On 11/16/2022 8:20 AM, John Clark wrote:
On Tue, Nov 15, 2022 at 9:50 PM Alan Grayson <agrayson2...@gmail.com>
wrote:
/> Please answer the question defining this thread./
The answer is yes, provided that the acceleration is produced by a
force, such as you'd get with a rocket. In General Relativity gravity
is not considered a force, it's just the way things move if Spacetime
is curved in a certain way, and to figure out what that curvature is
you need to know how much mass there is in the area and how it's
distributed, and you need to know General Relativity
/> Specifically, will the time dilation of a clock in an
accelerating frame, be the same as a clock as measured for a clock
in a the observer's accelerating frame/
I don't understand the question, if they're both accelerating at the
same rate then they're in the same reference frame. And again, Special
Relativity can't deal with gravity. According to Special Relativity if
you're sitting quietly in a gravitational well, as you would be if you
were on the Earth's surface, you're not accelerating, but according to
General Relativity you're accelerating upward at 9.8 meters per second
per second, and if you observe somebody in distant deep space far from
any source of gravity and they were keeping a constant distance from
you their wristwatch would seem to be moving slightly faster than
normal, and to them your wristwatch would seem to be moving slightly
slower than normal.
You need both Special Relativity and General Relativity to make the
corrections necessary for the Global Positioning Satellite system to
work.
That's the easy, engineer's way of doing it which works because the
corrections are small. But from a fundamental point of view all you
need is the proper length along the geodesics. This emphasizes that
there are not two different theories being overlaid. It's just
relativity in curved spacetime.
Brent
A GPS Satellite is moving fast compared to a clock on the ground so
Special Relativity says the clock on the satellite will lose 7210
nanoseconds a day, but the satellite clock is further from the Earth's
center so it's in a weaker gravitational field, and because of that
General Relativity says the satellite clock will gain 45850
nanoseconds a day relative to the clock on the ground. So the two
theories together predict the satellite clock will gain 45850 −7210 =
38,640 nanoseconds a day relative to a clock on the ground. If we
stuck with Newton and this relativistic correction was not taken into
account map positions would be off by about 6 miles a day, and the
error would be cumulative
John K Clark See what's on my new list at Extropolis
<https://groups.google.com/g/extropolis>
I1Il
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