Abstract
Two coupled oscillators provide a mathematical instrument for solving many problems in modern physics, including squeezed states of light and Lorentz transformations of quantum bound states. The concept of entanglement can also be studied within this mathematical framework. For the system of two entangled photons, it is of interest to study what happens to the remaining photon if the other photon is not observed. It is pointed out that this problem is an issue of Feynman’s rest of the universe. For quantum bound-state problems, it is pointed out the longitudinal and time-like coordinates become entangled when the system becomes boosted. Since time-like oscillations are not observed, the problem is exactly like the two-photon system where one of the photons is not observed. While the hadron is a quantum bound state of quarks, it appears quite differently when it moves rapidly than when it moves slowly. For slow hadrons, Gell-Mann’s quark model is applicable, while Feynman’s parton model is applicable to hadrons with their speeds close to that of light. While observing the temperature dependence of the speed, it is possible to explain the quark-to-parton transition as a phase transition.
Highlights
When Einstein developed his special relativity in 1905, he worked out a transformation law for a point particle
In his invited talk at the 1970 spring meeting of the American Physical Society held in Washington, DC (U.S.A.), Feynman noted first that the observed hadronic mass spectra are consistent with the degeneracy of three-dimensional harmonic oscillators
The longitudinal momentum distribution becomes wide-spread as the hadronic speed approaches the velocity of light. This is in contradiction with our expectation from nonrelativistic quantum mechanics that the width of the momentum distribution is inversely proportional to that of the position wave function
Summary
When Einstein developed his special relativity in 1905, he worked out a transformation law for a point particle He was aware that the hydrogen atom consists of one electron circling around a proton. In 1927 [1], Dirac noted that there is an uncertainty relation between time and energy variables but there are no excitations along the time axis He stated that this space-time asymmetry makes it difficult to make quantum mechanics consistent with relativity. If the variable exists and we are not able to measure it, the result is an increase in entropy and a temperate rise We treat this problem systematically with the existing rules of quantum mechanics and relativity. In the Appendix, we discuss where QFT stands with respect to our work
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