# Wavelength of light too long to measure electron position in double-slit experiment?

I'm a mathematician, so I am not familiar with experimental physics. I am watching MIT course on Quantum Mechanics, and they describe the two-slit experiment with electrons passing through the slits.

Here is my question: How do we measure the position of an electron with a light source? AND, why does longer wavelength mean we can't be as accurate in our measurement of the position. What is the apparatus? How does this actually work in a lab?

What I describe below is described in the video at 59:50 (https://youtu.be/TkJ_WgruM2g?t=59m50s)

They talk about trying to "cheat" and observe which slit the electron went through. They say to shine very weak light at the electrons before they pass through the slit. Sure, the light will impart some momentum and alter the path of the electron a little bit, but if the light is low energy enough, we could perhaps know which slit it went through, yet not change the diffraction pattern by very much. Great! Except weak light means low frequency, long wavelength. Then they say that long wavelength means we can't tell which slit the electron went through. We need wavelength on the order of the distance between the two slits to know which slit it went through. But increasing frequency by this amount is just enough to wash out any interference pattern at all, and so our experiment fails.

My question:

How do we measure the position of an electron with a light source? AND, why does longer wavelength mean we can't be as accurate in our measurement of the position. What is the apparatus? How does this actually work in a lab?

• Double slit experiments are a toy model system and are mostly used for teaching purposes. They are unsuitable as precision tests for quantum mechanics and so are photon scattering experiments. If I may suggest, try to learn quantum mechanics the right way and focus on atomic, molecular and nuclear physics. That't how physicists really use and test quantum mechanics. Jul 4, 2015 at 18:00
• @CuriousOne your remark is obsolete. Rather a number of very precise quantum experiments involving indirect observation of quantum properties of photons as they pass thru a double-slit. (This is not to say that the OP's questions aren't painfully naive -- not even understanding relationships between wavelength and precision of location is pretty bad) Jul 4, 2015 at 18:33
• @CarlWitthoft: A precision experiment in quantum mechanics has 10+ digits of precision. There is nothing in any version of the double slit experiment that can teach us something about quantum mechanics that we don't know, yet. Jul 4, 2015 at 18:35
• I did answer your question. You are simply not going to understand quantum mechanics this way. Strong and weak measurements are all well defined procedures in QM, but you need to understand the basics and a good deal more before you can develop the right intuition about these systems, especially weak measurements. QM wasn't invented to explain the double slit experiment. It was invented to explain atomic spectra. The electron double slit experiment wasn't even "performed" (as a physics act) until 1961, at a time when we already had an excellent handle on relativistic quantum field theory. Jul 4, 2015 at 19:08
• @CuriousOne The double slit experiment is very important from the conceptual point of view because it shows that the collapse of the wave function does indeed happen. QM wasn't invented to "explain atomic spectra": it was invented to explain and understand physics and in this respect the double slit experiment does the job. Jul 4, 2015 at 21:31

How do we measure the position of an electron with a light source?

Experiments with elementary particles are mostly scattering experiments. One needs the source of the particles and a detector that can identify particles. In this figure we see electrons one by one passing the slits and leaving a point (x,y) on a screen sensitive to electrons (deposition of ionization energy).

If the incoming electron energy is known and one scatters it very faintly before the slits, and at the same time measures the scattered photon one can tell from the angles the path the electron took: the point on the screen has to be consistent with the scattered photon's point in the photon detector ( energy and momentum conservation ).

AND, why does longer wavelength mean we can't be as accurate in our measurement of the position.

The photon is an elementary particle, elementary particles are point particles but their probability of interacting with the fields of the electron, atoms and molecules is affected by the frequency characterizing the photon , E=h*nu. Quantum mechanics tells us that the photon will be detected in a spherical region proportional to lambda, the wavelength ( otherwise known as the Heisenberg uncertainty principle) . If lambda is of the order of the distance between the two slits simple algebra on the scattering equations will tell you that the uncertainty is reflected in the uncertainty on which slit the electron went through, so the track cannot be known with an accuracy to choose a slit.

What is the apparatus? How does this actually work in a lab?

I do not think anybody would set up an experiment that the result is known with a bit of algebra. Have a look at this sophisticated experiment.