7 ms·

> Meanwhile, moving the height of anything a centimeter, the position of the moon, and a whole other host of noise sources have to be canceled out. Because tim

> Meanwhile, moving the height of anything a centimeter, the position of the moon, and a whole other host of noise sources have to be canceled out. Because time runs slower the stronger gravity becomes? I don't think it would be a problem, as long as the entire experimental apparatus is within the same gravity field for the duration of a particular measurement.

wongarsu 2y ago
The gravity field we are in isn't that constant. The gravitational influence of the moon is strong enough to move a lot of water here on Earth. The other planets are a lot further away, but not completely without gravitational influence. Earth's orbit around the sun isn't a perfect circle and has ~3% difference between lowest and highest point. The seasonal shift in mass distribution on Earth is big enough that we used to correct for it in astronomical time observations (the up to 30ms or so between UT1 and UT2). On the other hand, I don't think this experiment is really all that sensitive to gravity since we aren't really measuring time.
- incompatible 2y ago
  But it would depend on how long it takes to make a single measurement. Perhaps the moon wouldn't move far.
mikewarot 2y ago
Optical lattice clocks are so precise these days, you can detect the difference in clock rates caused by a 2 centimeter difference in height. The higher clock will run faster. In the famous thought experiment you can't tell the difference in an elevator in either a gravitational well, or accelerating frame. It turns out that is only true if the elevator is sufficiently small. Sufficiently small is getting smaller every year.
- incompatible 2y ago
  The lower gravity clock will run faster, but the experiment should give the same result, regardless of which frame it's running in. The same way that the caesium-133 atom transition frequency is 9192631770 Hz, regardless of the gravitational field.
  - deleted 2y ago
    [deleted]
  - mikewarot 2y ago
    The time shift of a Cesium beam atomic clock at different altitudes is a well established experimental result. With Optical Lattice clocks, they are much more stable, and the output is light, so a phase difference can be detected much, much quicker. According to [1], a difference of 1 centimeter can be measured. The quote of interest: An optical lattice clock with a frequency accuracy of 1 × 10^−18, which is currently the most accurate in the world, has a detectable gravitational potential equivalent to an elevation difference of approximately 1 cm. If you can access it, here's the related letter in Nature[2] from 2018. [1] https://www.rd.ntt/e/research/JN202304_21619.html https://www.rd.ntt/e/research/JN202304_21619.html [2] https://www.nature.com/articles/s41586-018-0738-2 https://www.nature.com/articles/s41586-018-0738-2
    - incompatible 2y ago
      Yes, nevertheless each clock in its own frame of reference is measuring 9192631770 Hz, or whatever. It's only with multiple communicating clocks that you'd observe the difference: that 9192631770 Hz in one place is different to 9192631770 Hz somewhere else.
      - deleted 2y ago
        [deleted]
      - magicalhippo 2y ago
        So if you have three clocks, one on the floor, one on a table and one at the ceiling, you could tell that relative to the clock on the table, the bottom one runs slower than the one at the ceiling, right? Is the statement then that if the elevator is sufficiently tall, this difference disappears if the elevator is accelerated by a rocket in outer (flat) space, vs hanging in an elevator shaft?
- moi2388 2y ago
  > It turns out that is only true if the elevator is sufficiently small. Do you have more context, explanation or source for this? This is the first time I’ve heard of this being the case and would love to learn more about it.
  - jungturk 2y ago
    This video w/ Dr Iva Fuentes, from two weeks ago, spends a few segments on the breakdown of the equivalence principle w/ quantum clocks. https://youtu.be/cUj2TcZSlZc?t=4006&si=Ykt0JDqEKk1ObMp3 https://youtu.be/cUj2TcZSlZc?t=4006&si=Ykt0JDqEKk1ObMp3 Video notes have lots of references to relevant papers (and the video itself surveys a few aspects of these issues).
  - stavros 2y ago
    I assume they mean that, in a gravity well, you get less acceleration as you get away from the well, whereas in an elevator you'll get the same acceleration in all places inside the elevator. Then again, the intent of the thought experiment was that you stay in one place.
  - patmorgan23 2y ago
    Time moves slower at the bottom of an elevator shaft because it is closer to the earth. We have instruments so precise we can measure that difference now.
    - moi2388 2y ago
      Yes I’ve always wondered about this. I thought the thought experiment basically dealt with points not regions though
  - DemocracyFTW2 2y ago
    1) what the others said, in a gravity well it depends on height above the floor, but not in an accelerating elevator; this limits the height according to the sensitivity of your instruments 2) additionally, we do not know of any disc-shaped objects of sufficient density and matter distribution to produce a uniformly linear gravity field; only galaxies come close but their gravity is small compared e.g. to that of Earth. Most of the time gravity is caused by spherical objects, meaning the lines of the fields diverge. If you had an elevator with a sufficiently large, completely flat floor, you could tell that you're hovering above a planet by observing that a plumb bob forms different angles with different (perfectly upright) walls of the cabin.

wongarsu 2y ago

The gravity field we are in isn't that constant. The gravitational influence of the moon is strong enough to move a lot of water here on Earth. The other planets are a lot further away, but not completely without gravitational influence. Earth's orbit around the sun isn't a perfect circle and has ~3% difference between lowest and highest point. The seasonal shift in mass distribution on Earth is big enough that we used to correct for it in astronomical time observations (the up to 30ms or so between UT1 and UT2). On the other hand, I don't think this experiment is really all that sensitive to gravity since we aren't really measuring time.

incompatible 2y ago
But it would depend on how long it takes to make a single measurement. Perhaps the moon wouldn't move far.

mikewarot 2y ago

Optical lattice clocks are so precise these days, you can detect the difference in clock rates caused by a 2 centimeter difference in height. The higher clock will run faster. In the famous thought experiment you can't tell the difference in an elevator in either a gravitational well, or accelerating frame. It turns out that is only true if the elevator is sufficiently small. Sufficiently small is getting smaller every year.

incompatible 2y ago
The lower gravity clock will run faster, but the experiment should give the same result, regardless of which frame it's running in. The same way that the caesium-133 atom transition frequency is 9192631770 Hz, regardless of the gravitational field.
- deleted 2y ago
  [deleted]
- mikewarot 2y ago
  The time shift of a Cesium beam atomic clock at different altitudes is a well established experimental result. With Optical Lattice clocks, they are much more stable, and the output is light, so a phase difference can be detected much, much quicker. According to [1], a difference of 1 centimeter can be measured. The quote of interest: An optical lattice clock with a frequency accuracy of 1 × 10^−18, which is currently the most accurate in the world, has a detectable gravitational potential equivalent to an elevation difference of approximately 1 cm. If you can access it, here's the related letter in Nature[2] from 2018. [1] https://www.rd.ntt/e/research/JN202304_21619.html https://www.rd.ntt/e/research/JN202304_21619.html [2] https://www.nature.com/articles/s41586-018-0738-2 https://www.nature.com/articles/s41586-018-0738-2
  - incompatible 2y ago
    Yes, nevertheless each clock in its own frame of reference is measuring 9192631770 Hz, or whatever. It's only with multiple communicating clocks that you'd observe the difference: that 9192631770 Hz in one place is different to 9192631770 Hz somewhere else.
    - deleted 2y ago
      [deleted]
    - magicalhippo 2y ago
      So if you have three clocks, one on the floor, one on a table and one at the ceiling, you could tell that relative to the clock on the table, the bottom one runs slower than the one at the ceiling, right? Is the statement then that if the elevator is sufficiently tall, this difference disappears if the elevator is accelerated by a rocket in outer (flat) space, vs hanging in an elevator shaft?
moi2388 2y ago
> It turns out that is only true if the elevator is sufficiently small. Do you have more context, explanation or source for this? This is the first time I’ve heard of this being the case and would love to learn more about it.
- jungturk 2y ago
  This video w/ Dr Iva Fuentes, from two weeks ago, spends a few segments on the breakdown of the equivalence principle w/ quantum clocks. https://youtu.be/cUj2TcZSlZc?t=4006&si=Ykt0JDqEKk1ObMp3 https://youtu.be/cUj2TcZSlZc?t=4006&si=Ykt0JDqEKk1ObMp3 Video notes have lots of references to relevant papers (and the video itself surveys a few aspects of these issues).
- stavros 2y ago
  I assume they mean that, in a gravity well, you get less acceleration as you get away from the well, whereas in an elevator you'll get the same acceleration in all places inside the elevator. Then again, the intent of the thought experiment was that you stay in one place.
- patmorgan23 2y ago
  Time moves slower at the bottom of an elevator shaft because it is closer to the earth. We have instruments so precise we can measure that difference now.
  - moi2388 2y ago
    Yes I’ve always wondered about this. I thought the thought experiment basically dealt with points not regions though
- DemocracyFTW2 2y ago
  1) what the others said, in a gravity well it depends on height above the floor, but not in an accelerating elevator; this limits the height according to the sensitivity of your instruments 2) additionally, we do not know of any disc-shaped objects of sufficient density and matter distribution to produce a uniformly linear gravity field; only galaxies come close but their gravity is small compared e.g. to that of Earth. Most of the time gravity is caused by spherical objects, meaning the lines of the fields diverge. If you had an elevator with a sufficiently large, completely flat floor, you could tell that you're hovering above a planet by observing that a plumb bob forms different angles with different (perfectly upright) walls of the cabin.