6 ms·

I guess you are confusing two things - think of a mark on a real line at x somewhere between 17 mm and 18 mm from the origin. If you measure its location with a

I guess you are confusing two things - think of a mark on a real line at x somewhere between 17 mm and 18 mm from the origin. If you measure its location with a ruler, you might only be able to say that it is somewhere between 17 mm and 18 mm from the origin, but this uncertainty in your measurement in no way constraints x to only be located at integer millimeter positions or something like that. There is not even a real limit imposed by the uncertainty principle, you can measure positions as precisely as you want, you just have to pay in momentum uncertainty. Where we really seem to run into a wall is that if you keep making the measurement more and more precise, you need higher and higher energies to achieve ever shorter wavelengths and dumping a lot of energy into a small volume to measure the position really precisely will eventually result in black holes.

naasking 4y ago
> There is not even a real limit imposed by the uncertainty principle, you can measure positions as precisely as you want, you just have to pay in momentum uncertainty. Yes, that's the current continuous model of how this works. That isn't necessarily reflective of reality though. > Where we really seem to run into a wall is that if you keep making the measurement more and more precise, you need higher and higher energies to achieve ever shorter wavelengths and dumping a lot of energy into a small volume to measure the position really precisely will eventually result in black holes. Exactly. In other words, all measurements necessarily have finite precision due to various uncertainties or other physical limits. I didn't pull this limit out of the aether, I came across it from one of Shor's posts [1] where he states that physical constants can't be defined to greater precision than what I specified above. If the physical constants can't have more than 60 digits of precision, then neither can any calculations or measurements based on them. The fact is, we seem to be bounded on all sides to finite precision. [1] https://physics.stackexchange.com/questions/16889/non-computable-numbers-in-physics#comment40236_16893 https://physics.stackexchange.com/questions/16889/non-comput...
- danbruc 4y ago
  My point is just that limited measurement precision does not imply anything about the underlying structure, could be continuous or not, I am not arguing for one side or the other.
  - naasking 4y ago
    Well then you seem to be agreeing with my original statement: > So yes, current theories use continuous real numbers, but I wouldn't generalize that to say that's confirmed because we're nowhere near being able to test that level of precision.
    - danbruc 4y ago
      Yes and no, I guess, depending on what exactly you intended to say. We agree, I guess, that we are currently using real numbers but that does not mean that the universe is actually continuous. Where I am not so sure that we agree is about the experimental side. We could run into some barrier when probing shorter and shorter distances, but this would not necessarily imply that space is not continuous. On the other hand we could also observe effects that clearly indicate a non-continuous structure of space without running into some measurement limit.
      - naasking 4y ago
        > Where I am not so sure that we agree is about the experimental side. We could run into some barrier when probing shorter and shorter distances, but this would not necessarily imply that space is not continuous Agreed, though I personally find continuous quantities implausible, despite preferring them at one point. As long as we had a discrete theory with equal predictive and explanatory power and it was equally parsimonious to a continuous theory, I would likely prefer it. I think the next revolution in physics will see an expansion of discretization or other forms of finitism. > On the other hand we could also observe effects that clearly indicate a non-continuous structure of space without running into some measurement limit. Agreed as well.
  - BlueTemplar 4y ago

naasking 4y ago

> There is not even a real limit imposed by the uncertainty principle, you can measure positions as precisely as you want, you just have to pay in momentum uncertainty. Yes, that's the current continuous model of how this works. That isn't necessarily reflective of reality though. > Where we really seem to run into a wall is that if you keep making the measurement more and more precise, you need higher and higher energies to achieve ever shorter wavelengths and dumping a lot of energy into a small volume to measure the position really precisely will eventually result in black holes. Exactly. In other words, all measurements necessarily have finite precision due to various uncertainties or other physical limits. I didn't pull this limit out of the aether, I came across it from one of Shor's posts [1] where he states that physical constants can't be defined to greater precision than what I specified above. If the physical constants can't have more than 60 digits of precision, then neither can any calculations or measurements based on them. The fact is, we seem to be bounded on all sides to finite precision. [1] https://physics.stackexchange.com/questions/16889/non-computable-numbers-in-physics#comment40236_16893 https://physics.stackexchange.com/questions/16889/non-comput...

danbruc 4y ago
My point is just that limited measurement precision does not imply anything about the underlying structure, could be continuous or not, I am not arguing for one side or the other.
- naasking 4y ago
  Well then you seem to be agreeing with my original statement: > So yes, current theories use continuous real numbers, but I wouldn't generalize that to say that's confirmed because we're nowhere near being able to test that level of precision.
  - danbruc 4y ago
    Yes and no, I guess, depending on what exactly you intended to say. We agree, I guess, that we are currently using real numbers but that does not mean that the universe is actually continuous. Where I am not so sure that we agree is about the experimental side. We could run into some barrier when probing shorter and shorter distances, but this would not necessarily imply that space is not continuous. On the other hand we could also observe effects that clearly indicate a non-continuous structure of space without running into some measurement limit.
    - naasking 4y ago
      > Where I am not so sure that we agree is about the experimental side. We could run into some barrier when probing shorter and shorter distances, but this would not necessarily imply that space is not continuous Agreed, though I personally find continuous quantities implausible, despite preferring them at one point. As long as we had a discrete theory with equal predictive and explanatory power and it was equally parsimonious to a continuous theory, I would likely prefer it. I think the next revolution in physics will see an expansion of discretization or other forms of finitism. > On the other hand we could also observe effects that clearly indicate a non-continuous structure of space without running into some measurement limit. Agreed as well.
- BlueTemplar 4y ago