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"Thus continuing my inability to understand [...]" You will enjoy this beautiful lecture given by Dr. Feynman entitled, "Probability and Uncertainty - The Quan

by Arjuna 13y ago

"Thus continuing my inability to understand [...]" You will enjoy this beautiful lecture given by Dr. Feynman entitled, "Probability and Uncertainty - The Quantum Mechanical View of Nature." [1] In this lecture, he describes the double-slit experiment, which is tied to the topic of quantum superposition. This particular section blows me away every time: "Here are the circumstances: source, strong light source; tell me, behind which hole will I see the electron? You say, 'Well, the reason you can't tell through which hole you're going to see the electron is, it's determined by some very complicated things back here: if I knew enough about that electron - it has internal wheels, internal gears, and so forth - and that this is what determines through which hole it goes. It's 50/50 probability because, like a die, it's set sort of at random - and if I were to have studied it carefully enough, your physics is incomplete: if you get a complete enough physics, then you'll be able to predict through which hole it goes.' That's the 'hidden variable' theory, so called. Well, that's not possible. It is not due to a lack of detailed knowledge that we cannot make a prediction, because I said that if I didn't turn on the light, I should get this interference pattern. If I have a circumstance in which I get that interference pattern, then it is impossible to analyze it in terms of saying, it goes through here or here, because that curve is so simple, mathematically - a different thing than the contribution of this and this as probabilities. So if it were possible for you to have determined through which hole it was going to go if I had the light on, the fact that I had the light on hasn't got anything to do with it! Whatever gears there are back here that you observe, which permitted you to tell me whether is was going to go through 1 or 2, you could have observed if I had the light off. And therefore you could have told me with the light off which hole - each time an electron goes - which hole it's going to go through. But if you can do this, then that curve would have to be represented as the sum of those that go through there and those that go through there - and it ain't. Therefore, it's impossible to have information ahead of time as to which hole it's going to go through when the light is out - or when the light is on, or out - in a circumstance where the experiment is set up that can produce this interference pattern. It is not a lack of unknown gears - a lack of internal complications - that makes nature have probability in it; it seems to be in some sense intrinsic. Someone has said it this way: 'nature herself doesn't know which way the electron is going to go.' A philosopher once said (a pompous one): 'it is necessary for the very existence of science that the same conditions always produce the same result.' Well, they don't: if you set up electrons in any way - I mean, you set up the circumstance here, in the same conditions every time, and you cannot predict behind which hole you'll see the electron. They don't - and yet the science goes on in spite of him." [1] https://www.youtube.com/watch?v=OCFX_NHBefI https://www.youtube.com/watch?v=OCFX_NHBefI

rjprins 13y ago
This is only true for local hidden variables. It is possible to explain this with hidden variables in broader sense. Which you could also call hidden connections.
- xenophanes 13y ago
  And could also call non-local (faster-than-light) magical thinking.
- Arjuna 13y ago
  "This is only true for local hidden variables. It is possible to explain this with hidden variables in broader sense. Which you could also call hidden connections." Can you explain further? The reason I ask is that, it would appear quite sound and logical (based on our knowledge of discrete objects in the real world) to say that the electron goes through either slit 1 or slit 2 in all cases, but this is not accurate. The reason is this: When an observation is made, then it can be determined which slit the electron went through; in this case, it always goes through one slit or the other. However, this observation is impossible to make without simultaneously disturbing the electron and destroying the interference pattern; that is to say, the resulting arrival distribution curve is not equal to the arrival distribution curve that is generated when no observations are made. Therefore, how can it be determined which slit the electron will go through, while at the same time, not destroying the interference pattern? To me, this is one of the "mystery of mysteries" of our universe.
  - jostylr 13y ago
    There is a perfectly good theory which allows one to have electrons just going through one slit at a time. It has a few names: de Broglie-Bohm theory/pilot-wave theory/Bohmian mechanics. The idea is that we have a wave AND a particle. The wave goes through both slits and interferes. The particle travels along the wave, like some wood on the ocean. Unlike an ocean wave, the quantum wave exists in 3N dimensional space where N is the number of particles in the universe (fundamentally) or the number of relevant particles in an experiment (practically). When an observation is made of which slit it went through, the environmental variables get entangled with the experimental system and separate the two branches of the wave functions (kind of like 2d waves that become separated vertically) and thus they can no longer interfere. The particle, always there and traveling along the wave, no longer is on a wave with an interference pattern. The system is no longer isolated from the environment and the behavior changes as a result. The weirdness is not the hidden variable (position of the particle!), but rather the quantum wave function. It lives on configuration space, meaning that, in theory, it uses the configuration of all the particles of the universe at a single time. This somewhat contradicts relativity. Bell, once he saw Bohm's theory, realized that nonlocality is the central issue. He tried to do better. He failed and then proved that nature itself is simply nonlocal. No one likes it, but that is simply the way nature is. Relativity lost to quantum nonlocality. As for randomness, one can prove in Bohm's theory that it is impossible to know the precise location of a particle. The best we can do, theoretically regardless of technology, is the quantum mechanical rule of psi-squared probability. The theory has global existence and uniqueness of solutions which classical mechanics does not even have. It agrees completely with standard quantum predictions. It is not very magical. It can even be derived more easily than the Schrodinger equation itself. In fact, all one has to do is assume that one has particles with positions and the guiding equation can be derived from at least five entirely different points of view.

by Arjuna 13y ago

rjprins 13y ago

This is only true for local hidden variables. It is possible to explain this with hidden variables in broader sense. Which you could also call hidden connections.

xenophanes 13y ago
And could also call non-local (faster-than-light) magical thinking.
Arjuna 13y ago
"This is only true for local hidden variables. It is possible to explain this with hidden variables in broader sense. Which you could also call hidden connections." Can you explain further? The reason I ask is that, it would appear quite sound and logical (based on our knowledge of discrete objects in the real world) to say that the electron goes through either slit 1 or slit 2 in all cases, but this is not accurate. The reason is this: When an observation is made, then it can be determined which slit the electron went through; in this case, it always goes through one slit or the other. However, this observation is impossible to make without simultaneously disturbing the electron and destroying the interference pattern; that is to say, the resulting arrival distribution curve is not equal to the arrival distribution curve that is generated when no observations are made. Therefore, how can it be determined which slit the electron will go through, while at the same time, not destroying the interference pattern? To me, this is one of the "mystery of mysteries" of our universe.
- jostylr 13y ago
  There is a perfectly good theory which allows one to have electrons just going through one slit at a time. It has a few names: de Broglie-Bohm theory/pilot-wave theory/Bohmian mechanics. The idea is that we have a wave AND a particle. The wave goes through both slits and interferes. The particle travels along the wave, like some wood on the ocean. Unlike an ocean wave, the quantum wave exists in 3N dimensional space where N is the number of particles in the universe (fundamentally) or the number of relevant particles in an experiment (practically). When an observation is made of which slit it went through, the environmental variables get entangled with the experimental system and separate the two branches of the wave functions (kind of like 2d waves that become separated vertically) and thus they can no longer interfere. The particle, always there and traveling along the wave, no longer is on a wave with an interference pattern. The system is no longer isolated from the environment and the behavior changes as a result. The weirdness is not the hidden variable (position of the particle!), but rather the quantum wave function. It lives on configuration space, meaning that, in theory, it uses the configuration of all the particles of the universe at a single time. This somewhat contradicts relativity. Bell, once he saw Bohm's theory, realized that nonlocality is the central issue. He tried to do better. He failed and then proved that nature itself is simply nonlocal. No one likes it, but that is simply the way nature is. Relativity lost to quantum nonlocality. As for randomness, one can prove in Bohm's theory that it is impossible to know the precise location of a particle. The best we can do, theoretically regardless of technology, is the quantum mechanical rule of psi-squared probability. The theory has global existence and uniqueness of solutions which classical mechanics does not even have. It agrees completely with standard quantum predictions. It is not very magical. It can even be derived more easily than the Schrodinger equation itself. In fact, all one has to do is assume that one has particles with positions and the guiding equation can be derived from at least five entirely different points of view.