Timeline for Stern-Gerlach experiment and probability theory
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
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| Dec 16, 2023 at 0:03 | answer | added | Cryo | timeline score: 1 | |
| Dec 15, 2023 at 17:29 | comment | added | user124910 | Does the Stern-Gerlach, or another experiment, force you to conclude the $\mathbb{E}(X)=\int_{\mathbb{R}}x|\psi(x)|^2dx$ approach is insufficient? Perhaps because the probabilities do not add subadditively as you would expect? Bell's inequality seems to imply hidden variables do not exist and quantum mechanics is non-local, but I'm not sure what this means in terms of classical probability theory. | |
| Dec 15, 2023 at 17:21 | comment | added | user124910 | @Cryo I'm not sure if it's a history of science problem. The Born rule works for computing probabilities, but I'd like to know why it is necessary. Why does the classical interpretation need this extension to work here? For example, you can imagine that position is a classical random variable and $|\psi(x)|^2$ is its density. Then $\mathbb{E}(X)=\int_{\mathbb{R}}x|\psi(x)|^2dx$. If $\hat{X}$ is the position operator, you can also write this as $<\psi,\hat{X}\psi>$. Why do we need to adopt this approach though? | |
| Dec 15, 2023 at 12:16 | comment | added | Cryo | Note that this rule is a postulate, on which everything is built. It was discovered as a result of multiple historical accidents and was retained as a minimal essence of what is needed for QM | |
| Dec 15, 2023 at 12:13 | comment | added | Cryo | @user124910, is this about history of science, or about science? Stern-Gerlach could have been the first one, but now quantum mechanics is a working horse in Physics and Chemistry, so not sure it matters which experiment was first. It may matter what is the minimal thing you need to get going. IMHO, that's Born Rule. This rule connects wavefunctions to probabilities and leads to situation where wavefunctions are combinable (since Schrodinger equation is linear), but probabilities are not | |
| Dec 15, 2023 at 7:30 | comment | added | user124910 | @Cryo The information on Bell's theorem that I've found, seems to suggest that if you have a probability space with 3 Bernoulli random variables defined on that space, then their inner-products satisfy $<X_1,X_2>+<X_2,X_3>\leq 1-<X_1,X_3>$. But, apparently this does not happen in the Stern-Gerlach experiment, which would be a reason to say we can't use classical probability. I still am reviewing that argument though, and I haven't made sense of it yet. | |
| Dec 15, 2023 at 7:26 | comment | added | user124910 | @Cryo My question is really why is this necessary though? I understand there is a non-commutative probability theory that is working here, but why is it necessary? What experiment made physicists realize that position and momentum cannot be modeled as random variables in the classical sense? | |
| Dec 15, 2023 at 6:36 | comment | added | Cryo | @PatoGalmarini, gave the relevant link above. In simple terms, probabilities of two independent events add up. That's how probabilities work. In quantum physics it is the probability amplitudes that add up, and since the amplitudes a complex-valued, the magnitude of their sum can be smaller than the individual component's magnitude. This is not possible with strictly non-negative probabilities | |
| Dec 15, 2023 at 0:40 | history | edited | Qmechanic♦ | CC BY-SA 4.0 |
added 10 characters in body; edited tags
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| Dec 15, 2023 at 0:30 | comment | added | Pato Galmarini | en.wikipedia.org/wiki/Bell%27s_theorem. | |
| S Dec 14, 2023 at 23:57 | review | First questions | |||
| Dec 15, 2023 at 5:43 | |||||
| S Dec 14, 2023 at 23:57 | history | asked | user124910 | CC BY-SA 4.0 |