Comments by "Dr Gamma D" (@DrDeuteron) on "The END of GPS for Aviation?! Spoofing At Work" video.

@Khetroid actually the time correction is just for the crappy clock in the receiver. The satellite clocks are good.
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3:10 you’re not just solving for the distance to all the satellites, you’re also solving for clock biases, since even thought the clocks are amazing, each microsecond of drift is 1000 ft of error. That’s why you need 4 satellites minimum. Einstein is a factor, but so is the atmospheric delay, esp the ionosphere. But they got tricks for that, too.
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@Khetroid gravitational force does,not cause time dilation, so the strength on orbit being weaker is not the cause. Time dilation is strictly due to different in potential energy. E.g, there is no gravity at the center of the earth, but is the most dilated place in the planet. For weak fields…I.e, far from the Schwarzschild radius,the time dilation formula is the same as the Lorentz factor formula, just replace the term for Newtonian kinetic energy Per mass, with Newtonian gravitational potential energy, per unit mass. Seems too simple for GR, but it works. Ofc that means the gravitational time dilation btw two heights is the same as the Lorentz factor the high one would gain falling to the lower one.
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@Khetroid OK, I have a PhD in physics, and I aced General Relativity taught by Kip Thorne--the world's top expert rn. So you can be wrong, or try to figure out why I am right, and learn something. To have time dilation depend on local acceleration would be a serious violation of the equivalence principle. Moreover: you can't travel close to the speed of light in flat spacetime. No matter how you move, inertially, it's flat. The time dilation occurs in other frames' clocks--and it is mutual. See: Twin Paradox I've also worked with GPS in many space borne applications. You need 4 sats: 3 for space position, and 1 to find the bias in your non-atomic clock in the receiver.
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@Khetroid well the gravitational accerlation doesn't matter. In weak fields, it's the difference between newtonian gravitational potential energy that leads to time dilation. Since you have a real degree, you know that in strong fields it's a non-linear mess, and you don't even need coordinates with a "time" axis, should you choose to do so. No if you do the twin paradox, the "missing time" is a product of the total velocity change at turnaround, times the distance back to earth (with a gamma in there). Basically changing clock bias on earth, as seen from space. If you frame (no pun intended) this as the space-twin being in universal uniform gravitational field (due to acceleration), that is equivalent to a "g", times a distance..as in mgh = gravitational potential energy. Of course the value of "g" matters, but it is uniform, so the variation does not.
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