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Integration of Dirac's Efforts to construct Lorentz-covariant Quantum Mechanics
Young S. Kim, Marilyn E. Noz
The lifelong efforts of Paul A. M. Dirac were to construct localized quantum systems in the Lorentz covariant world. In 1927, he noted that the time-energy uncertainty should be in…
Einstein's E = mc^2 derivable from Heisenberg's Uncertainty Relations
Sibel Baskal, Young S. Kim, Marilyn E. Noz
Heisenberg's uncertainty relation can be written in terms of the step-up and step-down operators in the harmonic oscillator representation. It is noted that the single-variable Hei…
Poincaré Symmetry from Heisenberg's Uncertainty Relations
Sibel Baskal, Young S. Kim, Marilyn E. Noz
It is noted that the single-variable Heisenberg commutation relation contains the symmetry of the group which is isomorphic to the Lorentz group applicable to one time-like…
Photons in the Quantum World
Sibel Baskal, Young S. Kim, Marilyn E. Noz
Einstein's photo-electric effect allows us to regard electromagnetic waves as massless particles. Then, how is the photon helicity translated into the electric and magnetic fields…
Entangled Harmonic Oscillators and Space-time Entanglement
Sibel Baskal, Young S. Kim, Marilyn E. Noz
The mathematical basis for the Gaussian entanglement is discussed in detail, as well as its implications in the internal space-time structure of relativistic extended particles. It…
Entropy and Temperature from Entangled Space and Time
Young S. Kim, Marilyn E. Noz
Two coupled oscillators provide a mathematical instrument for solving many problems in modern physics, including squeezed states of light and Lorentz transformations of quantum bou…
Dirac Matrices and Feynman's Rest of the Universe
Young S. Kim, Marilyn E. Noz
There are two sets of four-by-four matrices introduced by Dirac. The first set consists of fifteen Majorana matrices derivable from his four matrices. These fifteen matrices ca…
Feynman's Decoherence
Y. S. Kim, Marilyn E. Noz
Gell-Mann's quarks are coherent particles confined within a hadron at rest, but Feynman's partons are incoherent particles which constitute a hadron moving with a velocity close to…
Interferometers and Decoherence Matrices
D. Han, Y. S. Kim, Marilyn E. Noz
It is shown that the Lorentz group is the natural language for two-beam interferometers if there are no decoherence effects. This aspect of the interferometer can be translated int…
Does Lorentz Boost Destroy Coherence?
Y. S. Kim
It is shown that the time-energy uncertainty relation can be combined into the position-momentum uncertainty relation covariantly in the quark model of hadrons. This leads to a Lor…