






In the real world, this ellipse appears as


 You do not have to be a genius to combine the above two figures. This figure
means many different things in physics. Among them are
 Lornerzcovariant picture of bound states.

Quarks and partons as one Lorentzcovariant entity.
 Coupled Oscillators as a model for the Lorentzcovariant world.
 Squeezed states of light.
 Squeeze transformations in physics. Symplectic transformations.
 Feynman's rest of the universe.
 Role of entropy in the Lorentzcovariant world.
 Entropy and Lorentz transformations,
Physics Letters A 147, 343 (1990).
 Entangled space and time variables.
 Coupled oscillators, entangled oscillators, and Lorentzcovariant Oscillators
Journal of Optics B:
Qauntum and Semiclassical
7, s 459  467 (2005).
ArXiv.

I like this computer. It generates both quantum mechanics and
special relativity.

 Note added in 2018. After realizing that Dirac's
lifetime interest was in making quantum mechanics consistent with relativity,
I became interested what Dirac was really telling me when I met him 1962. In 1962,
he submitted his paper to the Journal of Mathematical Physics, in which he constructed,
from two harmonic oscillators,
the Lie algebra of the Lorentz group applicable to 3dimensional space with two time
variables.
Click here
for Dirac's 1963 paper.
The harmonic oscillator is the language of quantum mechanics. The Lorentz group is
the language of Einstein's special relativity. Does this mean that the special
relativity is derivable from quantum mechanics? For many years, this has been my
main interest in physics. Click here for my
list of publications.
 Note added in 2019.
I became quite excited about contracting Dirac's O(3,2) group
into the inhomogeneous Lorentz group, and wrote the following three papers.
 Einstein's E = mc^2 derivable from Heisenberg's Uncertainty Relations,
with Sibel Baskal and Marilyn Noz,
Quantum Reports [1] (2), 236  251 (2019),
doi:10.3390/quantum1020021.
ArXiv. For pdf with sharper images,
Click here.
 Role of Quantum Optics in Synthesizing Quantum Mechanics and Relativity,
Invited paper presented at the 26th
International Conference on Quantum Optics and Quantum Information
(Minsk, Belarus, May 2019).
ArXiv. For pdf with sharper images,
click here.
 Poincaré Symmetry from Heisenberg's Uncertainty Relations,
with S. Baskal and M. E. Noz,
Symmetry [11](3), 236  267 (2019),
doi:10.3390/sym11030409.
ArXiv.

