# Can an electron interact with itself to create interference?

I have been recently brushing up on my elementary physics concepts, specifically quantum physics. If I set up a single photon emitter and conducted the double slit experiment, it is possible for me to see interference. 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 this same effect observable when a single electron is fired at speeds much lower than the speed of light?

If so, how? For this to happen, the electron (which has mass and experiences time the way we do) has to be physically present at two locations at the same time (in both slits).

• 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

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

The electron you are thinking of is a localized particle in space. Instead, you have to consider the electron's position as a wave function. The wave function can be non-zero at both slits and interfere with itself afterward. 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.

• 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
• 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

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 slit experiment configuration one at a time, and the usual diffraction pattern was obtained. Proof, if any were necessary, that the electrons are delocalized when they pass through the slits.

• Very interesting paper! What strikes me most is that it appears as-if the single slit experiments also show some diffraction pattern (Figure 2). What is the explanation for that? – atlaste Mar 30 '18 at 5:48

I am adding this answer because the previous ones, though correct, do not emphasize that it is the probability of interaction of the electron that waves.

According to the well-validated theory of quantum mechanics, the wave function solution of a given potential or scattering problem, $Ψ$ is complex, i.e., not measurable. It is $Ψ^*Ψ$, a real number, that can be compared with the electron position measurement, and according to the postulates of quantum mechanics, it gives the probability for the electron to be measured at (x,y,z) at time t. It is not the electron's mass or energy that is waving, i.e., have sinusoidal behavior by showing interference patterns in the single electron double slit experiment.

electron build up over time

The electron is a point particle whenever it is measured, as in the pictures above, and this assumption is checked by experiments which give very tiny limits.

The accumulation of many electrons with the same scattering boundary conditions, as in the double slit experiment, shows a wave nature, confirming the probability behavior predicted by quantum mechanics.

So the electron interacts with the potentials and boundary conditions it is subjected to, and in interacting displays a probabilistic mechanical behavior, not deterministic as in classical mechanics interactions. This probability is what is predictable (determinable) in quantum mechanics, and is responsible for what is called the "wave" nature of a particle, which can only appear under accumulated interactions with the same boundary conditions.