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Feynman and Squeezed States Y. S. Kim Univ. of Maryland. Feynman’s Poem about Physical Laws. The artists of the Renaissance said that man’s main Concern should be for man, and there are other things of interest in the world. Even the artists
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Feynman’s Poem about Physical Laws The artists of the Renaissance said that man’s main Concern should be for man, and there are other things of interest in the world. Even the artists appreciate sunsets, the ocean waves, the march of the stars across the heavens. There is then some reason to talk of other things sometimes. As we look into these things we get an aesthetic pleasure from them directly on observation. There is also a rhythm and a pattern between the phenomena of nature which is not apparent to the eye, but only to the eye of analysis; and it is these rhythms and patterns which we call Physical Laws.
Feynman’s Interpretation of Physics 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.
Feynman’s Philosophical Base Feynman published approximately 150 papers on many different subjects of physics. Was he making his perpetual attempts to combine them into one paper? Then how? Did he know what he was talking about?
About Philosophers • Worker of all Lands Unite. • The philosophers have interpreted this world in various ways. The point however is to change it.
Physicists change the world by writing down one equation • Newton: one differential equation for both comets and planets. • Schroedinger: one equation for both running and standing waves. • How about Feynman? Where is his one equation?
How about Maxwell? • Four Equations = One set of Equations for electricty and magnetism.. • Applicable to the Lorentzian World.
Feynman said! • For Scattering problems, use Feynman diagrams. • For bound-state problems, use harmonic oscillators. • However, there were no Lorentz-covariant oscillators in 1970. • People said Feynman was absolutely crazy. • But, I became excited about what he said, and studied his physics systematically since then. I also became crazy.
Feynman talked about many things.Use harmonicoscillators for Step 1.
Feynman’s One Equation In his 1971 paper, Feynman wrote down one partial differential equation to cover both comets and planets. Where is the Squeezed State?
Hydrogen Atom becomes the Hadron (bound state of two quarks) in the Lorentz-covariant world.
Hadrons – Running wavesQuarks inside – Standing waves Harmonic oscillators
Feynman was successful in solving the mysteries of Regge poles, but totally failed in providing Lorentz-covariant solutions of his own equation for harmonic oscillators. From the Lorentzian point of view, his paper is total mess.
Feynman’s One Equation In order to handle the differential equation Feynman wrote down, we have to import both Wigner and Dirac.
Wigner’s Little Group • The space-time symmetry inside the hadron is smaller than the Lorentz group. It is isomorphic to O(3), three-dimensional rotation group.
1962. I had a private audience with Dirac like Nicodemus with Jesus I asked Dirac what I should do in Physics.Dirac told me to study Lorentz covariance. Americans should study more about this subject.
When Dirac was talking about Americans, he was talking about Feynman. He was talking with Feynman two months before I talked three months before I talked to him. Thus, one way to fix Feynman’s problem was to import Dirac’s work.
Dirac and Feynman in Poland (1962) • Dirac: construct a beautiful mathematics. • Feynman: mathematical instrument that will produce numbers which can be compared with numbers observed in the real world.
Back to two famous brothers-in-law • Dirac: Modern physics is the physics of harmonic oscillators. • Wigner: Modern physics is the physics of two-by-two matrices.
The same formula leads to Top: Squeezed State Bottom: Entangled State
Waves in Relativistic World • There are running waves and standing waves. • Running waves can be approximated by plane waves. Running waves can be made Lorentz-covariant through the Klein-Gordon equation. Thus, the S-matrix and Feynman diagrams. This is called Quantum Field Theory. Is the field theory capable of solving standing wave or bound-state problems?
Covariant Bound States (Standing Waves) • Bound States: Hydrogen Atom or Harmonic Oscillators. • Feynman chooses osc. wave functions to understand the covariant world. • Hadron consisting of two quarks. Overall coordinate and space-time separation.
This set of formulas is identical to the set we see in the coupled oscillators • Squeezed State • Entangled State
Dirac’s Quantum World Dirac 1927 Time-energy uncertainty without excitations. C-number T-E uncertainty. Space-time asymmetry.
