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In order for space to truly be continuous, particles would have to be represented with effectively infinite position information. Since particles seem to conta

In order for space to truly be continuous, particles would have to be represented with effectively infinite position information. Since particles seem to contain finite information, that seems unlikely.

danbruc 3y ago
That seems to me to be the wrong way to think about this. I don't think that we have any evidence that a particle stores its position in the same way we might do in a physics simulation, it just sits at some position in space time. What would its position even be, where would the origin of the coordinate system be? And even you could always just pick a coordinate system with the origin right where the particle is, then its coordinates would trivially be zero. If you have several or moving particles and you want to keep the coordinate system fixed, then this will of course no longer work.
- kromem 3y ago
  It also makes the assumption that the measurement of position must be continuously detailed, which we know in our universe is impossible because of the Plank length. So even if spacetime is continuous and particles do move within it in continuous ways, the combination of Heisenberg's uncertainty principle plus the Plank length means we can never observe such continuity anyways.
  - eigenket 3y ago
    > which we know in our universe is impossible because of the Plank length I think the statement that you are implying here is not known to be correct. We have no idea if it is (theoretically) possible to measure the position of a particle to a precision of less than a Plank length. In some formulations of quantum gravity there are fundamental limits like this, but quantum gravity is difficult at best and sketchy at worst and none of those versions of quantum gravity is without their flaws.
    - kromem 3y ago
      The problem is there's no way to measure it in actuality. If there's not enough energy in the universe to make the measurement, then there's no making the measurement no matter the theory of what would happen if there were more energy. We could discuss the theory of what happens to a virtual photon going down a split path between Everett or another interpretation, but if we can't ever actually measure the virtual photon, then it's just theorizing around an unanswerable question. Which is part of what leads to "shut up and calculate."
kromem 3y ago
Fun fact - as best we know, it's fundamentally impossible to know if space or time is actually continuous or discrete. We've known about the limitation in space for a while with the Plank length, and a similar limitation in time was discovered a year or two ago. So while we have successful models for the universe that rely on the notion of continuous spacetime, our measurable version of it effectively has a minimum pixel size beyond which we fundamentally cannot get any more detail. Fit the first time the other year I saw a psychics paper that actually presumed discrete spacetime based on simulation theory, which was pretty funny. I don't think the paper is that interesting beyond that aspect, but maybe you'll enjoy it given the presumption of discreteness: https://www.nature.com/articles/s41598-020-76301-0 https://www.nature.com/articles/s41598-020-76301-0

danbruc 3y ago

That seems to me to be the wrong way to think about this. I don't think that we have any evidence that a particle stores its position in the same way we might do in a physics simulation, it just sits at some position in space time. What would its position even be, where would the origin of the coordinate system be? And even you could always just pick a coordinate system with the origin right where the particle is, then its coordinates would trivially be zero. If you have several or moving particles and you want to keep the coordinate system fixed, then this will of course no longer work.

kromem 3y ago
It also makes the assumption that the measurement of position must be continuously detailed, which we know in our universe is impossible because of the Plank length. So even if spacetime is continuous and particles do move within it in continuous ways, the combination of Heisenberg's uncertainty principle plus the Plank length means we can never observe such continuity anyways.
- eigenket 3y ago
  > which we know in our universe is impossible because of the Plank length I think the statement that you are implying here is not known to be correct. We have no idea if it is (theoretically) possible to measure the position of a particle to a precision of less than a Plank length. In some formulations of quantum gravity there are fundamental limits like this, but quantum gravity is difficult at best and sketchy at worst and none of those versions of quantum gravity is without their flaws.
  - kromem 3y ago
    The problem is there's no way to measure it in actuality. If there's not enough energy in the universe to make the measurement, then there's no making the measurement no matter the theory of what would happen if there were more energy. We could discuss the theory of what happens to a virtual photon going down a split path between Everett or another interpretation, but if we can't ever actually measure the virtual photon, then it's just theorizing around an unanswerable question. Which is part of what leads to "shut up and calculate."

kromem 3y ago

Fun fact - as best we know, it's fundamentally impossible to know if space or time is actually continuous or discrete. We've known about the limitation in space for a while with the Plank length, and a similar limitation in time was discovered a year or two ago. So while we have successful models for the universe that rely on the notion of continuous spacetime, our measurable version of it effectively has a minimum pixel size beyond which we fundamentally cannot get any more detail. Fit the first time the other year I saw a psychics paper that actually presumed discrete spacetime based on simulation theory, which was pretty funny. I don't think the paper is that interesting beyond that aspect, but maybe you'll enjoy it given the presumption of discreteness: https://www.nature.com/articles/s41598-020-76301-0 https://www.nature.com/articles/s41598-020-76301-0