Feynman's Rest of the Universe


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.

Feynamn 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?

Two-mode Squeezed States

P. A. M. Dirac was quite fond of harmonic oscillators and the Lorentz group. He attempted to construct a representation of using two oscillators, and ended up with the O(3,2) deSitter group applicable to five dimensional space with three space and two time coordinates. Here is his paper.

Time Separation hidden in Feynman's Rest of the Universe.

They could have talked the Lorentz-boosted Bohr radius, but they did not. The time separation was a hidden variable to them.

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.


copyright@2009 by Y. S. Kim, unless otherwise specified.
The photos of Bohr and Einstein and of Dirac and Wigner are from the E. Segre Visual Archives of the American Physical Society.