Re: Going Around in circles - help!

From: RP (no_mail_no_spam_at_yahoo.com)
Date: 03/09/05 

Date: Wed, 09 Mar 2005 00:07:37 -0600

John Kennaugh wrote:
> Start with Twin Paradox type thought experiment.
>
> Earth and some fixed point say 1 light hour away. Moving clock transmits
> ticks. Speed say 0.866c.
>
> As far as the earth bound observer is concerned the moving observer's
> clock is going slow and he only receives half as many ticks as his one
> clock gives out.
>
> As far as the moving observer is concerned his clock keeps perfect time
> but the distance to the turn around point is only 0.5 light years away
> so the number of ticks his clock produces is half as many as it would if
> it travelled 1 light year each way.
>
> Thus there is no discrepancy between what the two observers reckon the
> number of ticks were but there is a difference in their perception. A
> tick is 'an event' it either takes place or it doesn't so it is
> fundamental that they agree.
>
> Note if you use the Doppler equation you find out about the spacing of
> the ticks but it does not affect the total number. - You can do it
> either way.
>
> OK here is my problem. Suppose the moving clock/observer is orbiting
> around the stationary observer. We expect the stationary observer to get
> less ticks from the moving clock than from his own clock. A tick is an
> event so the moving observer must also see the same number of ticks. Now
> in the above that was reconciled because for him the distance was
> shorter. i.e. A sees B's Time slower/B sees A's distance shorter =
> agreement on the number of ticks. If we apply the same then we would
> expect moving observer B to see the total circumference of his orbit as
> less than A sees it but that implies that he sees the radius of his
> orbit shorter. But the radius is at right angles to his direction of
> motion and length contraction is supposed to only take place in the
> direction of motion.
>
> I appreciate that B is not an inertial observer but I am under the
> impression that the time difference (in GPS for example) is usually put
> down to SR time dilation. Surely you cannot simply say B isn't an
> inertial observer so you can ignore what he perceives.

Yes you can, and must. In order to account for the observations in B's
accelerating frame you must account for the effects of boost in each
incremental step in his proper time. Because he is changing frames
from one instant to the next, the instantaneous reading on the other
clock no longer behaves according to the lorentz transform applied to
inertial observers. This is due to relativity of simultaneity, or IOW,
the fact that observers already located in these adjacent frames don't
agree on the instantaneous reading on that clock. Thus there is a
component of time offset due to boost and a component due to relative
velocity. During each vanishingly small step, SR time dilation

delta_t1 = delta_t2/gamma

applies, but not from one step to the next. IOW, the acceleration
cannot be gotten rid of even when applying instantaneously comoving
frames, because no matter how small the increment used there is always
an accelerating step between those adjacent inertial frames. When
taken to the limit, i.e. when sigma approaches zero, this fact
dissolves into the math and out of sight, and thus out of Dirk's mind.
IOW, SR isn't sufficient to resolve this problem. The rotating disk
argument, perfectly equivalent to your argument above, is used by
Einstein to derive the beginnings of GR, and the GR ticking rate
offset, and is done by applying SR and the premise of nonreciprocity
when there is relative acceleration between frames.

Richard Perry

Relevant Pages

  • Re: Time dilation
    ... No ticks can be lost or gained ... | There are two methods of calculating how many ticks the earth observer ...
    (sci.physics.relativity)
  • Re: The Single Experiment that Destroys Einstein.
    ... Both the OO and the ground observer count the number of ticks the ... GC (ground clock) emits PER ORBIT OF THE OO. ...
    (sci.physics.relativity)
  • Re: Time dilation
    ... >|>| an Earth clock as it leaves Earth, travels to a point a fixed distance, ... The moving clock transmits by radio its clocks ticks ... There are two methods of calculating how many ticks the earth observer ...
    (sci.physics.relativity)
  • Re: Time dilation
    ... |>| an Earth clock as it leaves Earth, travels to a point a fixed distance, ... The moving clock transmits by radio its clocks ticks ... In other words, time must be allowed for the ticks to reach the observer, ...
    (sci.physics.relativity)
  • Re: Time dilation
    ... >| an Earth clock as it leaves Earth, travels to a point a fixed distance, ... The moving clock transmits by radio its clocks ticks ... >| observer travelling with the moving clock, he will see his clock as ...
    (sci.physics.relativity)
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