The Anti-Infinity Parade

Nov 29, 2020

Quantum Mechanics in Your Face

Recently, a 1994 lecture by Sidney Coleman was transcribed and put on arXiv. The whole lecture is filled with wisdom, and clarity of thought regarding the conceptual framework of quantum mechanics. One particular point really struck me as something to permanently keep in my mind, and here described from my own perspective.

One of the worst pedagogical techniques involving quantum mechanics is talking about the wave-particle duality. This concept needs to die, because it only serves to confuse more than illuminate. The issue is that in quantum mechanics, the fundamental building blocks of matter (and massless particles) are these entities, whose state is modeled as a vector in Hilbert space. On the other hand, classical physics postulates that every entity in the universe is either a particle or a wave. The quantum entities have different behavior than particles or waves (obviously, otherwise what need is there for a new theory), but people continue to try to teach quantum mechanics by trying to pigeon hole quantum entities into the particle cubbyhole or the wave one.

For the last decade, I have wondered why, until Sidney Coleman puts the hammer on the nail. He says, people believe deep down that the world is really governed by classical mechanics, and therefore, they explain everything in terms of classical mechanics, or at least try to. (And let the student walk away even more confused). Instead, SC gives the correct pedagogy, aptly summarized on his slide:

"Every successful physical theory swallows its predecessor alive."

But it does so by interpreting the concepts of the old theory in terms of the new, NOT the other way around.

Thus our aim is NOT "the interpretations of quantum mechanics." It is the interpretation of classical mechanics

You can't say it much better than this. Once you have a more fundamental theory, you need to start your pedagogy from a clean slate. Construct the concepts of the new theory, and once they are fully defined, do you discuss how they reduce to the concepts of the old theory in certain circumstances.

He gives the example of thermodynamics and statistical mechanics, which subsumes the former. You don't want to explain the concept of molecular motion (only found within statistical mechanics) by appealing to the concept of heat. That is nonsensical. You explain heat in terms of molecular motion, the more fundamental quantity.

The final example he pulls out is one from the Fun to Imagine movie with Richard Feynman. In one segment, the host asks Feynman to explain why magnets attract or repel each other. Feynman simply answers that because "magnets repel each other". But the host insists on an explanation. Which results in Feynman monologuing on the what it means to explain something. I insist you listen to Feynman himself. But the short of it is that he says that, I can't explain it to you in terms of anything more fundamental that you understand (or even he understands). Electromagnetism is the most fundamental theory in its domain that explains a wealth of other phenomena, but we don't know why it is itself true. Our framework of explanation stops when we get to the axioms of electromagnetism. We can't explain electromagnetism in terms of everyday phenomena, because everyday phenomena is itself only explainable in terms of electromagnetism. The golden quote is,

"But I can't really do a good job, any job, of explaining magnetic force in terms of something else you are more familiar with, because I don't understand it in terms of anything else you are more familiar with."

Finally, to come back to quantum mechanics. Stop trying to explain the behavior of quantum entities in terms of classical entities, the fundamental quantity in terms of the derived. Instead, figure out how you can recover the conceptual framework of classical mechanics from that of quantum mechanics.