I would like to get an idea of what "quantum probability" means and how it differs from classical frequentist or Bayesian probability. Can anyone enlighten me in non-too-technical terms?
Asked
Active
Viewed 164 times
0
-
4possible duplicate of Why is the application of probability in QM fundamentally different from application of probability in other areas? – ACuriousMind Sep 19 '15 at 00:33
-
The best introduction I read to this were the Feynman lectures, which are online for free now, I think If you search for them. – Sep 19 '15 at 00:38
-
Feynman lectures online: http://www.feynmanlectures.caltech.edu/III_toc.html#Ch8-S6 – Gert Sep 19 '15 at 01:20
-
Quantum probability doesn't mean anything. Quantum systems aren't probabilistic, they are "uncertain", but that's not due to a probability built into the system but due to an unknowable quantum mechanical state of your measurement device. You go in with partial knowledge and you come out with partial knowledge, no probability needed. – CuriousOne Sep 19 '15 at 02:36
1 Answers
0
In Bayesian probability there is some objective truth that can be discovered with higher and higher certainty if we learn more information and update our distribution. The distribution does not fully describe the system. Rather it helps us to guess what the system might look like.
In the Copenhagen interpretation of quantum mechanics there is no objective truth beyond the wavefunction, which is essentially the distribution. If you know the wavefunction exactly, you have fully described the system.
In ordinary Bayesian probability when you do a measurement you learn more about the system and change the distribution. But that doesn't change the reality of the system. In quantum mechanics if you know the wavefunction you already know everything. In fact, in quantum mechanics when you do a measurement and change the distribution, you are actually changing the physical state of the system rather then only uncovering information about the system's previous state.
For another more technical discussion of quantum mechanics as a kind of probability theory with a 2-norm, see this interesting article. https://arxiv.org/abs/quant-ph/0101012
-
Conventional probability is just as much in the way of "knowing" the wavefunction as it is in the way of knowing classical trajectories etc.. This has nothing to do with uncertainty, it's just the same problem as with every other discrete measurement: $n$ independent measurements only lead to a statistical estimate that is good to about $1/\sqrt{n}$ in statistical error. Having said that, we rarely ever measure wavefunctions directly. There are much better spectral methods to get the actually relevant information about the system with extremely high precision. – CuriousOne Sep 19 '15 at 02:32
-
Are you disputing part of my answer? If so please clarify what you are disputing. I'm curious. Thanks! – Ian Sep 19 '15 at 02:44
-
Phrases like "objective truth" and "know exactly" are a dead giveaway that somebody hasn't internalized what physics does, it certainly doesn't do any of those things. Measurements don't change distributions in quantum mechanics because there are no distributions in quantum mechanics. There are only uncertainties and they have absolutely nothing to do with Bayesian (or any other) definition of probability. You are welcome, though, to find the central limit theorems of quantum mechanics, if you think otherwise. – CuriousOne Sep 19 '15 at 02:50
-
@CuriousOne So called measurements can definitely change the state (into an eigenstate) and since the answer above was conflating states and distributions (and being clear about it) and you can and do change the state ... that's it. – Timaeus Sep 19 '15 at 03:25
-
@Timaeus: My point was exactly that the post is conflating states and distributions. Distributions have this remarkable property of almost universal convergence into the Gaussian distribution, which is proven by a number of Central Limit theorems. Quantum mechanical systems do nothing like that. – CuriousOne Sep 19 '15 at 03:38
-
I was conflating distributions and wavefunctions intentionally. There are most definitely distributions in quantum mechanics if we define a distribution as a function that assigns a probability to each configuration of a system. I conflate distributions and wavefunctions since we can easily get the distribution from the wavefunction by writing the wavefunction in some basis and then squaring the modulus. This makes a distribution. – Ian Sep 19 '15 at 04:45
-
The information in the wavefunction is different from the information in a classical distribution that you might see in Bayesian probability. In QM the wavefunction contains all information about the system, while in classical probability the distribution only tells you what the system might look like, not what it actually does look like. – Ian Sep 19 '15 at 04:46
-
Finally, if you assume that quantum mechanics is truth as opposed to treating quantum mechanics as simply a useful predictive model, then the wavefunction can be thought of as the objective truth. – Ian Sep 19 '15 at 04:48
-
This is the kind of thinking you need to make sense of mixed states in quantum statistical mechanics, where we simultaneously need to consider quantum and statistical probabilities. – Ian Sep 19 '15 at 04:55