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I have been recently brushing up my elementary physics concepts, specifically quantum physics. So, if I set up a single photon emitter in the double slit experiment, it is possible for me to see interference (I am assuming), when I thought about this I realized that a photon is mass-less and travels at the speed of light, so time does not affect a photon, therefore a photon can interact with another instance of itself (which in our frame of reference exists in another time).

My question is, is the same effect observable when a single electron is fired at speeds much lower than the speed of light? If so, how? because for this to happen, the electron (which has mass and experiences time the way we do) has to physically be present at two locations at the same time (both the slits)?

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The fact that a photon can be nonlocalized has nothing to do with the fact that it doesn't have a varying proper time $\tau$. When we observe interference, it's because two different parts of the wave coincide at the same coordinates $(t,x,y,z)$ in some frame such as the lab. –  Ben Crowell Apr 30 '13 at 12:50

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Yes, electrons can be brought to interference with themselves. This can actually be shown in a double slit experiment, just as with photons.

The electron you think of is a localized particle in space. Instead, you have to consider the electron's position as a wave function. The wave funcion can be non-zero at both slits and interfere with itself afterwards. With electrons, you will also find the typical stripes (or rings, if you use a circular aperture as a single slit) that you found with photons.

This is one of the groundbreaking experiments that one can conduct in schools to prove that electrons actually are both, a wave and a particle.

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Well, right, except that the OP talks about "interaction" and the interference of two portions of a wave function isn't an interaction. –  Luboš Motl Apr 26 '13 at 13:14
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I suspect that the OP is using "interact" in a colloquial rather than formal sense. It is certainly true that electrons can generate two-slit interference patterns even when the rate is turned down low enough that the mean number in transit drops below unity, which is how I interpreted the question. –  dmckee Apr 26 '13 at 13:57
    
I see it as dmckee. The OP refers to a Photon's self-interaction in the double slit experiment. As uncharged particles, photons have no (tree-level) self-interaction which makes me interpret "interaction" as "superposition of wave function". –  Neuneck Apr 29 '13 at 5:55
    
I think I would add to "you have to consider the electron's position as a wave function. " 'whose square gives the probability of finding the electron at (x,y,z,t) ' . too often people think that the mass of the electron is spread all over the space. When one is given a probability for living to 80years one is not spread out from now to then ;) –  anna v Apr 30 '13 at 9:41

An electron and photon are quite different particles. However, they have something in common that makes them interfere in the double-slit experiments. This common feature is their wave function that means they obey the same laws describing their probabilistic propagation in space and time. In the double-slit experiments, their masses are particular properties influencing on interference patterns.

Thus, I would rather say not an electron interact with itself, but its possible trajectories of propagating interfere. If you set going an electron through a double-slit screen your detector indicates it as a single spot. But if the experiment will be repeated you will get an interference picture.

My question is, is the same effect observable when a single electron is fired at speeds much lower than the speed of light?

In quantum mechanics, speed (momentum) is related to the wavelength of the particle. So the interference is dependent on the momentum. At larger speeds, slits have to be smaller to observe interference.

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Yes, exactly the same happens with electrons. Indeed, the experiment has been done and is described in this paper. Electrons were sent through a Young's slits one at a time, and the usual diffraction pattern was obtained. Proof if any were necessary that the electrons are delocailsed when they pass through the slits.

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