Re: For Seto: Theories incompatible with relativity


Tom Roberts wrote:
[...]

No, there is no such violation. You have implicitly assumed that in
performing that acceleration of the two ends of the rod that you impart
the same force to both ends.

Yes.

In fact, you do not -- you must pull harder
on the front than on the back in order to make the two accelerations
equal, and the difference is just the strain in the rod.

That is, in
order to make those two accelerations equal in the inertial frame you
must stretch the rod.

Yes, but the instantaneous and simultaneous acceleration *caused* the
rod to stretch. That it _caused_ the stretching *is* the problem:

Consider:

[1] The lab-frame and the rods initial frame are the same.

[2] The simultaneity planes of the lab-frame and rod initial-frame are
the same

[3] The acceleration was applied _instantaneously_ and _simultaneously_
w.r.t lab-frame (and transtively, rod initial-frame)

[4] Due to [2] with [3], coordinate acceleration = proper acceleration

[5] Rod length remains invariant in lab-frame, which means proper
length changed.

That all this results in the stretching in [5] *IS* the problem - that
_only one_ special acceleration profile (i.e. born rigid) preserves
proper unit invariance *IS* the problem.

IMPORTANT:
If the acceleration was NOT instantaneous, then the
Born rigid acceleration is recovered because the Rod's
simultaneity plane begins to rotate as the acceleration is
applied.

The instantaneous property of the acceleration profile is
key to this 'bug'. I guess you can dismiss it as 'unphysical'
or whatever, but computer models still throw exceptions
irrespective!

This was originally posed as "Bell's paradox" involving two spaceships
and a string between them. For identical rockets the force is the same,
but the string breaks.

Thanks for pointing out the name. There is no point really discussing
this much more since it turns out to be a semi-well-known 'paradox':

http://math.ucr.edu/home/baez/physics/Relativity/SR/spaceship_puzzle.html

This is not a complete solution, because the delay must vary over time.
Even then I don't think you can accurately maintain the proper length of
the rod.[...]
Not quite. To really obtain Born rigid motion one must apply
different
_proper_ accelerations to the ends of the rod (and all along it). Using
different proper accelerations solves the variable delay problem
mentioned above.[...]

Sure.

So, how does SR prevent non-"Born rigid accelerations" other than
denying them because they violate SR?

They don't "violate SR", they just behave differently.

I don't debate the validity of SR, generally. I just contend that an
acceleration characterized by being _instantaneous_ and _simultaneous_
everywhere blows up the rod, when it shouldn't.

The usual case for Born rigid motion of an object made up of ordinary
matter is to apply a small acceleration to a single point of the object,
and to rely on the inter-atomic forces to maintain the shape of the
object; an example is an ordinary rocket. Here "small" must be small
enough so the inter-atomic forces of the material can maintain the
inter-atomic distances to sufficient accuracy; for all human-made
rockets this is reasonably accurate.


Tom Roberts

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Relevant Pages

  • Re: For Seto: Theories incompatible with relativity
    ... I don't see how SR prohibits the existence of a 'rigid rod', ... Yes, that is the proper lenght of the rod, by definition. ... Suppose that an instantaneous acceleration is applied ... profile is called a Born rigid acceleration. ...
    (sci.physics.relativity)
  • Re: How can this work in relativity?
    ... > that as long as you do your calculations in a single frame, ... >>> uniform acceleration by applying the appropriate compensating ... >From the moving FoR that includes the rod, ...
    (sci.physics.relativity)
  • Re: Deriving the contraction of a moving rod
    ... This is different to the problem of showing that a rod will ... If you have a rod at rest in some inertial frame, ... In Born rigid acceleration, you actually need to apply a ... You then *must* apply forces that give proper ...
    (sci.physics.research)
  • Re: SR Length Contraction - how do physicists explain this
    ... >> reference frame. ... >> accelerated rod stops accelerating, the rod is 5 meters longer than an ... >> change length during the acceleration. ... It takes more energy to accelerate something and stretch it ...
    (sci.physics.relativity)
  • Re: How can this work in relativity?
    ... >> that as long as you do your calculations in a single frame, ... the same at all points of the rod. ... >> Uniform acceleration means that the ...
    (sci.physics.relativity)