# Quick question about experiments done on spin detection

#### rede96

As I understand it, there is a certain probability associated with detecting spin states. Which if the spin state is unknown prior to testing is 0.5.

But if I prepare an electron with say spin up, then measure it again for spin up I will detected spin up 100% of the time.

Also, if I prepare my electron in spin up, but rotate my equipment by 90 degrees the results will show that I only detect spin up with a probability of 0.5 Also, the measuring process will affect the electron and change it's state to the direction of detection.

Prepare my electron again in the spin up state, but this time rotate my equipment by an angle θ, I can work out the probability by Cos2θ/2

So for example, if my equipment was rotated to say 60 degrees, it would give a 75% probability of detecting spin up for an electron that was prepared in the spin up state.

Have I understood that properly?

Also, have all different angels been tested experimentally against their predicted probabilities? Do they all give the expected results compared to the predicted probability or are there some small angles, like say 10 degrees, where the probability is that near to 1 (0.9924 I think), experimentally it just shows 100%?

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#### Nugatory

Mentor
Have I understood that properly?
Yes

Also, have all different angles been tested experimentally against their predicted probabilities? Do they all give the expected results compared to the predicted probability or are there some small angles, like say 10 degrees, where the probability is that near to 1 (0.9924 I think), experimentally it just shows 100%?
Observations match theory to the limits of experimental accuracy here, and we are way better than the third decimal point in accuracy so far. The only theoretical limit to the accuracy of these experiments is our ability to control the rotation of the apparatus itself; we can measure an arbitrarily small probability of the electron ending up spin down by running an arbitrarily large number of electrons through the apparatus.

In practice, experiments testing this behavior (measure on an in-between axis, see angle-dependent probability of one of two results, measured particle changes to the 100% state) are more often done with polarized light. It's easier and cheaper to generate polarized photons in enormous quantities, and they're easier to handle. The principle is the same though.

#### rede96

Yes

Observations match theory to the limits of experimental accuracy here, and we are way better than the third decimal point in accuracy so far. The only theoretical limit to the accuracy of these experiments is our ability to control the rotation of the apparatus itself; we can measure an arbitrarily small probability of the electron ending up spin down by running an arbitrarily large number of electrons through the apparatus.

In practice, experiments testing this behavior (measure on an in-between axis, see angle-dependent probability of one of two results, measured particle changes to the 100% state) are more often done with polarized light. It's easier and cheaper to generate polarized photons in enormous quantities, and they're easier to handle. The principle is the same though.
Ok, great. Thank you.

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