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?