In the first lecture of the MIT quantum-mechanics 2013 course, the professor develops basic abstract concepts, by inventing hypothetical binary measurable properties of electrons (hardness (H)= hard or soft (H/S), color (C)= black or white (B/W)) and apparatuses that measure them. Based on these, he explains a series of experiments with using apparatuses one after the other in various orders to establish an idea of the uncertainty principles (e.g. if you measure hardness twice, you get consistent results, if measure hardness, color and then hardness again, you get 50%/50%). The link to the lecture is here and he establishes these basics from the 11 minute mark to the 30 minutes mark (the whole lecture is rather entertaining).

Then at 33:20 min he develops and explains an apparatus, which measures one trait but joins the results before outputting them. This is done using a set of (hypothetical) mirrors and a beam-joiner. The whole apparatus is the purple box below. He then measures the output using one of the established simple apparatuses which determine either hardness or color. The lecture then goes trough a few such examples with certain variations.

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In the picture you see input of electrons with the White property, then a Hardness measurement device, but the two possible outputs Soft&Hard are reflected through mirrors and combined into a beam joiner and then the final output is put into a Color apparatus again. The question is about percentages of output black/white that are measured as final output. The result is somewhat surprising,

It still comes out 100% white

but the the result itself is is not my question, nor the potential interpretation. (For those of you who want to check, it's after the 45:30 mark or more precisely after the 50min mark after a audience vote.).

Instead, my question is more like: What would be an actual experiment that could be designed along these lines? (He mentions multiple times, that this has been done and verified in real experiments again and again.)

More Background: I'm obviously aware of the double slit experiments. I also know the photon experiments with horizontal and vertical polarizers (and the variant with a 45° polarizer in the middle). I'm aware of electron spin (measuring it by putting a prepared electron in a magnetic field and checking if a photon is emitted, this is from the Standford lectures with Norman Susskind). I'm also vaguely aware of "quantum-eraser"and heard of the quantum bomb-experiment (which seems to have a vaguely similar setup).

Actual Question: I'm wondering what an actual experiment would look like, where you send a particle that was prepared/selected to exhibit one property, then measure another property in a way that you first split the results but then are are able to merge them again. What properties could be measured in this form.

  • $\begingroup$ I'm aware that there is another question about the same experiment here physics.stackexchange.com/questions/609696/…, but mine is not about the result but about the actual experiment. $\endgroup$ Aug 8, 2023 at 9:26
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    $\begingroup$ This lecture is on the Stern/Gerlach experiment. IMO this is a very poor lecture .... if he just said when electron spin is measured it actually effects the measurement they could all go home wiser and have saved a couple of hours of their time. $\endgroup$ Aug 8, 2023 at 16:23
  • $\begingroup$ @PhysicsDave I did look at the Stern/Gerlach experiment on Wikipedia. While the Experiment 3 matches the intro versions of the Hardness/Color thought-experiment (Like measuring H->C->H) from the lecture, I don't see how it applies this special twist (of joining the results from the middle stage) from the version of the experiment I'm asking about. $\endgroup$ Aug 8, 2023 at 18:53
  • $\begingroup$ The wikipedia article talks about sequential measurements .... I believe the prof arbitrarily picked 2 variable names for basically the same effect in sequence. He was trying to make the point that it's all about probabilities .... which then leads to misleading statements (quite a few of those in QM)..... ignoring the real physics .... but feeling really proud of himself. $\endgroup$ Aug 8, 2023 at 21:20

1 Answer 1


A single slit experiment with photons would be the most common. Momentum and position are the two variables. The most common version of the uncertainty principle is that both of these have some uncertainty when measured.

Take a laser and shine it on a screen. It lights up a spot. This shows that the photons have a small transverse distance from the center of the beam. They also must have a small transverse momentum because the beam is close to cylindrical. Photons are traveling close to parallel to the axis. So uncertainty of both is small

Cut a slit or pinhole in the screen. The measured distance from the center of the beam is very small for photons that make it through.

When light from the pinhole strikes a wall, the beam is spread out. Some photons make a larger angle with respect to the axis. These photons have a larger uncertainty of transverse momentum.

We call this diffraction. Often it is explained as due to the wave nature of light. Another valid explanation is as a quantum mechanical effect. Photons are described by a wave equation, which gives rise to the same effect.

You can do more elaborate versions of this experiment. Use two slits. Now you not only get spreading, but interference.

You can do a $3$D many slit experiment using a crystal. The space between atoms is the slit. This is about the size of xray wavelengths, so xrays are used. This is X-ray crystallography.

Electrons also have a small wavelength. Electrons have been passed through a crystal and shown diffraction effects.

  • $\begingroup$ I think this lecture is about Stern Gerlach ....IMO not the greatest lecture. $\endgroup$ Aug 8, 2023 at 21:25

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