## Was Feynman a Kantian Physicist?

Einstein was!

*the adventure of our science of physics is a perpetual attempt to recognize that the different aspects of nature are really different aspects of the same thing.*

Why am I so crazy about what he said above? The reason is quite simple. I am a Kantianist, and Feynman talks like a Kantianist. I was able to talk to Wigner because he was a Kantianist. The most prominent Kantianist in physics was of course Albert Einstein.

- His 1969 paper on the parton picture.
- The 1971 paper he published with his students, on harmonic
oscillators for Lorentz-covariant bound states.
Click here for the paper.
- Chapter on density matrices in his 1972 book on statistical mechanics.
- In 1969, Feynman invented partons by observing hadrons moving with
velocity close to that of light. Hadrons are collection of partons
whose properties are quite different from those of the quarks.
Gell-Mann invented the quarks. According to the quark model, hadrons
are quantum bound states like the hydrogen atom. While quarks and
partons appear differently to us, are they the same covariant entity
in different limiting cases?
This is a typical Kantian question which Einstein addressed so brilliantly. The energy-momentum relation for slow particles is E = p

2 , while it is E = cp for fast-moving particles. Einstein showed that they come from the same formula in different limits. You may go to this webpage for a detailed story. - In his paper on harmonic oscillators, Feynman notes the existence of
Feynman diagrams for tools of quantum mechanics in the relativistic
regime. However, for bound-state problems, he suggests that harmonic
oscillator could be more effective. Needless to say, he knew that
these two methods should solve the same problem of combining quantum
mechanics and relativity. If Feynman was suggesting two different
methods for approaching the same problem, Feynman was a Kantianist.
The 1971 paper Feynman wrote with his students contains many original ideas. However, it is generally agreed that this paper is somewhat short in mathematics. With Marilyn Noz, I wrote a book on this subject, and its title is

*Theory and Applications of the Poincaré Group.*Our earliest paper on this subject was published in 1973. - In his book on statistical mechanics, Feynman
makes the following statement about the density matrix.
*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*.Here, Feynman divides the universe into two parts. He thinks we can obtain a better understanding of our observable system by considering the the universe outside the system. Presumably, Feynman was assuming the same set of physical law applied to this rest of the universe. Here, Feynman was talking about two entangled world.

If Feynman insists on gaining a better understanding of the world by making obervations from the two different directions, he is a Kantianist physicist.

The best way to understand the abstract concept of

*Feynman's rest of the universe*is to use two coupled harmonic oscillators, where one is the world in which we do physic, while the other belongs to the rest of the universe. If we choose observe both universes, we are led to the concept of entanglement.

According to what he said above, Feynman is saying or at least trying to say the same thing in his numerous papers. Thus, his ultimate goal was to combine all those into one paper. Feynman published about 150 papers. I am not able to combine all those into one paper. However, I was able to combine the following three papers he published during the period 1969-1972.

My long-time co-author in this program has been and still is Marilyn E. Noz. Our recent paper on coupled harmonic oscillators does the job. It is published in the J. Opt. B: Quantum Semiclass. Opt. 7 (2005) S458-S467. If you have subscription problem with this journal, you may look at its preliminary version arxived at quant-ph/0502096.

The basic advantage of coupled harmonic oscillators is that the physics is perfectly transparent thanks to mathematical simplicity. What is surprising is that all three of the above subjects can be formulated in terms of two coupled harmonic oscillators. In this way, we were able to combine all of them into a single physical problem.

Y. S. Kim (2006.5.12)

PS. Solving the coupled-oscillator problem is not much different from diagonalizing the quadratic equation

*x*

^{2}+ 2kxy + y^{2}= R^{2}.Many of my colleagues are complaining that I know nothing other than harmonic oscillators and digonal or 2-by-2 matrices. True! For this reason, I can do many things they cannot do. If you combine them, you end up with two coupled oscillators. I love coupled oscillators.

Feynman photo: courtesy of the Niels Bohr Library of the American Institute of Physics.