« on: 06/04/2020 20:40:34 »
First of all, my reply concerned the point of view of the observer, who we're trying to get to see an incoming clock tick at normal rate. You kind of worded it the other way around, but it can work that way as well.I'm not quite understanding this.QuoteAt what velocity do you have to be moving towards an observer to see their watch ticking at the same rate as yours after taking both time dilation and Doppler shift into account?Both observers would have to be stationary relative to each other.
Mind you, that's not the only solution. Two observers could circle each other at some rate, and thus have a relative velocity. You can get really creative and plot a funny spiral path in so the Earth guy sees a 1-1 rate between them, but then the incoming guy would still see a different rate.
If two observers are circling each other without the distance between them changing then of course they would each see the other's watch ticking at the same rate as their own watch but how could following a path that spirals inwards cause a different result than a direct path?Easiest case: From PoV of Earth, the remote clock is getting closer (blueshift) but is moving (redshift). If you adjust the angle just right, the two cancel. The relativistic effect is a function of speed, but the Doppler effect is a function of the rate of reduction of separation. A circular path would be red shifted (all dilation), but a direct path is dominated by Doppler. Somewhere between is a balance. The math isn't too hard to work out.
Imagine they are the only two objects in the universe. Any spiral path is now meaningless because there's no point of reference to create a spiralEarth is the reference. Remember, rotation is still absolute, not relative.
So no need for a 3rd object for it to be a spiral.
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