Interference between an electron and a photon?

[Sandeep T S]

Can we could interfere electron with photon, this question is come from logic both are waves. Is anyone did that before.?(I know that electron isn't a scalar wave)

 

[jtbell]

both are waves

However, they're different kinds of waves. In order to have interference, the quantities that are "waving" have to be able to be "added together". You can't add the photon field and the electron field together any more than you can add apples and elephants.

 

[Sandeep T S]

However, they're different kinds of waves. In order to have interference, the quantities that are "waving" have to be able to be "added together". You can't add the photon field and the electron field together any more than you can add apples and elephants.

So Theoretically not possible, anyone did any experiment to make theory is true, photon and electron can't interfere

 

[DrChinese]

... anyone did any experiment to make theory is true, photon and electron can't interfere

People will test various ideas in an attempt to prove a theory incorrect. However, ideas like yours would have been noticed already. There are many possible experiments, and scientists choose to perform those they deem useful.

As mentioned by by jtbell, there is no theoretical basis for such interference. So no one would know how to construct an experiment to test it in the first place.

 

[jtbell]

Can we could interfere electron with photon

Can you describe an experiment that would demonstrate this, at least in principle? Maybe what you're thinking about isn't what we would actually call "interference."

 

[tech99]

I was thinking that a semiconductor laser is close to electron/photon interaction.

 

[Sandeep T S]

Can you describe an experiment that would demonstrate this, at least in principle? Maybe what you're thinking about isn't what we would actually call "interference."

Take a double slit, shower one slit with electron and other with photon. Also notice pattern of single slit diffraction for electron and photon using one slit of double slit. Compare double slit pattern with single slit. If both pattern similar for photon/ electron there is no interference. If pattern is different there is a interference with photon and electron.

 

[vanhees71]

I was thinking that a semiconductor laser is close to electron/photon interaction.

One must distinguish between "interaction" and "interference" (or equivalently "superposition").

An interaction is a term in the Lagrangian of the quantum field theory (and as we discuss photons there's no other way than to use relativistic quantum field theory and the Standard Model!), and of course, in QED there's an interaction term between the electron and photon fields since of course the electromagnetic interaction is described as a U(1)-gauge theory with the electric charge as the gauge coupling. The corresponding interaction term is $\propto e \hat{A}^{\mu} \bar{\hat{\psi}} \gamma_{\mu} \hat{\psi}$, where $\psi$ is the Dirac-spinor field of electrons (or any other charged particles you like to describe concerning electromagnetism).

Interference occurs due to the superposition principle for Hilbert-space vectors, i.e., if you have two Hilbert-space vectors $|\psi_1 \rangle$ and $|\psi_2 \rangle$ you can usually also define another vector $\lambda_1 |\psi_1 \rangle+ \lambda_2 |\psi_2 \rangle$.

However, this is pure math, and there's also physics in Quantum Theory, which may restrict the possibility to make sense of some kinds of superpositions, i.e., for physical reasons it can be that some superpositions of state kets are "evil", making the theory nonsensical. If for physical reasons some superpositions are "forbidden", one calls it a "superselection rule", i.e., some physics selects these particular superpositions as "forbidden".

One very fundamental superselection rule is the charge superselection rule. Since electromagnetism is a local gauge theory, only gauge invariant mathematical objects are observable quantities, and since the gauge transformations for the matter fields (e.g., for electrons in QED $\hat{\psi}(x) \rightarrow \exp(+\mathrm{i} e \chi(\vec{x})) \hat{\psi}(x)$, \quad $\hat{A}^{\mu} \rightarrow \hat{A}^{\mu}+\partial^{\mu} \chi$) involve the gauge coupling. Note that it occurs in the transformation of the matter fields but not in that of the gauge fields, but that's only because in QED we deal with an Abelian U(1) gauge symmetry, which implies that from QED alone there's no reason for any kind of charge quantization, i.e., in principle the gauge coupling can be different to any particle species, and there's no reason that all particles have charges in integer multiples of the elementary charge $e$ (or $e/3$ for tha quarks).

However, to build gauge-invariant states from superpositions of other states the involved particles should all have the same charge, such that the states have a well-defined gauge-transformation property. Now an electron carries charge $-1$ (in units of the elementary charge $e$), while a photon carries charge $0$, and thus you must not use superpositions of single-electron and single-photon states.

Another superselection rule is the spin superselection rule, according to which one cannot superimpose states of integer spin with states of half-integer spin, because otherwise a rotation around $2 \pi$ don't make sense anymore. Another reason, related to this, is that there shouldn't be superpositions between bosonic and fermionic states.

 

[Nugatory]

Compare double slit pattern with single slit. If both pattern similar for photon/ electron there is no interference. If pattern is different there is a interference with photon and electron.

That does not follow, because any interaction between the photon and the electron (and as they both interact electromagnetically such interaction is pretty much assured) can disturb the pattern. Interference is something completely different.

 

[jtbell]

Take a double slit, shower one slit with electron and other with photon.

In that case, I would expect to see each kind of particle form a single-slit pattern, same as if you had sent them both through the same single slit.

[added after seeing Nugatory's comment] Ignoring, of course, any normal electromagnetic interaction involving photons and electrons. That's not "interference", in the meaning that we're using here.]

Suppose you first only send a batch of electrons through one of the slits. You get a single-slit pattern. It makes no difference whether you send them through all "at once" (during a very short time), or at the rate of one per hour. When you've accumulated enough electrons on the screen, the single-slit pattern will be easily visible.

The same thing happens if you use photons instead of electrons, through the other slit, or through the same slit.

Now suppose instead of sending one electron every hour, or one photon every hour, you send them alternately: first an electron, then after a half-hour, a photon, then after another half-hour, another electron, etc.

The point is that the particles don't interfere with each other. Instead, loosely speaking, each one interferes with itself.

 

[1977ub]

So, Let's say we fire a stream of electrons from left to right, and record the pattern which is detected.
Next we do it again, except there is a stream of photons from bottom to top. (perpendicular in the laboratory but in the same plane, in other words.)

Is there any type of interference caused of the electron paths other than what might be understood from the occasional close particle-to-particle interactions ?

 

[vanhees71]

Since the photons interact with the electrons, the interference pattern of the electrons might be disturbed by the photons. It's a nice example for the disturbance of measurement results by observation: In general, which-way information (measuring the position of the particle accurately) is incompatible with a sharp determination of momentum, and thus no interference occurs (or at least the interference/refraction pattern has less sharp contrast). See the brillant introductory chapter of Feynman's Lectures vol. III, which are legally available for free here:

http://www.feynmanlectures.caltech.edu/III_01.html