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http://en.wikipedia.org/wiki/Heisenberg_uncertainty_principle http://en.wikipedia.org/wiki/Heisenberg_uncertainty_principl... describes nature's limit to precis

by dexen 15y ago

http://en.wikipedia.org/wiki/Heisenberg_uncertainty_principle http://en.wikipedia.org/wiki/Heisenberg_uncertainty_principl... describes nature's limit to precision of measurement of position and speed vector of objects. In physics, it does not make sense to discuss position (nor boundaries) of object with infinite or absolute precision. There are suggestions that http://en.wikipedia.org/wiki/Planck_distance http://en.wikipedia.org/wiki/Planck_distance is the smallest distance (or size) nature handles. You could say nature has no concept of real numbers.

loup-vaillant 15y ago
> In physics, it does not make sense to discuss position (nor boundaries) of object with infinite or absolute precision. No, no, no, you are over interpreting. The fact that you cannot measure with infinite precision doesn't mean it doesn't even makes sense to talk infinitely precisely about positions. You can for instance make thoughts experiments, by imagining an initial state infinitely precisely, then conclude that subsequent measures will give such and such results, this time with finite precision. According to current models, nature runs on infinitely precise mathematics. (And according to most sensible current models, that math is also deterministic.) The fact that your access to those maths lack infinite precision doesn't mean the math itself is imprecise.
- mattheww 15y ago
  Actually, it's you who is doing the over interpreting. The Heisenberg uncertainty principle is a physical constraint that wave functions obey. If you define a state with an infinitely precise location, then the range of momentums is infinite. This result is fairly easy to reproduce, so it would probably be instructive to try it. The measurement interpretation of the Heisenberg uncertainty principle is both a useful way to understand it, and historically, a way to ease experimentalists into accepting and believing it.
  - sixbrx 15y ago
    I'm not sure what your argument really is here. Your very invocation of "the wave function" implies continuity in the evolution of the state vectors, described by the wave equation - it matters not that results of macroscopic measurements will only produce quantized results. You still used continuity of the more abstract (but no less "real") state vector evolution.
  - loup-vaillant 15y ago
    Just to be sure: the wave function is still a distribution of complex amplitude over a configuration space, right ? If I understand, you are saying is that if we have a Dirac peak at some point, then the momentum spread everywhere (the infinite momentum). I don't dispute that. I only meant that we could describe (in principle) a hypothetical wave function with infinite precision. Meaning, at each exact point in our hypothetical configuration space, we would specify an exact amplitude. (With the usual caveats due to the fact that we're talking about a distribution, not a function.) From then, we could predict the experimental results, which are bound to yield finite precision. Now, current physics say we will never infinitely accurately measure our wave function. But it also says that this wave function behaves lawfully, with infinite precision, from some (I think?) unknown initial state. Is there a problem left ? Edit: it just hit me that there is a problem if you don't believe in Many Worlds. Just know that I think the Copenhagen interpretation is crazy (I don't believe in the collapse of the wave function), and that currently, I find some form of Many World Interpretation most likely.

by dexen 15y ago

loup-vaillant 15y ago

> In physics, it does not make sense to discuss position (nor boundaries) of object with infinite or absolute precision. No, no, no, you are over interpreting. The fact that you cannot measure with infinite precision doesn't mean it doesn't even makes sense to talk infinitely precisely about positions. You can for instance make thoughts experiments, by imagining an initial state infinitely precisely, then conclude that subsequent measures will give such and such results, this time with finite precision. According to current models, nature runs on infinitely precise mathematics. (And according to most sensible current models, that math is also deterministic.) The fact that your access to those maths lack infinite precision doesn't mean the math itself is imprecise.

mattheww 15y ago
Actually, it's you who is doing the over interpreting. The Heisenberg uncertainty principle is a physical constraint that wave functions obey. If you define a state with an infinitely precise location, then the range of momentums is infinite. This result is fairly easy to reproduce, so it would probably be instructive to try it. The measurement interpretation of the Heisenberg uncertainty principle is both a useful way to understand it, and historically, a way to ease experimentalists into accepting and believing it.
- sixbrx 15y ago
  I'm not sure what your argument really is here. Your very invocation of "the wave function" implies continuity in the evolution of the state vectors, described by the wave equation - it matters not that results of macroscopic measurements will only produce quantized results. You still used continuity of the more abstract (but no less "real") state vector evolution.
- loup-vaillant 15y ago
  Just to be sure: the wave function is still a distribution of complex amplitude over a configuration space, right ? If I understand, you are saying is that if we have a Dirac peak at some point, then the momentum spread everywhere (the infinite momentum). I don't dispute that. I only meant that we could describe (in principle) a hypothetical wave function with infinite precision. Meaning, at each exact point in our hypothetical configuration space, we would specify an exact amplitude. (With the usual caveats due to the fact that we're talking about a distribution, not a function.) From then, we could predict the experimental results, which are bound to yield finite precision. Now, current physics say we will never infinitely accurately measure our wave function. But it also says that this wave function behaves lawfully, with infinite precision, from some (I think?) unknown initial state. Is there a problem left ? Edit: it just hit me that there is a problem if you don't believe in Many Worlds. Just know that I think the Copenhagen interpretation is crazy (I don't believe in the collapse of the wave function), and that currently, I find some form of Many World Interpretation most likely.