I really do want to apologize in advance, I know this question has been 'answered' before. I have this 'problem' of feeling negatively toward much of today's 'mystical' interpretations of physics, quantum physics in particular.
I am going through the Solid State Chemistry course provided by MIT's open-course-ware and I really like how the professor goes into some of the mathematical models. The current discussion is over Niels Bohr's quantization of the electron to support the planetary model of atoms. Very interesting.
So, this naturally brought me back to some of my pondering about quantum mechanics. I want to know: if one single photon, not a collection of them, is shot from a laser through the double slits, does it indeed physically go through both slits as a wave, only to "collapse" as a particle when it hits the screen? Will one single photon produce the interference pattern? Does it take many photons to build up the interference pattern?
See, I have this issue where I think that the wave function is just a mathematical model to represent the probability a particle will be in any given spot when measured. Basically, that it is not to say that a particle is actually in all places at once (as a wave), rather we can not know where it is because of the uncertainty of measurement at those scales, so we represent this as a mathematical model, on paper. Is this a correct interpretation, or do these mystical "quacks" actually have something right?
Update 1:
This answer here, https://physics.stackexchange.com/a/22934/46693 is what my question is about. There is the claim that "the photon simply doesn't have a position…because the photon's position is ill defined it occupies the whole experimental apparatus", and to me that seems like a logical fallacy, basically saying, "I don't know the location so it must not have one." Which interpretation is correct? I am saying that it does have a position, and that if we try to determine which slit the particle travels through, the measurement will have an impact on the outcome of the experiment, thus disrupting the interference pattern. While he is saying, that "it doesn't have a position, because I don't know what it is, so it must go through both slits."
I would be very grateful if this was clarified, thank you.
Update 2:
I understand that it is necessary for us to calculate things with the use of probability, and that assuming for the sake of equation that there are many worlds can be helpful. What I am asking is: Do professional physicists really use probabilistic models like these to "prove" that photons do not have location, or that there actually are "many worlds"? It seems to me that the fact that we use probability at all shows a lacking on our part as scientists, and not that nature is truly as strange as some hype it up to be. For instance, if movement caused time travel, people ought to be popping in and out of my experience, but that never happens.
Best Answer
It's all theory. The measure is how well it predicts. If you're looking for a concrete epistemology of what a photon is, you will not find it.
The way I think about your photon is the many-worlds interpretation, where instead of each "world" having a probability, it has a probability amplitude, which is a complex number.
If a world had only a probability, and you didn't know which world you were in, but knew you were in some set of possible worlds, then you would get the probability of that set by just adding the individual probabilities.
However, since worlds don't have probabilities, but amplitudes (which are square roots of probabilities), then to find the amplitude of a set of possible worlds, you add their amplitudes, and since those are complex numbers, they can reinforce, or cancel.
So you don't know if the world you are in has the photon going through slit A, or slit B, and landing at location C. But if you add the amplitudes of those two possibilities, you get a combined amplitude, when squared, that can be more, or less, than simply adding the probabilities.
So the question isn't, which slit did the photon come through, but what's the amplitude, and therefore the probability, of the set of possible worlds we are in. It's just a mathematical model, but it's the one that nature seems to follow.