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

[Fredrik]

If a lorentz contraction should not apply if the object is not in constant motion, please tell me why.

Lorentz contraction does apply to accelerated objects, but the Lorentz contraction formula won't help you calculate the length of an object in a certain frame if the object is also being stretched or squeezed while it's being accelerated. That's why the concept of "Born rigid acceleration" was invented.

An object is said to be doing Born rigid acceleration if the Lorentz contraction formulas can be used at any time during the acceleration to calculate the distance, in any frame, between any two points on the object.

Edit: [ The last sentence above should have said "any two points that are infinitesimally close to each other". This condition actually implies that e.g. the end points won't be moving at the same velocity, so we can't use the Lorentz contraction formula to calculate the distance between them. ]

That's what's so funny about Nakurusil's claims. He keeps saying that it's "Born rigidity" that shrinks an accelerating rocket, rather than Lorentz contraction, when in fact Born rigidity is just a name for a mathematical idealization of how solid objects get Lorentz contracted. It's extra funny since he's also rejecting mathematical idealizations.

 

[nakurusil]

Wow, it must have been like your birthday when you got a chance to quote one of my posts in its entirety before it was finished.

You still got it wrong. My solution is more general than the one you linked to. There's no need to postulate that the acceleration is constant, so I haven't used that detail.

Umm, no. You insist on using Lorentz transforms and length contraction.The Lorentz transforms are linear, the transforms that you need to use (if you read the reference I gave you) are hyperbolic (on linear). If you apply the correct mathyou will get the correct results.If you insist in applying the incorrect math , you will continue to get the incorrect results. The Lorentz transforms don't work with accelerated motion (contrary to your insitance), don't they teach that in Sweden? I think they do teach it but you must have missed the class.

 

[MeJennifer]

They don't work with accelerated motion, don't they teach that in Sweden? I think they do teach it but you must have missed the class.

This "Lorentz transformations don't work with accelerated motion" matra that you are proclaiming here is getting a bit old.

Perhaps it is time for you to explain what exactly does not work and why instead of insulting everybody here.

 

[nakurusil]

Lorentz contraction does apply to accelerated objects, but the Lorentz contraction formula won't help you calculate the length of an object in a certain frame if the object is also being stretched or squeezed while it's being accelerated. That's why the concept of "Born rigid acceleration" was invented.

An object is said to be doing Born rigid acceleration if the Lorentz contraction formulas can be used at any time during the acceleration to calculate the distance, in any frame, between any two points on the object.

That's what's so funny about Nakurusil's claims. He keeps saying that it's "Born rigidity" that shrinks an accelerating rocket, rather than Lorentz contraction, when in fact Born rigidity is just a name for a mathematical idealization of how solid objects get Lorentz contracted. It's extra funny since he's also rejecting mathematical idealizations.

You are mixing up two of my criticisms of your approach:

1. Your claims 5,6 that are in violation of Born rigid motion (looks like you read a lot on it in the last two days, this is good) as applied to calculating the the SPEED of individual parts as the rear and the front of a SINGLE rocket.

2. The fact that you cannot use the Lorentz transforms in order to calculate the SEPARATION distance between TWO rockets in ACCELERATED motion.

Try getting your facts straight, will you?

 

[nakurusil]

This "Lorentz transformations don't work with accelerated motion" matra that you are proclaiming here is getting a bit old.

Perhaps it is time for you to explain what exactly does not work and why instead of insulting everybody here.

I'm not insulting anybody. I explained this issue several times, go back and re-read my posts. You can also read the refence to the appropriate treatment of accelerated motion I gave Fredrick a few posts back.Here is another one, specially for you:
http://www.arxiv.org/PS_cache/physics/pdf/0405/0405038.pdf

 

[Fredrik]

You are mixing up two of my criticisms of your approach:

1. Your claims 5,6 that are in violation of Born rigid motion (looks like you read a lot on it in the last two days, this is good) as applied to calculating the the SPEED of individual parts as the rear and the front of a SINGLE rocket.

2. The fact that you cannot use the Lorentz transforms in order to calculate the SEPARATION distance between TWO rockets in ACCELERATED motion.

Try getting your facts straight, will you?

1. That's still not relevant, because 5 and 6 have nothing to do with the subject of this thread. And as I said before, I understood Born rigidity very well before I started this thread.

2. I'm not calculating any distances in an accelerated frame. I'm using inertial frames. (In my version of the problem the rockets have turned off their engines and are moving at constant velocity at the events where I do the calculation, but that's actually irrelevant. If they had been accelerating, I could have used a co-moving inertial frame).

I will explain to you one last time why my 5 and 6 (i.e. post #8) are valid. That post was a digression from the main topic of this thread. We were talking about SR in general, and not specifically about the spaceship problem. 5 and 6 deserve to be on that list because they are verbal descriptions of a set of curves in Minkowski space. That makes them valid. SR is the claim that space and time can be represented by Minkowski space, so 5 and 6 are definitely allowed by the rules of SR. They also have a pedagogical value, as I have explained before. They do not however have anything at all to do with the subject of this thread, so you can't "prove me wrong" by explaining that they are impossible in the real world, or that they don't help us solve the spaceship problem. We weren't talking about the real world, or about the spaceship problem. We were talking about SR.

 

[nakurusil]

1. That's still not relevant, because 5 and 6 have nothing to do with the subject of this thread. And as I said before, I understood Born rigidity very well before I started this thread.

2. I'm not calculating any distances in an accelerated frame. I'm using inertial frames. (In my version of the problem the rockets have turned off their engines and are moving at constant velocity at the events where I do the calculation, but that's actually irrelevant. If they had been accelerating, I could have used a co-moving inertial frame).

The string(rod) gets stretched starting from from time 0, doesn't it? Not only after the acceleration has stopped. If you want to compute the string
stretching during the acceleration phase you cannot use Lorentz transforms.OK?

If you are simply trying to calculate the rocket separation AFTER the engines have shut off, then you are making up your own, simplified problem. The string may have long snapped during the acceleration phase. Read the reference I gave you, would you?

I will explain to you one last time why my 5 and 6 (i.e. post #8) are valid. That post was a digression from the main topic of this thread. We were talking about SR in general, and not specifically about the spaceship problem. 5 and 6 deserve to be on that list because they are verbal descriptions of a set of curves in Minkowski space. That makes them valid. SR is the claim that space and time can be represented by Minkowski space, so 5 and 6 are definitely allowed by the rules of SR. They also have a pedagogical value, as I have explained before. They do not however have anything at all to do with the subject of this thread, so you can't "prove me wrong" by explaining that they are impossible in the real world, or that they don't help us solve the spaceship problem. We weren't talking about the real world, or about the spaceship problem. We were talking about SR.

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.

To which I answered that you can't do that to realistic objects (unless you attach a little motor to each atom in the object :-) ) Why do you persist? Why not admit that you were wrong. Especially since you are claiming that you understand Born rigidity?

 

[MeJennifer]

I'm not insulting anybody. I explained this issue several times, go back and re-read my posts. You can also read the refence to the appropriate treatment of accelerated motion I gave Fredrick a few posts back.Here is another one, specially for you:
http://www.arxiv.org/PS_cache/physics/pdf/0405/0405038.pdf

What has a document on the clock paradox to with your statement that Lorentz transformations do not work with accelerated motion?

This is getting ridiculous and is boosted by the fact that you are claiming expertise and making continious denigrating remarks to several members on this forum here without apparently even understanding the basic scope of the Lorentz transformations with regards to boosts, rotations and reflections in flat space-time.

 

[disregardthat]

We don't need to calculate what length the rope would be at every moment, we are merely trying to find proof that the string actually IS stretched when the spaceships are moving.

If you measured the average velocity of the spaceships in acceleration to a specific moment, you could use the lorentz contraction for velocity. This would only give you the amount of contraction at that specific point. But that's all you need. If the velocity faster than at the beginning, the string WILL get stretched.

Nakurusil, if you want a proper discussion, please answer on all the questions and statements stated here. You are not only ignoring the relevant parts of what Fredrik is saying, you are denying small irrelevant parts. That will not make this discussion advance any further.

And stop saying I need to take some classes, I can't, ok? I am only here to try to learn, and discuss and finding the correct answer. And I believe most of us here are...

 

[Fredrik]

The string(rod) gets stretched starting from from time 0, doesn't it? Not only after the acceleration has stopped.
...
If you are simply trying to calculate the rocket separation AFTER the engines have shut off, then you are making up your own, simplified problem. The string may have long snapped during the acceleration phase.

You're missing the point as usual. If the distance between the attachment points in the new inertial frame turns out to be larger than it was from the beginning, the stretching of that distance must have happened during the acceleration. Nothing interesting happens once the ships have turned off their engines, as we can show explicitly.

If you want to compute the string
stretching during the acceleration phase you cannot use Lorentz transforms.OK?

This is actually correct. The point of postulating constant acceleration (which I didn't) is that it makes it possible to explicitly calculate how much the string has stretched in the accelerating frame, at any time. (Edit: Hmm, is this really true? There's an infinite number of accelerating frames here. I'm not even sure if the proper distance is the same in the two frames defined by the attachment points. I need to think about this some more).

When I said that I could have used a co-moving inertial frame, I was actually making a mistake. (Note that I just refuted your claim that I never admit mistakes). It's actually not even obvious from what I wrote that I was making a mistake, so I didn't even have to admit this, but the mistake was to think that it's possible to calculate the proper distance between the attachment points during the acceleration in a co-moving inertial frame. The result of such a calculation would only have been a lower bound on the proper distance. (That's enough to prove that the string breaks of course, but my thoughts about it were still wrong).

To which I answered that you can't do that to realistic objects (unless you attach a little motor to each atom in the object :-) ) Why do you persist? Why not admit that you were wrong. Especially since you are claiming that you understand Born rigidity?

I wasn't wrong, and you know it. That's why this is trolling, and nothing else.

 

[nakurusil]

What has a document on the clock paradox to with your statement that Lorentz transformations do not work with accelerated motion?

This is getting ridiculous and is boosted by the fact that you are claiming expertise and making continious denigrating remarks to several members on this forum here without apparently even understanding the basic scope of the Lorentz transformations with regards to boosts, rotations and reflections in flat space-time.

It gives you the application and the proper formulas of hyperbolic motion. Try learning how to apply them, it solves the Bell paradox in a few lines.

 

[nakurusil]

You're missing the point as usual. If the distance between the attachment points in the new inertial frame turns out to be larger than it was from the beginning, the stretching of that distance must have happened during the acceleration. Nothing interesting happens once the ships have turned off their engines, as we can show explicitly.

Sure, you are making as if I didn't say the same thing. Problem with your derivation is that you are deriving the distance between the ships, during the acceleration phase incorrectly. Your derivation produces the incorrect result.

This is actually correct. The point of postulating constant acceleration (which I didn't) is that it makes it possible to explicitly calculate how much the string has stretched in the accelerating frame, at any time. (Edit: Hmm, is this really true? There's an infinite number of accelerating frames here. I'm not even sure if the proper distance is the same in the two frames defined by the attachment points. I need to think about this some more).

Well, thank you, you are starting to understand.

When I said that I could have used a co-moving inertial frame, I was actually making a mistake. (Note that I just refuted your claim that I never admit mistakes).

Indeed. If you managed to see your mistake in deriving the separation between rockets using Lorentz transforms next...

It's actually not even obvious from what I wrote that I was making a mistake, so I didn't even have to admit this, but the mistake was to think that it's possible to calculate the proper distance between the attachment points during the acceleration in a co-moving inertial frame.

Actually you can. But you need to learn how to use the proper formalisms.

I wasn't wrong, and you know it. That's why this is trolling, and nothing else.

Here you go again. I was thinking about showing you how to do things correctly but now I'll just show you again that you don't have a clue:

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.

 

[nakurusil]

We don't need to calculate what length the rope would be at every moment, we are merely trying to find proof that the string actually IS stretched when the spaceships are moving.

If you measured the average velocity of the spaceships in acceleration to a specific moment, you could use the lorentz contraction for velocity.

Bad idea. The rope doesn't break due to any "lorentz contraction", it breaks due to increased separation between rockets.

 

[Fredrik]

As far as I can tell, by only looking at a few of the external sources, they all seem to be focused on the detail of constant acceleration. There's nothing wrong with that of course. When the acceleration is constant, it's possible to calculate explicitly how much the has string has stretched at the time of any given event on one of the world lines. (In this post, I will sometimes be talking about the string as if it's able to stretch without breaking, and sometimes as if it breaks at the very first moment of stretching. I hope it's obvious what I mean. If it's not, ask). But it's not necessary to calculate this explicitly. All we need to prove is that the string breaks.

Since we don't need to calculate exactly how much the string breaks, we shouldn't have to postulate that the acceleration is constant. We should be able to show that the string breaks no matter how the spaceships accelerate.

There are many different versions of this problem, for example:

a) constant acceleration for ever (this is Bell's original version, I think)
b) arbitrary acceleration until a certain proper time when the engines shut off (my version)
c) arbitrary acceleration (the most general version)

I want to prove that the string breaks in version c). I have already proven that the string breaks in version b), by explicitly calculating the proper length of the string after the engines have been shut off. (See #76 and #88).

I think it's intuitively obvious that if the string breaks in b) it must also break in c), but I'd like to find a rigorous argument.

I think my solution of b) can be used as a starting point. This is the kind of reasoning I have in mind: The proper length doesn't increase once the engines have been turned off, so it must increase during the acceleration phase. This means that the string would also break in c).

I pretty sure this line of reasoning is valid, but as it stands, I don't think it's rigorous enough to prove that the string breaks in c). I'm kind of busy today, so I'm not going to try to work this out now. Maybe I'll try to fill in the missing details tomorrow. If anyone else feels like taking a shot at it in the mean time, go ahead...

 

[cincirob]

The Rope a Rocket Problem

This is an old problem first posed by JS Bell at a gathering of physicists. A number of physicists didn't get the right answer the first time. Because of this anti-relativists have latched onto it as a proof agianst relativity because relativity physicists sometimes disagree.

In any case, the outcome is a little strange. While most (even antirelativists) will agree the rope breaks, looking at the clocks on both ships is a bit confusing.

1. Before they accelerate the clocks on the ships are synchronized.

2. If the two ships stop accelerating at the same instant in the stationary frame, they will be going the same velocity and therefore it is possible to synchronize their clocks.

3. Since the clocks underwent the same process they will read identical times when compared to clocks in the stationary frame.

4. #3 seems problematical because,if the rocke clocks are synchronized, they shoud read differently for the stationary observers; that is, a stationary observer near the rear rocket will read Tr and because the clocks are moving at some v, Tf shoul read Tr-vd/c^2(1-(v/c)^2^-.5.

So it's a bit confusing that the clocks read the same. Lately I have been working on the math to see if I can predict this outcome but I'm not finished yet. You might try it as a challenge.

 

[nakurusil]

The proper length doesn't increase once the engines have been turned off, so it must increase during the acceleration phase. This means that the string would also break in c).

Correct. So if the rope breaks it breaks during the acceleration phase. This is why you must calculate the separation distance between the rockets during the acceleration phase. This is why you must not use Lorentz transforms, they do not apply to accelerated motion.

I pretty sure this line of reasoning is valid, but as it stands, I don't think it's rigorous enough to prove that the string breaks in c).

Correct. Except that your solution does not compute the separation distance between rockets correctly. You should not be using the Lorenz transforms, you schould be using hyperbolic motion. Using Lorentz transforms is akin to using the fact that the sum of the angles is 180 degrees in a planar triangle in order to calculate the third angle of a spherical triangle when you know the first two angles. In both cases there is no justification in blindly appliying a theory derived for one instance to a totally different instance.
By applying the correct theory (hyperbolic motion) you will get the correct answer. An it is not l=l_0\gamma. If you do the calculation correctly you will get a nonlinear expression that depends on acceleration and time.

 

[Fredrik]

I don't have to calculate the separation at all. I just have to show that it increases.

My calculation is exactly right for version b) of the problem, so stop denying that or at least try to prove that you're right. That hyperbolic motion stuff is specifically for version a).

 

[nakurusil]

I don't have to calculate the separation at all. I just have to show that it increases.

Yes, you do have to calculate the separation correctly, ESPECIALLY for "your case" (b) The question that was asked is: "will the rope snap". The rope has some elasticity, so it snaps only if the distance betwen the rockets increases beyond what the rope elasticity can accommodate DURING the acceleration phase. Without a correct calculation of the separation distance betwen the rockets, you cannot find out if the rope snaps. And in "your case" (b), the distance stops increasing after you shut off your engines.

My calculation is exactly right for version b) of the problem, so stop denying that or at least try to prove that you're right. That hyperbolic motion stuff is specifically for version a).

The hyperbolic motion is the rigurous solution for ALL cases.

 

[Fredrik]

Yes, you do have to calculate the separation correctly, ESPECIALLY for "your case" (b) The question that was asked is: "will the rope snap". The rope has some elasticity, so it snaps only if the distance betwen the rockets increases beyond what the rope elasticity can accommodate DURING the acceleration phase. Without a correct calculation of the separation distance betwen the rockets, you cannot find out if the rope snaps. And in "your case" (b), the distance stops increasing after you shut off your engines.

It's hard to tell if you're being serious. The rope will certainly snap if the proper length at any time exceeds the original proper length, and my calculation is more than sufficient to prove that it does in version b).

You're still insinuating that my solution of b) is incorrect. I suggest that you either stop doing that, or prove that you're right.

The hyperbolic motion is the rigurous solution for ALL cases.

Please explain yourself. Hyperbolic motion is constant proper acceleration. So how does a calculation that takes hyperbolic motion as a starting point solve the general case?

 

[ZapperZ]

This thread has gone long enough, and it is going nowhere long enough.

I will point out to everyone involved that to re-read the PF Guidelines that you have agreed to. If you do not think we meant everything we wrote in there, think again.

Consider this as your only warning before more drastic action is taken.

Zz.