6 ms·

That's right. While a day passes on earth, a day minus 58.721 μs passes on the moon (which is moving faster than the Earth). This multiplies, so after a millio

That's right. While a day passes on earth, a day minus 58.721 μs passes on the moon (which is moving faster than the Earth). This multiplies, so after a million days a clock on the moon will read 58 seconds behind a clock on the earth.

pdonis 2y ago
It's the other way around: while a day passes on Earth, a day plus 58.721 microseconds passes on the Moon. The Moon clock gradually gets ahead of the Earth clock. In an Earth-centered inertial frame, the Moon is moving faster than the Earth, but it is also at a very high altitude, and the altitude effect, which speeds up the Moon clock relative to Earth, is much larger than the speed effect, which slows it down. (Note that the above only takes into account the effects of the Earth's gravity. The paper also takes into account the effects of the Moon's gravity, which don't change the above answer qualitatively but do add small corrections numerically, so the 58.721 microseconds per day is not the actual value the paper ends up with.)
- alganet 2y ago
  Cool, thanks! I'm assuming this affects clocks (and things) but not time, right? Time itself is no different on the moon (it's not the future there). I know this must be true otherwise we would be surrounded by time travellers by now. So, where does this cancels out? My intuition says that if we have two clocks, each clock with a display and a laser pointing to each other, and we put one of them on the moon and the other on earth, someone observing it from a third equidistant point would see both lasers blinking at the same rate. If that's true (I don't know if it is) both of your answers are kinda right, aren't they? From earth, the moon clock ticks slower compared to earth clocks, therefore it lags behind. From the moon, the moon clock ticks faster compared to earth clocks, therefore it skips ahead, and vice-versa. I am not sure though, I feel like I'm missing something.
  - pdonis 2y ago
    > I'm assuming this affects clocks (and things) but not time, right? What's the difference? > otherwise we would be surrounded by time travellers by now I'm not sure what your reasoning is here. > where does this cancels out? I don't understand the question. What is supposed to cancel out? > someone observing it from a third equidistant point would see both lasers blinking at the same rate. No, they wouldn't. > From earth, the moon clock ticks slower compared to earth clocks No, it ticks faster. That was my point.
    - alganet 2y ago
      Consider this scenario: - I get into a spacecraft, go into orbit around earth. - Once in orbit, I start accelerating until my clock ticked faster for long enough to be 1s ahead of earth. - Once I'm 1s ahead of earth, I capture transmissions my buddy sent to me of the stock exchange rates. - My buddy, on the ground, has a telescope and is ready to invest or sell stocks depending on whether I stop or keep accelerating. - My buddy now has knowledge about the future, I land and share the money we stole from the future with him. My intuition says this should be impossible, but it seems that I got the "why" wrong. Or maybe everything wrong.
      - pdonis 2y ago
        > Consider this scenario Let me re-describe your scenario properly: Your buddy sends you information about stock exchange rates when his clock reads 12 noon exactly. You are one light-second away from him, so his message is received by you at 12 noon + 1 second, his time. That is also 12 noon + 2 seconds, your time, but that doesn't matter; it's still information about rates when his clock said 12 noon, not rates when his clock said 12 noon + 1 second, 1 second after he sent the message. In other words, the fact that your clock ticks faster and gets "ahead" of your buddy's does not mean you receive information from your buddy's future.
        alganet 2y ago
        Your example makes sense, the distance for light to arrive makes it impossible (also, the distance for the light from the craft to reach the telescope in step 4, it's a round trip). Going further than this is way above my skillset :D Thanks for the time to indulge my curiosity, I'll study more and try to develop a better intuition.
  - doctorpangloss 2y ago
    It might be easier to think about this as “if you are on the moon and point a telescope at a clock on earth, clock hands move slower on earth than on the moon." This is distinct from "all humans everywhere have a normative experience that the clock hands right next to them move at the same speed.” Or "you never experience falling into a black hole, but you do fall in." You can also watch the movie Interstellar, it has clock hands moving slower in gravity wells as a minor plot point.
    - alganet 2y ago
      You mean the descent into the water planet? If I modify that scene a little bit, it serves to showcase my doubts. 4 astronauts are on orbit around the water planet, but Brand is sick. Cooper, Brand and Doyle go down so Romily can spend 20 years researching a cure. After an hour, Cooper, the sick Brand and Doyle go back to orbit and reunite with Romily. For Romily, 20 years passed and he completed the sythesis for the cure. Romily has "stolen" some information about the future by "walking it" in a relatively different pace, and it was able to share that information with someone that "walked it" in a slower pace. Now, this is for gravity. This was possible because of Gargantua. But gravity is not the only component of the "microseconds per day" formula, there's seems to be more. So I'm interested perhaps in an illustrative scenario where the speed is highlighted (whatever the outcome is, doesn't matter), not the gravity, and there is an attempt at information exchange (don't care if can be successful or not, as long as the example actually explains it).
      - pdonis 2y ago
        > I'm interested perhaps in an illustrative scenario where the speed is highlighted That would be something like the standard twin paradox. You could set that up so that, for example, Cooper, Brand, and Doyle go out in their spaceship at very high speed and don't come back until 20 years have passed on Earth, where Romily has spent that time finding a cure. With the right numbers for the speed of the spaceship and the distance it travels out and back, it could be arranged that only an hour would pass for those aboard the ship. The downside of this is that the rocket power you would need to boost the ship to the required speed, and then turn it around and come back and decelerate to land on Earth again, would be huge, way, way beyond what would normally be considered reasonable. The reason a supermassive black hole was used instead in Interstellar was to allow Cooper, Brand, and Doyle to be able to travel at much more reasonable speeds using much more reasonable rockets, and take advantage of the spacetime geometry of the hole to get the extreme time dilation effect. The reason a rapidly rotating hole was used (aside from the fact that we believe most supermassive holes in our universe are rapidly rotating in this way) was that it allows free-fall orbits to exist very close to the hole's horizon that have very large time dilation factors like 1 hour to 20 years, so that a planet in a free-fall orbit could plausibly exist in that region. For a non-rotating hole that is not possible; to get that close to the horizon and get the time dilation factor you would need, you would have to use rockets to "hover" and the rocket power involved would be of the same order of unreasonableness, if not more so, as what would be needed for the "twin paradox" trip I described above.
  - IIAOPSW 2y ago
    I think what you are trying to say here is that if both the Earth and Moon reference frame were blinking out a 1-second clock signal via a laser pointer to a neutral 3rd party reference frame, the third party would see pulses at 1-second intervals from both sources. This is false. Time itself is in fact progressing at a different rate in both frames, and a second in one is not the same as a second in the other. But, time still "works the same way" for both reference frames in the sense that its not like the clocks in one appear to move in "slow motion". An observer on Earth or the Moon still sees clocks ticking at one second per second, and objects appear to move and react in the ordinary physical ways at the same rate you expect them to. But this is because the observer is also an object in that reference frame, so their perception of everything is in the same "slow motion" as the objects they observe. Now, if an observer on the Moon was to watch an observer on Earth with a telescope or vice versa, then they would indeed see "the video playing at a slightly wrong speed". The effect is relative between observers, not local to an observer. That's why its called relativity.
    - alganet 2y ago
      Thanks! I'm not trying to say anything :D I'm just trying to understand it better. That's why I sprinkled all my comments with healthy doses of "I don't know". I really don't know. The 3rd party seeing blinks at the same rate was just a guess, I'm happy to learn that this guess is false.
      - MaxikCZ 2y ago
        The fact you mentioned you are talking about your intuitionn not verified knowledge, was what kept the diacussion grounded, thanks for it. Otherwise, as you have been told, your intuition was trully false, and spacetime behaves in some unintuitive ways. Whats weird about it is that it seem to behave differently depending on where you are observing something from, thats cruical. Its all about point of view, literally. Wherever you are (earth, moon, space, near of blackhole), time and space will work normaly for you because you are there. But if you are looking how things are happening somewhere else, it suddenly starts looking very weird. You said that you would be surrounded by time travellers, and you indeed literally are. The boring answer is we are all tkme travelers, but the interesting part of it that if we accelerate differently (one going up the tower while other waits down), their times literally start moving different amounts, and when they meet, one is younger than another. The reason we dont notice is because we keep moving at very, very, very low fractions of speed of light where time dilatation is easy to ignore (must be mathematically compensated for GPS sattelites to even work, tho), but that doesnt mean its not ever-presently there.
  - loa_in_ 2y ago
    It's always future, where we are not
mr_mitm 2y ago
Moves faster than than the Earth relative to what? Isn't it the gravitational time dilation that is the relevant effect here?
alganet 2y ago
Thanks!

pdonis 2y ago

It's the other way around: while a day passes on Earth, a day plus 58.721 microseconds passes on the Moon. The Moon clock gradually gets ahead of the Earth clock. In an Earth-centered inertial frame, the Moon is moving faster than the Earth, but it is also at a very high altitude, and the altitude effect, which speeds up the Moon clock relative to Earth, is much larger than the speed effect, which slows it down. (Note that the above only takes into account the effects of the Earth's gravity. The paper also takes into account the effects of the Moon's gravity, which don't change the above answer qualitatively but do add small corrections numerically, so the 58.721 microseconds per day is not the actual value the paper ends up with.)

alganet 2y ago
Cool, thanks! I'm assuming this affects clocks (and things) but not time, right? Time itself is no different on the moon (it's not the future there). I know this must be true otherwise we would be surrounded by time travellers by now. So, where does this cancels out? My intuition says that if we have two clocks, each clock with a display and a laser pointing to each other, and we put one of them on the moon and the other on earth, someone observing it from a third equidistant point would see both lasers blinking at the same rate. If that's true (I don't know if it is) both of your answers are kinda right, aren't they? From earth, the moon clock ticks slower compared to earth clocks, therefore it lags behind. From the moon, the moon clock ticks faster compared to earth clocks, therefore it skips ahead, and vice-versa. I am not sure though, I feel like I'm missing something.
- pdonis 2y ago
  > I'm assuming this affects clocks (and things) but not time, right? What's the difference? > otherwise we would be surrounded by time travellers by now I'm not sure what your reasoning is here. > where does this cancels out? I don't understand the question. What is supposed to cancel out? > someone observing it from a third equidistant point would see both lasers blinking at the same rate. No, they wouldn't. > From earth, the moon clock ticks slower compared to earth clocks No, it ticks faster. That was my point.
  - alganet 2y ago
    Consider this scenario: - I get into a spacecraft, go into orbit around earth. - Once in orbit, I start accelerating until my clock ticked faster for long enough to be 1s ahead of earth. - Once I'm 1s ahead of earth, I capture transmissions my buddy sent to me of the stock exchange rates. - My buddy, on the ground, has a telescope and is ready to invest or sell stocks depending on whether I stop or keep accelerating. - My buddy now has knowledge about the future, I land and share the money we stole from the future with him. My intuition says this should be impossible, but it seems that I got the "why" wrong. Or maybe everything wrong.
    - pdonis 2y ago
      > Consider this scenario Let me re-describe your scenario properly: Your buddy sends you information about stock exchange rates when his clock reads 12 noon exactly. You are one light-second away from him, so his message is received by you at 12 noon + 1 second, his time. That is also 12 noon + 2 seconds, your time, but that doesn't matter; it's still information about rates when his clock said 12 noon, not rates when his clock said 12 noon + 1 second, 1 second after he sent the message. In other words, the fact that your clock ticks faster and gets "ahead" of your buddy's does not mean you receive information from your buddy's future.
      - alganet 2y ago
        Your example makes sense, the distance for light to arrive makes it impossible (also, the distance for the light from the craft to reach the telescope in step 4, it's a round trip). Going further than this is way above my skillset :D Thanks for the time to indulge my curiosity, I'll study more and try to develop a better intuition.
- doctorpangloss 2y ago
  It might be easier to think about this as “if you are on the moon and point a telescope at a clock on earth, clock hands move slower on earth than on the moon." This is distinct from "all humans everywhere have a normative experience that the clock hands right next to them move at the same speed.” Or "you never experience falling into a black hole, but you do fall in." You can also watch the movie Interstellar, it has clock hands moving slower in gravity wells as a minor plot point.
  - alganet 2y ago
    You mean the descent into the water planet? If I modify that scene a little bit, it serves to showcase my doubts. 4 astronauts are on orbit around the water planet, but Brand is sick. Cooper, Brand and Doyle go down so Romily can spend 20 years researching a cure. After an hour, Cooper, the sick Brand and Doyle go back to orbit and reunite with Romily. For Romily, 20 years passed and he completed the sythesis for the cure. Romily has "stolen" some information about the future by "walking it" in a relatively different pace, and it was able to share that information with someone that "walked it" in a slower pace. Now, this is for gravity. This was possible because of Gargantua. But gravity is not the only component of the "microseconds per day" formula, there's seems to be more. So I'm interested perhaps in an illustrative scenario where the speed is highlighted (whatever the outcome is, doesn't matter), not the gravity, and there is an attempt at information exchange (don't care if can be successful or not, as long as the example actually explains it).
    - pdonis 2y ago
      > I'm interested perhaps in an illustrative scenario where the speed is highlighted That would be something like the standard twin paradox. You could set that up so that, for example, Cooper, Brand, and Doyle go out in their spaceship at very high speed and don't come back until 20 years have passed on Earth, where Romily has spent that time finding a cure. With the right numbers for the speed of the spaceship and the distance it travels out and back, it could be arranged that only an hour would pass for those aboard the ship. The downside of this is that the rocket power you would need to boost the ship to the required speed, and then turn it around and come back and decelerate to land on Earth again, would be huge, way, way beyond what would normally be considered reasonable. The reason a supermassive black hole was used instead in Interstellar was to allow Cooper, Brand, and Doyle to be able to travel at much more reasonable speeds using much more reasonable rockets, and take advantage of the spacetime geometry of the hole to get the extreme time dilation effect. The reason a rapidly rotating hole was used (aside from the fact that we believe most supermassive holes in our universe are rapidly rotating in this way) was that it allows free-fall orbits to exist very close to the hole's horizon that have very large time dilation factors like 1 hour to 20 years, so that a planet in a free-fall orbit could plausibly exist in that region. For a non-rotating hole that is not possible; to get that close to the horizon and get the time dilation factor you would need, you would have to use rockets to "hover" and the rocket power involved would be of the same order of unreasonableness, if not more so, as what would be needed for the "twin paradox" trip I described above.
- IIAOPSW 2y ago
  I think what you are trying to say here is that if both the Earth and Moon reference frame were blinking out a 1-second clock signal via a laser pointer to a neutral 3rd party reference frame, the third party would see pulses at 1-second intervals from both sources. This is false. Time itself is in fact progressing at a different rate in both frames, and a second in one is not the same as a second in the other. But, time still "works the same way" for both reference frames in the sense that its not like the clocks in one appear to move in "slow motion". An observer on Earth or the Moon still sees clocks ticking at one second per second, and objects appear to move and react in the ordinary physical ways at the same rate you expect them to. But this is because the observer is also an object in that reference frame, so their perception of everything is in the same "slow motion" as the objects they observe. Now, if an observer on the Moon was to watch an observer on Earth with a telescope or vice versa, then they would indeed see "the video playing at a slightly wrong speed". The effect is relative between observers, not local to an observer. That's why its called relativity.
  - alganet 2y ago
    Thanks! I'm not trying to say anything :D I'm just trying to understand it better. That's why I sprinkled all my comments with healthy doses of "I don't know". I really don't know. The 3rd party seeing blinks at the same rate was just a guess, I'm happy to learn that this guess is false.
    - MaxikCZ 2y ago
      The fact you mentioned you are talking about your intuitionn not verified knowledge, was what kept the diacussion grounded, thanks for it. Otherwise, as you have been told, your intuition was trully false, and spacetime behaves in some unintuitive ways. Whats weird about it is that it seem to behave differently depending on where you are observing something from, thats cruical. Its all about point of view, literally. Wherever you are (earth, moon, space, near of blackhole), time and space will work normaly for you because you are there. But if you are looking how things are happening somewhere else, it suddenly starts looking very weird. You said that you would be surrounded by time travellers, and you indeed literally are. The boring answer is we are all tkme travelers, but the interesting part of it that if we accelerate differently (one going up the tower while other waits down), their times literally start moving different amounts, and when they meet, one is younger than another. The reason we dont notice is because we keep moving at very, very, very low fractions of speed of light where time dilatation is easy to ignore (must be mathematically compensated for GPS sattelites to even work, tho), but that doesnt mean its not ever-presently there.
- loa_in_ 2y ago
  It's always future, where we are not

mr_mitm 2y ago

Moves faster than than the Earth relative to what? Isn't it the gravitational time dilation that is the relevant effect here?

alganet 2y ago

Thanks!