Re: Before Now
Hal Finney (hal@rain.org)
Thu, 23 Jan 1997 22:36:24 -0800
From: Damien Broderick <damien@ariel.ucs.unimelb.edu.au>
> Hal comments:
>
> > A commercial jet flying at 10000 m will therefore have a
> >speedup due to GR of about 10^-10. This is an order of magnitude more
> >than the relativistic slowdown of even the mile per second plane, so
> >it will swamp that effect in normal situations.
>
> This has been an empirical issue for many years. A quick hunt of my shelves
> does not locate the detailed account, which I recall showed a (very small)
> overall loss of time in the airborne clock. Britannica says: `The
> clock-paradox effect also has been substantiated by experiments comparing
> the elapsed time of an atomic clock on Earth with that of an atomic clock
> flown in an airplane. The latter experiments. furthermore, have confirmed a
> gravitational contribution to time dilation, as predicted by the theory of
> general relativity.' No plus or minus signs, damn it, but presumably if the
> joint effect had conformed with Hal's estimate this would have deserved
> mention in the EB.
I'm sorry, I made a numerical error and used a value of c that was a
factor of 10 too low. Actually g/c^2 is about 10^-16 per meter and
so at 10000 m the gravitational speedup would be 10^-12. This puts
the relativistic slowdown back in the lead since it was about 10^-11,
although Eliezer's plane was going pretty darn fast (nearly at orbital
velocity). For ordinary commercial jets it looks like the relativistic
slowdown just about cancels the gravitational speedup!
Hal