Double slit experiments - basic pondering I have some ponderings about the double slit experiment(s) and mainly their interpretations. Some of my questions may exhibit insufficient scholarship so please bear along, or please point out the fallacies wherever they are instead.


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*Why is it commonly said that it is impossible to know in advance which slit any single particle will go through, and all that can be said is that there will be a probability distribution that can describe many particle's aggregate behavior. Isn't it more humbly correct to say that we just don't know how to predict that?

*Say that the experiment is held with electrons. And photons are used to detect whether an electron passed through one of the slits. And of course, this detection collapses the wave function etc. What however should be the effect of the photons on the electron? is an electron totally and entirely oblivious to having interacted with a photon? is only the photon affected by an electron (in the classical model to start with) and not vice versa?

*When the particle beam is being shot, or a a single particle is shot at a time, what can be said about the direction of the particles or the angle of the beam? are those of a probabilistic nature, and what would happen if they are not probabilistic but rather if the direction of each particle is known in advance? this is probably the most straightforward to answer of my questions.
Thanks! I just find it very interesting, and yet in a sense basic.
 A: *

*It is said that it's impossible to predict "which slit" in advance because it's impossible to predict "which slit" in advance. All predictions in QM are demonstrably probabilistic, the final locations of the particles are random, and hidden-variable theories may be shown to be incompatible with observations. In fact, you are clearly misunderstanding what is "commonly said" about the "which slit" information. What is commonly said is another, stronger truth – that it is impossible to determine the "which slit" information even after the particle is absorbed at a point of the photographic plate or detector (i.e. well after it goes through the slits)! This is the real issue in the wave-particle duality. I guess that this is so counter-intuitive for you and you are so eager to argue about things you don't understand that it makes no sense to try to explain to you why this claim is right.

*When a photon collides with an electron, the interaction is mutual and both particles are affected. The electron's impact on the photon is what allows us to learn something about the electron by looking at the photon; the photon's impact on the electron is what disturbs the interference pattern. Indeed, if the photon is capable of learning the position of the electron, its influence on the electron is also strong enough so that the electrons treated in this way won't make any interference pattern – it will be destroyed.

*The direction of the particle's motion, i.e. given by $\vec p / |\vec p|$, is an observable and like every other observable in any system obeying the laws of quantum mechanics, this observable is mathematically represented by a linear operator on the Hilbert space which means that one can only make probabilistic predictions about its values (unless the predicted probabilities of certain properties are 0 or 100 percent which is extremely rare and surely can't occur in a double slit experiment).
A: *

*This gets into the whole question of when do we ever get to say "that's impossible" as opposed to just "we have no idea how to do it". Instead, I'll give you an "if only" non-answer: we do have a very good idea how to use quantum entanglement to send messages faster than the speed of light, if only we knew how to make predictions about quantum events that are better than random guessing. And we do have a very good idea how to send messages  backwards in time, if only we knew how to send messages faster than light. 

*I don't have anything to add to what Luboš Motl said.

*When it comes to sending particles one at a time, and whether they might not just be pre-determined: you may instead be interested in Elitzur and Vaidman's bomb detector. It involves a hypothetical type of tamper-proof bomb which can be live or dud. It's not exactly the two-slit experiment, but it does involve the quantum self-interference of single photons, and manages to distinguish some live bombs from duds without necessarily detonating them. This would be impossible if it was just a case of the photon path being determined in advance -- then, the only way to distinguish live from dud would be to detonate all the live ones. This thought experiment has been performed. (Okay, minus the bomb detenator, which makes it way less dramatic. But, safety first, folks!)
