Does SR actually forbid FTL travel?

[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!