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I still don't get it. In Bell's thought experiment, the angle between the axes of two particles is well known before any particle is fired. Why do you say the

I still don't get it. In Bell's thought experiment, the angle between the axes of two particles is well known before any particle is fired. Why do you say the following? > you can't tell what angle the other particle will be measured with If the angle is 90 degrees, the correlation would be 50%, if the angle is 180 degrees, the correlation would be 100%, and when the angle is 0 degrees, the correlation would be 50%. What are you saying (or rather, the theory says) is that since we have the above numbers, if there were local variables, then the correlation, for example, at 90 degrees should have been 25%, and the correllation at 270 degrees should have been 75%, but since in both cases the correlation isn't that, we can't have local variables? Edit: What about this algorithm? struct ParticleState { double otherAngle; }; double algorithm(ParticleState state, double angle) { return -cos(abs(angle - state.otherAngle)); } 'other angle' is the angle of the other entangled particle. This algorithm returns precisely -cos(|oA - oB|) as you suggested.

cyphar 7y ago
> In Bell's thought experiment, the angle between the axes of two particles is well known before any particle is fired. Why do you say the following? The relative angles I'm referring to are of the measurements (or rather, the relative angle between the two measurement vectors). Those angles can be thought of as being unknown when the particles are created (because you can imagine the experimenters for A and B randomly picking an angle after the particles have been separated). We do "know" that the particles have a particular spin along a particular axis when they're created (more accurately, we know that the spin axes have a particular property -- that they have opposite spins along some axis), but we aren't necessarily measuring along that axis (and if you measure a quantum state along a different axis, you get random-looking results that follow a particular statistical distribution which is predicted by quantum mechanics). To give an example of this property. Imagine a particle which we measure to have a +1/2 spin in the Z-axis. If you then measure it along the X-axis you'll get a result of +1/2 50% of the time (note though, that subsequent measurements of the same particle in the same state will give you the same result because measuring the particle collapsed its state to be along the axis you measured). Now, we aren't measuring along the Z-axis in this experiment (instead we're depending on a different property of the particles to calculate their correlation) but the idea is very similar. > If the angle is 90 degrees, the correlation would be 50%, if the angle is 180 degrees, the correlation would be 100%, and when the angle is 0 degrees, the correlation would be 50%. Sure, but if particle A is measured along -47 degrees from the Z-axis (angle chosen at random after the particles are separated), and particle B is measured along +133 degrees from the Z-axis (also a random angle chosen after the particles are separated), how would A (or B) individually know what statistical distribution to produce when you measure it? All the A particle knows is that you measured it at -47 degrees from the Z-axis and it doesn't know what angle B was measured against (heck, the scientist doing the measurement might not know what angle B is being measured against). > 'other angle' is the angle of the other entangled particle. The angle is not a property of the particle, it's a property of the measurement we take.

cyphar 7y ago

> In Bell's thought experiment, the angle between the axes of two particles is well known before any particle is fired. Why do you say the following? The relative angles I'm referring to are of the measurements (or rather, the relative angle between the two measurement vectors). Those angles can be thought of as being unknown when the particles are created (because you can imagine the experimenters for A and B randomly picking an angle after the particles have been separated). We do "know" that the particles have a particular spin along a particular axis when they're created (more accurately, we know that the spin axes have a particular property -- that they have opposite spins along some axis), but we aren't necessarily measuring along that axis (and if you measure a quantum state along a different axis, you get random-looking results that follow a particular statistical distribution which is predicted by quantum mechanics). To give an example of this property. Imagine a particle which we measure to have a +1/2 spin in the Z-axis. If you then measure it along the X-axis you'll get a result of +1/2 50% of the time (note though, that subsequent measurements of the same particle in the same state will give you the same result because measuring the particle collapsed its state to be along the axis you measured). Now, we aren't measuring along the Z-axis in this experiment (instead we're depending on a different property of the particles to calculate their correlation) but the idea is very similar. > If the angle is 90 degrees, the correlation would be 50%, if the angle is 180 degrees, the correlation would be 100%, and when the angle is 0 degrees, the correlation would be 50%. Sure, but if particle A is measured along -47 degrees from the Z-axis (angle chosen at random after the particles are separated), and particle B is measured along +133 degrees from the Z-axis (also a random angle chosen after the particles are separated), how would A (or B) individually know what statistical distribution to produce when you measure it? All the A particle knows is that you measured it at -47 degrees from the Z-axis and it doesn't know what angle B was measured against (heck, the scientist doing the measurement might not know what angle B is being measured against). > 'other angle' is the angle of the other entangled particle. The angle is not a property of the particle, it's a property of the measurement we take.