Relativity in engineering

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It helps to estimate the pre-launch adjustment of the clocks, but that's about it. No orbit is exactly circular, the field is not exactly spherical and all orbits change over time. The real operational adjustment is done periodically based on comparison with a group of ground-based clocks, not based on theory.

>>7705342
Interesting, thanks.
I thought that the internal clocks were set to operate at a slightly different rate than on Earth, not that they corrected them periodically.

Any other systems where relativity needs to be taken into account?

>>7705357
They do tick slower. From what I've read they adjust to effects from special relativity using an onboard computer; effects from general relativity due to altitude changes might require more manual adjustments.

>>7705382
>They do tick slower.

Slower than what? The SR component (motion) is -7µs per day while the GR component (potential) is +45µs per day. Without pre-launch adjustment the on-board clock would get ahead of the ground-based clock by 38µs per day. The neutral orbit (SR+GR=0) is at r≈(3/2)*R_Earth (see OP's pic). Clocks in a lower orbit tick slower than on the surface, above that clocks tick faster. The mean orbital radius of GPS satellites is about 26560 km.

The adjustment of the GPS clocks has little to do with positioning accuracy, it is done because the clock also serves as a global time reference and to alleviate the calculations at the receiver end should the (many) GPS clocks fall out of sync. The receiver uses its own clock only as a (very) short term reference.

A little off topic, but maybe relative (groan). I have two quantum clocks. One here on erth, and one in a rocket. The object is to maintain erth time on the rocket for reference.
The clocks are designed with particles that are always entangled, and the spin is 'counted'.
Within the framework of GR, will the pilot of the rocket see the spin of the particle in his clock change the farther from erth he/she gets?
Will the spin of the particle in the erth clock change?
(I am having problems getting my head around this).

>>7706153
I'm not sure what your question is however I think it's as the rocket increases in distance from earth will the clock on earth and the clock on the rocket maintain the same time?

The answer is no. According to relativity time does not act in the same fashion on earth as space.

>>7706153
Entanglement doesn't work like that. Entangled particles don't change in any classical sense. You can't even tell anything is happened without communicating with earth.

>>7706241
>Measurements of physical properties such as position, momentum, spin, polarization, etc. performed on entangled particles are found to be appropriately correlated. For example, if a pair of particles is generated in such a way that their total spin is known to be zero, and one particle is found to have clockwise spin on a certain axis, then the spin of the other particle, measured on the same axis, will be found to be counterclockwise; because of the nature of quantum measurement.

>>7706241
Thus, we have two entangled particles, one spinning clockwise and the other anti-clockwise (total spin is zero). Oe is in an earth clock with a counter - the other on a rocket with a counter.
The spin count will remain the same for both particles DESPITE the time and distance covered.

Therefore. Will an observer on the rocket see the angular momentum of the particle decrease?

Will the earth observer see the spin count increase? change?

Or - Do we have a clock that works and tells earth time in perpetuity (not that there is any reason to create this clock - its a thought experiment). I hope you understand it now?

>>7706185
But, quantum entanglement does not conform to GR? Therefore the clocks will stay synchronised.

>>7705657
>The adjustment of the GPS clocks has little to do with positioning accuracy
That's not what I heard. I heard (from somebody who actually worked on the GPS project) that without compensation there would be a position drift.

>>7706569
But of course, all of this was word of mouth, I read nothing supporting this.