Getting Lost in the Quantum Sauce

Patrick Bryant, Ph.D.
April 2025

Quantum mechanics is truly bizarre and wonderful. Perhaps most counterintuitive once you start to wrap your head around it, is that anything like our lived experience can come from the equations. You learn about superpositions, particles behaving like waves and vice versa, entanglement, quantum tunneling and teleportation. It’s not surprising that many physicists occasionally get lost in the sauce. In a recent and excellent Veritasium video, the popular YouTube channel’s host (Derek Muller) and story producer (Casper Mebius) briefly fell into the swirling psychedelic trap of quantum magic.

I encourage you to watch the video, it provides a lovely introduction to the conceptual basis for one of the most important tools in modern physics: The Path Integral. Unfortunately, the video leaves out two very important considerations when using path integration and misinterprets the result of a demonstration as a result.

Quantum measurement

At 25:33 in the video, Muller states “...[objects] don’t really have a precise trajectory, instead everything explores all possible paths…”, this is only applicable if the object in question is not “being observed” by which I mean, it is so well isolated from its environment, that it is not constrained to be physically consistent with other observable quantities. When you continually “observe” an object, its position and velocity are constrained to the values “you” observe. In this case the “you” is a hypothetical version of you which is capable of taking in every single bit of information about the object which reaches its environment and using it to perform the measurement. Even if you turn your back, the object is shooting out photons and sound waves, etching its past trajectory irreversibly in the surrounding environment.

Conservation Laws

Assuming you manage to isolate your test subject from its environment, it will now undergo the messy process of exploring “all possible paths” as described in the video, but the final outgoing energy and momentum is 100% guaranteed to be exactly the same as the total energy and momentum the system started with. This means that if you shoot a laser into a box where it is totally isolated and left to do the quantum nasty, it will still come shooting out of the box going in the same direction with the same number and color of photons. At 29:12 in the video Mebius performs an experiment where he shoots a laser at a black bit of paper covering half a mirror and a diffraction grating covering the other half.

He then gets very excited when he sees light from the laser coming from the diffraction grating side of the mirror, “proof that light takes all paths!” Unfortunately this is wrong, what is actually happening is that a small amount of the laser beam is poorly focused and scatters off the aperture of the laser pointer, sending out light in all directions. This spatially incoherent portion of the laser light does indeed bounce off the mirror after going through the diffraction grating, allowing it to reach the camera above. The primary portion of the laser shoots directly into the black paper where it is mostly absorbed as heat and some scatters in all directions.

If Mebius had performed this experiment with an appropriately designed aperture he would see that no light was visible from the diffraction grating. This is a simple consequence of momentum and energy conservation. The photons leaving the laser are produced in a special coherent state with well defined momentum headed straight for the paper and all of the energy of the laser is being “measured” by the environment when it hits the black paper. The only allowed paths for the light are those which leave the laser in the direction they started and end at the paper.

Conclusion

The video is still great and the first demonstration in the video is a beautiful example of the classical wave dynamics of light! Veritasium is a superb resource and a master class in science communication. Just remember when someone is excited about quantum weirdness, check that they appreciate the subtlety of measurement and conservation laws.

P.S. If you want a more technical introduction to path integration, check out Appendix A of my PhD thesis, page 259. I explain how this applies to quantum fields in Chapter 2.3.2, page 25.

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