Why is the Wikipedia article about Bell's spaceship paradox disputed at all?

[Fredrik]

Why is the Wikipedia article about Bell's spaceship "paradox" disputed at all?

Link to the article

This problem is ridiculously simple. The condition that the spaceships experience the same acceleration implies that their world lines will have the same shape. (The acceleration doesn't have to be constant. It's sufficient that both spaceships accelerate the same way). This implies that the length of the rope will remain constant in the launcher's frame. Think about that for a second. After a while, the rope is moving at a high velocity in the launcher's frame, and must therefore be Lorentz contracted, but it's still the same length! That means that it must have been stretched. If it was already stretched to its maximum length when the acceleration began, it must break. It's as simple as that.

This is all very basic stuff that belongs in an introductory level class about special relativity. So why is this article disputed at all?

Is it because of the common (but silly) misunderstanding that you can't solve a problem involving any kind of acceleration entirely in SR? (It's really weird how many people who have studied SR still believe that you need GR for problems like this).

Or is it because some people who understand that the rope gets stretched are arguing that SR somehow also implies that the rope gets stronger, so it can handle getting stretched?

I can't think of a third reason.

I know that some people here have been working on this article. Perhaps one of you can explain this to me.

 

[quantum123]

Perhaps as one poster said, there is no stretching at all - just a matter of siumultaneity.
To measure length, you need to know two points at the same time.

 

[Boustrophedon]

Bell's spaceships is didputed because Bell was wrong !

You're right about the problem being simple but it is rather important to use special relativity and not Lorentz's pre-1905 theory, which postulates actual physical contraction of solid lengths in the direction of motion. It should be remembered that Einstein's SR is a fundamentally different theory even though it leads to the same Lorentz transformations.

Einstein's theory involves a purely kinematical approach involving no physical "shrinkage" but achieving contracted measurements by means of the relativity of simultaneity. That is to say, the shift in simultaneity causes the front end to be measured first with respect to the rear end a moment later, resulting in a reduced measurement.

What this means is that a rod initially at rest with respect to an observer does not, in SR, change its length with respect to that same observer, as it is accelerated to some fraction of c. What happens is that the length of the rod defined by another observer moving with it will appear to get longer with respect to the "stationary" observer who sees the rear end marked increasingly before the front end, as the moving observer's simultaneity shifts.

Einstein's 1905 paper only concludes that a length defined in K' appears shorter in K by the Lorentz factor, and vice versa, where K' and K are in relative uniform motion. It does not say nor suggest that a body would change its physical length during acceleration.

The idea of a rod "shrinking" as it accelerates is an unfortunate anachronism - a "hang-over" from Lorentz's earlier theory that still lingers on a century later and even finds its way into textbooks now and then.

If you read Bell's original article you will see that he makes it clear throughout that he is using Lorentz's theory in preference to SR. He was a quantum physicist with no track record in relativity and it's not clear whether he disliked Einstein's SR or whether he didn't realize the significant difference between the two approaches.

 

[Fredrik]

Boustrophedon, you're wrong. I don't know how you got the idea that everyone who's making correct claims about SR is actually wrong because they're using some pre-SR theory that we've barely heard about, but I can assure you that's not what I'm doing, and it's not what the people in the other thread are doing either.

 

[Fredrik]

Perhaps as one poster said, there is no stretching at all - just a matter of siumultaneity.

If someone said that, he or she was either talking about Lorentz contraction in general, or hasn't understood SR at all. Lorentz contraction can be said to be "just a matter of simultaneity", but in this case the rope is clearly being forcefully stretched. Otherwise its length wouldn't remain the same when it gets Lorentz contracted.

To measure length, you need to know two points at the same time.

That obvious. What's your point?

 

[Ich]

The problem has nothing do with whether you choose Einstein or Lorentz. When people here are speaking of actual stretching/compression, they mean actual stretching.
There is confusion about what exactly "accelerating a rod" means. I can think of 4 substantial different scenarios:
1. The rod is being pulled. It will first get stretched, stay so during acceleration, and finally come to "rest" at its initial proper length when the acceleration ceases. There are no internal stresses then.
2. The same with a rod being pushed; just replace "stretched" with "compressed".
3. The rod is being pushed and pulled in a way that the proper accelerations of both ends are the same. It will experience stretching and compression (depending on the position) during acceleration. It will come to "rest" with a greater proper length, actually stretched.
4. Every single point of the rod is being accelerated with a carefully chosen proper acceleration such that no internal stresses occur. Its length, as measured in in a suitable comoving frame, will stay constant. It will come to rest with its original proper length an no stresses.[

 

[quantum123]

OK.
I see the problem here.
There is a rigid rod to the co-moving observers.
But the lab observers see a contracting rod.
So shall I say that the spring constant has also got be relativistically transformed.

 

[Fredrik]

Just adding to the list...

5. Every point of the rod is instantaneously (or near instantaneously) boosted to a new velocity, all at the same time in the frame where the rod was at rest before the boost. This stretches the rod to a longer proper length.
6. Every point of the rod is instantaneously (or near instantaneously) boosted to a new velocity, all at the same time in the frame where the rod will be at rest after the boost. This compresses the rod to a shorter proper length.

 

[Ich]

OK.
I see the problem here.
There is a rigid rod to the co-moving observers.
But the lab observers see a contracting rod.
So shall I say that the spring constant has also got be relativistically transformed.

If you measure the rod contracted according to Length Contraction, you know that it has not changed at all. No need to consider spring constants.

 

[Fredrik]

I think he's trying to argue that the string/rope/rod in the Bell's spaceship scenario won't break even though it's getting stretched. Any such argument would have to say something about the properties of the material.

 

[nakurusil]

Just adding to the list...

5. Every point of the rod is instantaneously (or near instantaneously) boosted to a new velocity, all at the same time in the frame where the rod was at rest before the boost. This stretches the rod to a longer proper length.
6. Every point of the rod is instantaneously (or near instantaneously) boosted to a new velocity, all at the same time in the frame where the rod will be at rest after the boost. This compresses the rod to a shorter proper length.

Both 5 and 6 are not possible. Forces travel at finite speed (the speed of sound) in rigid materials. This is a pretty slow speed , so you cannot have "instantaneous (or near instantaneous) velocity boost". This is what Born rigidity is all about.
So, the rear of the rocket , where the engine is, is boosted earlier than the front.
So, the rear of the leading rocket is boosted earlier than the front of the trailing rocket.
So, the rod anchored between the rear of the leading rocket and the front of the trailing rocket gets STRETCHED (if the two rockets motors exhibit the same uniform acceleration) .
If you would like the mathematical tratment that goes with it, you can check wiki on the "Bell's paradox" or I can add a reference to a college course notes on hyperbolic motion/Born rigidity. They show the conditions under which the rod breaks.

Now, why is the wiki article disputed? I am sure CH can explain this a lot better, the short of it is that it takes one kook (Rod Ball in this case) to slap the "NPOV disputed" on any wiki article. If you click on "discussion", you will find the never ending argument with Rod Ball.

 

[Fredrik]

Both 5 and 6 are not possible. Forces travel at finite speed (the speed of sound) in rigid materials.

They're possible. You just have to find a way to push every atom at the same time.

I'm not saying it's easy. 5 and 6 are not reasonable ways to accelerate objects, but they have a pedagogical value.

 

[nakurusil]

They're possible. You just have to find a way to push every atom at the same time.

Physics says that the above is not possible. (unless you decide to attach a miniature rocket motor to each atom)

I'm not saying it's easy. 5 and 6 are not reasonable ways to accelerate objects, but they have a pedagogical value.

If you use absurd premises don't be surprised to get absurd conclusions.

 

[Fredrik]

Physics says that the above is not possible. (unless you decide to attach a miniature rocket motor to each atom)

So it is possible. What's interesting is what's possible in principle, not what's easy.

5 and 6 are interesting mainly because thinking about those only for a few seconds is by far the easiest way to understand the claim that there are no rigid bodies in SR.

 

[nakurusil]

So it is possible. What's interesting is what's possible in principle, not what's easy.

5 and 6 are interesting mainly because thinking about those only for a few seconds is by far the easiest way to understand the claim that there are no rigid bodies in SR.

Sounds like an attempt to justify why you got the solution wrong at post #1

 

[Fredrik]

Are you one of those guys who just tries to deliberately misunderstand everything?

 

[nakurusil]

Are you one of those guys who just tries to deliberately misunderstand everything?

No, not at all. I tried to help you see your own mistakes. Look at your initial post and at your persistence that all atoms in a rigid object can be accelerated in sync.

 

[pervect]

Link to the article

This problem is ridiculously simple. The condition that the spaceships experience the same acceleration implies that their world lines will have the same shape. (The acceleration doesn't have to be constant. It's sufficient that both spaceships accelerate the same way). This implies that the length of the rope will remain constant in the launcher's frame. Think about that for a second. After a while, the rope is moving at a high velocity in the launcher's frame, and must therefore be Lorentz contracted, but it's still the same length! That means that it must have been stretched. If it was already stretched to its maximum length when the acceleration began, it must break. It's as simple as that.

This is all very basic stuff that belongs in an introductory level class about special relativity. So why is this article disputed at all?

Is it because of the common (but silly) misunderstanding that you can't solve a problem involving any kind of acceleration entirely in SR? (It's really weird how many people who have studied SR still believe that you need GR for problems like this).

Or is it because some people who understand that the rope gets stretched are arguing that SR somehow also implies that the rope gets stronger, so it can handle getting stretched?

I can't think of a third reason.

I know that some people here have been working on this article. Perhaps one of you can explain this to me.

You are assuming that the reason articles get tags is based on logic and an actual substantial objection. It's actually more of a political process.

It's disputed mainly because of Rod Ball, although the detailed history of how it got that tag is a little more complicated. If you're really curious, and have enough time, you can see the history of the evolution of the article, and the talk pages for the article.

I believe that I actually tagged the article with an NPOV tag when it was in a significantly different form - the history page shows my September 2006 edit below as adding the tag.

http://en.wikipedia.org/w/index.php?title=Bell's_spaceship_paradox&oldid=76280528

I don't feel that there are any NPOV problems with the current article either, but as a very involved party in writing the current version of the article, I don't feel it's appropriate for me to remove the NPOV tag. In fact, I'm not quite sure what the wikipedia process for reomving a tag is (if there is one).

From my POV, the biggest open question with some (small) amount of merit was the debate over whether or not a man named Petkov and his opinions should be mentioned. AFAIK Rod Ball is the only one who feels this particular author's contributions are notable.

I'm happy to have what I think is a reasonably good article with a NPOV tag stuck on it, as opposed to having a very bad article with a NPOV tag stuck on it, so I haven't really investigated closely what it would take to get the tag removed.

 

[disregardthat]

Both 5 and 6 are not possible. Forces travel at finite speed (the speed of sound) in rigid materials. This is a pretty slow speed , so you cannot have "instantaneous (or near instantaneous) velocity boost". This is what Born rigidity is all about.

How about gravity, are the atoms not accelerated equally (or nearly equally because of longer distances from back to front of the object to the pulling object) The atoms are equally gaining acceleration, but the atoms are organizing themselves so the object will be compressed, but if the atoms did not interact with each other, the object would be stretched in a frame equal to the original frame before the objects starts moving. This is making these points real:

5. Every point of the rod is instantaneously (or near instantaneously) boosted to a new velocity, all at the same time in the frame where the rod was at rest before the boost. This stretches the rod to a longer proper length.
6. Every point of the rod is instantaneously (or near instantaneously) boosted to a new velocity, all at the same time in the frame where the rod will be at rest after the boost. This compresses the rod to a shorter proper length.

The only difference is that it is looked upon at a different frame of movement.



Anyway, I don't see the reason why the rope is not being snapped.

If one spaceship is being pulled from behind by it's rocked engine, it is contracted, and observed as compressed in a rest frame. But this is only if it is accelerated from one point, or plane of the object. If it was pulled from the front, it would also get a compressed form.
If each atom now were accelerated equally with respect to the REST frame the object would indeed be the SAME size in the rest frame, but larger in the moving frame. (Each atom has a greater distance to each other in the moving frame) This makes it true that if an object were pulled by two or more points of the object, the object would appear larger.

Now, if we see the two spaceships as ONE object, it would be true that the object "stretches". Because both ships are simoultaneously accelerated in the rest frame. As the acceleration continue, the distance in the rest frame will appear un-changed (although each spaceship will look contracted). In the moving frame however, the distance will be enlargened.
The rope that is tied together between these ships (assuming that the ships are accelerating the same direction, but the one slightly ahead of the other, with respect to the direction of acceleration) will be accelerated equally in both front and back in the rest frame. As the distance between the ships remain unchanged in the rest frame, the distances will, as said, increase in the moving frame. The same applies for the rope. It is accelerated at the same time equally in the rest frame, which means it will be larger in the moving frame. (If you apply te atoms interaction with each other, they will make the object stretch, but as acceleration continue, the object will inevitably snap, since the atoms cannot hold the stretching. This will happen at the place where the atoms hold on each other least. (a weak spot in the rope for example)

This explanation is only true if the spaceships are NOT accelerating in a directioin showed here:

"S"=spaceship
"-"=rope
^=direction of acceleration
"_"=empty space(no effect on the situation, only added because of to make the direction sign be in the correct position)

____^____
S---------S

It must be something like this, (actually, anything except the situation above)

"S"=spaceship
"."=rope
"-"=rope
"^"=direction of acceleration
"_"=empty space(no effect on the situation, only added because of to make the direction sign be in the correct position)

______^________
S---...
______ ---...
____________---S


I just want to say, that I have given a lot of thought into this, and find it correct. If you believe I am wrong, please elaborate why. But please make sure which frame I am basing my statements on, before you argument over it...
I am relatively new to the concept of general relativity

 

[nakurusil]

How about gravity, are the atoms not accelerated equally (or nearly equally because of longer distances from back to front of the object to the pulling object) The atoms are equally gaining acceleration, but the atoms are organizing themselves so the object will be compressed, but if the atoms did not interact with each other, the object would be stretched in a frame equal to the original frame before the objects starts moving. This is making these points real:

The only difference is that it is looked upon at a different frame of movement.

Your post is not understandable, are you asking for the GR treatment of the problem instead of the treatment under SR with accelerated motion? Of course we can treat it using GR but the gravitational field difference between the two ends of the rockets is so small that we can neglect it wrt the much higher effect due to the thrust acceleration. Would you care to repost such that your question is more understandable?

 

[disregardthat]

Your post is not understandable, are you asking for the GR treatment of the problem instead of the treatment under SR with accelerated motion? Of course we can treat it using GR but the gravitational field difference between the two ends of the rockets is so small that we can neglect it wrt the much higher effect due to the thrust acceleration. Would you care to repost such that your question is more understandable?

First of all, I have read my post through a couple of times, and find it fairly understandable.

What is the difference between the GR and SR treatment of the problem?

And the gravitational field between the objects ARE so small that they are unmeasurable, I didn't state it were significant factors. I only implied the factor excisted. What I wrote did not have anything directly to do with the spaceship situation. I only stated that this:

Both 5 and 6 are not possible. Forces travel at finite speed (the speed of sound) in rigid materials. This is a pretty slow speed , so you cannot have "instantaneous (or near instantaneous) velocity boost". This is what Born rigidity is all about.

Is incorrect. My upper paragraph which is "translated" under, had only one point, to argument that statement.

OK, I can make it more understandable:

How about gravity, are the atoms not accelerated equally (or nearly equally because of longer distances from back to front of the object to the pulling object) The atoms are equally gaining acceleration, but the atoms are organizing themselves so the object will be compressed, but if the atoms did not interact with each other, the object would be stretched in a frame equal to the original frame before the objects starts moving. This is making these points real:

How about gravity? When gravity are interracting with an object, it pulls every atom at the SAME rate. (if we overlook the insignificant difference in the gravity field) In practice, the force between the atoms will make them stay at their normal places. (as if you stretched a string, it wants to go back to normal size, because of the atom interraction, it does not wish to stay stretched (This got nothing to do with the spaceship situation!) ).
So during the acceleration of gravity, the atoms will organaize so it will behave like it was pushed from one point of the object, as it reaches a high velocity(in rest frame!(it will stay the same size in the moving frame)). But that is not the point here. The point is that an object can indeed be accelerated at the same rate for each atom.

Bottom line: In a gravitational pull, the object is not pushed from behind, or pulled at the back, each atom is taking effect directly from the gravitational force. As the distance between them in the objects frame, the atoms will automatically interact with each other, and making the distance between each other, normal for their frame. (If atoms had no force in between themselves, the object would in the objects frame be stretched, and each atom would be further and further away from their neighbour atoms)

 

[nakurusil]

OK, I can make it more understandable:


How about gravity? When gravity are interracting with an object, it pulls every atom at the SAME rate.

Gravity is a force like any other force. It propagates at FINITE speed in VACUUM (c). Inside a body it will propagate at the much lower speed of sound. So, you are wrong, it will not propagate thru a body instantaneously. Therefore, the effect of gravitational force on the two rockets on the acceleration will be very similar (albeit much weaker) than the force due to engine thrust. To recap:

1. The rear of the rocket(s) reaches a higher speed than the front of the rockets during the acceleration phase.

2. Because of that, the rod beween rockets gets stretched.

3. The above is not a kinematic effect, cannot be treated as "length contraction" , either in SR or in LET.

So during the acceleration of gravity, the atoms will organaize so it will behave like it was pushed from one point of the object, as it reaches a high velocity(in rest frame!(it will stay the same size in the moving frame)).

You are trying to treat the problem as a kinematic problem,as frame-dependent "length contraction" , this is wrong, see points 1-3 above.

But that is not the point here. The point is that an object can indeed be accelerated at the same rate for each atom.

I suggest that you read on "Born rigidity" before making such claims. Because your claims are wrong.

 

[disregardthat]

Gravity is a force like any other force. It propagates at FINITE speed in VACUUM (c). Inside a body it will propagate at the much lower speed of sound. So, you are wrong, it will not propagate thru a body instantaneously.

Did I use the word instantaneously? If I did, I deeply regret it, because it was not what I meant. On the other hand, THAT was not my point at ALL. I think you search for a single thing that is insigninficantly incorrect, and then point it out, and make it sound like everything is wrong. The acutal point was that each atom interract with the gravitational pull, and not just the end of the object, making it push the rest of it with it. (that makes point 5. and 6. correct, which was my main intention. I didn't question wether the gravitational waves had a finite speed or not...

Therefore, the effect of gravitational force on the two rockets on the acceleration will be very similar (albeit much weaker) than the force due to engine thrust. To recap:

Again, my text about gravity had no link to the paradox stated.

1. The rear of the rocket(s) reaches a higher speed than the front of the rockets during the acceleration phase.
[/quote] Well, if the object fell long enough, this diference would be irrelevant.

2. Because of that, the rod beween rockets gets stretched.

3. The above is not a kinematic effect, cannot be treated as "length contraction" , either in SR or in LET.

Why is that, I have been told that gravitational movement is the same as movement by push and pull, just that the force is excerted at each atom, rather than on a point of the object.

You are trying to treat the problem as a kinematic problem,as frame-dependent "length contraction" , this is wrong, see points 1-3 above.





I suggest that you read on "Born rigidity" before making such claims. Because your claims are wrong.

If I got you correctly, the rigidy has insignificant meaning here. The atoms may use some time to reorganize, but this will happen constantly throughout acceleration. You might have misunderstood my meaning.

 

[nakurusil]

If I got you correctly, the rigidy has insignificant meaning here. .

You got it exactly backwards.

 

[complexPHILOSOPHY]

http://www.nizkor.org/features/fallacies/

Read through this site and learn all of the axioms of logic and their fallicious counter-parts. This way, the debate can be more structured and you can easily identify the logical constructions and postulates that are being posited.

 

[disregardthat]

You got it exactly backwards.

And why is that? What does rigidy excactly have to do with the pull of gravity?
I did say that the object IS observed smaller in a rest-frame when it is pulled by gravity. When I said that it wouldn't, that was under the circumstances of no interaction between the atoms.

I believe that we just misunderstand each other...

Anyway, the gravity points has nothing to do with the main point of this thread...

EDIT: Ok, even though I do not understand your point, let's just let it go...
The thread was about the stated paradox...

 

[Fredrik]

Sounds like an attempt to justify why you got the solution wrong at post #1

No, not at all. I tried to help you see your own mistakes. Look at your initial post and at your persistence that all atoms in a rigid object can be accelerated in sync.

I didn't get #1 wrong, and what I said about the items 5 and 6 that I added to Ich's list has nothing to do with post #1.

And what's up with that "...all atoms in a rigid object..." comment?! I never said anything like that! So don't say that I did.

 

[nakurusil]

I didn't get #1 wrong, and what I said about the items 5 and 6 that I added to Ich's list has nothing to do with post #1.

And what's up with that "...all atoms in a rigid object..." comment?! I never said anything like that! So don't say that I did.

This problem is ridiculously simple. The condition that the spaceships experience the same acceleration implies that their world lines will have the same shape. (The acceleration doesn't have to be constant. It's sufficient that both spaceships accelerate the same way). This implies that the length of the rope will remain constant in the launcher's frame.After a while, the rope is moving at a high velocity in the launcher's frame, and must therefore be Lorentz contracted, but it's still the same length! That means that it must have been stretched.

Ummm, no, nothing to do with "Lorentz length contraction", sorry.This is not a kinematics problem, this is why I tried (and unfortunately failed) to explain it to you from the point of view of dynamics. If you still don't get it after all the explanations, there is nothing that I can do for you.

 

[Chris Hillman]

I really hope this not yet another troll...

Fredrik asked about Link to the article. I am no longer participating in Wikepedia, but I was principle author of a previous version (see http://en.wikipedia.org/wiki/User:Hillman/Archive) . The reason for the flags is that this article has been the subject of a long running "edit war" between members of WikiProject Physics (a group of Ph.D. physicists and mathematicians to which I formerly belonged) and a single crank who asserts, in the face of all proof to the contrary, that the mainstream analysis is wrong.

Perhaps one of you can explain this to me.

My horrible experience with the article in question was responsible for my abandoning my attempts to add content to the Wikipedia; thereafter I stayed on for a few months to trying to help formulate proposed policy reforms aimed at streamlining cruft eradication and so on, but harrassment from embittered cranks led me to abandon this effort as well. So it should not be necessary for me to explain why I decline to discuss this matter further.

Anyone interested in the actual physics/math is urged to consult my last version (see the link in my archive page to a quartet of closely related articles I wrote on the Bell and Ehrenfest "pardoxes" plus the Rindler and Born coordinates) and then to study the papers cited in these articles, then the papers cited in the review paper by Gron, and so on. A related webpage by Greg Egan (see gregegan.customer.netspace.net.au/SCIENCE/Rindler/RindlerHorizon.html) is also well worth reading. It is sad that this lovely subject has been permanently spoiled for me by my awful experience at Wikipedia.

 

[Fredrik]

Ummm, no, nothing to do with "Lorentz length contraction", sorry.This is not a kinematics problem, this is why I tried (and unfortunately failed) to explain it to you from the point of view of dynamics. If you still don't get it after all the explanations, there is nothing that I can do for you.

What are you talking about? You haven't tried to explain anything to me except the trivial and irrelevant fact that 5 and 6 are practically impossible. (It's trivial in the sense that any moron understands it, and it's irrelevant because it's what's possible in principle that's interesting in a discussion about a theory). You have however invented opinions for me that I don't have, and falsely claimed that I'm wrong about more important things (post #1) without providing a shred of evidence, or anything that resembles an explanation.

 

[Fredrik]

Thank you Chris and Pervect for your answers. They are both interesting.

However, I noticed that neither of you answered the question about what kind of objections have been presented against the obvious conclusion. Do they claim a) that GR is needed since acceleration is involved, b) that SR somehow implies that the rope will not break even though it's getting stretched, or c) some other kind of crank nonsense?

 

[nakurusil]

Thank you Chris and Pervect for your answers. They are both interesting.

However, I noticed that neither of you answered the question about what kind of objections have been presented against the obvious conclusion. Do they claim a) that GR is needed since acceleration is involved,

No, SR handles accelerated motion, you need to understand hyperbolic motion.

b) that SR somehow implies that the rope will not break even though it's getting stretched,

No again, you need to understand that forces applied to an object propagate at finite speed (speed of sound). This is why, when you couple SR hyperbolic motion with Born rigidity you get the CORRECT explanation of the problem . I gave it to you three times, here it is one more time:

1. The rear of the rocket (where the motor is) reaches the cruising speed v BEFORE the front of the rocket (due to ...Born rigidity)

2. Therefore the rear of the leading rocket reaches the cruising speed v BEFORE the front of the trailing rocket.

3. Therefore the rod connecting the rear of the front rocket and the front of the rear rocket stretches

4. All of the above has NOTHING to do with Lorentz contraction, contrary to your repeated claims.

5. All of the above shows that your claims 5-6 are physically impossible, contrary to your insistance to the contrary. You cannot "accelerate all the points in a real rigid object simultaneously" Born rigidity theory precludes this from happening.

 

[nakurusil]

I didn't get #1 wrong, and what I said about the items 5 and 6 that I added to Ich's list has nothing to do with post #1.

And what's up with that "...all atoms in a rigid object..." comment?! I never said anything like that! So don't say that I did.

Why don't you re-read your post #8?

5. Every point of the rod is instantaneously (or near instantaneously) boosted to a new velocity, all at the same time in the frame where the rod was at rest before the boost. This stretches the rod to a longer proper length.
6. Every point of the rod is instantaneously (or near instantaneously) boosted to a new velocity, all at the same time in the frame where the rod will be at rest after the boost. This compresses the rod to a shorter proper length.

The situations that you list are unphysical, they violate the way forces propagate in a solid.

 

[yogi]

For any of you that have a copy of the 2nd addition of Spacetime physics, you can see the problem and its explanation on pages 117 - 119. The authority embraces the solution championed by Nakurusil (also Hillman and pervect)

 

[nakurusil]

For any of you that have a copy of the 2nd addition of Spacetime physics, you can see the problem and its explanation on pages 117 - 119. The authority embraces the solution championed by Nakurusil (also Hillman and pervect)

Thank you!

 

[pervect]

Thank you Chris and Pervect for your answers. They are both interesting.

However, I noticed that neither of you answered the question about what kind of objections have been presented against the obvious conclusion. Do they claim a) that GR is needed since acceleration is involved, b) that SR somehow implies that the rope will not break even though it's getting stretched, or c) some other kind of crank nonsense?

I'd say that c) is the closest answer. If you're really curious, check out the talk page, and wade through it:

http://en.wikipedia.org/wiki/Talk:Bell's_spaceship_paradox

I'm not really interested in rehashing these old arguments, and I think Chris is even less interested than I am - I wouldn't be surprised Chris would rather have a root canal without any anesthetic than rehash this again.

So let's forget about those old arguments as a whole (if you bother to read the talk page, and have some SPECIFIC question you want answered, go ahead and ask it though).

But, since there appears to be some interest, let's wipe the slate clean and start some new discussion, hopefully one that is more sensible and even-handed.

I think a lot of the underlying dispute is over distance measures. It seems that everyone has their own ideas on this topic, even excluding the cranks, and that even in the literature we don't see complete unanimity. For instance, their is a paper by Demystifier that talks about these issues that was discussed recently. I like my approach better than his, though :-). While my approach isn't published in any specific papers that I'm aware of, it's inspired by several common textbooks (specifically Wald and MTW).

With these caveats about a lack of complete unanimity in mind, the way I would describe the usual definition of distance would go like this. First, one needs to perform a global 3+1 split of space-time, by assigning every event in space-time a time coordinate. This can be done in many different ways. In the context of special relativity, every inertial frame of reference will have it's own 3+1 split. If two inertial observers in a flat Minkowski space-time are moving with respect to each other, they will assign different events as being simultaneous, generating a different space-time split. Only if two observers are stationary with respect to each other will they arrive at the same space-time split.

There are even more ways to perform a global 3+1 split in GR. The very first thing one must realize is that every different 3+1 split generates a different distance measure.

Given that one has this global 3+1 split, the mathematical process of defining a distance measure then becomes reasonably straightforward. Given this split, one defines a 3-d hypersurface of simultaneity as the set of points sharing the same time coordinate.

The 4-d metric, the invariant "Lorentz interval" will "induce" a 3-d spatial metric on every hypersurface of simultaneity. Any two nearby points on the 3-d hypersurface will have a space-like separation. The value of this space-like separation is just the space-like Lorentz interval between these points calculated via the 4-d metric, or physically by the Lorentz interval, which is an observer independent invariant that does not depend on any choice of coordinates.

Thus, given a global 3+1 split, we can use the Lorentz interval between nearby points to calculate the "induced" metric on the hypersurface, in terms of any convenient spatial coordinates we like.

This gives us a reasonably unambiguous notion of distance between two nearby points at any given "time", where "time" is the global time coordinate that we assigned to every event.

The process of defining a distance between two far-away points is slightly more complex. To define the distance between two far-away points, one must specify a specific curve connecting them. The length of this curve can be calculated by calculating the distance between each pair of nearby points on the curve (as above) and adding them together, i.e. via an integral.

The usual curve chosen is one which lies entirely in one particular hypersurface of simultaneity defined by the global 3+1 split, and it is a geodesic on that hypersurface - i.e. the curve generally comprises the set of points that gives the "shortest distance" between two points when the connecting curve is constrained to lie entirely within the hypersurface of simultaneity.

Here is where one must pay close attention, to make sure that this is indeed the curve being used to compute the distance by any particular author. It seems like the "obvious" choice, at least to me, but sometimes people (for whatever reason) don't make this "obvious" choice. So beware when you read a paper.

In curved geometries, you may have to worry about the fact that there can in general be more than one geodesic between any two points. For instance, on the surface of the Earth at the equator, is that coffee cup 1 meter to your west, or 40075159 meters to the east :-).

OK, this was the general approach. Now let's go to specifics. If we have an accelerated point-like observer, I suggest from my general analysis above that we have to first define some notion of simultaneity in order to be able to define distances. How do we do this? While there are many possible choices, one of the most common choices is to chose at any given instant, the notion of simultaneity of an instantaneously co-moving inertial observer as the appropriate notion of simultaneity for the global time coordinate 't'. This choice, when elaborated, ultimately winds up with the usual "Rindler" coordinates for an accelerated observer.

 

[quantum123]

I find it strange that problems can be classified as SR or GR.
Doesn't GR => SR?
If SR deals only with uniform velocity and GR deals with gravity, then acceleration in SR would be some intermediate form, which I suspect even Einstein used to arrive inductively at GR.

 

[yogi]

Quantum 123: In its initial inception, Einstein considered only Inertial motion. But the Lorentz transforms can be used to evaluate the time lost by objects which undergo acceleration so long as we take the view of the inertial unaccelerated observer. 13 years after Einstein published "On the Electrodynamics of Moving Bodies" he authored a paper explaining the twin's aging differential as consequent to an effective pseudo G field. As it turns out, most present authors take the position that, properly interpreted, SR is fully adequate to predict the correct results. While both theories give the exact same numerical results, the underlying physical causes "appear" to be different. Some have interpreted this as indicative of a deeper unity

 

[Fredrik]

OK Nakurusil, now you have proven that you're just a troll. No one could possibly have that poor reading comprehension. I don't know why I even bother to answer your increasingly absurd statements. This will probably be the last time.

No, SR handles accelerated motion...

No again, you need to understand that forces applied to an object propagate at finite speed (speed of sound).

I was asking Chris and Pervect what the cranks think are valid reasons to disagree with the physicists. Why do you pretend that I have made these objections? Seriously, what's wrong with you?

I gave it to you three times, here it is one more time:

The previous stuff proves that you're a troll. This claim proves that you're also a liar. We have not discussed the details of the spaceship scenario before. This is the first time you've made a post answering me, that makes any attempt to discuss the details.

It seems that your attempt to explain what happens in the spaceship scenario is meant to be serious though, so I will answer that as if we're actually having a discussion.

One thing you need to realize is that no one has said anything about the spaceships being "Born rigid", or in fact anything at all about the details about the spaceships. In the absence of such specifications, it is natural to treat them as point particles. If you are uncomfortable with this, then at least try to imagine the rope (or whatever) being attached to the same point on the two identical spaceships. Then it doesn't matter if the ships are Born rigid or not.

The rope will get Lorentz contracted in the launcher's frame, because its speed is changing! Its length in that frame will remain unchanged however, because the world lines of the two attachment points are identical except for their starting points in space. This means that the rope is being forcefully stretched to a proper length that when Lorentz contracted is equal to the original proper length. That's why the rope must break.

As for some of your specific claims...

1. The rear of the rocket (where the motor is) reaches the cruising speed v BEFORE the front of the rocket (due to ...Born rigidity)

If we assume that the rockets are Born rigid (and a real rocket would be, since the acceleration would not be so high that the speed has changed significantly in the time it takes a sound wave to propagate from one end of the rocket to another), then yes, this is true. However, we're talking about an extremely short time.

2. Therefore the rear of the leading rocket reaches the cruising speed v BEFORE the front of the trailing rocket.

3. Therefore the rod connecting the rear of the front rocket and the front of the rear rocket stretches

That would be part of the reason, in your version of the spaceship scenario, but if you're going to use 2 to motivate 3, then you should have mentioned that 2 also holds for any intermediate velocity u<v.

However, your 3 isn't the only reason the rope/rod/string stretches. The space between the rockets has stretched as well, and that's what this problem is really about. (If your 3 is the only reason the rope stretches in your version of the spaceship scenario, then the rope wouldn't stretch in everyone else's version of it. Everyone else thinks of the rope as being attached to the same point on both rockets, remember).

This is one thing you've missed: In the launcher's frame both rockets always have the same velocity. But in an inertial frame that's co-moving with the rocket in front, the trailing rocket will have a lower velocity during the acceleration. And if the rockets turn off their engines after a certain proper time T, the rocket in front is turning off its engine before the rocket behind it, in the co-moving frame. At this time (still in the co-moving frame), the rocket in front has reached its "cruising speed", but the rocket behind still hasn't.

4. All of the above has NOTHING to do with Lorentz contraction, contrary to your repeated claims.

That's where you're wrong. You're making a major blunder here. This has everything to do with Lorentz contraction. In fact, this is Lorentz contraction. Born rigidity was invented as a way to approximate how actual physical objects become Lorentz contracted. You have obviously completely misunderstood that.

5. All of the above shows that your claims 5-6 are physically impossible, contrary to your insistance to the contrary. You cannot "accelerate all the points in a real rigid object simultaneously" Born rigidity theory precludes this from happening.

Now you're really being a troll again. And you're wrong. What you call "all of the above" has nothing to do with my 5 and 6. And I've told you repeatedly that both 5 and 6 would require a simultaneous push to every single part of the object, something that's possible in principle. You don't seem to understand what "in principle" means, so maybe you should look it up or something.

Why don't you re-read your post #8?

No, you need to read it again, and then read the specific piece of criticism you made that started this part of the "discussion". You claimed that I had claimed that the objects in those idealized situations are rigid! I said no such thing! In fact I said the exact opposite.

 

[Fredrik]

I find it strange that problems can be classified as SR or GR.
Doesn't GR => SR?

The relationship between SR and GR is that you can obtain SR from GR by postulating that there is no matter or energy at all, anywhere in the universe. The only solution of Einstein's equation (the fundamental equation of GR) that satisfies these conditions is Minkowski space, i.e. the flat space-time of SR.

It is possible to deal with accelerated motion entirely in SR, contrary to what some people believe. It's pretty obvious really, if you think about the fact that "accelerated motion" is just a curve through Minkowski space that isn't a straight line.

 

[Fredrik]

I'd say that c) is the closest answer. If you're really curious, check out the talk page, and wade through it:

http://en.wikipedia.org/wiki/Talk:Bell's_spaceship_paradox

OK, thanks. I'll probably read some of it, but there seems to be a lot to read. I totally understand that you and Chris don't want to get into a discussion about "alternative" solutions.

...the way I would describe the usual definition of distance would go like this. First, one needs to perform a global 3+1 split of space-time

You made a very careful and very good explanation. As far as I'm concerned though, you could have saved some time by just saying that you're considering this problem in the context of GR and then skipped to this part:

While there are many possible choices, one of the most common choices is to chose at any given instant, the notion of simultaneity of an instantaneously co-moving inertial observer as the appropriate notion of simultaneity for the global time coordinate 't'. This choice, when elaborated, ultimately winds up with the usual "Rindler" coordinates for an accelerated observer.

Everything in between is more or less obvious to a Wald reader. (I'm sure that many others needed to see the details to understand what you were talking about though).

I have to admit that I hadn't even thought about this problem in the context of GR until now. I'm going to start now.

One more question though: Is everyone involved, including that Rod Ball character, in agreement about what happens in the context of SR?

 

[Boustrophedon]

No need for complications, just get the fundamentals right first !

I have to say that both Pervect and Chris Hillman are quite wrong. To show this (yet another) way, consider the following scenario...

The spaceships/string combination remains at first unlaunched while an observer accelerates up to constant velocity v in some extra 'mother ship'. From here the spaceships will appear closer by the Lorentz factor, gamma, with the string equally so, i.e.still taut.

Next launch the spaceships so as to accelerate up to join the 'mother ship' at constant v. According to incorrect Bell-type reasoning the ships will maintain constant distance, i.e. L/gamma, as they speed up to join the mother-ship but the string will un-contract back to original length L.

Now start again but reverse the launch order so that the spaceships/string first speeds up to v, where again we are supposed to believe that the string this time snaps under contraction ( let's say it's trailing end detaches from the rear ship ) while the spaceship distance stays constant. When the mother ship now accelerates up to join them at velocity v the string will regain it's original length L, but the spaceship distance will increase to gamma*L.

So taking the whole thing from the point of view of the mother-ship observer, in both cases they end up together again at the same velocity v, having accelerated identically in each case. However depending on which went first and which followed later, we get two completely different and contradictory conclusions. In one the spaceships are closer together than the string length by gamma and in the other they are further apart than the string length by gamma !

As I said before, "physical shrinkage" type contraction (as proposed by Fitzgerald & Lorentz) is outmoded by a century and plays no part in special relativity.

 

[Fredrik]

Boustrophedon, your explanation is hard to follow because it's often difficult to understand what frame you're using. Anyway, it certainly doesn't matter if the mother ship is brought to speed v before or after the other two ships.

Suppose the distance between the spaceships in the launcher's frame before they start is K. (I'm defining my own variable since I don't know what frame you used to define your L). This is what happens:

The distance between the ships will be constant (=K) in the launcher's frame, but not in the mother ship's frame. In the mother ship's frame, the distance will grow from K to gamma*K. That's why the string must break. If it breaks by detaching itself from the trailing ship at the beginning of the acceleration phase, then its length in the launcher's frame will change from K to K/gamma. In the mother ship's frame, its length will change from K/gamma to K. This is just Lorentz contraction.

Where exactly do you see a contradiction?

By the way, this is SR. It has nothing to do with the pre-SR theory that you keep mentioning.

 

[disregardthat]

Nakurusil, as far as I know, you have only discussed wether gravity happens instantly or not. That has nothing to do with this paradox.

If you think of that the spaceships are accelerated simultanously in the rest-frame, they would NOT be accelerated simultanously in the the frame of the point when they turn of their motors. In this frame, the front ship accelerates BEFORE the back ship, and this just states that the length between the ships have grown. MEaning the rope will get stretched, and snap.

 

[nakurusil]

<personal attack and ranting snipped as irrelevant to the subject>

It seems that your attempt to explain what happens in the spaceship scenario is meant to be serious though, so I will answer that as if we're actually having a discussion.

One thing you need to realize is that no one has said anything about the spaceships being "Born rigid", or in fact anything at all about the details about the spaceships.

But :

1. The ships are NOT point particles, they have dimensions
2. Born rigidity is germaine to the problem, I tried (and obviously failed) to explain to youhow it intervenes in stretching the rod.
3. Born rigidity is germaine in refuting your claims 5 and 6 as unphysical. This is how our little discussion started, with your insistance that scenarios 5 and 6 are possible. I proved you wrong but you wouldn't listen.

In the absence of such specifications, it is natural to treat them as point particles. If you are uncomfortable with this, then at least try to imagine the rope (or whatever) being attached to the same point on the two identical spaceships. Then it doesn't matter if the ships are Born rigid or not.

But the rope is not attached to the SAME point of both ships. It is attached to the front of the rear ship and to the tail of the leading ship. So you need to take Born rigidity into consideration. You are still trying to cover up for the nonsense in your claims 5 and 6.

The rope will get Lorentz contracted in the launcher's frame, because its speed is changing!
Its length in that frame will remain unchanged however, because the world lines of the two attachment points are identical except for their starting points in space. This means that the rope is being forcefully stretched to a proper length that when Lorentz contracted is equal to the original proper length. That's why the rope must break.

The correct solution to this problem has nothing to do with Lorentz contraction (even in the absence of the Born rigidity issue). It has to do with the fact that a line of simulataneity intercepts the two spacetime trajectories at a REAL (as opposed to apparent) distance that is LARGER than the length of the rod. This is your second misconception that I tried to correct but you are too stubborn to get it. It is really very simple, if you look at the wiki picture.

As for some of your specific claims...

If we assume that the rockets are Born rigid (and a real rocket would be, since the acceleration would not be so high that the speed has changed significantly in the time it takes a sound wave to propagate from one end of the rocket to another), then yes, this is true. However, we're talking about an extremely short time.

Seems that you took some time to read on Born rigidity, this is good. Now you can hopefully understand that claims 5-6 are incorrect.
What do you mean by However, we're talking about an extremely short time.? Can you quantify it? Because I can show you , mathematically, not with armwaving, how ANY amount of time taken into accelerating the ships contributes to stretching the rope. Actually, it can ve argued that the disparity in propagating the thrust forces between the rear of leading rocket and the front of the other contribute MORE to the rope stretching than the relativity of simultaneity discussed above.

That would be part of the reason, in your version of the spaceship scenario, but if you're going to use 2 to motivate 3, then you should have mentioned that 2 also holds for any intermediate velocity u<v.

However, your 3 isn't the only reason the rope/rod/string stretches. The space between the rockets have stretched as well, and that's what this problem is really about. (If your 3 is the only reason the rope stretches in your version of the spaceship scenario, then the rope wouldn't stretch in everyone else's version of it. Everyone else thinks of the rope as being attached to the same point on both rockets, remember).

I was tempted to say : "who is the troll here?". My very first post was a refutation of your claims 5 and 6 as unphysical because they contradict Born rigidity. Of course I am aware that the stretching is a superposition of BOTH relativity of simultaneity (nothing to do with any length contraction, buster) AND Born rigidity. I have shown you that you cannot ignore BORN rigidity, that's all.

This is one thing you've missed: In the launcher's frame both rockets always have the same velocity.

Not at all, I've been telling you that this is not true: during the acceleration period the rear of the leading rocket is FASTER than the front of the trailing rocket. So, do you understand Born rigidity or not? I am still not sure.

But in an inertial frame that's co-moving with the rocket in front, the trailing rocket will have a lower velocity during the acceleration.

See above, for a the complete and correct explanation.

And if the rockets turn off their engines after a certain proper time T, the rocket in front is turning off its engine before the rocket behind it,
in the co-moving frame. At this time (still in the co-moving frame), the rocket in front has reached its "cruising speed", but the rocket behind still hasn't.

Hmm, this "turning off its engine before" is a function of the way the two rockets clocks are synchronised, iyou surely knew that. If they use a light signal coming from the ground, as in the wiki example, the light signal will hit the more proximate rocket (the "rocket behind" in your text) BEFORE it hits the leading rocket, so the trailing rocket will turn off its engine BEFORE the leading rocket, further stretching the rope. So , it appears that you got it backwards.

But what is the relevance to all this in light of my refutation of your claims 5 and 6?

That's where you're wrong. You're making a major blunder here. This has everything to do with Lorentz contraction. In fact, this is Lorentz contraction. Born rigidity was invented as a way to approximate how actual physical objects become Lorentz contracted. You have obviously completely misunderstood that.

Looks like you may have made the error, see the paragraph above.

Now you're really being a troll again. And you're wrong. What you call "all of the above" has nothing to do with my 5 and 6. And I've told you repeatedly that both 5 and 6 would require a simultaneous push to every single part of the object, something that's possible in principle. You don't seem to understand what "in principle" means, so maybe you should look it up or something.

No need for personal attacks. If pigs had wings, they would fly. Born rigidity says exactly the opposite, that what you are claiming in principle, is NOT possible. IN REALITY. This IS the main disagreement between us.

No, you need to read it again, and then read the specific piece of criticism you made that started this part of the "discussion". You claimed that I had claimed that the objects in those idealized situations are rigid! I said no such thing! In fact I said the exact opposite.

Still trying to justify 5 and 6?

 

[Boustrophedon]

It doesn't matter what frame you use - I made it clear that for simplicity I used the mother-ship frame throughout. If the mother-ship takes off first to reach constant v the spaceship distance and the string length will both then be L/gamma. Then the spaceships take off to eventually join the mother ship at same velocity, during which Bell's reasoning would have the string un-contract to L while the spaceships stay L/gamma apart.

Now simply consider the same scenario again only in reverse order: The spaceships take off first and remain at constant distance L from the (unlaunched) mother-ship while the string a la Bell shrinks to L/gamma.
Now when the mother-ship speeds up to join the spaceships/string at the same constant v, the string will un-contract to L and the spaceship distance increase from L to gamma*L.

Thus we have arrived at a contradiction. The same situation ( s'ships, string & mothership back at rest w.r.t. each other ) is obtained by exactly the same acceleration processes but gives totally different comparisons depending on which order they went in. The first case ends with spaceships L/gamma apart while in the second they are gamma*L apart.

 

[quantum123]

Why must the rod obey Born rigidity? Is it just an assumption of a special case?

 

[nakurusil]

Why must the rod obey Born rigidity? Is it just an assumption of a special case?

Because all real life objects do. Forces do not propagate instantaneously in rigid or objects. (they obviously do not propagate instantaneously in semi-rigid ones). Another way of looking at this, there is no infinitely rigid material. When one pushes on a rod, the rod acts as a train, it compresses a little (because the cars are connected with spring-like devices). When one pulls a rod, it stretches, exactly like a train. The "locomotive" part gets going earlier in both cases.
Note: not only the rod but also the two rockets in the problem are affected by the Born rigidity. The rockets are NOT points, they have dimensions that need to be accounted for in solving the problem.

 

[Boustrophedon]

What rod ?, what train ?, what cars ? Do try and keep up !

 

[nakurusil]

What rod ?, what train ?, what cars ? Do try and keep up !

quantum123 asked for an explanation of Born rigidity. Do you know what it is and what role it plays in Bell's paradox? No?