regardless of its acceleration history...”

This is a worthy belief if you can show it on a Minkowski diagram (or through SR transformation equations).

I mentioned it before and I will mention it again. Google "Born rigid" motion or acceleration. It will give you the equations and Minkowski diagrams for how to accelerate an object without introducing stresses and maintaining the proper length of the object. Any other acceleration scheme (e.g. the method used in Bell's rocket paradox) will subject the object to stress.

 

[Eli Botkin]

To All:
A bit more about our connection to SR’s message.

The reason we call these SR results paradoxes is because they seem so strange to us as beings who never got even close to leaving the frame we live in and entering a frame that has a great velocity relative to the one we left. All our experiences drive us to believe that the length of a rod will always retain that length no matter how we toss it, move it , or whatever, so long as we don’t heat or cool it, or squeeze or pull on it. That’s what the experience in our cocoon tells us. Remember how difficult it was for people to accept, when you tried to tell them, that if they had left their current place and then returned, their age would then be less than it would be if they had stayed and not traveled. We still don’t have an internalized feeling that this occurs, but we accept it because of our confidence in SR. Maybe after much time we will begin to accept (though un-internalized) that rest-frame lengths also depend on previous travel history.

As to the Bell paradox, I tend to be fixated on the need to show that if the string does break, it must do that for all observer. For some observers the ship separation increases and we can happily say that the string breaks, providing we also assume that the string doesn’t follow the same SR transformation which would avoid breakage. Some claim it doesn’t follow those transformations because it’s “rigid”. But there is nothing in SR that says thou shalt not transform “rigid” items.

For those observers who see the ships approaching each other, the string, if again deemed to be “rigid” would break under compression (or otherwise sag). Here again SR transformation would avoid compression.

Also the oft stated EM field contraction, drawing the object’s atoms closer, as reason for breakage, would have a frame relative-velocity dependence and would still leave the question: Does every observer see the same event (breakage, if it takes place)?

It may turn out that if breakage does occur in every frame’s view, it is because the string is undergoing an acceleration as viewed from all frames.

It’s been fun.

 

[harrylin]

harrylin (162):
This hypothesis (which turned out to be a good guess) of a Lorentz contraction to explain the Michelson-Morley experimental result was overshadowed by SR’s explanation that this same contraction could be derived from the hypothesis of an invariant speed of light. SR is what leads us more firmly to understanding the reason for length contraction, and SR does not say that it is “because the EM fields that hold the matter together contract…”

Hi Eli, surely you realize that many different "because" answers on a single question can be correct. In particular, SR is based on the assumption that Maxwell's laws are valid. According to those laws the EM fields that hold the matter together contract (and that was the basis for Fitzgerald's assumption of length contraction. I don't have the reference, but I think that the correctness of that assumption has been verified in more recent times with computer simulation aids.
SR is not magic, every physical principle must relate to physical means by which it works.

 

[harrylin]

[...] As to the Bell paradox, I tend to be fixated on the need to show that if the string does break, it must do that for all observer.

We all agree that the string must break according to every inertial reference system - and this is indeed the case for any perspective that I analyzed (happily so, for else SR would be defect!).

For some observers the ship separation increases and we can happily say that the string breaks, providing we also assume that the string doesn’t follow the same SR transformation which would avoid breakage. Some claim it doesn’t follow those transformations because it’s “rigid”. [..]

For sure all people in this discussion claim that the string does obey the Lorentz transformation between inertial frames - that's the "SR transformation" that must be obeyed. If the distance between the space ships is 100 m before departure, it will remain 100 m after departure until cruising speed according to measurements in the launch pad frame S. Consequently, according to SR this distance will be measured as γ*100 m in the new co-moving frame S' in which also the string is in rest. This distance defines the length of the string, which now is greater than that of the same string without constraints.

Thus it's just the contrary of what you think. For those co-moving observers the ship separation has increased and they can happily confirm that the string may have been broken, providing we also assume that the string does follow the same SR transformation which in this case implies proper stretching (and ultimately breakage).

Did that help?

 

[A.T.]

For some observers the ship separation increases and we can happily say that the string breaks, providing we also assume that the string doesn’t follow the same SR transformation which would avoid breakage.

There are no SR transformations which would avoid breakage.

Some claim it doesn’t follow those transformations because it’s “rigid”

Nobody claimed this here.

Also the oft stated EM field contraction, drawing the object’s atoms closer, as reason for breakage, would have a frame relative-velocity dependence

Yes, "reasons" for something can be frame-dependent. In my frame I die because the bullet hits me. In the bullets frame I die because I hit the bullet.

and would still leave the question: Does every observer see the same event (breakage, if it takes place)?

No, it doesn't leave leave that question. Physics predicts that all observes observe it to break. But physics doesn't care what informal "reasons" human observes come up with, to rationalize the result in terms of their intuitive cause-effect thinking.

 

[Dale]

DaleSpam (173 & 174):
You really needn’t have spent so much of your time enlightening me about those “core concepts.” But thanks for your concern. PS, my degree in physics is 61 years old, undilated ;-)

OK, so you understand that proper length is frame invariant now? In particular you understand the difference between constant (over time) and invariant (across frames)? You pretty clearly did not understand it a couple of days ago, so I wasn't sure how far to go.

 

[A.T.]

In particular you understand the difference between constant (over time) and invariant (across frames)?

He obviously doesn't, because in post #182 he still confuses rigidity (constancy of proper length over time) with coordinate transformations (which relate lengths across frames).

 

[ghwellsjr]

To All:
A bit more about our connection to SR’s message.

The reason we call these SR results paradoxes is because they seem so strange to us as beings who never got even close to leaving the frame we live in and entering a frame that has a great velocity relative to the one we left.

No, the reason we have so-called paradoxes in SR is because of an incorrect assumption about what happens when the same scenario is viewed from different frames. If you correctly apply the Lorentz Transformation process, not just the idea of Length Contraction or Time Dilation while ignoring the Relativity of Simultaneity, then there can never be a paradox.

All our experiences drive us to believe that the length of a rod will always retain that length no matter how we toss it, move it , or whatever, so long as we don’t heat or cool it, or squeeze or pull on it.

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

That’s what the experience in our cocoon tells us. Remember how difficult it was for people to accept, when you tried to tell them, that if they had left their current place and then returned, their age would then be less than it would be if they had stayed and not traveled. We still don’t have an internalized feeling that this occurs, but we accept it because of our confidence in SR. Maybe after much time we will begin to accept (though un-internalized) that rest-frame lengths also depend on previous travel history.

Rest-frame lengths don't depend on previous travel history but if you pull separately on both ends of an object, you can change its rest-frame length or break it if it won't stretch which is the meaning of rigid.

As to the Bell paradox, I tend to be fixated on the need to show that if the string does break, it must do that for all observer. For some observers the ship separation increases and we can happily say that the string breaks, providing we also assume that the string doesn’t follow the same SR transformation which would avoid breakage. Some claim it doesn’t follow those transformations because it’s “rigid”. But there is nothing in SR that says thou shalt not transform “rigid” items.

You are overlooking the fact that although the ship separation can be different in different frames, these events have different times associated with them. If you instead calculate the separation in these different frames with events that have the same time associated with them, then you will understand why they all show that the string breaks. You can't ignore the Relativity of Simultaneity.

For those observers who see the ships approaching each other, the string, if again deemed to be “rigid” would break under compression (or otherwise sag). Here again SR transformation would avoid compression.

Also the oft stated EM field contraction, drawing the object’s atoms closer, as reason for breakage, would have a frame relative-velocity dependence and would still leave the question: Does every observer see the same event (breakage, if it takes place)?

It may turn out that if breakage does occur in every frame’s view, it is because the string is undergoing an acceleration as viewed from all frames.

It’s been fun.

If a string or any object undergoes an acceleration in one (inertial) frame, then it undergoes an acceleration in all (inertial) frames. If you accelerate the object at just one point (which means you apply a force at just one point), then you can use SR to determine how all the other points on the object accelerate so that the object maintains the same shape as it had before, as long as it is rigid. That's what we mean by rigid. If you separately accelerate the object at two different points (which means applying two forces at two different points), and that second point accelerates the object differently than what SR would have determined it to be if you had only applied one force, then the object is either rigid and will break, or it is not rigid and will be stretched or compressed.

 

[Eli Botkin]

yuiop (181):
Thanks loads for this suggestion. Though I am totally familiar with the math in Born rigidity, I confess that I hadn’t thought to apply it to adjacent particles in the rod. I clearly need to rethink my position which, at first glance, seems incorrect. If so, then I owe all breakage enthusiasts an apology.

 

[Dale]

I tend to be fixated on the need to show that if the string does break, it must do that for all observer.

And I have encouraged you multiple times to do so. All you have to do is to take the valid proof I posted and Lorentz transform into any other frame in order to get an equivalent proof in a different frame.

providing we also assume that the string doesn’t follow the same SR transformation which would avoid breakage. Some claim it doesn’t follow those transformations because it’s “rigid”. But there is nothing in SR that says thou shalt not transform “rigid” items

This statement is badly wrong. Again you seem to be not understand proper length and its relationship to strain and reference frames.

A strain is a change in the proper length of an object over time, so strain is frame invariant. Length contraction is a disagreement between two different frames about the coordinate length of an object at a single point in time.

The concept of "Born rigidity" defines a strain-free motion. A stiff object in SR is one which will remain Born rigid regardless of external forces, at least until it breaks.

Again, rigidity relates the length at one time to the length at another time, and length contraction relates the length in one frame to the length in another frame. They are independent concepts and it is incorrect that rigid objects are exempt from length contraction.

 

[Austin0]

Hi Eli,
I would like to try a different approach and see what you think. Let us say we have two rockets, A and B, with the same proper length L that are at rest alongside each other. Rocket B accelerates off in the x direction, until it reaches a velocity of 0.8c relative to rocket A and then switches off the drive. The observers onboard rocket B measure the coordinate length of rocket A to be 0.6L. The observers on board rocket A report the proper length of rocket A to still be L. There is no reason for the proper length of rocket A be anything other than L because we have not done anything to rocket A. If we had stress gauges on the rockets, then they would indicate that rocket A is unstressed. If you agree with all the above then you should agree that in order for rocket A to be unstressed when it has a velocity relative to rocket B, then the rocket B observers must measure the coordinate length of rocket A to less than L. For the length of rocket A to still be L when it has motion relative to B then rocket A would have to be physically stretched and probably break. Agree?

You might argue that it would be different if we accelerated rocket A instead of rocket B, but once the rockets engines are switched off and the stresses are allowed to settle down, then SR tells us that the proper length of both rockets is still L and they each measure the coordinate length of the other ship to less than L, so it makes no difference which rocket actually accelerates.

If you agree with the above, then you should conclude that if you accelerate an object while maintaining its coordinate length in the initial reference frame, then its proper length must be increasing (which I think you have already figured out) AND it must be under increasing stress and eventually break.

Yes, here you clearly exemplified the difference between the kinematic and physical EM field contraction interpretations of contraction.
If we assume the EM contraction of ship B it is clear that we cannot apply that explanation to the contraction of ship A as measured in B. We must assume a purely kinematic source in this case.
If we consider a third ship C with an inertial velocity equal to the final velocity of B then we see B expanding relative to that frame as it accelerates.


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

If we assume the EM interpretation in frame C then the expansion is a result of decreasing contraction from the initial velocity as the velocity decreases with deceleration.
This is not a problem with the kinematic interpretation but is an obvious contradiction if we assume actual physical contraction. If the contraction is the result of actual tensile forces due to light speed interactions within the structure, then it logically is directly dependent on the velocity, relative not to any frame, but to the absolutely invariant speed of light.
it then follows that if a system is changing velocity it must be either increasing or decreasing it's speed relative to light. Contracting or expanding but not both.
So assuming that the EM contraction is correct there is still no way to determine how it would apply. It could only be a partial cause for the observed phenomena with the necessary assumption of purely kinematic effects also.
With no way to tell which is which.

In the case here. Ship B is both contracting and expanding. EM contraction works fine if we assume frame A is at rest and B is actually increasing in velocity. EM expansion works fine in C if we assume C is at rest and B is actually decreasing in velocity.
But both depictions of the physics occurring in the ship during acceleration cannot be accurate.
Make sense??

 

[Eli Botkin]

To all who set me straight: Mea culpa!

I am now convinced that I erred in thinking that SR was not adequate to show that the string in Bell's Paradox will break. The clincher was the Born rigidity solution that yuiop had suggest that I review. My new understanding also removed my concern about inertial frames wherein the ships approach each other.

Thanks again,
Eli

 

[harrylin]

To all who set me straight: Mea culpa!

I am now convinced that I erred in thinking that SR was not adequate to show that the string in Bell's Paradox will break. The clincher was the Born rigidity solution that yuiop had suggest that I review. My new understanding also removed my concern about inertial frames wherein the ships approach each other.

Thanks again,
Eli

Nice to hear that this discussion was useful.

 

[harrylin]

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

I did not see yuiop show such a thing... I see no such problem.

If we consider a third ship C with an inertial velocity equal to the final velocity of [ship] B then we see B expanding relative to that frame as it accelerates. If we assume the EM interpretation in frame C then the expansion is a result of decreasing contraction from the initial velocity as the velocity decreases with deceleration.
This is not a problem with the kinematic interpretation but is an obvious contradiction if we assume actual physical contraction. If the contraction is the result of actual tensile forces due to light speed interactions within the structure, then it logically is directly dependent on the velocity, relative not to any frame, but to the absolutely invariant speed of light.

Perhaps you forgot that the speed of light relative to an atom depends on the chosen frame? It's a direct result of our definition of simultaneity. The speed of light relative to an object (also called "closing speed") is not invariant but frame dependent, just as the EM effects.

it then follows that if a system is changing velocity it must be either increasing or decreasing it's speed relative to light.

Well, obviously this is necessarily so (as described from any inertial frame). That follows from the second postulate - no need for such a complex consideration! As interpreted from frame C, the rockets fly along with light that is going in one direction and counter the light going in the other direction.

Contracting or expanding but not both.
So assuming that the EM contraction is correct there is still no way to determine how it would apply. It could only be a partial cause for the observed phenomena with the necessary assumption of purely kinematic effects also.
With no way to tell which is which. In the case here. Ship B is both contracting and expanding.

It applies just the same as most other things in physics, such as electric and magnetic fields as well as energy. Kinetic energy is perhaps the clearest:

1. a rocket takes off, so that -according to the launch pad frame calculations- its length contracts and the rocket's kinetic energy increases.
2. you choose another reference frame, and in the new reference frame the rocket's length "is" contracted and the rocket "has" more kinetic energy.

Hopefully it is clear that 1. and 2. are physically completely different cases, and also that these effects are "relative" to the frame of observation; "is" and "has" are not absolutes.
Else you would have that the energy increases AND decreases, which is a contradiction.

It is similarly wrong to say that ship B is both contracting and expanding; that's an error due to flip-flopping reference systems (a major cause of errors, like mixing dollars and euros!). We should say that ship B is contracting and gaining energy according to system A, and expanding and loosing energy according to system B.

[..] EM expansion works fine in C if we assume C is at rest [..]

The laws of physics are defined relative to a reference system that is presumably "in rest".

But both depictions of the physics occurring in the ship during acceleration cannot be accurate.
Make sense??

They cannot both be "absolutely true". That makes perfect sense, and it's the starting point of SR and already of classical relativity (such as in Newton's mechanics) that we cannot determine "who is right". See the introduction here:
http://www.fourmilab.ch/etexts/einstein/specrel/www/

 

[Dale]

To all who set me straight: Mea culpa!

I am now convinced that I erred in thinking that SR was not adequate to show that the string in Bell's Paradox will break. The clincher was the Born rigidity solution that yuiop had suggest that I review. My new understanding also removed my concern about inertial frames wherein the ships approach each other.

Thanks again,
Eli

Awesome! That is the core educational purpose of PF at work then!

 

[Doc Al]

Yay!

 

[Austin0]

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

I did not see yuiop show such a thing... I see no such problem.

You did not comment on the previous sentences.

If we assume the EM contraction of ship B it is clear that we cannot apply that explanation to the contraction of ship A as measured in B. We must assume a purely kinematic source in this case.

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

If we consider a third ship C with an inertial velocity equal to the final velocity of [ship] B then we see B expanding relative to that frame as it accelerates. If we assume the EM interpretation in frame C then the expansion is a result of decreasing contraction from the initial velocity as the velocity decreases with deceleration.
This is not a problem with the kinematic interpretation but is an obvious contradiction if we assume actual physical contraction. If the contraction is the result of actual tensile forces due to light speed interactions within the structure, then it logically is directly dependent on the velocity, relative not to any frame, but to the absolutely invariant speed of light.

Perhaps you forgot that the speed of light relative to an atom depends on the chosen frame? It's a direct result of our definition of simultaneity. The speed of light relative to an object (also called "closing speed") is not invariant but frame dependent, just as the EM effects.

I would say that any quantitative evaluation of the speed of light relative to an atom depends on the chosen frame.
But I made no such evaluation . I simply talked about a change in velocity with no implication that it was even determinable whether it was an increase or decrease.
When I said invariant wrt light I was not not talking about the frame invariance of measured speed but the independent isotropic constancy that we assume. That all photons absent the influence of gravity are moving at the same "absolute speed"
In your opinion does this or does this not imply some indeterminate, but actual, change in velocity relative to light resulting from a change of velocity through acceleration
??

it then follows that if a system is changing velocity it must be either increasing or decreasing it's speed relative to light.

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

Well, obviously this is necessarily so (as described from any inertial frame). That follows from the second postulate - no need for such a complex consideration! As interpreted from frame C, the rockets fly along with light that is going in one direction and counter the light going in the other direction.

Contracting or expanding but not both.
So assuming that the EM contraction is correct there is still no way to determine how it would apply. It could only be a partial cause for the observed phenomena with the necessary assumption of purely kinematic effects also.
With no way to tell which is which. In the case here. Ship B is both contracting and expanding.

It applies just the same as most other things in physics, such as electric and magnetic fields as well as energy. Kinetic energy is perhaps the clearest:

1. a rocket takes off, so that -according to the launch pad frame calculations- its length contracts and the rocket's kinetic energy increases.
2. you choose another reference frame, and in the new reference frame the rocket's length "is" contracted and the rocket "has" more kinetic energy.

Hopefully it is clear that 1. and 2. are physically completely different cases, and also that these effects are "relative" to the frame of observation; "is" and "has" are not absolutes.
Else you would have that the energy increases AND decreases, which is a contradiction.

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

In any case i don't think this is quite analogous. Momentum and KE are both inherently kinematic evaluations. Applying to interactions with external entities. Completely relative values that say nothing about the internal conditions of the particle in question.
As far as the contraction , as I stated previously; viewed kinematically there is no problem with the ship contracting relative to one frame and expanding relative to another.

It is similarly wrong to say that ship B is both contracting and expanding; that's an error due to flip-flopping reference systems (a major cause of errors, like mixing dollars and euros!). We should say that ship B is contracting and gaining energy according to system A, and expanding and loosing energy according to system C (I assume not B as you wrote).

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

I was not flipping between reference frame but rather looking at the implications of the purely physical interpretation of contraction as applied to both frames at once.

Consider the fictitious paradox of contraction.
Length A is smaller than length B AND length B is smaller than length A
Obviously the correct application of the L transformation resolves this in a completely logically consistent way. But that resolution is a kinematic one. It includes the relativity of simultaneity.
Now we can say that some physical EM contraction is happening in addition to the kinematic factors and still be logically consistent.
But to propose that both A and B are physically contracted as a result of EM forces ,to me at least, brings it right back to a logical contradiction.

[..] EM expansion works fine in C if we assume C is at rest [..]

The laws of physics are defined relative to a reference system that is presumably "in rest".

Yes of course.But to my understanding the relevant physics in this case is the maths of the Lorentz transformation.This is a kinematic description that predicts the expected measurements of relative frames .
As I said I assume this to be a totally accurate description of reality. But the maths do not per se, directly describe or entail any physics interpretation. Does not make any statement regarding the physical cause of contraction or provide a definition to determine what is due to actual EM forces and what is a consequence of relative simultaneity or pure relative motion.
This is a matter of interpretation.

But both depictions of the physics occurring in the ship during acceleration cannot be accurate.
Make sense??

They cannot both be "absolutely true". That makes perfect sense, and it's the starting point of SR and already of classical relativity (such as in Newton's mechanics) that we cannot determine "who is right".

I never implied that it was a question of determining who was right.
What I was suggesting was that it was also impossible to determine what was due to actual EM forces and what was due to kinematic effects.

 

[Austin0]

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




If you accelerate the object at just one point (which means you apply a force at just one point), then you can use SR to determine how all the other points on the object accelerate so that the object maintains the same shape as it had before, as long as it is rigid. That's what we mean by rigid. If you separately accelerate the object at two different points (which means applying two forces at two different points), and that second point accelerates the object differently than what SR would have determined it to be if you had only applied one force, then the object is either rigid and will break, or it is not rigid and will be stretched or compressed.

this question is not related to the string scenario. i already stated long before that I assume the string will break.That was a case of two effectively independent systems
But you are apparently relating this to a single strong physical structure. SO I would like to clarify.
If we assume the two ships are connected with a massive cable or some structurally strong lattice and the ships have identical mechanical drives with equal thrust (remove the complication of equal proper acceleration), obviously there is going to be stress.
After initial application of thrust we can assume a stress gradient , compression at the rear transitioning to extension at the front. But after a stable equilibrium is achieved can you explain why there would be an overall net expansive force or why there would be an increasing expansive force over time?
Thanks

 

[yuiop]

Hi AustinO,

Have you tried analysing your question with Lorentz Ether Theory (LET)? LET and SR are mathematically identical and predict the same things but differ philosophically. In my Humble opinion, LET gives a more physical intuition of what is going on. Perhaps it might be worth starting a new thread as I think we are danger of going off topic here and I will contribute as and when I have time, although I am bit busy at the moment.

 

[ghwellsjr]

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


If you accelerate the object at just one point (which means you apply a force at just one point), then you can use SR to determine how all the other points on the object accelerate so that the object maintains the same shape as it had before, as long as it is rigid. That's what we mean by rigid. If you separately accelerate the object at two different points (which means applying two forces at two different points), and that second point accelerates the object differently than what SR would have determined it to be if you had only applied one force, then the object is either rigid and will break, or it is not rigid and will be stretched or compressed.

this question is not related to the string scenario. i already stated long before that I assume the string will break.That was a case of two effectively independent systems
But you are apparently relating this to a single strong physical structure. SO I would like to clarify.
If we assume the two ships are connected with a massive cable or some structurally strong lattice and the ships have identical mechanical drives with equal thrust (remove the complication of equal proper acceleration), obviously there is going to be stress.
After initial application of thrust we can assume a stress gradient , compression at the rear transitioning to extension at the front. But after a stable equilibrium is achieved can you explain why there would be an overall net expansive force or why there would be an increasing expansive force over time?
Thanks

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

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

 

[yuiop]

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

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

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

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

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

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

 

[harrylin]

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

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

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

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

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

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

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

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

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

[comment moved up:]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

 

[Austin0]

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

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

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

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

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

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

I don't know about everyone else But I totally agree. That is exactly my analysis.
The assumption that a rigidly connected system would have equal coordinate acceleration and maintain a constant separation in the launch frame simply because of equal thrust,is in my opinion, not founded in realistic physics.
Also in the case of the independent systems there is a physical basis for an assumption of increasing separation wrt other frames moving in the same direction.
For instance a frame at 0.8c In this frame the earlier ignition of the lead ship would result in in a velocity differential that would actually increase over time because the coordinate acceleration in that frame would be increasing by a factor of 1/$\gamma$³ and the lead ship would be infinitesimally ahead on the acceleration curve.
This would not be the case with the connected system. The prior ignition of the lead ship would not lead to significant actual coordinate motion relative to the back of the system while the momentum was propagating back through the system. With any kind of realistic acceleration ,for simplicity say 1 g, the system would begin actual motion as a whole with any infinitesimal differential between the front and back equalizing as full acceleration was achieved and internal tensile forces realized a stable stress gradient.
To me it appears to be a simple situation: There are the tensile forces of L contraction acting inward toward the center of mass and the forces of thrust directed forward. So from the middle to the front the two forces are in oppositon which would result in a minute retardation of the acceleration of the front (in launch frame). From the center backward the forces are aligned ,so would result in a comparable increase in the coordinate acceleration of the rear.
The end result being the expected contraction in the launch frame with a coordinate differential of acceleration and velocity between the front and the back without a necessary precise scaling of distributed acceleration with a larger acceleration appllied to the rear as proposed by the Born hypothesis.
I agree with the premise that if a constant separation could be maintained in the launch frame that this would result in physical disruption of the system. But my feeling is that not only would this be impossible but to even attempt it would require massive thrust with some degree of actual reverse thrust being applied to the rear . IMHO

 

[yuiop]

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

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

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

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

 

[Austin0]

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

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

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

Originally Posted by ghwellsjr

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

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

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

 

[Austin0]

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

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

 

[phyti]

austinO post 191

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

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

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