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

[nakurusil]

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.

You get a contradiction only if you don't understand the physics at work and you oversimplify the problem as above. There are multiple places where the problem is solved correctly . Try Wheeler and Taylor's Spacetime Physics pages 117-119 (second edition).

 

[Boustrophedon]

Yes and No. Yes I know perfectly well what it is and No it doesn't play any role in Bell's problem.

 

[disregardthat]

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.

Uhm, yes they are. I recommend you read the very paradox before you make your claims.

This is from the Wikipedia artcile Fredrik posted:

"Analysis
In the following analysis we will treat the spaceships as point masses and only consider the length of the string. We will analyze the variant case previously mentioned, where both spaceships shut of their engines after some time period T."

That makes me pretty sure at least THEY treat the spaceships as point masses

Which makes this incorrect:

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.

The correct solution to this problem has nothing to do with Lorentz contraction (even in the absence of the Born rigidity issue).

Do you really know what Lorentz contraction is? After reading your large post, I suspect you confuse contraction with mechanical compression.

--------------------------

I suppose we are only searching for if the string will break, and not if the space between the ships have grown after they shut their engines off. Because the moment they turn it off, depends on which frame you look at it. If they keep accelerating towards infinity, the string will eventually break.

 

[nakurusil]

Yes and No. Yes I know perfectly well what it is and No it doesn't play any role in Bell's problem.

you may want to rethink your second answer

 

[nakurusil]

Uhm, yes they are. I recommend you read the very paradox before you make your claims.

This is from the Wikipedia artcile Fredrik posted:

"Analysis
In the following analysis we will treat the spaceships as point masses and only consider the length of the string. We will analyze the variant case previously mentioned, where both spaceships shut of their engines after some time period T."

That makes me pretty sure at least THEY treat the spaceships as point masses

Can you distinguish between a pedagogical simplification and reality? Of course you do. The ships are NOT point sources. wiki shows a simplified model for the problem. I brought this fact into discussion in order to refute Fredrik's claims 5 and 6 as unphysical. His claims have to do with physical rockets, not point approximations.

BTW: The SR length contraction has nothing to do with this problem. And yes, I understand length contraction.

 

[nakurusil]

I suppose we are only searching for if the string will break, and not if the space between the ships have grown after they shut their engines off.

The way to find that out is by calculating the variation of the distance betwen the two rockets and comparing it to the length of the unstretched string (rod).

Because the moment they turn it off, depends on which frame you look at it. If they keep accelerating towards infinity, the string will eventually break.

Interestingly enough, the string will get stretched even if the two rockets accelerate only for a finite time.

 

[disregardthat]

Can you distinguish between a pedagogical simplification and reality? Of course you do. The ships are NOT point sources. wiki shows a simplified model for the problem. I brought this fact into discussion in order to refute Fredrik's claims 5 and 6 as unphysical. His claims have to do with physical rockets, not point approximations.

Ok, so you mean that in the original situation stated by the article, really mean that the string were attached to different places on each ship? Find evidence first. Here I think we are talking about the article...

And the 5. and 6. point to fredrik has absolutely zero to do with this paradox...

BTW: The SR length contraction has nothing to do with this problem. And yes, I understand length contraction.

this is nonsense, lorentz contraction has everything to do with this! Why would you say otherwise?

Interestingly enough, the string will get stretched even if the two rockets accelerate only for a finite time.

Correct, but since we know nothing of the material the string is made of, we cannot jump to conclusions when the rope will be snapped. It will happen in a finite time, but you cannot know when. That's just the reason I said "If they keep accelerating towards infinity, the string will eventually break.", somewhere along the line the string will snap...

Why are you posting so many posts after another, why not keep it to 1 post each time?

 

[nakurusil]

Ok, so you mean that in the original situation stated by the article, really mean that the string were attached to different places on each ship? Find evidence first. Here I think we are talking about the article...

And the 5. and 6. point to fredrik has absolutely zero to do with this paradox...

You still don't get it. See my first post in this thread.

Why are you posting so many posts after another, why not keep it to 1 post each time?

Because you seem unable to follow really simple stuff, so I matrying to make it easier for you to understand.

 

[nakurusil]

this is nonsense, lorentz contraction has everything to do with this! Why would you say otherwise?

There is a very good, comprehensive treatment of the problem in the external links of the wiki article. On second thoughts, someone should bite the bullet and turn that external link into an article. It shows a much higher level of detail and it includes the Born rigidity treatment as well as the hyperbolic motion. No Lorentz contraction, sorry

 

[disregardthat]

You still don't get it. See my first post in this thread.

Ok, that just shows that aren't listening to what I am saying. I said that: "And the 5. and 6. point to fredrik has absolutely zero to do with this paradox..."
Then you show a link to a post where you explain why these points are unreal. Don't you see why that is no answer? You argument to things i didn't say. That makes it impossible to discuss with you.

There is a very good, comprehensive treatment of the problem in the external links of the wiki article. On second thoughts, someone should bite the bullet and turn that external link into an article. It shows a much higher level of detail and it includes the Born rigidity treatment as well as the hyperbolic motion. No Lorentz contraction, sorry

Uhm, ok. I see we have found the root... So, you believe that there is no lorentz contraction when an object moves at higher velocities? It is contracted! That is what this very paradox is going on about.

From the wiki article:
"According to discussions by Dewan & Beran and also Bell, in the spaceship launcher's reference system the distance between the ships will remain constant while the elastic limit of the string is length contracted, so that at a certain point in time the string should break!"

That shows that contraction is the main part of the paradox...

And this quote from the article should give you proper understanding that it IS really lorentz contraction that is being talked about:

"Finally, we can say that the proper distance between spaceships A and B after the end of the acceleration phase in a comoving frame is equal to the Lorentz length of the line segment A`B``. The line A`B`` is defined to be a line of constant t', where t' is the time coordinate in the comoving frame, a time coordinate which can be computed from the coordinates in frame S via the Lorentz transform:"

Read the article before you come with statements. Because I have seen many of your statements to be wrong. And you don't even answer to your own mistakes. That is also making it very difficult to discuss with you.

 

[Fredrik]

Nakurusil,

Why don't you answer my question about why you pretended that I had made claims in post #31?

Why don't you say anything about the fact that you claimed to have discussed the details of #1 with me before, when in fact you had not?

Why don't you say anything about the fact that you claimed that I had said that the object in #8 is rigid, when in fact I had never done so?

You have no right to whine about "personal attacks" as long as you talk to me as if I have opinions that you know I don't have. If you stop doing that, I won't call you a troll again.

I'm done discussing the "in principle" vs. "in reality" issue with you. I'm just going to tell you that you are going to have a very hard time understanding physics unless you're willing to think about stuff that's only possible in principle.

I see you still claim that Lorentz contraction is irrelevant. I'm going to have to quote Penn Gillette: "You couldn't be more wrong if your name was Wrong Wrongy Wrongenstein". I don't know if I can explain it to you though. It's not that I'm not willing to explain stuff. It's that you don't seem to be able to even consider the possibility that you might be wrong about something.

1. The ships are NOT point particles, they have dimensions

Only in your version of the problem. Look at the space-time diagram in Wikipedia for example. Do you see four world-lines or two? I see two. One for each ship.

2. Born rigidity is germaine to the problem,...

Wrong. It has a small part to play in your version of the problem though.

3. Born rigidity is germaine in refuting your claims 5 and 6 as unphysical.

Wrong. If I had said that the objects in #8 are Born rigid, then you would have had a point, but I clearly said that they are not.

I proved you wrong but you wouldn't listen.

I have no doubt that you will continue to think that's what happened.

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.

Only in your version of this problem. This additional assumption that you introduced is just an irrelevant complication that obscures the real issue. The real issue can be seen by simply considering curves in Minkowski space, and ignoring the spaceships altogether.

You are still trying to cover up for the nonsense in your claims 5 and 6.

BS. I was trying to explain to you what the real issue is in this problem, but you obviously ignored it.

The correct solution to this problem has nothing to do with Lorentz contraction (even in the absence of the Born rigidity issue).

If you think so, then you don't know what Lorentz contraction is.

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 Lorentz contraction!

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.

I understood Born rigidity a lot better than you do now a long time before I wrote #8, and 5-6 are still possible in principle.

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.

Maybe it's not a small amount. I can't see this part as clearly as the rest right now, and I don't think it's relevant enough to be worth spending time on. Anyway we seem to agree about the important details about what happens to your Born rigid spaceships. But all of that stuff is irrelevant to the real problem anyway.

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.

The stuff about the rear moving faster than the front is true, in your version of this problem. My claim that both rockets (not both ends of one rocket) have the same velocity in the launcher's frame is correct in both versions, so I don't know why you think I was contradicting you. But ok, let's rephrase it specifically for your version of the problem: "Consider a specific part of rocket A. In the launcher's frame, at any given time, that part of rocket A has the same velocity as the same part of rocket B".

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.

Light signal from Earth?! Don't bring any more unnecessary complications into this! Just imagine two identical ships controlled by their onboard computers (identical computers, running identical programs). This will guarantee that the two world lines are identical except for their starting position in space. (If the world lines aren't identical, there must be something fundamentally different about the starting positions, and that would contradict SR).

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

I have no idea why you're asking this. I have told you repeatedly that 5 and 6 have absolutely no relevance to the spaceship problem.

 

[Fredrik]

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

The string/rope/rod that connects the spaceships in this problem is not Born rigid. That would contradict the description of the problem.

Because all real life objects do.

This certainly explains a lot. When I was answering you earlier I was thinking "I wonder if he thinks that all objects are Born rigid" and now I know that you do.

First of all, there's no such thing as an object that just is Born rigid. Born rigidity isn't a property of a material, it's a property of the world lines of the different parts of the object.

This is the definition:

An object is said to be going through Born rigid motion if the distance between any two points on the object, as measured by co-moving inertial observers, is constant.

A rubber band that's being pulled in two opposite directions at once certainly isn't Born rigid.

A rocket is approximately Born rigid, but it can't be exactly Born rigid through the entire acceleration phase, since the force that accelerates it is applied only to the rear of the rocket.

 

[Fredrik]

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.

OK, this time I understand you. But the spaceships don't stay L/gamma apart in the mother ship's frame. The distance between them is always L in the launcher's frame, so it can't be a constant in the mother ship's frame. (This is easy to see in the space-time diagram). It will be "uncontracted" from L/gamma to L.

I will stop here. There may be other mistakes in what you said, but I'm not going to look for them, since one mistake is enough to invalidate the conclusion.

 

[nakurusil]

Nakurusil,

Why don't you answer my question about why you pretended that I had made claims in post #31?

Why don't you say anything about the fact that you claimed to have discussed the details of #1 with me before, when in fact you had not?

Why don't you say anything about the fact that you claimed that I had said that the object in #8 is rigid, when in fact I had never done so?

What's your problem? Look at the nonsense you put forward in your claims 5 and 6. I even boldened them for you and you still persist?

You have no right to whine about "personal attacks" as long as you talk to me as if I have opinions that you know I don't have. If you stop doing that, I won't call you a troll again.

You only need to look at the ridiculous claims 5,6.

I'm done discussing the "in principle" vs. "in reality" issue with you. I'm just going to tell you that you are going to have a very hard time understanding physics unless you're willing to think about stuff that's only possible in principle.

So after I called you on the silliness of those two claims you have persistently tried to justify them. They are ridiculous, they contradict physical reality.

I see you still claim that Lorentz contraction is irrelevant.

...for solving this partcular problem, yes.

Wrong. If I had said that the objects in #8 are Born rigid, then you would have had a point, but I clearly said that they are not.

Go back and re-examine your unphysical claims 5 and 6.

Only in your version of this problem. This additional assumption that you introduced is just an irrelevant complication that obscures the real issue. The real issue can be seen by simply considering curves in Minkowski space, and ignoring the spaceships altogether.

Umm, no. There is a comprehensive solution in the "External links" of the wiki page. Read it.

BS. I was trying to explain to you what the real issue is in this problem, but you obviously ignored it.

So , you still think that your claims 5,6 are physical? Once you get exposed, you seem unable to admit error.

If you think so, then you don't know what Lorentz contraction is.
This is Lorentz contraction!

Maybe where you went to school.

I understood Born rigidity a lot better than you do now a long time before I wrote #8, and 5-6 are still possible in principle.

Of course, why admit to error. When caught, do everything possiblle to cover it up, even if you are digging yourself deeper.

Maybe it's not a small amount. I can't see this part as clearly as the rest right now, and I don't think it's relevant enough to be worth spending time on. Anyway we seem to agree about the important details about what happens to your Born rigid spaceships. But all of that stuff is irrelevant to the real problem anyway.

Maybe if you tried to put it in a mathematical form you might get surprised. Try writing down the equations.

The stuff about the rear moving faster than the front is true, in your version of this problem. My claim that both rockets (not both ends of one rocket) have the same velocity in the launcher's frame is correct in both versions, so I don't know why you think I was contradicting you. But ok, let's rephrase it specifically for your version of the problem: "Consider a specific part of rocket A. In the launcher's frame, at any given time, that part of rocket A has the same velocity as the same part of rocket B".

But this is exactly the version that disagrees with your claims 5,6

Light signal from Earth?! Don't bring any more unnecessary complications into this! Just imagine two identical ships controlled by their onboard computers (identical computers, running identical programs). This will guarantee that the two world lines are identical except for their starting position in space.

Umm, no. You can't do that. The two rockets have DIFFERENT speeds , therefore their onboard clocks, computers, oscillators would be DESYNCHRONIZED. You need a common reference. Try googling "Cassini".

(If the world lines aren't identical, there must be something fundamentally different about the starting positions, and that would contradict SR).

Don't you think that the two pilots need a signal to tell them when to shut off the engines? This is exactly what happens in the picture of wiki version, you know, the one that you keep quoting. I pointed that out to you but you snipped it. Whatever you do, don't admit to error. Ever.

I have no idea why you're asking this. I have told you repeatedly that 5 and 6 have absolutely no relevance to the spaceship problem.

5,6 have no relevance whatsoever since they violate physical reality. This was my point all along. Finally we agree on something.

 

[nakurusil]

The string/rope/rod that connects the spaceships in this problem is not Born rigid. That would contradict the description of the problem.


This certainly explains a lot. When I was answering you earlier I was thinking "I wonder if he thinks that all objects are Born rigid" and now I know that you do.

Umm, no. You are twisting my words. I went on to explain that there is no such thing as an ifinitely rigid object, this is why I objected so strongly to your claims 5,6.

A rocket is approximately Born rigid, but it can't be exactly Born rigid through the entire acceleration phase, since the force that accelerates it is applied only to the rear of the rocket.

And this is exactly why I objected repeatedly to 5,6. Finally you caught up on reading on the subject, congratulations.

 

[Fredrik]

OK, that does it. I'm done talking to you Nakurusil. You're a troll. (Definition here).

 

[nakurusil]

OK, that does it. I'm done talking to you Nakurusil. You're a troll. (Definition here).

You insult me because I exposed your erroneous claims and you ran out of logical and pertinent arguments?

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.

...and you would want people to believe that you understand Born's theory of rigidity? Let's be serious.

 

[nakurusil]

OK, this time I understand you. But the spaceships don't stay L/gamma apart in the mother ship's frame. The distance between them is always L in the launcher's frame, so it can't be a constant in the mother ship's frame. (This is easy to see in the space-time diagram). It will be "uncontracted" from L/gamma to L.

I will stop here. There may be other mistakes in what you said, but I'm not going to look for them, since one mistake is enough to invalidate the conclusion.

Lorentz transforms do not apply to accelerated motion. Didn't you know that?
Now I understand your insistance in claiming that "The distance between them is always L in the launcher's frame, so it can't be a constant in the mother ship's frame. (This is easy to see in the space-time diagram). It will be "uncontracted" from L/gamma to L."

You can't simply brute force the problem and apply length contraction, you need to use the equations of hyperbolic motion in order to calculate the proper distance. Didn't you know that? Apparently not.

 

[MeJennifer]

Lorentz transforms do not apply to accelerated motion.

That is incorrect, they apply to all relative motion.
An accelerated user is at rest with a sequence of comoving inertial frames that each have a different relative speed.

 

[nakurusil]

That is incorrect, they apply to all relative motion.
An accelerated user is at rest with a sequence of comoving inertial frames that each have a different relative speed.

Don't think so. Think about how the Lorentz transforms have been derived.
You are talking about the fact that you can apply a sequence of Lorentz transforms over a sequence of infinitesimal changes in speed in order to derive the equations of hyperbolic motion. This doesn't mean that you can replace the equations of hyperbolic motion with a single Lorentz transform. I think that this is what is done on the wiki page of the Bell's paradox and it most probably led to an incorrect solution. All this bickering with Fredrick about his misunderstanding of the Born theory of rigidity may have uncovered something interesting after all.
Either way, the safe way is to use the equations of hyperbolic motion. I don't think that you get the same results using the correct eqiuations (hyperbolic motion) as using the Lorentz transforms. Try it on the wiki solution of the Bell paradox, do the calculations.
I also think that Chris Hillman had a link to his solution in the wiki archives. It treats the complete case correctly, I think that it should be put back in.

 

[quantum123]

If Lorentz transform does not apply to accelerating observers, will he/she still experience the Doppler effect of SR?

 

[nakurusil]

If Lorentz transform does not apply to accelerating observers, will he/she still experience the Doppler effect of SR?

Yes, there was another thread on this subject. The equations of the relativistic Doppler effect under accelerated motion will be different from the ones for inertial motion.

 

[quantum123]

It would be nice to see more diagrams, mathematical equations, clear definitions and logic in this discussion. Words are very vague and can be misused easily.
I thought Latex is rather easy to use and you can even send in attachment of pictures?

 

[Fredrik]

You insult me because I exposed your erroneous claims and you ran out of logical and pertinent arguments?

No, I have already explained why I'm calling you a troll. Here's a repost of that:

Why don't you answer my question about why you pretended that I had made claims in post #31?

Why don't you say anything about the fact that you claimed to have discussed the details of #1 with me before, when in fact you had not?

Why don't you say anything about the fact that you claimed that I had said that the object in #8 is rigid, when in fact I had never done so?

You have no right to whine about "personal attacks" as long as you talk to me as if I have opinions that you know I don't have. If you stop doing that, I won't call you a troll again.

Your reply to that was pathetic. You just brought up #8 again, even though your objections to it is just a bunch of stuff that I understood better than you do now when I wrote #8.

What I said in post #8 is still possible in principle. It has nothing to do with Born rigidity though, and nothing to do with what this thread is about. Hmm, I have a feeling I've told you that already.

You gave me plenty of new reasons to call you a troll in #64 and #65. Specifically, you keep returning to my #8 over and over again when we're discussing things that we both know have absolutely nothing to do with #8. You also ignored everything I said about what we were really talking about. That's troll behavior.

By the way, I still want answers to those questions above.

 

[Fredrik]

Lorentz transforms do not apply to accelerated motion. Didn't you know that?
Now I understand your insistance in claiming that "The distance between them is always L in the launcher's frame, so it can't be a constant in the mother ship's frame. (This is easy to see in the space-time diagram). It will be "uncontracted" from L/gamma to L."

I don't think you do. The reason I'm so sure about that is that the specifications of the problem imply that both spaceships will have identical world lines in the launcher's frame, except for their starting position.

You can't simply brute force the problem and apply length contraction, you need to use the equations of hyperbolic motion in order to calculate the proper distance. Didn't you know that? Apparently not.

You need those equations in the version of the problem where the acceleration goes on forever (aren't you dismissing that scenario as "unphysical"?). You don't need them if the rockets turn off their engines after a predefined proper time. (OK, you need them if you want to know the final velocity, but what I said is true no matter what the final velocity is). Once the engines have been turned off the rockets are moving at a constant velocity, so now it's only a matter of comparing the spatial distances in two inertial frames. That's Lorentz contraction, no matter what you want to call it.

 

[Fredrik]

It would be nice to see more diagrams, mathematical equations, clear definitions and logic in this discussion. Words are very vague and can be misused easily.
I thought Latex is rather easy to use and you can even send in attachment of pictures?

OK, let me try to define the problem more clearly.


The problem (my version)

Two spaceships are stationary in a certain inertial frame (the launcher's frame), with their engines turned off. The spaceships are identical in every way in this frame, except of course for their position in space. (Note that this includes clock synchronization, and that they are aimed in the same direction).

The distance between them is L. A string of length L has been attached to the spaceships. To avoid irrelevant complications, we assume that both end points of the string are attached to the same point on both spaceships.

The string is very weak and would break if it's stretched to a length longer than L. The force it exerts on the spaceships is assumed to be negligible.

The engines of both spaceships are controlled by computers on the ships. The computers are of course identical and running identical programs. The program was written to make sure that the engines will start at certain time, and shut off after a finite proper time T. When the engines are on, the ships will accelerate in one of the two directions defined by a straight line between the attachment points of the string.

Will the string break?


Other versions

It is usually postulated that the engines will cause a constant acceleration. I've chosen not to postulate that because it restricts our attention to a special case without making the problem easier.

It's sometimes postulated that the acceleration will go on forever.

It's sometimes not postulated that the engines will shut off.

Apparently there are people who postulate that the string is attached to the front of one ship and to the rear of the other. That only adds a complication to the problem that obscures the real issue.

The problem can also be considered in other space-times than Minkowski space. That makes the problem more complicated. Pervect made a post about this.


The solution

The world lines of the attachment points of the string must be identical in the launcher's frame, except for their starting position in space. (If they weren't, there would be something fundamentally different about those two points in space, and that would violate special relativity). This implies that the distance between the attachment points, and hence the length of the string, in the launcher's frame will be constant. However, since the spaceships' velocity has changed, the string must now be Lorentz contracted. It's Lorentz contracted and it's the same length! This means that its proper length must have increased.

So the string must break.

I'm not going to draw a space-time diagram. The one in the Wikipedia article is good enough.

 

[Boustrophedon]

Your description is acceptable up to the point where you just "throw in" the casual "the string must now be Lorentz contracted". I understand that you mean 'from the launcher frame' but the snag is - where does this glib assumption come from ? Certainly not from Einstein's SR: it is, in fact, the central postulate of Lorentz's theory that was supplanted by SR, and the postulate itself supplanted by Einstein's "constant velocity of light for all inertial observers" postulate instead ( i.e. not 'as well as' ).

The reason acceleration was for a long time not dealt with in SR was because all the original papers dealt only with constant uniform motion from which we knew that lengths in A measured shorter in B and vice versa etc. but it was an open question what would happen if A accelerated to B's frame or vice versa.

Although Bell prefers to champion Lorentz's approach by assuming a length here and now becomes shorter from here when accelerated but constant for a co-mover, it is equally possible to consider the co-mover's lengths becoming longer whilst the length from 'here' stays constant.

The latter is preferable for three reasons:
1) It's consistent with SR being "kinematical" and involving no 'physical' effects - everything follows from the constant c postulate.
2)It's consistent with the 'changing' length effect being associated with the accelerated system rather than the system that is undisturbed.
3)It's consistent with the behaviour of two separate, identically accelerated bodies - particularly in view of the fact that the derivation of SR makes no distinction between solid lengths and separated bodies - it deals abstractly with two points a distance apart moving at certain velocity.

 

[nakurusil]

No, I have already explained why I'm calling you a troll.

Every time you respond with unwarranted abuse I will remind you of your "understanding" (better said lack of thereof) of elementary physics:

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.

What I said in post #8 is still possible in principle. It has nothing to do with Born rigidity though, and nothing to do with what this thread is about. Hmm, I have a feeling I've told you that already.

Never admit to your errors, even if it means embarassing you furthr.

 

[nakurusil]

I don't think you do. The reason I'm so sure about that is that the specifications of the problem imply that both spaceships will have identical world lines in the launcher's frame, except for their starting position.


You need those equations in the version of the problem where the acceleration goes on forever (aren't you dismissing that scenario as "unphysical"?). You don't need them if the rockets turn off their engines after a predefined proper time. (OK, you need them if you want to know the final velocity, but what I said is true no matter what the final velocity is). Once the engines have been turned off the rockets are moving at a constant velocity, so now it's only a matter of comparing the spatial distances in two inertial frames. That's Lorentz contraction, no matter what you want to call it.

You may continue claiming that you can use Lorentz transformations and , subsequently, Lorentz contraction all you want. As a matter of fact, you can even use binary arithmetic and Fortran programming. The thing is that you will not get the correct answer to the problem. Lorentz transforms cannot be applied to accelerated motion and expect correct results. Do you know why? Didn't they teach you that in your school? Apparently not.

 

[nakurusil]

Although Bell prefers to champion Lorentz's approach by assuming a length here and now becomes shorter from here when accelerated but constant for a co-mover, it is equally possible to consider the co-mover's lengths becoming longer whilst the length from 'here' stays constant.

The latter is preferable for three reasons:
1) It's consistent with SR being "kinematical" and involving no 'physical' effects - everything follows from the constant c postulate.
2)It's consistent with the 'changing' length effect being associated with the accelerated system rather than the system that is undisturbed.
3)It's consistent with the behaviour of two separate, identically accelerated bodies - particularly in view of the fact that the derivation of SR makes no distinction between solid lengths and separated bodies - it deals abstractly with two points a distance apart moving at certain velocity.

Yep, this is the mess of contradictions that one gets into when one insists on using a mathematical formalism (Length contraction/Lorentz transforms) that should NOT be used because it does NOT apply to accelerated motion.

 

[disregardthat]

What applies to the accelerated motion?

Do you deny that an object has a certain velocity that is higher than at the start at one point during the acceleration?

 

[nakurusil]

What applies to the accelerated motion?

Hyperbolic motion. Was designed specifically to deal with accelerated motion in SR.

Do you deny that an object has a certain velocity that is higher than at the start at one point during the acceleration?

What makes you think that I did that? I am just saying that the equations of hyperbolic motion should be used in order to accurately describe accelerated motion in SR.Do you understand why?

 

[disregardthat]

Don't you think it is a little weird that you are the only one that think that lorentz length contraction does not apply?

You are saying that lorentz contraction does not apply here, the only reason for that must be that you are denying that the velocities of the spaceships are the same as the rest-frame... I cannot see any other reason.

 

[quantum123]

Fred:
I have just drawn some spacetime pictures and I think I got you mean - simple enough.
One suggestion - redraw the picture from the frame of one of the rockets when it is very close to the speed of light. Post it as attachment if possible. The picture should highlight the different rates of acceleration of the rockets at the same time, and also the increase in separation of the rocket. Wiki didn't do that.

 

[nakurusil]

Don't you think it is a little weird that you are the only one that think that lorentz length contraction does not apply?

Physics is not a popularity contest.

You are saying that lorentz contraction does not apply here, the only reason for that must be that you are denying that the velocities of the spaceships are the same as the rest-frame... I cannot see any other reason.

I think that you need to take some classes, your post above makes no sense.

 

[disregardthat]

Ok...

You are saying that the lorentz contraction does not apply in this "paradox"
The only reason that you would say that is to me because:
You are denying that the object moving actually is changing velocities when it is accelerating.
Because any object in a different velocity thant in another frame, is contracted by the factor of root'(1+v^/c^2))

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

 

[nakurusil]

Ok...

You are saying that the lorentz contraction does not apply in this "paradox"
The only reason that you would say that is to me because:
You are denying that the object moving actually is changing velocities when it is accelerating.

Umm, no.I am not denying that an object is changing speed. I am telling you that you cannot apply length contraction in order to solve this problem. You need to take some classes before attempting to discuss this subject.

Because any object in a different velocity thant in another frame, is contracted by the factor of root'(1+v^/c^2))

You got the factor wrong and you got the idea of applying length contraction wrong. Everything else is right

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

Based on your prior posts, this subject is far too advanced for you to grasp. Your buddy Fredrik might be able to explain this to you once he gets it.

 

[Fredrik]

Your description is acceptable up to the point where you just "throw in" the casual "the string must now be Lorentz contracted". I understand that you mean 'from the launcher frame' but the snag is - where does this glib assumption come from ? Certainly not from Einstein's SR

I'm not using anything except the fact that the space-time we're talking about is Minkowski space, and that the two world lines are identical in the launcher's frame except for their starting position.

I will try to explain it in more detail. Look at the space-time diagram in the Wikipedia article. The distance between A and B is the same as the distance between A' and B'. This illustrates how the distance between the two attachment points remains the same in the launcher's frame.

When I said that "the string must now be Lorentz contracted", the "now" I had in mind is the time of event A'. (It would work just as well if I had chosen another event, but then I would have had to draw a new space-time diagram). It was also kind of misleading to say "the string". What I really had in mind was the distance between the two attachment points. That's what's getting Lorentz contracted.

My statement that the distance between the attachment points is Lorentz contracted to length L in the launcher's frame, means that its proper length, i.e. it's length as measured by a co-moving inertial observer is gamma*L.

What we need to understand to see this is to a co-moving observer, the distance between the attachment points is the space-time distance along the dotted line between A' and B'', because that line is the subset of Minkowski space that the co-moving observer considers "space" at the time of event A'.

It is straightforward to calculate what distance the co-moving observer would measure. The math is the same as for any other Lorentz contraction and the result is gamma*L.

This is one way to do it explicitly.

The slope of the solid lines are 1/v. The slope of the dotted line is v. We are looking for the space-time distance between A' and B''. Let's call this quantity M(A',B''). By definition (of special relativity), this quantity is frame-independent, so we can choose any frame for the calculation. I choose one that's co-moving with the launcher and has it's origin at A'.

M(A',B'')^2=-t(B'')^2+x(B'')^2=x(B'')^2 \big(1-\frac{t(B'')^2}{x(B'')^2}\big)
=x(B'')^2 (1-v^2)=\gamma^{-2} X(B'')^2

I used the fact that the slope of the dotted line is v. Now we have to calculate x(B'').

x(B'')=x(B')+K=L+K

where K satisfies

\frac{t(B'')}{K}=\frac{1}{v}

I used the fact that the slope of the solid line is 1/v. Now we see that

K=vt(B'')=v^2x(B'')

I used the fact that the slope of the dotted line is v. Insert this into the equation where we first used the variable K=x(B'')-x(B').

x(B'')=L+K=L+v^2x(B'')

and solve for x(B'').

x(B'')=\frac{L}{1-v^2}=\gamma^2L

Now use this in the calculation of the invariant distance.

M(A',B'')^2=\gamma^{-2} X(B'')^2=\gamma^{-2} \gamma^4 L^2=\gamma^2 L^2

M(A',B'')=\gamma L

...and we're done.

 

[nakurusil]

I'm still editing this post. Don't bother replying to it yet.I'm not using anything except the fact that the space-time we're talking about is Minkowski space, and that the two world lines are identical in the launcher's frame except for their starting position.

I will try to explain it in more detail. Look at the space-time diagram in the Wikipedia article. The distance between A and B is the same as the distance between A' and B'. This illustrates how the distance between the two attachment points remains the same in the launcher's frame.

When I said that "the string must now be Lorentz contracted", the "now" I had in mind is the time of event A'. (It would work just as well if I had chosen another event, but then I would have had to draw a new space-time diagram). It was also kind of misleading to say "the string". What I really had in mind was the distance between the two attachment points. That's what's getting Lorentz contracted.

My statement that the distance between the attachment points is Lorentz contracted to length L in the launcher's frame, means that its proper length, i.e. it's length as measured by a co-moving inertial observer is gamma*L.

What we need to understand to see this is to a co-moving observer, the distance between the attachment points is the space-time distance along the dotted line between A' and B'', because that line is the subset of Minkowski space that the co-moving observer considers "space" at the time of event A'.

It is straightforward to calculate what distance the co-moving observer would measure. The math is the same as for any other Lorentz contraction and the result is gamma*L.

This is one way to do it explicitly.

The slope of the solid lines are 1/v. The slope of the dotted line is v. We are looking for the space-time distance between A' and B''. Let's call this quantity M(A',B''). By definition (of special relativity), this quantity is frame-independent, so we can choose any frame for the calculation. I choose one that's co-moving with the launcher and has it's origin at A'.

M(A',B'')^2=-t(B'')^2+x(B'')^2=x(B'')^2 (1-\frac{t(B'')^2}{x(B'')^2})=x(B'')^2 (1-v^2)=\gamma^{-2} X(B'')^2

I used the fact that the slope of the dotted line is v. Now we have to calculate x(B'').

x(B'')=x(B')+K=L+K

where K satisfies

\frac{t(B'')}{K}=\frac{1}{v}

Here I'm using that the slope of the solid line is 1/v. So we have that

K=vt(B'')=v^2x(B'')

Here I'm using that the slope of the dotted line is v. Insert this into the equation that defined our K

x(B'')=L+v^2x(B'')<br /> <br /> and solve for x(B'').<br /> <br /> x(B'')=\frac{L}{1-v^2}=\gamma^2L<br /> <br /> Now use this in the calculation of the invariant distance.<br /> <br /> M(A',B'')^2=\gamma^{-2} X(B'')^2=\gamma^{-2} \gamma^4 L^2=\gamma^2 L^2<br /> <br /> M(A',B'')=\gamma L

You are still using Lorentz transforms.<br /> Try using the appropriate instruments, you might be able to get the correct result. Here:<br /> <a href="http://www.ph.utexas.edu/~gleeson/NotesChapter13.pdf" target="_blank" class="link link--external" rel="nofollow ugc noopener">http://www.ph.utexas.edu/~gleeson/NotesChapter13.pdf</a>

 

[Fredrik]

You are still using Lorentz transforms.
Try using the appropriate instruments, you might be able to get the correct result. Here:
http://www.ph.utexas.edu/~gleeson/NotesChapter13.pdf

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.

 

[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.