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