3 ms·

> an observer may have much less information than physically possible, but it can't have more information about some system than a physical limit. Still the pr

by kgwgk 2y ago

> an observer may have much less information than physically possible, but it can't have more information about some system than a physical limit. Still the probability represents the uncertainty of the observer. You say that "the most possible information" is still not enough because "measurement is a time-consuming process" and it's not "possible to measure" with infinite precision. I'd say that you're just confirming that "the lack of knowledge" happens but that doesn't mean the physical state is undefined. You call that uncertainty a property of the system but that doesn't seem right. The evolution of the system will happen according to what the initial state was - not according to what we thought it could have been. Maybe we don't know if A or B will happen because we don't know if the initial state is a or b. But if later we observe A we will know that the initial state was a. (Maybe you would say that at t=0 the physical state is not well-defined but at t=1 the physical state at t=0 becomes well-defined retrospectively?)

tsimionescu 2y ago
I would say that any state that we can't measure is not a physical state. So if we can only measure, even in theory, a system up to precision dx, then the system being in state a means that some quantity is x±dx. If the rules say that the system evolves from states where y>=x to state A, and from states where y<x to state B, then whether we see it in state A or state B, we still only know that it was in state a when it started. We don't get any extra retroactive precision. This is similar to quantum measurement: when we see that the particle was here and not there, we don't learn anything new about its quantum state before the measurement. We already knew everything there was to know about the particle, but that didn't help us predict more than the probabilities of where it might be.
- kgwgk 2y ago
  > I would say that any state that we can't measure is not a physical state. Ok, so if I understand correctly for you microstates are not physical states and it doesn't make sense to even consider that at any given moment the system may be in a particular microstate. That's one way to look at things but the usual starting point for statistical mechanics is quite different.
  - tsimionescu 2y ago
    That would be a bit too strong a wording. I would just say that certain theoretical microstates (ones that assume that position and velocity and so on are real properties that particles possess and can be specified by infinitely precise numbers) are not in fact physically distinguishable. Physical microstates do exist, but they are subject to the Heisenberg limit, and possibly other, less well defined/determined precision limits. Beyond some level of precision, the world becomes fundamentally non-deterministic again, just like it appears in the macro state description.

by kgwgk 2y ago

tsimionescu 2y ago

I would say that any state that we can't measure is not a physical state. So if we can only measure, even in theory, a system up to precision dx, then the system being in state a means that some quantity is x±dx. If the rules say that the system evolves from states where y>=x to state A, and from states where y<x to state B, then whether we see it in state A or state B, we still only know that it was in state a when it started. We don't get any extra retroactive precision. This is similar to quantum measurement: when we see that the particle was here and not there, we don't learn anything new about its quantum state before the measurement. We already knew everything there was to know about the particle, but that didn't help us predict more than the probabilities of where it might be.

kgwgk 2y ago
> I would say that any state that we can't measure is not a physical state. Ok, so if I understand correctly for you microstates are not physical states and it doesn't make sense to even consider that at any given moment the system may be in a particular microstate. That's one way to look at things but the usual starting point for statistical mechanics is quite different.
- tsimionescu 2y ago
  That would be a bit too strong a wording. I would just say that certain theoretical microstates (ones that assume that position and velocity and so on are real properties that particles possess and can be specified by infinitely precise numbers) are not in fact physically distinguishable. Physical microstates do exist, but they are subject to the Heisenberg limit, and possibly other, less well defined/determined precision limits. Beyond some level of precision, the world becomes fundamentally non-deterministic again, just like it appears in the macro state description.