4 ms·
> what the accumulation of "microseconds per day" means Let's try this scenario: You are in your spaceship in free-fall orbit around the Earth at the altitude
by pdonis 2y ago
> what the accumulation of "microseconds per day" means
Let's try this scenario:
You are in your spaceship in free-fall orbit around the Earth at the altitude of the Moon. Your buddy remains on Earth, and every day, when you in your ship pass directly overhead, he sends you a light signal with a time stamp. More precisely, he will do this every 24 hours and 50 minutes by his clock, since that's how long it takes from one overhead passage of the Moon to the next. (We'll ignore all the variations in the Moon's orbit and assume your ship is in a circular orbit at the appropriate altitude and in the right plane to pass directly over your buddy each day.)
Let's say that on day 0, you pass over your buddy at 12 noon precisely by his clock. He sends you his signal at that instant, and you receive it 1.25 seconds later, the light travel time to the Moon. And let's say you've adjusted your clock so it reads exactly 12 noon + 1.25 seconds when you receive that signal.
Then, 24 hours and 50 minutes later, you pass over your buddy again and he sends you his next signal at 12:50 pm by his clock. You receive it at 12:50:01.250058 pm by your clock, i.e., 1.25 seconds of light travel time + 58 microseconds that your clock gained. But, as I've said, the information in the light signal is still the information from 12:50 pm by your buddy's clock, not 12:50:000058.
24 hours and 50 minutes after that, you pass over your buddy again and he sends you another signal, this time at 1:40 pm by his clock. You receive it at 1:40:01.250116 by your clock, since your clock has now gained 116 microseconds. But, again, the information in the signal is still from 1:40 pm by your buddy's clock, not from 1:40:000116.
And so on, for as long as you want to run the experiment.
In other words, the light signals your buddy sends you are "markers" in spacetime: they govern what information your buddy can send you. The difference in your clock rates is not in "how fast you go into the future"--your clock moving faster doesn't mean you get your buddy's light signals "in advance". All it means is that there are more ticks of your clock--58 microseconds more--in between each "marker" light signal. Or, to put it in the geometric language that is common in General Relativity, the length of your worldline between two successive "markers" is 58 microseconds longer than the length of your buddy's worldline between those same two "markers". But the causal structure of spacetime--what information you and your buddy can exchange--doesn't depend on your clock rates, it only depends on the "markers", the light signals, between you.
- alganet 2y ago> your clock moving faster doesn't mean you get your buddy's light signals "in advance" Thanks, this helps a lot! I think I have just one more question :D I can send him a signal too, right?: I can stop accelerating, or beam him back at the speed of light. When I receive the signal at 12:50:01.250058 I stop accelerating. 1.25 seconds later at 12:50:02.500000 (his clock) my buddy sees that I sent him a response by stopping my acceleration. Or does he see me stopping when his clock is at 12:50:02.500058? If he sees it at 12:50:02.500000, no one gets information in advance, but I gained 58 microseconds that I could use to run a computer program for a little longer, as an example, and make a better statistical prediction than he could do on the ground. Or do I lose the ability to use those 58 microseconds in some way?
- pdonis 2y ago> I can send him a signal too, right? Yes. Rather than stop accelerating (you weren't in the first place, you were in a free fall orbit in my scenario), you can just send a light signal back, which is a lot simpler--and uses a lot less rocket fuel. :-) Suppose you receive your buddy's signal at 12:50:01.250058 and immediately send one back. Your buddy will receive that signal at 12:50:02.5000000 by his clock. No 58 microsecond gain, since his clock didn't gain that time, only yours did. > gained 58 microseconds that I could use to run a computer program for a little longer, as an example Yes. The Interstellar scenario discussed upthread gives a much more extreme example (and in my response I gave a similar scenario but involving speed instead of using the gravity of a supermassive rotating black hole to get the time dilation effect).
- alganet 2y agoCool, thanks! That was exactly what I was trying to wrap my head around.