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> Spacecraft, acceleration to pick up speed (not to go higher) That would mean you would no longer be in a free-fall orbit, you would be moving faster than fre

by pdonis 2y ago

> Spacecraft, acceleration to pick up speed (not to go higher) That would mean you would no longer be in a free-fall orbit, you would be moving faster than free-fall orbit speed, and your clock would run slower. Depending on how much you sped up, you might even end up having your clock run slower than Earth clocks. > stock-exchange cheaters Nothing you can possibly do with your rocket will enable you to cheat on the stock exchange. No matter what you do, you can't have your buddy's light signals contain information from his future. > I don't get the "don't need" or "don't want". You don't need or want to fire rockets to speed up if your objective is to have your clock run as fast as possible relative to Earth's at a given altitude. Indeed, if you really want your clock to run as fast as possible relative to Earth's clock at a given altitude, you should use your rocket to "hover" motionless (meaning zero speed relative to Earth's center of mass) at that altitude, not to speed up relative to free-fall orbital speed.

alganet 2y ago
> Nothing you can possibly do with your rocket will enable you to cheat on the stock exchange. I'm not trying to come up with an experiment that enables stock-exchange cheating. I'm trying to come up with a thought experiment that highlights the effect of speed on time dilation, with the purpose of understanding what the accumulation of "microseconds per day" means, and in the spirit of the paper posted I want to put an element of information/communication there (clocks with laser beams, stock exchange, doesn't matter what it is, for this purpose they're equivalent). > Depending on how much you sped up, you might even end up having your clock run slower than Earth clocks. So there is at least a component of the "microseconds per day" offset formula that contributes to a slowing down compared to what is being orbited, is that correct? If I got this right, speed matters but it is negligible compared to other factors for objects like the moon or a human made satellite. That's OK. Like I said, I don't want to actually cheat in the stock exchange, I want to understand that effect.
- pdonis 2y ago
  > So there is at least a component of the "microseconds per day" offset formula that contributes to a slowing down compared to what is being orbited I'm not sure what you mean by "compared to what is being orbited". We are comparing a clock in a free-fall orbit to a clock on Earth. > speed matters but it is negligible compared to other factors for objects like the moon or a human made satellite For the Moon, yes, the speed effect is small compared to the altitude effect. For human made satellites, it isn't. For example, as I have already said, clocks on the ISS run slow compared to Earth clocks--because in low Earth orbit, the slowdown due to speed is greater than the speedup due to altitude.
  - alganet 2y ago
    If the moon orbited earth a little bit faster, would the number of microseconds per day accumulated change (even if ever so slightly)? In other words, is the speed a determining factor in the offset? Your answer seems to indicate that yes. So, in principle, I should be able to come up with a thought experiment that highlights what that speed means. Would this hypothetical faster moon, billions of years orbiting earth at a different speed, look geologically younger than our regular speed moon? (genuine don't know, but that's the kind of coloquial illustrative example I'm looking for).
    - pdonis 2y ago
      > If the moon orbited earth a little bit faster, would the number of microseconds per day accumulated change (even if ever so slightly)? Meaning, if you attached rockets to the Moon to speed it up while not changing its orbital radius? In that case the speedup relative to Earth clocks would be less, yes. > in principle, I should be able to come up with a thought experiment that highlights what that speed means I gave you one upthread, in the subthread where the movie Interstellar was being discussed. > Would this hypothetical faster moon, billions of years orbiting earth at a different speed, look geologically younger than our regular speed moon? Meaning, if you compared the two after billions of years of Earth clock time had elapsed? Yes.
- 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?

by pdonis 2y ago

alganet 2y ago

> Nothing you can possibly do with your rocket will enable you to cheat on the stock exchange. I'm not trying to come up with an experiment that enables stock-exchange cheating. I'm trying to come up with a thought experiment that highlights the effect of speed on time dilation, with the purpose of understanding what the accumulation of "microseconds per day" means, and in the spirit of the paper posted I want to put an element of information/communication there (clocks with laser beams, stock exchange, doesn't matter what it is, for this purpose they're equivalent). > Depending on how much you sped up, you might even end up having your clock run slower than Earth clocks. So there is at least a component of the "microseconds per day" offset formula that contributes to a slowing down compared to what is being orbited, is that correct? If I got this right, speed matters but it is negligible compared to other factors for objects like the moon or a human made satellite. That's OK. Like I said, I don't want to actually cheat in the stock exchange, I want to understand that effect.

pdonis 2y ago
> So there is at least a component of the "microseconds per day" offset formula that contributes to a slowing down compared to what is being orbited I'm not sure what you mean by "compared to what is being orbited". We are comparing a clock in a free-fall orbit to a clock on Earth. > speed matters but it is negligible compared to other factors for objects like the moon or a human made satellite For the Moon, yes, the speed effect is small compared to the altitude effect. For human made satellites, it isn't. For example, as I have already said, clocks on the ISS run slow compared to Earth clocks--because in low Earth orbit, the slowdown due to speed is greater than the speedup due to altitude.
- alganet 2y ago
  If the moon orbited earth a little bit faster, would the number of microseconds per day accumulated change (even if ever so slightly)? In other words, is the speed a determining factor in the offset? Your answer seems to indicate that yes. So, in principle, I should be able to come up with a thought experiment that highlights what that speed means. Would this hypothetical faster moon, billions of years orbiting earth at a different speed, look geologically younger than our regular speed moon? (genuine don't know, but that's the kind of coloquial illustrative example I'm looking for).
  - pdonis 2y ago
    > If the moon orbited earth a little bit faster, would the number of microseconds per day accumulated change (even if ever so slightly)? Meaning, if you attached rockets to the Moon to speed it up while not changing its orbital radius? In that case the speedup relative to Earth clocks would be less, yes. > in principle, I should be able to come up with a thought experiment that highlights what that speed means I gave you one upthread, in the subthread where the movie Interstellar was being discussed. > Would this hypothetical faster moon, billions of years orbiting earth at a different speed, look geologically younger than our regular speed moon? Meaning, if you compared the two after billions of years of Earth clock time had elapsed? Yes.
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?