Feynman's Rest of the Universe

Do you know how to do
quantum mechanics of this system?
In his book on statistical mechanics, Feynman says

When we solve a quantum-mechanical problem, what we really do is divide the universe into two parts - the system in which we are interested and the rest of the universe. We then usually act as if the system in which we are interested comprised the entire universe. To motivate the use of density matrices, let us see what happens when we include the part of the universe outside the system.

Feynman then used the density matrices and Wigner functions to illustrate his rest of the universe. However, he used only one oscillator to illustrate what he said about the rest of the universe. Yes! The harmonic oscillator is the basic tool to illustrate the Wigner function. But how could he explain two different worlds with one oscillator?

The single harmonic oscillator is the backbone of the present form of quantum mechanics. However, do you know how to do quantum mechanics of two oscillators? Indeed, Paul A. M. Dirac did not know how to do quantum mechanics of this system until he submitted his paper on on two oscillators in 1962 (published in 1963).

The time Separation is hidden in Feynman's Rest of the Universe.

We are quite familiar with the electron-proton separation in the in the hydrogen atom. It is called the Bohr radius. If the hydrogen atom moves, the Bohr radius picks up its time-separation, as shown in this figure.
They could have talked about the Lorentz-boosted Bohr radius, but we do not know anything about their conversation if it took place. Thus, the time separation is a hidden variable in the present form of quantum mechanics.
Niels Bohr (1885-1962) was born six years after Einstein. Whenever Bohr mentions the word "space" in his philosophical writings, he adds "time." This is how much Bohr respected Einstein. Einstein also had a great respect for Bohr. At the same time, Einstein had his objections to the Copenhagen interpretation of quantum mechanics. This aspect is well known and is still actively debated by the present generation of physicists.

I hope you enjoyed my cartoons. When did I realize the the cartoon is a powerful language? Click here. Webapges are also powerful. When did I learn this? Click here.

I still have to proof-read this page thoroughly. Like you, I am a busy person. I hope I will be able to clean up the mess soon.

copyright@2018 by Y. S. Kim, unless otherwise specified.
The photo of Bohr and Einstein is from the E. Segre Visual Archives of the American Physical Society.