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How to incorporate HEP into the naive picture of QM?

Physics Asked on August 21, 2020

When I explain QM to non-physicists, I sometimes say that quantum effects are typically noticeable on very small scales. For example, a QM particle in the harmonic potential behaves mostly classically, up to effects of order $hbar$ (think of the spread of coherent states!), which becomes especially clear if the particle is almost at rest. Those, of course, are the intro words that precede diving into the wonderful world of unusual and exciting phenomena taking place at the scales of $hbar$.

But then I realized that within this simple intro, I cannot really give a big picture of significance of quantum effects at high energies. Maybe it would make sense to right away separate strongly and weakly interacting systems? Then we could say that the behavior of electric particle beams is indeed mostly explained by E&M. But what about confinement? How should we explain the relation between the importance of QCD and $hbar$? Also, what about (phenomenological) strongly interacting systems in Condensed Matter?

I understand that answers may be somewhat opinionated yet believe that there should be a more or less general argument. I just really like to be accurate with my words, and I don’t want to say anything conceptually wrong, even to amateurs. Especially to amateurs.

UPDATE

Apparently I got so confused that even asked a separate question on the Planck constant.

One Answer

In quantum mechanics, as in classical mechanics, we need special relativity when the energy is comparable to or larger than the rest energy $mc^2$ of the system we're studying. (This is the point at which we stop calling ourselves quantum physicists and start calling ourselves high energy physicists.) In relativistic quantum mechanics, there are two dimensionful constants, $hbar$ and $c$. Given a length scale $ell$, we associate it with an energy scale by taking begin{align} E = frac{hbar c}{ell} end{align} The smaller a length scale we want to probe, the larger the energy of the particles we need to send in to probe it. So if you accept that quantum mechanics applies at small length scales, then you also accept that it applies at high energy scales!

I think the question about many-body quantum systems deserves to be a separate question, and I'm not quite sure what you're asking about QCD and confinement.

Answered by d_b on August 21, 2020

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