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I've seen this a handful of times, but I don't know enough about physics to understand the specifics of the theorem to make meaningful statements about it. Can

by noahlt 16y ago

I've seen this a handful of times, but I don't know enough about physics to understand the specifics of the theorem to make meaningful statements about it. Can anyone explain the free will theorem to laymen?

Qz 16y ago
Here is my layman's understanding of it: Say we have two people performing similar experiments who are far enough apart from each other that the information from one experiment can't affect the result of the other person's experiment. The experiment they are performing is to measure the 'spin' of a particle that has been 'entangled' with the particle measured by the other experimenter. Since the particles are entangled, if the experimenters measure the spin in the same direction, they will both get the same result. The theorem then states that if the experimenters are 'free' (as in will) to choose which direction to measure the spin of their particle, then the result of measuring the spin cannot be determined by anything previous to the experiments (and can't be determined by the other experimenter, as established above). Put into everyday terms, its impossible for the universe to be fully determinate and still have actors capable of free will, and vice versa: if people have free will then the world can't be fully determinate.
- mbateman 16y ago
  > The theorem then states that if the experimenters are 'free' (as in will) to choose which direction to measure the spin of their particle, then the result of measuring the spin cannot be determined by anything previous to the experiments (and can't be determined by the other experimenter, as established above). Yes, and this is because if it could be determined by anything, it would imply something like a hidden variable theory of quantum mechanics, which violates the Kochen-Specker theorem. This is the part of the argument that I don't understand. If anyone could help I'd be grateful.
  - Qz 16y ago
    Well basically the KS paradox says that for certain types of measurements (which not-coincidentally happens to be the exact type of measurement in the free will theorem), the result of the measurement is based on the direction of the measurement, not on anything prior to that measurement. Specifically, if you measure the 'spin' in 3 orthogonal directions, then the resulting values will always be the same (1,0,1 in some order), but that there is no function which can determine those values prior to the actual measurement, hence there is no possible hidden variable that can explain the quantum mechanical result. The free will theorem extends that result because the fundamental issue of the KS paradox hinges on the direction in which the spin is measured relative to the universe. The direction of the particular measurement is 'decided' upon by the person or thing doing the measuring, in this case the experimenter. But is that direction pre-determined, or does the person have free will in choosing the direction? The situation is tricky because we now have two experimenters who are measuring a pair of entangled particles, which we thus know will give the same result, if measured in the same direction. Because of the KS paradox, we know that the result of the measurement hinges on the direction chosen by the experimenter, not on anything prior to the experiment. If we take that the experimenters have 'free will' then the entangled nature of the particles means that the result of the spin measurement can't be 'random' but it is also 'non-determinate' because of KS, and thus the result of the measurement must have the same quality of 'freedom' as the 'freedom' experienced by the experimenters in choosing the direction of measurement.

by noahlt 16y ago

Qz 16y ago

Here is my layman's understanding of it: Say we have two people performing similar experiments who are far enough apart from each other that the information from one experiment can't affect the result of the other person's experiment. The experiment they are performing is to measure the 'spin' of a particle that has been 'entangled' with the particle measured by the other experimenter. Since the particles are entangled, if the experimenters measure the spin in the same direction, they will both get the same result. The theorem then states that if the experimenters are 'free' (as in will) to choose which direction to measure the spin of their particle, then the result of measuring the spin cannot be determined by anything previous to the experiments (and can't be determined by the other experimenter, as established above). Put into everyday terms, its impossible for the universe to be fully determinate and still have actors capable of free will, and vice versa: if people have free will then the world can't be fully determinate.

mbateman 16y ago
> The theorem then states that if the experimenters are 'free' (as in will) to choose which direction to measure the spin of their particle, then the result of measuring the spin cannot be determined by anything previous to the experiments (and can't be determined by the other experimenter, as established above). Yes, and this is because if it could be determined by anything, it would imply something like a hidden variable theory of quantum mechanics, which violates the Kochen-Specker theorem. This is the part of the argument that I don't understand. If anyone could help I'd be grateful.
- Qz 16y ago
  Well basically the KS paradox says that for certain types of measurements (which not-coincidentally happens to be the exact type of measurement in the free will theorem), the result of the measurement is based on the direction of the measurement, not on anything prior to that measurement. Specifically, if you measure the 'spin' in 3 orthogonal directions, then the resulting values will always be the same (1,0,1 in some order), but that there is no function which can determine those values prior to the actual measurement, hence there is no possible hidden variable that can explain the quantum mechanical result. The free will theorem extends that result because the fundamental issue of the KS paradox hinges on the direction in which the spin is measured relative to the universe. The direction of the particular measurement is 'decided' upon by the person or thing doing the measuring, in this case the experimenter. But is that direction pre-determined, or does the person have free will in choosing the direction? The situation is tricky because we now have two experimenters who are measuring a pair of entangled particles, which we thus know will give the same result, if measured in the same direction. Because of the KS paradox, we know that the result of the measurement hinges on the direction chosen by the experimenter, not on anything prior to the experiment. If we take that the experimenters have 'free will' then the entangled nature of the particles means that the result of the spin measurement can't be 'random' but it is also 'non-determinate' because of KS, and thus the result of the measurement must have the same quality of 'freedom' as the 'freedom' experienced by the experimenters in choosing the direction of measurement.