Magnetic Fields in Fundamental Quantum Experiments

Consider the classical double-slit experiment. If any detection is made as to “which way� the particle went, then the wave function collapses and the pattern of particles striking the dety7ector does not create an interference pattern. My understanding is that for a particle to be “detected�, this does not require an actual intelligence observing it, but merely that the particle has some effect, no matter how minute, on the environment through which it passes. In other words, the particle only has to be “detectable� not actually detected, for the wave function to collapse. My question has to do with the double-slit experiment done with a stream of electrons, which I understand is just as valid for the experiment as photons. Alternatively, this could be an experiment with a Stern-Gerlack machine measuring the spin-up or spin-down state of a stream of electrons. The problem I see is that a moving electron is by definition an electric current, since it is a moving electric charge. And a moving current generates an E-M field. After all, an ampere is a coulomb of charge moving per second. So if the very nature of a moving electron creates an electric current, then whether an electron was moving along a certain path or not would always be detectable, since the moving electron gives rise to a current and a corresponding E-M field, which is inherently detectable. So, how can electrons ever act as being in a super-position state, since they always “give-away� their presence?
- Dick Byrd (age 75)
Mirror lake, NH, USA

Hi Dick,

Fantastic question!

As you say, a moving electron creates a measurable magnetic field, which could in principle tell you something about the particles position and/or momentum.

Let's say I shoot an electron through a beamsplitter, which has a 50-50 chance of deflecting the electron to the right or the left. The electron's momentum is now a superposition of rightwards and leftwards. The magnetic field is also in a superposition! It is simultaneously centered on the right-moving and the left-moving electron. Basically, you have entangled the "magnetic field" and "electron direction" variables.

If you try to find the electron's position by measuring the magnetic field, you will randomly collapse the field superposition into right or left, and the particle will always be on the same side. This is entanglement, and isn't particularly exciting since it is local.

I would say it is no weirder than single-electron interference (which is an experimental ). However, the problem gets more exciting if you consider not the field, but instead the radiation of a charged particle. For example: If you do the two-slit experiment with electrons, each electron diffracts through each slit. Through this interaction with the slit, the electron gains a spread in momentum, a corresponding spread in acceleration, and a corresponding spread in radiation*.

Here's the argument you may be worried about: could someone see a diffraction pattern on a screen beyond the slits, and then afterwards detect the radiated fields to determine which slit the electron went through? Since the radiated fields aren't coupled to the electron anymore, one might measure them independently without disturbing the electron, and so perhaps measure the position and momentum of the particle.

Actually, this can't be done. Just as in the above case, the fields are entangled with the path taken, except in this case the entanglement is nonlocal (as in the EPR experiment). So the measurements are always consistent, but don't give you any additional information.

Actually, according to a colloquium I heard, explicit calculations show that the radiation field doesn't actually give you enough information to figure out which slit the electron went through. For example, if the wavelength of the radiation is long enough, then by standard optical resolution limitations you cannot resolve which slit the electron was in. In this case, you don't even need to understand quantum mechanics to see how the paradox is resolved: there just isn't enough information in the radiation fields to determine where the particle is.

Hope that wasn't too confusing! :)
David Schmid

(published on 05/08/2013)