On 04/01/2010 03:08 PM, Jed Rothwell wrote: > Stephen A. Lawrence wrote: > >> >> Can someone refresh my memory about the precise time measurements >> >> conducted with atomic clocks positioned at different elevations on the >> >> surface of Earth. >> > >> > Gravity or acceleration slow down time. >> >> *WRONG* >> >> A momentarily comoving inertial observer who is colocated with an >> accelerating observer will find that their clocks are ticking AT THE >> SAME RATE. > > Well, for those of us not co-moving, the clock in Boulder, CO gains 15 > ns per day compared to the one in Washington DC, because it is 1,600 m > higher, and this is widely cited as proof of relativity. Special > relativity I should have said.
No, not special, special relativity doesn't address gravity at all. That is, in fact, the difference between SR and GR -- SR applies only to the "special case" of no gravity. And again, the difference in clock rate has to do with the depth in the gravity well, *not* with the difference in the local G field strength, which is really, truly, miniscule when you're talking about a few thousand feet at Earth's surface. > > Perhaps my way of expressing this does not strictly comport with theory, I'd say, rather, that what you said about acceleration slowing time is strictly wrong. > but there is no doubt that the higher you go, and the weaker gravity > becomes, the faster clocks go. Again, the *strength* of the field has no direct effect on time. You'd get exactly the same gravitational dilation difference between sea level and a 20,000 foot mountain peak if the Earth were 10 times larger and just enough less dense so that surface gravity was the same as it is here and now -- but in that case the difference in gravitational *strength* between sea level and mountain top would be far less. Gravitational time dilation has to do with the actual values of the metric components. Gravitational field strength has to do with the FIRST DERIVATIVES of the metric components. They are related, but indirectly. > This becomes a real problem with the GPS > satellite clocks. Well, not really a "problem", because the engineers who designed them knew about GR. Just like Y2K was, in the end, not a "problem" because everybody prepared in advance. > > - Jed >
