Does SR actually forbid FTL travel?

[DrSnarl]

(4) All clocks read zero. This is frame independent. According to home rocket,'your clock' is now in its PAST, but still reads zero. According to "your perspective", all clocks are still zero and in the PRESENT - "your clock" is still in same frame as home stationary clock, just teleported.

(5) All clocks still read zero for everyone (we are assuming effectively instant accelerations and effectively zero time betweein (4) and (5)). "your clock" is in past compared to "home rocket", and "home clock" is now in future compared to "away clock" (and also according to "your clock"). But they all stil read zero. Note, home rocket thinks teleport was into past from its 'present', away rocket (now that it is going .9c) thinks teleport was to its present from its future.

(6) Teleport back, in away rocket's frame, to away rocket's now simultaneous point on home world line. This will bring you to, say, -1 on this world line. What everyone agrees: your orginal world line ended at its reading of zero. Your 0 time self is now located at -1 on the home world line. Your past self clock reads -1, your coincident present self clock reads 0. All agree on this. Home rocket and away rocket both think the second teleport was a simultaneous teleport (in (5), they both considered the first teleport to be in the past direction). Home stationary observer thinks the second teleport was into the past.

You are right.

In the first thought experiment, I was not treating the time shift due to acceleration as being frame invariant (as you and others pointed out, but I now understand what you meant). In the second thought experiment, I for some reason decided that accelerating causes remote observers to think you traveled in time, which is incorrect.

So it seems that unless you invoke some kind of science fiction type sub-space (that has the property of normalizing time everywhere when you enter it), then SR does indeed forbid FTL travel or information transfer.

Thank you everyone who responded in this thread (especially you PAllen - you're awesome!).

 

[DrSnarl]

...then SR does indeed forbid FTL travel or information transfer.

Or more accurately, SR does indeed dictate that FTL travel or information transfer IS time travel, as we have been discussing.

 

[parthchavo]

First of all you cannot travel at the speed of light or faster than it is because the equations of relativity itself forbid it. When you travel with a velocity v with respect to something, mass increases by underoot(1-v^2/c^2), time speeds up by underoot(1-v^2/c^2) and length contracts by underoot(1-v^2/c^2). So if we add c or something greater in the equation, all the equations of mass, time and length will fall apart. This will mean the collapse of everything around you.

 

[parthchavo]

I would also like to point out that teleportation is not forbaded by relativity. It is actually quantum mechanics which allows it because of the connection and pairing of particles. If somehow we could feed all the information about the quantum state of particles in your body in a computer, then transfer that information to another computer which would rebuild your body with the particles paired to the particles of your body, then you would have actually been teleported. Amazingly a physicist in Hawaii actually teleported a photon from one island to another.

 

[DaveC426913]

I would also like to point out that teleportation is not forbaded by relativity. It is actually quantum mechanics which allows it because of the connection and pairing of particles. If somehow we could feed all the information about the quantum state of particles in your body in a computer, then transfer that information to another computer which would rebuild your body with the particles paired to the particles of your body, then you would have actually been teleported.

There's been a bit of confusion. When we've been talking about teleportation, we've been talking about it as instant - or at least faster than light. The observer is here, then the observer is there, instantly.

What you are talking about is collecting data about something and then sending it by conventional slower-than-light communications to another place and then reassembling it.

 

[parthchavo]

Oh I get it now, no I don't think that is possible. It could have been possible if we could travel faster or at the speed of light, since in that case time would completely stop with respect to us. But we know we can't, so there's no point in talking about it.

 

[DrSnarl]

(4) All clocks read zero. This is frame independent. According to home rocket,'your clock' is now in its PAST, but still reads zero. According to "your perspective", all clocks are still zero and in the PRESENT - "your clock" is still in same frame as home stationary clock, just teleported.

OK, I now remember why I thought that accelerating causes a remote observer to think you've traveled through time. I thought that the resulting time shift depending on distance was what created the perception of length contraction.

So after step 4), wouldn't "home rocket" be in the future from your perspective (with CLOCK=FUTURE) and not in the PRESENT? It seems like this would be necessary or else you would not perceive "home rocket" as being length contracted. By the same reasoning, after you have teleported, it should appear that home rocket is no longer home, but much closer to you.

 

[PAllen]

OK, I now remember why I thought that accelerating causes a remote observer to think you've traveled through time. I thought that the resulting time shift depending on distance was what created the perception of length contraction.

So after step 4), wouldn't "home rocket" be in the future from your perspective (with CLOCK=FUTURE) and not in the PRESENT? It seems like this would be necessary or else you would not perceive "home rocket" as being length contracted. By the same reasoning, after you have teleported, it should appear that home rocket is no longer home, but much closer to you.

Your accelerating will never cause someone else to conclude anything about you other than:

- your clock rate has changed (not theirs)
- your rocket/rulers etc. have changed in length (not theirs).

SR is strange at first exposure, but not nearly as strange as you propose. Nobody else's clocks, rulers, or division of past and future change by virtue of what you do.

As for 'your perception' of home rocket in step (4) of your scenario, I am using your definition of teleporting as a pure shift in in position in your rest frame, with no other effects. So, in (4) you have teleported, but are still in the same rest frame. That the home rocket has started accelerating has no consequence for you at all - except for effects like I noted above.

The accelerating rocket does experience home rest frame distances as changing, and (using conventional SR simultaneity) a shift in what home rest frame events are in its future versus its past. It is the accelerating observer that experiences the changes, not any inertial observer.

You seem to have a number of things about SR backwards.

 

[Austin0]

The difference from classical correlation is that your results are influenced not only by the set up of the state, but also by decisions made by the other experimenter. What prevents signalling, according to current understanding, is that you cannot actually deduce the other experimenter's decisions from your results. You can only find out that they mattered later by comparing results. Why you can't specify a plausible causality hypothesis is that it is frame dependent which measurement occurred first (if they are done far enough apart).

Hi Somhow I missed your reply until now.

I understand regarding the necessity of transferring information after the fact to establish the results.
And of course generally, correlation dosn't necessarily imply causation.
But in this instance, if their is repeatable correlation between the actions of the experimanters and the results, I don't see why establishing temporal order is a necessary requirement for an inference of a causal connection.
In this thread you are positing FTL translation violating temporal order, but do you think this implies there is no causality happening?

 

[DrSnarl]

Your accelerating will never cause someone else to conclude anything about you other than:

- your clock rate has changed (not theirs)
- your rocket/rulers etc. have changed in length (not theirs).

If that is true, then consider what would happen when a rocket on the far side of a distant wall accelerates away from you. Due to Lorentz contraction, it would appear to you as though the rocket contracted backwards THROUGH the wall.

If, on the other hand, Lorentz contraction was just an illusion caused by relativity of simultaneity, you would instead see the rocket accelerate gradually (ie. slower than it really was accelerating) as it shifted through time from your perspective, with the back of the rocket seeming to accelerate slightly faster than the front. While this was happening, you would also see their clock moving much more slowly than yours - slower than could be accounted for with time dilation (ie. it would be moving into your future). Once they stopped accelerating from your perspective, their clock would speed up to the normal dilated rate, and their length would not contract any further.

In this second scenario, you would not see the rocket come back through the wall, even if the acceleration was instantaneous. (That would be bizarre - you would actually see the rocket disappear, then reappear in your future fully length contracted and without having moved before flying away.)

 

[PAllen]

Hi Somhow I missed your reply until now.

I understand regarding the necessity of transferring information after the fact to establish the results.
And of course generally, correlation dosn't necessarily imply causation.
But in this instance, if their is repeatable correlation between the actions of the experimanters and the results, I don't see why establishing temporal order is a necessary requirement for an inference of a causal connection.
In this thread you are positing FTL translation violating temporal order, but do you think this implies there is no causality happening?

Which action caused which consequence? Causality, as I understand it, has a direction. If you want to define some idea 'causal linkage', without specification of what caused what, then I might well agree with it, but would not call it causality.

As for FTL, I have tried to show that (if SR remains true), there is inherently the possibility of causal paradoxes despite Novikov (complex information without cause). Therefore, I personally don't believe it will ever happen.

 

[DrSnarl]

(That would be bizarre - you would actually see the rocket disappear, then reappear in your future fully length contracted and without having moved before flying away.)

Actually, the entire rocket would not reappear at once; you would see the back appear before the front.

 

[PAllen]

If that is true, then consider what would happen when a rocket on the far side of a distant wall accelerates away from you. Due to Lorentz contraction, it would appear to you as though the rocket contracted backwards THROUGH the wall.

No, this is just plain false. If the wall is in your frame, the distance between you and the back of the rocket is always increasing, the distance to the wall never changes, and the distance between the wall and the back of the rocket always increases. The only thing length contraction predicts is that the (if the rocket maintains same length in its own frame), the front will accelerate less than the back, such the rocket is getting shorter. What, exactly, have you studied on SR? These are the fundamentals you are misunderstanding. It really seems you should read one of the basic books on SR (or Einstein's paper on line) before making pronouncements.

[Edit: several of your other statements in the post I replied to were also wrong, but this is the starting point, indicating that you need to study/review the fundamentals.]

 

[DrSnarl]

No, this is just plain false. If the wall is in your frame, the distance between you and the back of the rocket is always increasing, the distance to the wall never changes, and the distance between the wall and the back of the rocket always increases. The only thing length contraction predicts is that the (if the rocket maintains same length in its own frame), the front will accelerate less than the back, such the rocket is getting shorter. What, exactly, have you studied on SR? These are the fundamentals you are misunderstanding. It really seems you should read one of the basic books on SR (or Einstein's paper on line) before making pronouncements.

[Edit: several of your other statements in the post I replied to were also wrong, but this is the starting point, indicating that you need to study/review the fundamentals.]

Let's place the rocket and the wall at distance "x". After acceleration has finished, the perceived distance of the rocket should be:

x' = γ(1-v/c)x​

x' will be less than x - in other words, the rocket will have moved backwards through the wall in your perception.

This is flat out wrong, as you said, but it seems to be what you get if you simply treat Lorentz contraction as physically real and not just a symptom of relativity of simultaneity.

Regarding my background, since you brought it up, I am obviously not a physicist (I am an engineer). I was exposed to relativity at a cursory level in school (ie. here are the equations for the transformations, etc.), but I have recently begun to try to understand the resolution of the various paradoxes which I have come across. This has led me to read up on various explanations of the theory - some better than others. I posted here because I was finding that available literature was not addressing my questions, and one cannot engage in dialogue with a book.

 

[Austin0]

Teleportation trivially leads to time travel in SR as follows (again, also assuming principle of relativity - same laws in all inertial frame):

1) Teleport to a rocket traveling at .9c. Pure coordinate shift in the home frame.2) Teleport back home from the rocket. Pure coordinate shift in the rocket frame.

You arrive home before you left. Teleportation is pure FTL. How can it be different from tachyons in the phenomena it allows?

Hi
Certainly after the fact , when you suddenly appear on the rocket, an observer in your initial frame can establish an event. Pure coordinate shift wrt your frame.

But before the fact: You have decided on a destination within the rocket frame but how do you determine where and when that point is at the instant you depart??

Right off the bat you have two contradictory locations depending on the frame.

Is there some characteristic of teleportation that would indicate the preferred frame on which to base your arrival time and place ?
Which is the actually simultaneous location??

Or in fact any reason to suppose that either location is absolutely simultaneous with your location at that instant?

If you choose the initial frame for calculations , do you believe that conventionally synchronized clocks are actually or absolutely simultaneous??

That if you teleport to a distant location in this same frame you will arrive there with the same local proper time reading as your departure point?

If this is so then would it not follow that instantly returning to your initial location you would also arrive there at the same proper time ??

So if we assume that that distant location was proximate to the spaceship then the round trip would still take no proper time wrt home.

If we take the further step of simply moving the destination from right outside the ship to inside it for a momentary appearence , what justification could there be for now assuming that the arrival home would occur before leaving??

That the phenomenon of teleportation would be affected by the synchronicity of the ships clocks . That the destination of its instantaneous translation would now be determined by a different set of absolutely synchronous clocks?

0f course overlooked in this discussion is the factor that teleportation into a ship at 0.9c would be messy for any time over an instantaneous appearence as you would still be going 0.9c relative to the ship , ouch.

If on the othr hand you don't assume the initial frames clocks are absolutely synchronized then what basis do you have for guessing what the local arrival time would be for even an inframe hop let alone one to another frame ?

 

[PAllen]

Let's place the rocket and the wall at distance "x". After acceleration has finished, the perceived distance of the rocket should be:

x' = γ(1-v/c)x​

x' will be less than x - in other words, the rocket will have moved backwards through the wall in your perception.

This is flat out wrong, as you said, but it seems to be what you get if you simply treat Lorentz contraction as physically real and not just a symptom of relativity of simultaneity.

Regarding my background, since you brought it up, I am obviously not a physicist (I am an engineer). I was exposed to relativity at a cursory level in school (ie. here are the equations for the transformations, etc.), but I have recently begun to try to understand the resolution of the various paradoxes which I have come across. This has led me to read up on various explanations of the theory - some better than others. I posted here because I was finding that available literature was not addressing my questions, and one cannot engage in dialogue with a book.

Ok, you don't understand the meaning of the x and x' in these equations. x,t describe events in one frame. Having specified this, you use Lorentz transform to see how these would look in another frame (x',t'). Given some inertial frame seeing some sequence of events, x' is never used to describe what this inertial frame sees. It is used to transform to what would be seen by some other inertial frame. If you want to posit accelerated frames, that is a whole other ball of wax, which I wrote several long posts about in this thread - but you are not really ready for that until you understand inertial frames. (Further, I don't really recommend ever using accelerated frames in special relativity).

To get at the length contraction of an accelerating rocket, the correct approach is to define Born rigidity for object in general. However, an adequate approach is to require that the length of the rocket stays the same in the instantaneously comoving inertial frame of the back of the rocket. Then you would find (as I said before) that (in the inertial frame) the front of the rocket would accelerate less than the back, and length of the rocket (in the inertial frame) would get shorter. However, at all times, (in the inertial frame) the front and back of the rocket are always accelerating, moving away from some starting point. There is no shrinkage of distance to the rocket.

I really suggest, as a starting point, read part I of:

http://www.fourmilab.ch/etexts/einstein/specrel/www/

then come back and ask more questions.

 

[PAllen]

Hi
Certainly after the fact , when you suddenly appear on the rocket, an observer in your initial frame can establish an event. Pure coordinate shift wrt your frame.

But before the fact: You have decided on a destination within the rocket frame but how do you determine where and when that point is at the instant you depart??

Right off the bat you have two contradictory locations depending on the frame.

Is there some characteristic of teleportation that would indicate the preferred frame on which to base your arrival time and place ?
Which is the actually simultaneous location??

Or in fact any reason to suppose that either location is absolutely simultaneous with your location at that instant?

If you choose the initial frame for calculations , do you believe that conventionally synchronized clocks are actually or absolutely simultaneous??

That if you teleport to a distant location in this same frame you will arrive there with the same local proper time reading as your departure point?

If this is so then would it not follow that instantly returning to your initial location you would also arrive there at the same proper time ??

So if we assume that that distant location was proximate to the spaceship then the round trip would still take no proper time wrt home.

If we take the further step of simply moving the destination from right outside the ship to inside it for a momentary appearence , what justification could there be for now assuming that the arrival home would occur before leaving??

That the phenomenon of teleportation would be affected by the synchronicity of the ships clocks . That the destination of its instantaneous translation would now be determined by a different set of absolutely synchronous clocks?

0f course overlooked in this discussion is the factor that teleportation into a ship at 0.9c would be messy for any time over an instantaneous appearence as you would still be going 0.9c relative to the ship , ouch.

If on the othr hand you don't assume the initial frames clocks are absolutely synchronized then what basis do you have for guessing what the local arrival time would be for even an inframe hop let alone one to another frame ?

I am not going to get involved in answering all these points. Most, have been dealt with, in passing, in this thread. The OP proposed a hypothetical model of teleportation which, it happens, is effectively the zero energy limit of tachyons, for which there is well established theory. That is what I used for analysis. Obviously, in such thought experiments, one ignores issues like teleporting to the inside of a rapidly moving spaceship and then surviving 'instant' acceleration to .9c as you hit the floor/wall of the ship.

No physicist I know of would take teleportation seriously; many, if not most, doubt tachyons. However, the intent of the OP was to inquire whether, and if so, why, SR would equate FTL and/or teleportation to time travel. That question is well defined once you define your flavor of FTL or teleportation - and the OP, at various points, did define their conception enough so it it could be analyzed.

 

[Austin0]

Which action caused which consequence? Causality, as I understand it, has a direction. If you want to define some idea 'causal linkage', without specification of what caused what, then I might well agree with it, but would not call it causality.

As for FTL, I have tried to show that (if SR remains true), there is inherently the possibility of causal paradoxes despite Novikov (complex information without cause). Therefore, I personally don't believe it will ever happen.

Of course I would agree causality as we know and understand it in the real world has direction.
But here we are discussing FTL and EPR so in one case we're out of this world completely and in the other case into a new real world.

In your Shakspeare scenario (great BTW) wouldn't you agree that the arrival of the manuscript back in time was a purely causal consequence of your action?? That Shakespeare
wrote/transcribed it was the cause of your consequent action?
SO what caused what? And if this is indeterminate does this mean there was no causality at all??
In the case of the entangled photons: It is true we cannot say in a frame independent way which occurred first but there are really only two possibilities.
In the first: A precedes B = normal causality is preserved.
In the second: B precedes A and causality is reversed . Demonstrating the very premise of the FTL +SR =time travel hypothesis.
I agree regarding the improbability of FTL or teleportation.

 

[yuiop]

Let's place the rocket and the wall at distance "x". After acceleration has finished, the perceived distance of the rocket should be:

x' = γ(1-v/c)x​

x' will be less than x - in other words, the rocket will have moved backwards through the wall in your perception.

This is flat out wrong, as you said, but it seems to be what you get if you simply treat Lorentz contraction as physically real and not just a symptom of relativity of simultaneity.

This is wrong, but not for the reasons you think. Where did you get the equation? It is not the Lorentz transformation and it is not the length contraction equation.

 

[PAllen]

Of course I would agree causality as we know and understand it in the real world has direction.
But here we are discussing FTL and EPR so in one case we're out of this world completely and in the other case into a new real world.
.

Well, entanglement is very much of the world we live in. Further, I think it tells us something very fundamental about our world.

In your Shakspeare scenario (great BTW) wouldn't you agree that the arrival of the manuscript back in time was a purely causal consequence of your action?? That Shakespeare
wrote/transcribed it was the cause of your consequent action?
SO what caused what? And if this is indeterminate does this mean there was no causality at all??
.

If you use an entropic definition of time ordering, as Demystifier suggested (and I agree), then it is clear that the text of the play appeared at some point in 1600s (without authorship or origin), then Shakespeare transcribed it, then someone in the future sent it back in time). Of course, I didn't invent this scenario, I don't know who first proposed it. Brian Greene has argued, that like it or not (he likes it more than me, I think), such causeless information is a necessary possibility in GR, and Novikov does nothing to relieve this.

In the case of the entangled photons: It is true we cannot say in a frame independent way which occurred first but there are really only two possibilities.
In the first: A precedes B = normal causality is preserved.
In the second: B precedes A and causality is reversed . Demonstrating the very premise of the FTL +SR =time travel hypothesis.
I agree regarding the improbability of FTL or teleportation.

How on Earth do you distinguish that A precedes B is normal causality??!

 

[Austin0]

Well, entanglement is very much of the world we live in. Further, I think it tells us something very fundamental about our world.

I totally agree. I was just suggesting that it is the edge of a new world we are entering.
What started out ,not that long ago really ,as a reductio ad absurdum argument against certain QM concepts has turned out to be a reality that we are just beginning to empiracally explore.

If you use an entropic definition of time ordering, as Demystifier suggested (and I agree), then it is clear that the text of the play appeared at some point in 1600s (without authorship or origin), then Shakespeare transcribed it, then someone in the future sent it back in time). Of course, I didn't invent this scenario, I don't know who first proposed it. Brian Greene has argued, that like it or not (he likes it more than me, I think), such causeless information is a necessary possibility in GR, and Novikov does nothing to relieve this.

IMHO It is debatable whether or not entropy can be applied so directly in this fashion. Which seems to necessitate an assumption that the flow in a complex open system is going to globally, steadily increase without flux. In the case of the Earth fluctuations could occur over many millenia or longer and 400 years is a hiccup.
You can say the content of the manuscript itself was in some fashion authorless. But the physical object itself did in fact have an origin. It was sent from the future so the complete chain of events as I described applies. You can say it is paradoxical but it is still causal even if it does not follow our normal expectations of temporal ordering. No?

How on Earth do you distinguish that A precedes B is normal causality??!

I don't distinguish. That is the point. You maintained that no inference of causality could be made because we could not establish temporal order. I.e. because we could not tell if A preceeded B or vice versa. I was simply proposing that it didn't make any difference because there were only two possibilities; normal causality or inverse causality.
So the order I presented was purely arbitrary as it doesn't make any difference which preceeds the other as we can't tell any way.
Does this make it any clearer?

 

[DrSnarl]

This is wrong, but not for the reasons you think. Where did you get the equation? It is not the Lorentz transformation and it is not the length contraction equation.

Yes, I agree, I was wrong. The source of my error lies in how I was attempting to explain why length contraction occurs.

I think here is the basic thing I do not understand: what happens to the rocket on the other side of the wall when it accelerates? Assume instantaneous acceleration. Immediately after accelerating, from your perspective, where is the back of the rocket and the front of the rocket? If there was a clock at the back and at the front of the rocket, they would not equal each other from your perspective, would they?

Also, the equation I should have used is x'=x(sqrt(1-v^2/c^2)), but even with that, it doesn't fix the problem with my analysis.

 

[PAllen]

Yes, I agree, I was wrong. The source of my error lies in how I was attempting to explain why length contraction occurs.

I think here is the basic thing I do not understand: what happens to the rocket on the other side of the wall when it accelerates? Assume instantaneous acceleration. Immediately after accelerating, from your perspective, where is the back of the rocket and the front of the rocket? If there was a clock at the back and at the front of the rocket, they would not equal each other from your perspective, would they?

Also, the equation I should have used is x'=x(sqrt(1-v^2/c^2)), but even with that, it doesn't fix the problem with my analysis.

Immediately after acceleration, the back of the rocket will have moved closer to the front, according the length contraction formula for the now constant speed of the rocket. Your formula is for length contraction, not coordinate transformation, and is usually written L' = L sqrt(1-v^2/c^), where L is rest length and L' is contracted length. Using x just confuses matters, making it look like the Lorentz transform, which is a different set of formulas (for coordinate transformation).

So, the back of the rocket will have moved away from the wall, while the front will not have moved yet (for this 'instant' acceleration). After this instant acceleration, front and back move from here at new constant speed.

As for clocks, we now have to come back to minimal reality. SR prohibits instant acceleration of a rigid body, just as strongly as it prohibits matter moving FTL. The analysis above shows why - the back of the rocket will have moved a finite distance in zero time. For any length of rocket, you can derive a specific maximum acceleration consistent with (Born) rigid motion - that avoids any part of the rocket moving FTL. If we consider this maximum allowed acceleration (noting also that the front continues accelerating after the back has stopped - to arrive at final rigid motion at constant speed), then for clocks that started in synch on starting inertial frame, both will be end up behind corresponding inertial frame clocks, the back further behind than the front.

 

[DrSnarl]

Yes, I agree, I was wrong. The source of my error lies in how I was attempting to explain why length contraction occurs.

I do not feel so bad now - it appears that the problem I have with this rocket experiment is illustrated by the Bell spaceship paradox. A quick internet search reveals conflicting explanations that yield conflicting results. Is there a scientific consensus on whether or not the "string would break"?

 

[DrSnarl]

So, the back of the rocket will have moved away from the wall, while the front will not have moved yet (for this 'instant' acceleration). After this instant acceleration, front and back move from here at new constant speed.

The thing that is confusing about that is this: what makes the front of the rocket special? Why would the front of the rocket "not have moved yet"? If you added a nose needle to the rocket, would it now be the front of the nose needle that had not yet moved? It doesn't seem like adding something to the front of the rocket should affect the way the rocket contracts.

I was attempting to reconcile this by thinking that the entire frame of reference contracts towards the observer (hence the wall problem), and I was trying to reconcile that by explaining the contraction as an illusion caused by relative simultaneity. Somewhere in there I got off the rails.

 

[PAllen]

I do not feel so bad now - it appears that the problem I have with this rocket experiment is illustrated by the Bell spaceship paradox. A quick internet search reveals conflicting explanations that yield conflicting results. Is there a scientific consensus on whether or not the "string would break"?

There is no controversy on this. If the front and back maintain the same distance apart seen from the inertial frame, the string breaks. If the string remains taut, but under fixed tension, and no breakage occurs (by properly coordinated acceleration of its constituents), then it gets shorter during acceleration as seen from the inertial frame.

 

[PAllen]

The thing that is confusing about that is this: what makes the front of the rocket special? Why would the front of the rocket "not have moved yet"? If you added a nose needle to the rocket, would it now be the front of the nose needle that had not yet moved? It doesn't seem like adding something to the front of the rocket should affect the way the rocket contracts.

I was attempting to reconcile this by thinking that the entire frame of reference contracts towards the observer (hence the wall problem), and I was trying to reconcile that by explaining the contraction as an illusion caused by relative simultaneity. Somewhere in there I got off the rails.

Instant acceleration is not really possible. Real acceleration is limited by speed of sound in materials (displacement propagates at the speed of sound, and if more than a critical force is applied, the material will deform or break). Born rigid acceleration (such that there are no stresses in the body as it accelerates) requires each piece 'knowing' when and how to accelerate to achieve this. It is this artifice that leads to things like the front knowing when and how to accelerate compared to the back.

 

[DrSnarl]

Instant acceleration is not really possible. Real acceleration is limited by speed of sound in materials (displacement propagates at the speed of sound, and if more than a critical force is applied, the material will deform or break). Born rigid acceleration (such that there are no stresses in the body as it accelerates) requires each piece 'knowing' when and how to accelerate to achieve this. It is this artifice that leads to things like the front knowing when and how to accelerate compared to the back.

So if a rocket had side boosters near the front - so that both the front and the back were accelerating independently but at the same rate - then the rocket would break in half as the front portion and back portion were contracted away from each other?

 

[PAllen]

Here are two recent papers giving an accessible treatment of rigid body motion in SR. There are more elegant, robust, treatments involving e.g. an expansion tensor, but these papers are basically accessible at advanced high school/undergrad level, and cover all the essential ideas.

http://arxiv.org/abs/0906.1919
http://arxiv.org/abs/1105.3899

[EDIT: I should note that I, and many (but not all) knowledgeable participants on this forum, disagree with the emphasis in the first paper on length contraction. It remains very useful for understanding rigid motion, nonetheless.

My disagreements focus on the following:

1) Granting reality only to rest length, and basically claiming contracted length is analogous to 'relativistic mass' which is an increasingly disfavored concept in SR. I think this goes too far, for while relativistic mass is useless (IMO), total energy is not. To deal with the geometry of a moving object, you need a description in the inertial system. This must use some something essentially like length contraction.

2) He briefly mentions Terrell's result for a photograph of a moving sphere. He fails to mention that for non-spherical objects, the conclusions are different - photographs will show a contracted object depending on the relative position of camera and object. In particular, a photograph of a moving rod taken adjacent to its center (in the configuration known as the barn pole paradox) will show the rod completely inside the barn with both doors closed, even though the rod is longer (rest length) than any dimension of the barn (that is, longer even than any diagonal).]

 

[DrSnarl]

Here are two recent papers giving an accessible treatment of rigid body motion in SR. There are more elegant, robust, treatments involving e.g. an expansion tensor, but these papers are basically accessible at advanced high school/undergrad level, and cover all the essential ideas.

http://arxiv.org/abs/0906.1919
http://arxiv.org/abs/1105.3899

Thank you, I will take a look.

 

[DaveC426913]

So if a rocket had side boosters near the front - so that both the front and the back were accelerating independently but at the same rate - then the rocket would break in half as the front portion and back portion were contracted away from each other?

Only inasmuch as any rocket would suffer these kinds of stresses. Remember, in the rocket's reference fame, it is stationary.

If a rocket is sitting in orbit, and it turns on its bow thrusters, well technically, its front end and its rear end are undergoing two stresses:
1] the thrusters are pulling on one end and only moving the other end via normal mechanical forces that are transmitted at the speed of sound (yeah, crafts will creak when their propulsion is turned on.)

2] So, for a brief fraction of a second, the bow of the craft is moving relative to the stern of the craft. Technically, this does mean that there is a theoretical relativistic contraction effect. But it is difficult to express just how small this effect is.

 

[PAllen]

So if a rocket had side boosters near the front - so that both the front and the back were accelerating independently but at the same rate - then the rocket would break in half as the front portion and back portion were contracted away from each other?

It depends on how they accelerate. If they accelerate independently so as to maintain constant distance as measured in an inertial frame, the rocket will break. If they accelerate independently so as to maintain absence of stress (or minimal stress) throughout the rocket, there will be no breakage, but the inertial frame will measure the rocket shrinking, and will measure different acceleration profiles for the front and back.

 

[DrSnarl]

Thank you for the explanations, Dave and PAllen! I think I get it now. I will read through those papers to try to iron out the remaining kinks.

Thanks for being patient!