[net.misc] Clock Problem

faustus (01/19/83)

I think the problem with the clock problem is that you are assuming
that the special theory of relativity will apply to a clock swinging
in a circle. In fact, it won't: it only applies to INERTIAL reference
frames, whereas the clock is in an ACCELERATED reference frame, or,
continuously moving between reference frames. I have not worked out
the details of how this affects the phenomenon of time dilation, but
I am confident that it will show there is no time loss. This dis-
tinction between inertial and accelerated reference frames is also
the resolution to the famous twin paradox, by the way. 


              -Wayne Christopher
               faustus@berkeley
               decvax!ucbvax!faustus

bobr (01/19/83)

OK, here's my two bits.  Even in special relativity, a time dialation occurs
only between two reference frames whose velocity w.r.t. each other approaches
the speed of light.  Since the cord is very strong, a simple rotational
transform will reduce the problem to one where their velocity is 0, thus no
time dilation occurs.  Of course, since the reference frames are undergoing
acceleration, all bets are off.

tektronix!iddic!bobr   Robert Reed

woods (01/20/83)

   Admittedly, my relativity is scanty and old, but I'll bet the
relativistic effects in an accelerated frame over a time (?) period
have something to do with the integral of the acceleration (hey, that's
average velocity!) over that period. Since the acceleration of the object
moving in a circle is always towards the center of the circle, the net
integral of the acceleration will be nearly zero.
  Wow. Why am I going through all this? THe obvious thing is that velocity
is a VECTOR. Thus the object whirlig in a circle may have a lot of SPEED,
but not much velocity when averaged over time. If I am not mistaken,
relativistic effects depend on velocity, not on speed.

                        GREG
			ucbvax!hplabs!hao!woods
			menlo70!hao!woods
			harpo!seismo!hao!woods
			decvax!brl-bmd!hao!woods

thomson (01/21/83)

Wayne Christopher claims that special relativity is not applicable to
the soon-to-be-famous "whirling digital clock" problem because the clock
(display) is accelerated.  SR requires only that the OBSERVER be in a
local inertial frame, if the clock hypothesis is accepted (i.e. that time
dilation effects depend only on instantaneous velocities, not on 
acceleration) and this hypothesis has been verified for very large
accelerations.  SR is certainly applicable, and if the whole clock
were whirled rather than just the display it would indeed run slow.

mark (01/22/83)

the problem's solution (that the "clock" is only a display for a distant,
fixed, clock) has already been posted by several people.

to those claiming that special relativity does not apply, since the clock
is accelerated:  this is true, but the motion still causes time dilation,
AND THE ACCELERATION DOES TOO.  if you swung a real clock about your head,
it would lose time faster than SR alone leads you to expect.

the experiment was done some years ago (sorry, i have no references):
someone carried an atomic clock around the world by commercial airliner.  it
lost time wrt the one left on the ground.

				mARK bLOORE
				univ. of toronto

faustus (01/23/83)

I never said that SR doesn't apply, just that you cannot necessarily
apply the law for time dilation without regard for accelerating 
reference frames. In this case, it is not hard to apply it properly,
in others, such as the Twin Paradox, it is much harder to use in the
correct manner.

             -Wayne Christopher
	      faustus@berkeley
	      ucbvax!faustus

bob (01/28/83)

Why doesn't someone simply try spinning the clock to see what happens?