157,056 research outputs found
Can you do quantum mechanics without Einstein?
The present form of quantum mechanics is based on the Copenhagen school of
interpretation. Einstein did not belong to the Copenhagen school, because he
did not believe in probabilistic interpretation of fundamental physical laws.
This is the reason why we are still debating whether there is a more
deterministic theory. One cause of this separation between Einstein and the
Copenhagen school could have been that the Copenhagen physicists thoroughly
ignored Einstein's main concern: the principle of relativity. Paul A. M. Dirac
was the first one to realize this problem. Indeed, from 1927 to 1963, Paul A.
M. Dirac published at least four papers to study the problem of making the
uncertainty relation consistent with Einstein's Lorentz covariance. It is
interesting to combine those papers by Dirac to make the uncertainty relation
consistent with relativity. It is shown that the mathematics of two coupled
oscillators enables us to carry out this job. We are then led to the question
of whether the concept of localized probability distribution is consistent with
Lorentz covariance.Comment: Latex 11 pages, 7 figures; invited paper presented at the
International Conference on Foundations of Probability and Physics (Vaxjo,
Sweden, June 2006); to be published in the proceedings (AIP Conference
Proceedings Series); Minor correction
Standing waves in the Lorentz-covariant world
When Einstein formulated his special relativity, he developed his dynamics
for point particles. Of course, many valiant efforts have been made to extend
his relativity to rigid bodies, but this subject is forgotten in history. This
is largely because of the emergence of quantum mechanics with wave-particle
duality. Instead of Lorentz-boosting rigid bodies, we now boost waves and have
to deal with Lorentz transformations of waves. We now have some understanding
of plane waves or running waves in the covariant picture, but we do not yet
have a clear picture of standing waves. In this report, we show that there is
one set of standing waves which can be Lorentz-transformed while being
consistent with all physical principle of quantum mechanics and relativity. It
is possible to construct a representation of the Poincar\'e group using
harmonic oscillator wave functions satisfying space-time boundary conditions.
This set of wave functions is capable of explaining the quantum bound state for
both slow and fast hadrons. In particular it can explain the quark model for
hadrons at rest, and Feynman's parton model hadrons moving with a speed close
to that of light.Comment: LaTex 20 pages, presented at the 2004 meeting of the International
Association of Relativistic Dynamincs, to be published in the proceeding
Structure and correlation effects in semiconducting SrTiO₃
We have investigated the effects of structure change and electron correlation on SrTiO₃ single crystals using angle-resolved photoemission spectroscopy. We show that the cubic to tetragonal phase transition at 105 K is manifested by a charge transfer from in-plane (dyz and dzx) bands to out-of-plane (dxy) band, which is opposite to the theoretical predictions. Along this second-order phase transition, we find a smooth evolution of the quasiparticle strength and effective masses. The in-plane band exhibits a peak-dip-hump lineshape, indicating a high degree of correlation on a relatively large (170 meV) energy scale, which is attributed to the polaron formation
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