Nature is Intrinsically Probabilistic

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.

The light as a particle/wave duality make it impossible to predict where an electron will emerge in an experiment.