Is Lorentz Contraction Indistinguishable from Standard Relativity?

[cfrogue]

cfrogue,

Try thinking of what happens in the launch frame as a sort of inverse of what happens in the ship frame.

In the ships frame(s) the gap is increasing but the length of the thread is not. In the launch frame the gap is constant but the length of the thread is not. Both cases lead to stress in the thread and eventually breaksge.

Matheinste.

Can't.

There exists the SR acceleration equations.

These equations show the ships do not change in distance.

Further, there does not exist a mainstream paper that proves the string breaks in the calculations of the launch frame.

If you can prove this within the launch frame, please show me.

 

[cfrogue]

As Jesse mentioned, the author of that webpage (Kevin Brown) is talking about a different kind of acceleration that keeps the gap between the rockets constant from the point of view of the rocket observers, but now observers in the launch frame see the gap as length contracting at the same rate as anything connecting the two rockets. In that context an instantaneous rest frame for the accelerating rockets makes sense.

As an aside, I like this interesting quote from Kevin Brown in the linked webpage:

Interesting, this author draws the following conclusion.

4 Conclusion
We have seen that the physical length of an object is the rest frame length as
measured in the instantaneous rest frame of the object. For two spaceships
having equal accelerations, as in Bell’s spaceship example, the distance between
the moving ships appears to be constant, but the rest frame distance between
them continually increases.

http://arxiv.org/PS_cache/arxiv/pdf/0906/0906.1919v2.pdf

 

[JesseM]

How?

You said he did not specify the launch frame, but he did specify what he thought was going on in the launch frame. I didn't say I agreed that his explanation was complete.

It is talking about how to reduce the acceleration of the front ship to equate the effect of the string's length contraction.

What do you mean by "equate the effect"? In Born rigid acceleration the distance between the ships does not change in their own instantaneous rest frame from one moment to the next, if that's what you mean, so a string between them which was also accelerating in a Born rigid way would not snap. But if you meant something else, please explain.

 

[matheinste]

Can't.

There exists the SR acceleration equations.

These equations show the ships do not change in distance.

Further, there does not exist a mainstream paper that proves the string breaks in the calculations of the launch frame.

If you can prove this within the launch frame, please show me.

But the specifications of the problem state that the distance is constant in the launch frame and it follows logically in SR that if the gap is constant in the launch frame then it cannot be constant in the ship frame(s).
The usual acceleration laws do not apply because the constancy of the gap is is not a natural consequence of normal acceleration but imposed upon the system by the problem designer.

Matheinste.

 

[cfrogue]

You said he did not specify the launch frame, but he did specify what he thought was going on in the launch frame. I didn't say I agreed that his explanation was complete.

What do you mean by "equate the effect"? In Born rigid acceleration the distance between the ships does not change in their own instantaneous rest frame from one moment to the next, if that's what you mean, so a string between them which was also accelerating in a Born rigid way would not snap. But if you meant something else, please explain.

Did you operate on the launch frame yet, that is what I am after.

If you look early on, you said I was "a crackpot" for considering the launch frame.

Yet, we are all finding a problem using this frame.

 

[matheinste]

Did you operate on the launch frame yet, that is what I am after.

If you look early on, you said I was "a crackpot" for considering the launch frame.

Yet, we are all finding a problem using this frame.

Not all.

 

[cfrogue]

But the specifications of the problem state that the distance is constant in the launch frame and it follows logically in SR that if the gap is constant in the launch frame then it cannot be constant in the ship frame(s).
The usual acceleration laws do not apply because the constancy of the gap is is not a natural consequence of normal acceleration but imposed upon the system by the problem designer.

Matheinste.

Sorry, acceleration is absolute motion under SR.

You are trying to apply relativity for acceleration which is not applicable.
Thus, most solutions apply a "theoretical rest frame logic" to prove consequences of the accelerating frame.

Yet, none operate from the launch frame which does not calculate a distance differential.

This is the issue at hand.

SR must solve this problem logically from both the launch frame and the accelerating frame and arrive at the same exact conclusion.

 

[matheinste]

Sorry, acceleration is absolute motion under SR.

You are trying to apply relativity for acceleration which is not applicable.
Thus, most solutions apply a "theoretical rest frame logic" to prove consequences of the accelerating frame.

Yet, none operate from the launch frame which does not calculate a distance differential.

This is the issue at hand.

SR must solve this problem logically from both the launch frame and the accelerating frame and arrive at the same exact conclusion.

Point 1. Sorry, acceleration is absolute motion under SR.

Aceleration is absolute.

Point 2.You are trying to apply relativity for acceleration which is not applicable.
Thus, most solutions apply a "theoretical rest frame logic" to prove consequences of the accelerating frame.

No idea what you are talking about. Too technical for me.

Point 3. Yet, none operate from the launch frame which does not calculate a distance differential.

No idea what operate from the launch frame means.

Point 4. SR must solve this problem logically from both the launch frame and the accelerating frame and arrive at the same exact conclusion.

That is obvious, and several people have already done it for you.

Matheinste

 

[JesseM]

Did you operate on the launch frame yet,

Why do you keep repetitively asking me this question when I've already told you several times that proving it in the launch frame would require calculating the electromagnetic forces between atoms, and I don't have the specific math for this but I am sure it would work? Did you really forget that I already gave you this answer more than once, or do you have problems comprehending it or something?

If you look early on, you said I was "a crackpot" for considering the launch frame.

Um, no I did not, your memory is playing tricks on you. I just did a search for posts by me using the word "crackpot", there were none on this thread.

 

[cfrogue]

Why do you keep repetitively asking me this question when I've already told you several times that proving it in the launch frame would require calculating the electromagnetic forces between atoms, and I don't have the specific math for this but I am sure it would work? Did you really forget that I already gave you this answer more than once, or do you have problems comprehending it or something?

Are you claiming SR does not answer this?

Um, no I did not, your memory is playing tricks on you. I just did a search for posts by me using the word "crackpot", there were none on this thread.

LOL

 

[JesseM]

Are you claiming SR does not answer this?

SR alone does not answer questions about strings breaking in any frame, you always need additional assumption about materials science. This is what I already told you in post 114 and post 122, and A.T. said the same thing in post 125.

 

[cfrogue]

Um, no I did not, your memory is playing tricks on you. I just did a search for posts by me using the word "crackpot", there were none on this thread.

Post $21

If you think there is any dispute among modern physicists about what would happen in this thought-experiment, you need to post some actual peer-reviewed literature, not a reference to an informal poll taken back when the idea was totally new. I am quite confident that there is no actual dispute about the fact that the stress increases, although as I said there could be types of accelerations where the stress increases but the string doesn't break (maybe because in certain types of accelerations the stress would approach a fixed limit rather than increasing without bound).


The implication you presented is that the consensus all agree the string will break. You implied by this post I was a crackpot. Thank goodness science is not conducted by consensus.

Yet no one thought to ask the launch frame.

I am doing that and with validity I might add.

 

[cfrogue]

SR alone does not answer questions about strings breaking in any frame, you always need additional assumption about materials science. This is what I already told you in post 114 and post 122, and A.T. said the same thing in post 125.

I posted mainstream papers that decide the string can only stretch or contract from the context of the accelerating frame.

Yet, we are trying to evaluate the launch frame.

 

[JesseM]

The implication you presented is that the consensus all agree the string will break.

Yes, and that is entirely true.

You implied by this post I was a crackpot.

How did I "imply" that? You're being oversensitive, I just thought you weren't aware that this was a settled issue among scientists so I was pointing that out to you.

Yet no one thought to ask the launch frame.

Sure they did. As pointed out by atyy (see posts 89-93), Bell did a calculation of the expected equilibrium length in the launch frame using classical electromagnetism, and showed the equilibrium length would shrink with increasing velocity, showing that if the string's length in the launch frame is constant it must be getting further and further past its equilibrium length.

Also, since we know that the electromagnetic laws governing atomic bonds are Lorentz-symmetric, that shows a priori that electromagnetic calculations done in different frames must always arrive at the same conclusions about local events, like whether the atomic bonds in the string are broken.

 

[JesseM]

I posted mainstream papers that decide the string can only stretch or contract from the context of the accelerating frame.

No, none of the papers said it could only be decided in an accelerating frame and couldn't be decided in the launch frame, they just didn't bother to do a calculation in the launch frame since the problem is easier to evaluate in other frames. As with the GPS thread, you seem to have trouble distinguishing between denying that something is true vs. just not addressing it one way or another.

 

[cfrogue]

No, none of the papers said it could only be decided in an accelerating frame and couldn't be decided in the launch frame, they just didn't bother to do a calculation in the launch frame since the problem is easier to evaluate in other frames. As with the GPS thread, you seem to have trouble distinguishing between denying that something is true vs. just not addressing it one way or another.

OK, then do the calcs and prove your case from the launch frame.

 

[atyy]

OK, then do the calcs and prove your case from the launch frame.

As follows:

In the launch frame the laws of physics have Lorentz symmetry. Thus from the launch frame we can switch frames, and show it breaks.

 

[cfrogue]

Also, since we know that the electromagnetic laws governing atomic bonds are Lorentz-symmetric, that shows a priori that electromagnetic calculations done in different frames must always arrive at the same conclusions about local events, like whether the atomic bonds in the string are broken.

Now, I like this

But, the launch frame does not have stress logic.

Give yourself any point between the ships and the acceleration equations do not show contraction.

Maybe I am wrong.


Can you show me?

 

[cfrogue]

As follows:

In the launch frame the laws of physics have Lorentz symmetry. Thus from the launch frame we can switch frames, and show it breaks.

Show me the math please.

Thanks.

 

[atyy]

Now, I like this

But, the launch frame does not have stress logic.

Give yourself any point between the ships and the acceleration equations do not show contraction.

Maybe I am wrong.


Can you show me?

BTW, the acceleration equations are not SR equations.

I hope you are aware of phenomena such as:
http://www.cco.caltech.edu/~phys1/java/phys1/MovingCharge/MovingCharge.html

Historically, electrodynamics gave rise to SR, not the other way round.

 

[atyy]

Show me the math please.

Thanks.

That was the math!

 

[JesseM]

OK, then do the calcs and prove your case from the launch frame.

I've told you a bunch of times that I don't know how to do the specific electromagnetic calculations, but I know this approach would work just based on the Lorentz-symmetry of electromagnetic laws. And if you read the link to Bell's book in post #5 as well as the comments in post 89-93, you'll see that Bell did apparently show that the equilibrium length of an unattached string would get shorter as its velocity increased in the launch frame, which shows that the string attached to the ships was steadily going farther and farther past its equilibrium length, a reasonable basis for concluding it will snap.

 

[atyy]

Now, I like this

But, the launch frame does not have stress logic.

Give yourself any point between the ships and the acceleration equations do not show contraction.

Maybe I am wrong.


Can you show me?

Compare the field lines for the linear (ie. constant velocity) case with v=0 and v=0.9 at http://www.cco.caltech.edu/~phys1/java/phys1/MovingCharge/MovingCharge.html

 

[Fredrik]

In the launch frame the distance between the ships is constant whereas it[/color] should be continually contracting in the launch frame due to increasing velocity of the ships relative to[/color] the launch frame . The thread occupies the distance between the ships and so too should appear contracted in the launch frame. It does not appear so and therefore must be increasingly stressed. Simple as that?

I hope the red "it" means "the string" and not the distance, which you have already said is constant, so it would be inconsistent to say that it should be contracting.

The blue "relative to", should be "in". An object has a velocity in a frame, and relative to another object. So you could also have said "relative to the launch platform" or something like that.

The last two sentences are a bit weird too. You shouldn't be saying that a length "appears" to have a certain value. It has that value in the frame you're talking about. It only makes sense to talk about how it "appears" if you're describing what it would look like in a photograph or something like that. What you should be saying instead is that since the problem specifies that the string won't influence the motion of the rockets, and that the endpoints of the string will remain attached to the rockets, the endpoints will be the same distance apart at all times in the launch frame.

And to finish it off you have to add that the string would be getting shorter as its speed increases if it hadn't been for the constraint that the endpoints remain a distance d apart, and explain why that is. (As I said in my previous post, it's an axiom in SR with matter added "manually", and a derived result in SR with matter added by specifying a Lagrangian or something equivalent to that).

 

[Fredrik]

OK, then do the calcs and prove your case from the launch frame.

Are you saying that you want someone to show you how to calculate how the length of an object in a particular inertial frame changes when the object's velocity in that frame changes? The easiest way to do this by far is to just take its length in the co-moving inertial frame and just Lorentz transform to the inertial frame you're interested in. What you're asking for is just a more complicated way to do the calculation. Why would you want to see a complicated way to find the same result when you already have an easy way to get it? Anyone who understands SR knows that the result can't be any different.

Are you also seriously suggesting that the string wouldn't really break?

 

[pervect]

I have no idea what "stress logic" is. I find it a bit disturbing that our poster seems to be rather demanding and attempting to have others do things the hard way. I'm not quite sure what the point of this all is - I don't get the sense that he's actually interested in learning relativity, but I don't get a clear sense of what he's actually after.

There isn't any such thing in relativity as rigid motion - any actual measuring rod will have a rigidity limited by the speed of sound in the material. The behavior of a non-ideal measuring rod being "squished" isn't particularly interesting, though.

The most possible rigid physical body would probably be the SI standard for length - which is defined in terms of a light beam. (This is an offhand remark, but I believe it to be a correct observation).

The ideal of rigidity, as SR understands it, is widely understood to be "Born rigidity",

It would be relatively easy to post some calculations about what happens to a Born rigid body being accelerated, but I'm not sure there's any purpose in doing so at this point. Unless we have someone who is actually interested in this and would be convinced by the results...

 

[Fredrik]

Well said Pervect. I was thinking the same thing. I especially liked this part:

I don't get the sense that he's actually interested in learning relativity, but I don't get a clear sense of what he's actually after.

 

[Al68]

Did you operate on the launch frame yet, that is what I am after.

If you look early on, you said I was "a crackpot" for considering the launch frame.

Yet, we are all finding a problem using this frame.

Nobody has had any problem using the launch frame that I can see.

If the string stays attached to both ships, its proper length as calculated in the launch frame is coordinate length/sqrt(1-v^2/c^2), where coordinate length is equal to the distance between the ships in the launch frame.

If the distance between the accelerating ships is constant in the launch frame, then the string's proper length will increase (stress) with time per the above calculation in the launch frame.

Just in case its not clear, all of the above is determined in the launch frame.

What else would you like to determine in the launch frame with SR?

 

[matheinste]

Fredrik may I offer this as a paraphrase of your description in #126, the SR resolution.

In the launch frame the distance between the ships is constant whereas IT should be continually contracting in the launch frame due to increasing velocity of the ships relative to the launch frame . The thread occupies the distance between the ships and so too should appear contracted in the launch frame. It does not appear so and therefore must be increasingly stressed. Simple as that?

Matheinste

I hope the capital IT means "the string" and not the distance, which you have already said is constant, so it would be inconsistent to say that it should be contracting.

The blue "relative to", should be "in". An object has a velocity in a frame, and relative to another object. So you could also have said "relative to the launch platform" or something like that.

The last two sentences are a bit weird too. You shouldn't be saying that a length "appears" to have a certain value. It has that value in the frame you're talking about. It only makes sense to talk about how it "appears" if you're describing what it would look like in a photograph or something like that. What you should be saying instead is that since the problem specifies that the string won't influence the motion of the rockets, and that the endpoints of the string will remain attached to the rockets, the endpoints will be the same distance apart at all times in the launch frame.

And to finish it off you have to add that the string would be getting shorter as its speed increases if it hadn't been for the constraint that the endpoints remain a distance d apart, and explain why that is. (As I said in my previous post, it's an axiom in SR with matter added "manually", and a derived result in SR with matter added by specifying a Lagrangian or something equivalent to that).

Thanks for your continued efforts to help. Perhaps I could make it a little clearer. Can I take one point at a time. Of course when I do it may still be incorrect but here goes.

My original words----------In the launch frame the distance between the ships is constant whereas it should be continually contracting in the launch frame due to increasing velocity of the ships relative to the launch frame . ----------

What this was meant to convey is that the constancy of the length of the gap in the launch frame means that the length of the gap in the ship's frame(s) is increasing. If the length of the gap was constant in the ship's frame(s) it would be increasingly contracted in the launch frame because of the continued increase in relative velocity between the launch frame and the ship's frame(s).

I accept that your comments about "in a frame" and "relative to a frame" and "appears" are correct and helpful. That usage was sloppiness on my part.

Is that Ok for starters?

Thanks. Matheinste.

 

[A.T.]

Let us abandon the logic of breakage.

But why? Just because it has been shown to you that the launch frame will also conclude that the string breaks, if it applies SR consequently?

So, the theory concludes the rod experiences change from the accelerating frame and from the launch frame, no such conclusion can be drawn.

Wrong. SR applied consequently in the launch frame concludes a change of the string: All elements the string is made of are moving and are therefore contracted, so they cannot fill the constant distance between the ships anymore.

...implied by this post I was a crackpot.

You are not even a crackpot. Let me summarize this discussion:

"Show me the string breaks, in the launch frame"

It breaks in it's own frame due to elongation, so it breaks in every frame.

"But you are not allowed to use other frames, just launch frame"

In the launch frame all elements the string is made of are moving and are therefore contracted, so they cannot fill the constant distance between the ships anymore

"But you are not allowed to use 'material science'"

"Without some 'material science' you cannot show that a material will break"

"Then I don't care anymore if the string breaks. I just want to repeat the same nonsense, that SR concludes no change of the string in the launch frame, over and over again, and ignore all explanations. La la la, I don't see them ..."

 

[cfrogue]

BTW, the acceleration equations are not SR equations.

I hope you are aware of phenomena such as:
http://www.cco.caltech.edu/~phys1/java/phys1/MovingCharge/MovingCharge.html

Historically, electrodynamics gave rise to SR, not the other way round.

I am not really sure what you mean.

 

[cfrogue]

I have no idea what "stress logic" is. I find it a bit disturbing that our poster seems to be rather demanding and attempting to have others do things the hard way. I'm not quite sure what the point of this all is - I don't get the sense that he's actually interested in learning relativity, but I don't get a clear sense of what he's actually after.

There isn't any such thing in relativity as rigid motion - any actual measuring rod will have a rigidity limited by the speed of sound in the material. The behavior of a non-ideal measuring rod being "squished" isn't particularly interesting, though.

The most possible rigid physical body would probably be the SI standard for length - which is defined in terms of a light beam. (This is an offhand remark, but I believe it to be a correct observation).

The ideal of rigidity, as SR understands it, is widely understood to be "Born rigidity",

It would be relatively easy to post some calculations about what happens to a Born rigid body being accelerated, but I'm not sure there's any purpose in doing so at this point. Unless we have someone who is actually interested in this and would be convinced by the results...

If "Born rigidity" is the standard, then what are the calculations from the launch frame that would break the rod?

 

[cfrogue]

But why? Just because it has been shown to you that the launch frame will also conclude that the string breaks, if it applies SR consequently?

Wrong. SR applied consequently in the launch frame concludes a change of the string: All elements the string is made of are moving and are therefore contracted, so they cannot fill the constant distance between the ships anymore.

You are not even a crackpot. Let me summarize this discussion:

"Show me the string breaks, in the launch frame"

It breaks in it's own frame due to elongation, so it breaks in every frame.

"But you are not allowed to use other frames, just launch frame"

In the launch frame all elements the string is made of are moving and are therefore contracted, so they cannot fill the constant distance between the ships anymore

"But you are not allowed to use 'material science'"

"Without some 'material science' you cannot show that a material will break"

"Then I don't care anymore if the string breaks. I just want to repeat the same nonsense, that SR concludes no change of the string in the launch frame, over and over again, and ignore all explanations. La la la, I don't see them ..."

Then I don't care anymore if the string breaks. I just want to repeat the same nonsense, that SR concludes no change of the string in the launch frame, over and over again, and ignore all explanations. La la la, I don't see them ..."

I want to see the math from the launch frame.

Why is this wrong to ask?

 

[cfrogue]

Nobody has had any problem using the launch frame that I can see.

If the string stays attached to both ships, its proper length as calculated in the launch frame [/B]is coordinate length/sqrt(1-v^2/c^2), where coordinate length is equal to the distance between the ships in the launch frame.

If the distance between the accelerating ships is constant in the launch frame, then the string's proper length will increase (stress) with time per the above calculation in the launch frame.

Just in case its not clear, all of the above is determined in the launch frame.

What else would you like to determine in the launch frame with SR?

The latest paper posted shows the ships drift apart as the explanation.

How is the consistent?

Though, I would tend to agree with your analysis above.

 

[cfrogue]

Nobody has had any problem using the launch frame that I can see.

If the string stays attached to both ships, its proper length as calculated in the launch frame is coordinate length/sqrt(1-v^2/c^2), where coordinate length is equal to the distance between the ships in the launch frame.

If the distance between the accelerating ships is constant in the launch frame, then the string's proper length will increase (stress) with time per the above calculation in the launch frame.

Just in case its not clear, all of the above is determined in the launch frame.

What else would you like to determine in the launch frame with SR?

I have an additional problem thinking with this.

The space between the rockets is that of the launch frame space since the distance between the ships does not change and thus is Euclidian.

However, if any rod exists between the space of the two ships, that is Minkowsky space-time.
Thus, it appears that the space between the two ships is Euclidian while at the same time it is Minkowsky also.

Does this seem correct?

 

[JesseM]

I want to see the math from the launch frame.

Why is this wrong to ask?

And if the math was a detailed calculation of the electromagnetic forces between atoms in a rod moving at different velocities in the launch frame, do you think you'd be able to follow it? Or are you just challenging people to show that the calculations have been done?

As mentioned several times before, if you look at the book linked to in post #5 and check pages 68-74, you'll see that Bell does provide some calculations from classical electromagnetism to show that a simplified solid object like a rod or string will have a shorter equilibrium length at higher velocities, with the calculations done not from the object's rest frame but from the frame in which it is moving (the launch frame).

 

[yuiop]

Thus, it appears that the space between the two ships is Euclidian while at the same time it is Minkowsky also.

You have discovered that observers in different reference frames have different points of view. Welcome to relativity :)

 

[cfrogue]

And if the math was a detailed calculation of the electromagnetic forces between atoms in a rod moving at different velocities in the launch frame, do you think you'd be able to follow it? Or are you just challenging people to show that the calculations have been done?

As mentioned several times before, if you look at the book linked to in post #5 and check pages 68-74, you'll see that Bell does provide some calculations from classical electromagnetism to show that a simplified solid object like a rod or string will have a shorter equilibrium length at higher velocities, with the calculations done not from the object's rest frame but from the frame in which it is moving (the launch frame).

Oh, this is not correct about what I am doing.

What do you think about the overlapping space argument?

 

[cfrogue]

You have discovered that observers in different reference frames have different points of view. Welcome to relativity :)

Can you specify the conditions under which this statement is true?


Is this statement true when considering the light cone and events in the absolute past?

 

[JesseM]

Oh, this is not correct about what I am doing.

Then what are you doing? Do you disagree that the only way to show why it snaps in the rest frame would be to calculate the changing electromagnetic forces between atoms in this frame? If you agree that such a calculation would show it snaps, but you are somehow unsatisfied with this, can you explain why?

 

[yuiop]

Can you specify the conditions under which this statement is true?

Is this statement true when considering the light cone and events in the absolute past?

Observers in different reference frames will disagree on some measurements such as the length of an object or the time interval between two spatially separated events. Other measurement are invariant such as the speed of light or the spacetime interval between two events. I am not sure, but I think invariant quantities are usually four vectors. As for the light cone, all observers will agree which event occurred first if the events are causally connected i.e. one event is within the light cone of the other event, but they might disagree on which event happened first if the events are outside each others light cones.

Also, as I explained in an earlier post, observers in different reference frames will have different explanations for an observation such as in the famous pole and barn paradox. The observer at rest with the barn says the the pole fits within the barn because it is length contracted. The observer at rest with the pole says the pole is longer than the barn, but gets through the barn unscathed, because the doors at the back and front do not open and close simultaneously from his point of view.

 

[cfrogue]

Then what are you doing? Do you disagree that the only way to show why it snaps in the rest frame would be to calculate the changing electromagnetic forces between atoms in this frame? If you agree that such a calculation would show it snaps, but you are somehow unsatisfied with this, can you explain why?

Oh, this is a valid question.

I am not satisified that it appears that the space between the two ships is Euclidian while at the same time it is Minkowsky also.

 

[cfrogue]

Observers in different reference frames will disagree on some measurements such as the length of an object or the time interval between two spatially separated events. Other measurement are invariant such as the speed of light or the spacetime interval between two events. I am not sure, but I think invariant quantities are usually four vectors. As for the light cone, all observers will agree which event occurred first if the events are causally connected i.e. one event is within the light cone of the other event, but they might disagree on which event happened first if the events are outside each others light cones.

Also, as I explained in an earlier post, observers in different reference frames will have different explanations for an observation such as in the famous pole and barn paradox. The observer at rest with the barn says the the pole fits within the barn because it is length contracted. The observer at rest with the pole says the pole is longer than the barn, but gets through the barn unscathed, because the doors at the back and front do not open and close simultaneously from his point of view.

I agree with all you said above.

But, one cannot just blindly conclude because there exists a difference under SR that it is normal.

In particular, one solution has the ships drifting apart.

Yet the launch frame does not see this.

This is not a normal disagreement.

Now, if R of S is involved and two light cones are involved, then many observers can disagree on the ordinality of when they are struck by the two different light cones and that is normal.

But, the above is not normal.

 

[JesseM]

I am not satisified that it appears that the space between the two ships is Euclidian while at the same time it is Minkowsky also.

Space cannot be Minkowski, Minkowski describes a geometry of spacetime. The spatial part of Minkowski spacetime is Euclidean in the sense that all of Euclid's laws work (parallel lines never meet, the sum of angles in a triangle is 180 degrees, etc.)

 

[atyy]

I have an additional problem thinking with this.

The space between the rockets is that of the launch frame space since the distance between the ships does not change and thus is Euclidian.

However, if any rod exists between the space of the two ships, that is Minkowsky space-time.
Thus, it appears that the space between the two ships is Euclidian while at the same time it is Minkowsky also.

Does this seem correct?

Space is Euclidean in every inertial frame. The crucial thing is that the relation between inertial frames is given by Lorentz transformations, not Galilean transformations, so eg. what is deemed simultaneous in one inertial frame isn't in another.

 

[cfrogue]

Space cannot be Minkowski, Minkowski describes a geometry of spacetime. The spatial part of Minkowski spacetime is Euclidean in the sense that all of Euclid's laws work (parallel lines never meet, the sum of angles in a triangle is 180 degrees, etc.)

OK, you are right, but they must overlap and cannot which is my point based on the launch frame and the accelerating frame.

You must know, when operating from A to relative frame B, Minkowski must be used.

That presents a problem under this analysis.

 

[JesseM]

OK, you are right, but they must overlap and cannot

What must overlap and cannot?

 

[A.T.]

I want to see the math from the launch frame.

That is the math:

In the launch frame all elements the string is made of are moving and are therefore contracted, so they cannot fill the constant distance between the ships anymore

Just because something is not a symbolic formula, doesn't mean it is not math. But here the symbolic version anyway:

N : number of string elements placed in line to span the length of the string
d : distance a single resting string element can span
D = N*d: distance the string can span at rest = distance between the rockets in the launch frame

When the string moves at velocity v all elements are contracted by 1/gamma(v) (Lorentz factor) according to SR:

D' = N*d/gamma(v): distance the string can span while moving at v

since

gamma(v) > 1

it follows that

D' < D

So the string cannot span the distance between the rockets D when it is moving. It brakes.

 

[Al68]

I want to see the math from the launch frame.

Why is this wrong to ask?

The math for what? What specifically do you want to see the calculation for?

The latest paper posted shows the ships drift apart as the explanation.

How is the consistent?

Consistent with what? The distance between the ships increasing in the co-moving frame of the string is consistent with the distance between them being constant in the launch frame. In fact, the proper distance between the ships must increase with velocity to maintain their constant distance in the launch frame.

 

[Dale]

BTW everyone, there is a FAQ on Bell's spaceship: http://math.ucr.edu/home/baez/physics/Relativity/SR/spaceship_puzzle.html