I don’t know off the top of my head the magnitude of both effects, but GPS has to take into account both General as well as Special relativity to provide accurate results - which is frakking awesome!
General relativity (which was described after special relativity, interestingly) because the satellites are further from the Earth (mass body) than we and our devices are at. This results in our “clocks” running slower than theirs.
Special relativity because of the high speed the satellites are orbiting at which slows down their “clocks” relative to us (comparitvely stationary) on the Earth.
I use “clocks” in quotes, because it is the actual rate that time passes which can be compared with clocks in each perspective. Both of these effects are small, but meaningful enough that it is accounted for to result in accurate measurements.
So is it possible to be at a point in space, a sort of relativistic lagrangian point, where special and general relativity cancel each other out? Or is this a situation where even if the effects are of equal magnitude the ‘clocks’ will still be off because goddamn relativity?
Yes and no. Special relativity depends on speed, so it’s not a point, more like an orbit. “Reference frame” is usually how physicists define it.
But yes, you could pick two frames such that their special and general relativistic effects cancel out.
But but, in relativistic regimes, simultaneity doesn’t work intuitively. So you could have the two frames “running at the same rate”, but depending on which frame you’re in, the same event could be observed first in frame A, or simultaneously, or in frame B first.
And all frames always observe their local clocks running at 1 second = 1 second.