Length Contraction in Special Relativity

[Metroid]

I have a seemingly simple question about length contraction in SR.   Suppose that you have two particles (A and B) at rest relative to each other and separated by a distance L.  Now suppose particle C traveling at a velocity (4/5)c from A to B.  Particle C travels to and arrives at particle B at a later time.   We know that time recorded by C (i.e., T') and the length it has traveled L' are reduced relative to those recorded by observers in the reference frame of A & B.     Let's focus on L'.     From SR, we all know that L' = 1/gamma x L.  So particle C, from its perspective, has traveled L' upon arriving at B.      Now consider the following -- immediately (or very quickly) stop particle C upon its arrival at B.    The instant before particle C stopped, it will have registered a length L', whereas the instant after it has stopped, it presumably registers a length L for the A-B separation.  

Now I know that SR should only be applied to inertial reference frames (RFs), but we all know that it can also be applied to accelerating RFs.  But we do not need the equations to address this issue -- from one instant to the next (i.e., prior to after arrival at B), the measured length changes from L' to L.   I also know a second distance measurement is necessary after the arrival and cessation of C's travel.  But regardless, are we supposed to believe that the measured length goes discontinuously (i.e., jumps) from L' to L in  this short interval of time?  Or does a series of distance measurements show a distance the varies somewhat more continuously from L' to L after stoppage?  I know that L is the "proper length", but just stating that this length should be applied to C after its stoppage does not fully address the question.

 

Thoughts?

 

[swansont]

You can't have an instantaneous change in velocity (a is not infinite), so the length will not have a discontinuity

[Metroid]

Thanks for the response.  Yes, I expected someone would say this.  This is a good thing to bring up.  But alright, let's spread out the deceleration to a small value, say 100x the Planck time.  You will then have the measured length changing by the same amount, but not instantaneously.  The result is the sam though, and I think that it is unphysical.  I am most interested in this issue, in the context of discrete spacetime.

[swansont]

38 minutes ago, Metroid said:

Thanks for the response.  Yes, I expected someone would say this.  This is a good thing to bring up.  But alright, let's spread out the deceleration to a small value, say 100x the Planck time.  You will then have the measured length changing by the same amount, but not instantaneously.  The result is the sam though, and I think that it is unphysical.  I am most interested in this issue, in the context of discrete spacetime.

Yes. As long as the acceleration is unphysical, results depending on it will also likely be unphysical. But if spacetime is discrete, then why is there a problem if the length change is as well? Why would a large change in length be at odds with anything?

[Metroid]

By unphysical, I mean the change in the measured length (that C measures) as C decelerates.   If space is discrete, then it is discrete at the Planck scale.  I have to work through the equations, but I doubt that the length changes from L' to L over an arbitrary time of deceleration.  I would appreciate a citation of such a calculation.  Namely, uniform deceleration and the associated change in L' to L.      Thank you one and all.

[mathematic]

The deceleration time is irrelevant.  The point is before C stops he measures L' and after C stops, he measures L.  If he is continuously measuring while he is stopping, the measured distance will change continuously.

[Metroid]

Yes, as per my original formulation of the question, I do not care about the deceleration time since it does not impact the answer.  I guess that I need to derive L' for a uniform deceleration.  I am sure that this has been done, but I guess I should do it myself.   I guess I just assumed that this may not yield the expected result.  But I should check this.

[swansont]

13 hours ago, Metroid said:

If space is discrete, then it is discrete at the Planck scale.

No, that does not follow.

13 hours ago, Metroid said:

  I have to work through the equations, but I doubt that the length changes from L' to L over an arbitrary time of deceleration.

Since L' depends on v, how can it be anything else? If you want to know the rate at which L' is changing, you take the derivative with respect to t. The result will contain dv/dt, which is acceleration

13 hours ago, Metroid said:

  I would appreciate a citation of such a calculation.  Namely, uniform deceleration and the associated change in L' to L.      Thank you one and all.

Do the math described above.

[mathematic]

17 hours ago, Metroid said:

Yes, as per my original formulation of the question, I do not care about the deceleration time since it does not impact the answer.  I guess that I need to derive L' for a uniform deceleration.  I am sure that this has been done, but I guess I should do it myself.   I guess I just assumed that this may not yield the expected result.  But I should check this.

You can compute the distance before he starts slowing down and after he stops.  These depend only on the relative speed at that time.  What happens in between doesn't matter.

[discountbrains]

You have hit upon a paradox of this whole theory. No discontinuity needs to be considered. I hope my post on this made it on this board and wasn't deleted. You see u are not allowed to go against this Einstein religion. Distances that are immutable somehow magically change when u start calculating them using relativity. This is a fantacy. Yet SR predicts some things quite well like E=mc²

[beecee]

32 minutes ago, discountbrains said:

You have hit upon a paradox of this whole theory. No discontinuity needs to be considered. I hope my post on this made it on this board and wasn't deleted. You see u are not allowed to go against this Einstein religion. Distances that are immutable somehow magically change when u start calculating them using relativity. This is a fantacy. Yet SR predicts some things quite well like E=mc²

Well  blow me down! Now tell me why if you are so sure of what you claim, why you do not write up a paper for professional peer review. Or better still, before doing that, at least look at the answers already given in this thread, instead of empty rhetoric and denial.

I'll let those more attuned to SR point out your error in the other thread of yours, which obviously and purposely you seem to have posted in the wrong section. Afterall this is mainstream science.

[discountbrains]

Please, please give a cogent refutation of what I claim. None of you have given any solid proof that what I claimed is wrong. You realize all you're using is conventional wisdom don't you.As for writing a paper, I recently came up with something in math that I think is pretty profound, but the proof is only about 4 lines. I wrote The Journal of the American Mathematical Society to see if I could get an opinion and got back it wasn't in the format nor met the criteria of an article. I knew that. I don't know where to go with my stuff. 

[Mordred]

First off its a rules violation to post non mainstream replies into someone else thread. You already have your own thread that length contraction is invalid according to your view. Do not contaminate another OPS thread with non mainstream replies based on your lack of understanding of how length contraction is applied under the Minkowskii skew symmetry. Post those mathematics into the other thread and we will discuss it there please.

Edited June 29, 2018 by Mordred

[discountbrains]

I hope u come over to my thread and we'll discuss Minkowki's spaces or whatever u want.

[Mordred]

Thank you, I am already involved there.

[swansont]

7 hours ago, discountbrains said:

You have hit upon a paradox of this whole theory. No discontinuity needs to be considered. I hope my post on this made it on this board and wasn't deleted. You see u are not allowed to go against this Einstein religion.

It's not religion.

7 hours ago, discountbrains said:

Distances that are immutable somehow magically change when u start calculating them using relativity. This is a fantacy.

And yet there is experimental confirmation of it.

7 hours ago, discountbrains said:

Yet SR predicts some things quite well like E=mc²

Again, we have experimental confirmation of this relationship.

6 hours ago, discountbrains said:

Please, please give a cogent refutation of what I claim.

How about making a rigorous claim? You claim that L' will not depend on acceleration. Well, take the derivative of L' with respect to t, and show us!

6 hours ago, discountbrains said:

None of you have given any solid proof that what I claimed is wrong.

You are claiming things to be true, and the burden of proof is on you to support these claims. They are not true simply because you don't accept the refutation of them. 

 

[Strange]

9 hours ago, discountbrains said:

Distances that are immutable

It turns out, they are mutable. Surprise!