Coupled oscillators and Feynman's three papers

According to Richard Feynman, 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. It is therefore interesting to combine some, if not all, of Feynman's papers into one. The first of his three papers is on the ``rest of the universe'' contained in his 1972 book on statistical mechanics. The second idea is Feynman's parton picture which he presented in 1969 at the Stony Brook conference on high-energy physics. The third idea is contained in the 1971 paper he published with his students, where they show that the hadronic spectra on Regge trajectories are manifestations of harmonic-oscillator degeneracies. In this report, we formulate these three ideas using the mathematics of two coupled oscillators. It is shown that the idea of entanglement is contained in his rest of the universe, and can be extended to a space-time entanglement. It is shown also that his parton model and the static quark model can be combined into one Lorentz-covariant entity. Furthermore, Einstein's special relativity, based on the Lorentz group, can also be formulated within the mathematical framework of two coupled oscillators.Comment: 31 pages, 6 figures, based on the concluding talk at the 3rd Feynman Festival (Collage Park, Maryland, U.S.A., August 2006), minor correction

Einstein, Wigner, and Feynman: From E = mc^{2} to Feynman's decoherence via Wigner's little groups

The 20th-century physics starts with Einstein and ends with Feynman. Einstein introduced the Lorentz-covariant world with E = mc^{2}. Feynman observed that fast-moving hadrons consist of partons which act incoherently with external signals. If quarks and partons are the same entities observed in different Lorentz frames, the question then is why partons are incoherent while quarks are coherent. This is the most puzzling question Feynman left for us to solve. In this report, we discuss Wigner's role in settling this question. Einstein's E = mc^{2}, which takes the form E = \sqrt{m^{2} + p^{2}}, unifies the energy-momentum relations for massive and massless particles, but it does not take into account internal space-time structure of relativistic particles. It is pointed out Wigner's 1939 paper on the inhomogeneous Lorentz group defines particle spin and gauge degrees of freedom in the Lorentz-covariant world. Within the Wigner framework, it is shown possible to construct the internal space-time structure for hadrons in the quark model. It is then shown that the quark model and the parton model are two different manifestations of the same covariant entity. It is shown therefore that the lack of coherence in Feynman's parton picture is an effect of the Lorentz covariance.Comment: LaTex 15 pages, 1 figure, presented at the Wigner Centennial Conference held in Pecs, Hungary (July 2002), published in the proceedings (Acta Physica Hungarica, 2003), minor corrections to the original versio

QCD. What else is needed for the Proton Structure Function?

While QCD can provide corrections to the parton distribution function, it cannot produce the distribution. Where is then the starting point for the proton structure function? The only known source is the quark-model wave function for the proton at rest. The harmonic oscillator is used for the trial wave function. When Lorentz-boosted, this wave function exhibits all the peculiarities of Feynman's parton picture. The time-separation between the quarks plays the key role in the boosting process. This variable is hidden in the present form of quantum mechanics, and the failure to measure it leads to an increase in entropy. This leads to a picture of boiling quarks which become partons in their plasma state.Comment: Latex 9 pages, 4 figure