Sci.Physics.Foundations

FrediFizzx wrote: ↑Fri Jan 26, 2024 12:06 pm

Joy Christian wrote: ↑Fri Jan 26, 2024 9:50 am

FrediFizzx wrote: ↑Fri Jan 26, 2024 8:57 am
After eq. (13) you say "...where k is an arbitrary unit vector...". k is the spin vector of the particles so not exactly arbitrary. The direction of k is arbitrary. You might want to make that more clear.

Thanks! Yes, k is a unit spin vector with arbitrary direction and a unit magnitude.

Ok, you're welcome. Now, I don't quite understand eq. (15). What do sigma_1 and sigma_2 represent?

sigma_1 and sigma_2 represent spins at the two observation stations 1 and 2 at the two ends of the experiment.

The spins in quantum mechanics are not represented by ordinary vectors like k but by Pauli matrices, such as sigma_1 and sigma_2.
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Joy Christian wrote: ↑Fri Jan 26, 2024 1:01 pm

FrediFizzx wrote: ↑Fri Jan 26, 2024 12:06 pm

Joy Christian wrote: ↑Fri Jan 26, 2024 9:50 am
Thanks! Yes, k is a unit spin vector with arbitrary direction and a unit magnitude.

Ok, you're welcome. Now, I don't quite understand eq. (15). What do sigma_1 and sigma_2 represent?

sigma_1 and sigma_2 represent spins at the two observation stations 1 and 2 at the two ends of the experiment.

The spins in quantum mechanics are not represented by ordinary vectors like k but by Pauli matrices, such as sigma_1 and sigma_2.

Why bother with the 1 and 2 designations? They are exactly the same and eq. (15) is a matrix.
.

FrediFizzx wrote: ↑Sat Jan 27, 2024 7:28 am

Joy Christian wrote: ↑Fri Jan 26, 2024 1:01 pm

FrediFizzx wrote: ↑Fri Jan 26, 2024 12:06 pm
Ok, you're welcome. Now, I don't quite understand eq. (15). What do sigma_1 and sigma_2 represent?

sigma_1 and sigma_2 represent spins at the two observation stations 1 and 2 at the two ends of the experiment.

The spins in quantum mechanics are not represented by ordinary vectors like k but by Pauli matrices, such as sigma_1 and sigma_2.

Why bother with the 1 and 2 designations? They are exactly the same and eq. (15) is a matrix.

Because, while mathematically the same, they belong to two different spins, or particles, arriving at the spacelike separated observation stations 1 and 2.
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Joy Christian wrote: ↑Sat Jan 27, 2024 7:49 am

FrediFizzx wrote: ↑Sat Jan 27, 2024 7:28 am

Joy Christian wrote: ↑Fri Jan 26, 2024 1:01 pm
sigma_1 and sigma_2 represent spins at the two observation stations 1 and 2 at the two ends of the experiment.

The spins in quantum mechanics are not represented by ordinary vectors like k but by Pauli matrices, such as sigma_1 and sigma_2.

Why bother with the 1 and 2 designations? They are exactly the same and eq. (15) is a matrix.

Because, while mathematically the same, they belong to two different spins, or particles, arriving at the spacelike separated observation stations 1 and 2.

Sure, that is obvious so really no need for the sub 1 and 2. So, we have a Pauli vector interacting with a direction vector. Seems screwy as we don't get a cross product (a x sigma).

Why is lambda all of a sudden appearing in eq. (16)?
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FrediFizzx wrote: ↑Mon Jan 29, 2024 12:34 pm

Joy Christian wrote: ↑Sat Jan 27, 2024 7:49 am

FrediFizzx wrote: ↑Sat Jan 27, 2024 7:28 am
Why bother with the 1 and 2 designations? They are exactly the same and eq. (15) is a matrix.

Because, while mathematically the same, they belong to two different spins, or particles, arriving at the spacelike separated observation stations 1 and 2.

Sure, that is obvious so really no need for the sub 1 and 2. So, we have a Pauli vector interacting with a direction vector. Seems screwy as we don't get a cross product (a x sigma).

Why is lambda all of a sudden appearing in eq. (16)?

The eigenvalues omega are determined by lambda in Bell's proof. The discussion in Section III is a continuation of the discussion in Section II.
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