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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 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 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? Who writes Interpretations? 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, Washington, 1970 Based on Feynman’s 1970 Talk 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 harmonic oscillators for Step 1. Feynman said 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? Feynman’s One Equation Hydrogen Atom becomes the Hadron (bound state of two quarks) in the Lorentz-covariant world. Hadrons – Running waves Quarks 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. Two famous brothers in law Feynman said Running waves and Standing Waves 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 twoby-two matrices. Theory of Everything in Physics 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 Lorentzcovariant 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? We started writing papers on Feynmanism from 1973 2003 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 spacetime separation. Time separation Feynman said 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. Dirac’s Light-cone System (1949) Lorentz-squeezed Hadron Squeezed States in Quantum Optics Parton Picture Coherence to Incoherence Lorentz-covariant Picture of Feynman’s Parton Model Parton Distribution Function Time Dilation External signal sees quarks as free independent particles. Feynman’s decoherence Since Einstein’s energy-momentum relation (1905) Register ownership with authorities Phys. Rev. Letters Two different aspects (quarks and partons) of nature coming from one thing! 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 was a Kantianist, so was Einstein. Entropy Problem • First, let us look at what he says about the density matrix. In his 1973 book, Feynman says Here again, Feynman talks like a philosopher • Here again, we can use harmonic oscillators to see what he really had in mind. • In his original paper he uses a single oscillator. • We should use coupled oscillators to decode what he was saying. Rest of the universe -Entanglement • X variable: we do physics with. • Y variable: we do not observe. – rest of the universe. Two worlds are entangled. Time separation hidden in the present form of quantum mechanics Back to Space-time physics • Time separation variable between the quarks exists, but they are not observed deeply hidden in the present form of quantum mechanics . • It indeed belongs to Feynman’s rest of the universe. 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. New Words in Physics • Frogs: most of are frogs. • Birds; Feynman is a bird. Birds see the world as one world. To Feynman, quantum optics and the quark model belong to one world. For more details, visit the following webpages. • http://www.ysfine.com • http://www.ysfine.com/feynman