- #36
rubi
Science Advisor
- 847
- 348
Spacetime isn't communicating. What is going wrong is the following:
Intuitively, we would think that objects carry around with them some numbers ##\lambda_1,\lambda_2,\ldots## that characterize all their properties. For example, their spin in ##z## direction may be calculated from these numbers by a function ##S_z(\lambda_1,\lambda_2,\ldots)##. You can prove that this naive idea is incompatible with quantum mechanics. However, our intuition for statistics derives from this idea. Only objects, whose spin can be calculated in such a way are forced to obey the statistics that we would find intuitive.
As I said, the previous naive idea is incompatible with QM. However, there are ways to fix it:
1. Give up the idea that objects have spin. The notion of spin changes depending on the situation. There are many observables ##S_z^{(1)}(\lambda_1,\lambda_2,\ldots), S_z^{(2)}(\lambda_1,\lambda_2,\ldots), \ldots## and you need to use a different one depending on the context. This is what hidden variable theories do.
2. Give up the idea that there is a (potentially transfinite) list of numbers ##\lambda_1, \lambda_2, \ldots## that characterizes the situation of the physics. Particles still have spin, but the naive way to describe it mathematically fails. This may produce statistics that is incompatible with our intuition, since the statistics that we would find intuitive is derived from the idea that there are numbers ##\lambda_1,\lambda_2,\ldots## that describe the situation completely.
The first way gives up locality. The second way gives up classicality. Some people call it "realism", but I don't think this is a good name. The universe is still real, but its mathematical description is less naive.
The reason for why we find quantum statistics non-intuitive is that in our daily life, we are used to statistics that can be derived from some underlying list of numbers. However, it is only a problem with our intuition and not with physics itself.
Intuitively, we would think that objects carry around with them some numbers ##\lambda_1,\lambda_2,\ldots## that characterize all their properties. For example, their spin in ##z## direction may be calculated from these numbers by a function ##S_z(\lambda_1,\lambda_2,\ldots)##. You can prove that this naive idea is incompatible with quantum mechanics. However, our intuition for statistics derives from this idea. Only objects, whose spin can be calculated in such a way are forced to obey the statistics that we would find intuitive.
As I said, the previous naive idea is incompatible with QM. However, there are ways to fix it:
1. Give up the idea that objects have spin. The notion of spin changes depending on the situation. There are many observables ##S_z^{(1)}(\lambda_1,\lambda_2,\ldots), S_z^{(2)}(\lambda_1,\lambda_2,\ldots), \ldots## and you need to use a different one depending on the context. This is what hidden variable theories do.
2. Give up the idea that there is a (potentially transfinite) list of numbers ##\lambda_1, \lambda_2, \ldots## that characterizes the situation of the physics. Particles still have spin, but the naive way to describe it mathematically fails. This may produce statistics that is incompatible with our intuition, since the statistics that we would find intuitive is derived from the idea that there are numbers ##\lambda_1,\lambda_2,\ldots## that describe the situation completely.
The first way gives up locality. The second way gives up classicality. Some people call it "realism", but I don't think this is a good name. The universe is still real, but its mathematical description is less naive.
The reason for why we find quantum statistics non-intuitive is that in our daily life, we are used to statistics that can be derived from some underlying list of numbers. However, it is only a problem with our intuition and not with physics itself.
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