Re: TomTom's stupidity (re: was always TomTom's stupidity)


Daryl McCullough wrote:
> schoenfeld1@xxxxxxxxx says...
>
> >Yeah, I did the math before, Daryll. I specfically asked you, in that
> >other post, if a stationary 1 unit ruler accelerates to velocity 0.866c
> >(acceleration was simultaneous everywhere in stationary frame) what
> >will be the ruler's proper length and rulers length in stationary
> >frame.
>
> The answer given by SR is that if the length
> of the rod is 1 meter in frame A (the initial
> rest frame) then its length will be two meters
> in frame B (the final rest frame). This makes
> perfect sense from the standpoint of frame B,
> because according to frame B, one end of the
> rod comes to rest *before* the other end.
> If one end of the rod is moving, and the other
> is not, then that means that the rod is stretching.

This just isn't true. The rod is initially stationary relative to frame
A. The rod detects the simultaneous acceleration everywhere on the rod
at the same time as frame A (assuming you synchronized the clocks). The
rod thus stops accelerating simultaneously everywhere from the rod's
frame as well. Now this does not happen in usual treatments of
noninertial SR because they always conspire the transformations to
preserve the proper length of the noninertial frame - and this is
consistent with GR - but not justifiable from SR postulates.


> >THAT RESULT IS A BOGUS RESULT
>
> Bogus how?

Because it implies that a noninertial frame can detect it's own
relativistic length contractions, and this causes all sorts of problems
with energy conservation and causality. Again, in the usual treatments
of noninertial SR the authors always preserve the noninertial proper
lengths but this is not justifiable from SR postulates. Basically, the
situation which you described never occurs under this treatment.

> >THAT RESULT VIOLATES ENERGY CONSERVATION (why did the ruler break,
> >daryll, why did it break?)
>
> Because a rocket is *pulling* on it. If you pull hard enough
> on any object, it will break. Try it with a piece of taffy.

It's not "pulling on it" at all. You need to understand that all points
on the rod simultaneously accelerate and stop accelerating.

> >THAT RESULT DEMONSTRATES SR'S CLEAR FAILURE TO DESCRIBE A NONINERTIAL
> >FRAME
>
> My calculation was all done using inertial frames. I didn't
> use any noninertial frames. There are two inertial frames:
> the initial rest frame, A, and the final rest frame B.

And your final rest frame is able to measure a relativistic length
contraction of itself which is a false result. In GR you can't do this
at all.

> >> However, you can use the Lorentz transformations to
> >> conclude the following:
> >>
> >> If the rod's proper length is constant, *then*
> >> the left and right ends cannot accelerate identically.
> >
> >Correct.
> >hint: the left and right ends don't _simultaneously_
> >accelerate in the stationary frame, they accelerate at different
> >times SUCH THAT THE PROPER LENGTH REMAINS PRESERVED.
>
> That's a different problem. Yes, if the two ends accelerate
> so as to maintain a constant proper length, then the rod
> will maintain a constant proper length. That's certainly
> true. I was addressing the case in which the two ends
> accelerate simultaneously, as viewed in the initial
> rest frame A.

Now if you go read any treatment of noninertial SR, like MTW, they
always preserve this proper length. Ever wondered why?

> >This is trivially true from GR, but from SR, is not.
>
> Neither GR nor SR says that proper lengths remain preserved
> when you accelerate an object. GR and SR don't say anything
> in this regard. If you think they make different predictions,
> write down the formulas for the prediction of GR, and
> write down the formula for the prediction of SR. They
> had *better* make the same predictions, because the
> equations of GR and SR are the *same* in the limit
> as G --> 0.

Not the case. In GR, the proper unit length of the frame is constant.
In SR, as you've learned, you don't get this result in all scenarios
and this can lead to major problems. Also, I don't see any relation
with SR and G --> 0. G is a constant and it's value depends only on
arbitrary units. G is 0 in the planck scale and this is where most
Quantum Gravity research takes place.

> In both GR and SR, if a rocket accelerates so as to maintain
> a constant proper length, then (by definition) its proper
> length doesn't change. I don't see why you think there is
> a difference between GR and SR in this regard.

Err, in your own post you determined that the proper length of the rod
changed. This doesn't ever happen in GR.

[...]

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Relevant Pages

  • Re: TomToms stupidity (re: was always TomToms stupidity)
    ... >The ruler instantaneously accelerates to velocity 0.866c. ... >What is the length of the ruler in A's frame? ... For example, if you accelerate ... If the proper length of the rod remains constant, ...
    (sci.physics.relativity)
  • Re: Is there length contraction in SRT, uncle Ben?
    ... length of the rod, setting up measurements at their will, ... manner, each in his frame. ... and L is the measured (and at the same time the proper) length ... it doesn't matter whether the measurements ...
    (sci.physics.relativity)
  • Re: TomToms stupidity (re: was always TomToms stupidity)
    ... >(acceleration was simultaneous everywhere in stationary frame) what ... rod comes to rest *before* the other end. ... >> the left and right ends cannot accelerate identically. ... write down the formula for the prediction of SR. ...
    (sci.physics.relativity)
  • Re: TomToms stupidity (re: was always TomToms stupidity)
    ... >>> own reference frame. ... Let there be a rod initially at rest ... will be the ruler's proper length and rulers length in stationary ... > the left and right ends cannot accelerate identically. ...
    (sci.physics.relativity)
  • Re: Rigid rod problem
    ... >> I don't see in what sense your first statement could ... If you choose a point on the rod a use its current speed as your FOR, ... exactly as it fits in our "rest" frame at the ... and will accelerate forever. ...
    (sci.physics.relativity)