4 ms·

> 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 unce

> 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
  Because if position and momentum are not quantized like this, you cannot get discrete bits of information (aka negative entropy) and the whole (so-called) "2nd law of thermodynamics" becomes impossible to derive, which is kind of a problem ? http://www.av8n.com/physics/thermo/entropy-more.html#sec-phase-space http://www.av8n.com/physics/thermo/entropy-more.html#sec-pha... Note that this underlying structure is subjective, relative to the observer, not something objective... (but we already know that there's no such thing as an "objective underlying structure" from elsewhere from quantum mechanics and also from relativity)
  - naasking 4y ago
    > (but we already know that there's no such thing as an "objective underlying structure" from elsewhere from quantum mechanics and also from relativity) No we don't. Don't confuse the map with the territory.
    - BlueTemplar 4y ago
      In the sense that physics is about "map-making", not the "true nature of reality", and has been for a while now (since it split from philosophy ? since the beginning of postmodern physics in 1905 ?). Even philosophy has pretty much given up that claim : with Gödel/Church/Turing having blown up to smithereens the positivist project of a "theory of everything" for mathematics, and Wittgenstein/Kuhn/Derrida/Foucault/Chomsky having redirected the rest of philosophy towards "the naming of things". And that project had been ironically doomed from before its start anyway : Descartes both laid the groundwork for it by elevating epistemology to "fist philosophy" and for solipsism - which, while a dead-end, cannot be ruled out ! (Also honorable mention for Max Tegmark's Mathematical Universe I guess, which, in a way, indirectly achieves the claim by positing a mathematical multiverse so vast that "our" reality can only be contained inside it.) So the only discipline left that still lays claim on Truth and the True Nature of Reality is theology. (Note that this is how Descartes "solved" the problem of solipsism.)
      - danbruc 4y ago
        Physics is map making, but from that your claims - subjective nature of reality, no objective structure - do not follow, at best you could claim that physics has nothing to say about the nature of reality. And I have doubts about that, at least to some extend. What kind of answer would you expect for a question like what is the true nature of an electron? You can describe the properties of an electron, what more do you want? What is a thing above and beyond the sum of its properties?

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
Because if position and momentum are not quantized like this, you cannot get discrete bits of information (aka negative entropy) and the whole (so-called) "2nd law of thermodynamics" becomes impossible to derive, which is kind of a problem ? http://www.av8n.com/physics/thermo/entropy-more.html#sec-phase-space http://www.av8n.com/physics/thermo/entropy-more.html#sec-pha... Note that this underlying structure is subjective, relative to the observer, not something objective... (but we already know that there's no such thing as an "objective underlying structure" from elsewhere from quantum mechanics and also from relativity)
- naasking 4y ago
  > (but we already know that there's no such thing as an "objective underlying structure" from elsewhere from quantum mechanics and also from relativity) No we don't. Don't confuse the map with the territory.
  - BlueTemplar 4y ago
    In the sense that physics is about "map-making", not the "true nature of reality", and has been for a while now (since it split from philosophy ? since the beginning of postmodern physics in 1905 ?). Even philosophy has pretty much given up that claim : with Gödel/Church/Turing having blown up to smithereens the positivist project of a "theory of everything" for mathematics, and Wittgenstein/Kuhn/Derrida/Foucault/Chomsky having redirected the rest of philosophy towards "the naming of things". And that project had been ironically doomed from before its start anyway : Descartes both laid the groundwork for it by elevating epistemology to "fist philosophy" and for solipsism - which, while a dead-end, cannot be ruled out ! (Also honorable mention for Max Tegmark's Mathematical Universe I guess, which, in a way, indirectly achieves the claim by positing a mathematical multiverse so vast that "our" reality can only be contained inside it.) So the only discipline left that still lays claim on Truth and the True Nature of Reality is theology. (Note that this is how Descartes "solved" the problem of solipsism.)
    - danbruc 4y ago
      Physics is map making, but from that your claims - subjective nature of reality, no objective structure - do not follow, at best you could claim that physics has nothing to say about the nature of reality. And I have doubts about that, at least to some extend. What kind of answer would you expect for a question like what is the true nature of an electron? You can describe the properties of an electron, what more do you want? What is a thing above and beyond the sum of its properties?