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### 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

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