On 10/13/2020 6:18 AM, John Clark wrote:
On Tue, Oct 13, 2020 at 1:20 AM Alan Grayson <agrayson2...@gmail.com
<mailto:agrayson2...@gmail.com>> wrote:
/> How does gravity cause the difference between what the theories
predict? AG /
There is no contradiction about what the theories predict because
Special Relativity can make no prediction at all about what a clock
will do when it is in a gravitational field or is accelerated in any
other way; that's why it's called "special", it's only applicable in
certain special circumstances. But General Relativity can handle
acceleration and gravity. 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,
That's a kind of engineering way of looking at it which works well to
first order. But remember "moving fast" is relative and one could
naviely conclude the ground clock must run slow compared to the satellite.
but the satellite clock is further from the Earth's center so it's in
a weaker gravitational field, and because of that general relatively
says the satellite clock will gain 45850 nanoseconds a day relative to
the clock on the ground.
The more fundamental way to look at it is the spacetime is curved, but
locally it's Minkowski. So every clock just measures the proper
distance along it's world line. Acceleration only enter indirectly
since it deviates the path from geodesic which is the extremum. In
spacetime the acceleration is just seen as a geometric factor. In this
way of looking at it there are not two theories SR and GR, it's just SR
on a curved background.
Brent
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 this were not taken into account the GPS system would be in
error by 6 miles every day and the error would add up, soon the entire
GPS system would be useless.
John K Clark
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