From Superluminal Velocity To Time Machines?

Various experiments have shown superluminal group and signal velocities recently. Experiments were essentials carried out with microwave tunnelling, with frustrated total internal reflection, and with gain-assisted anomalous dispersion. According to text books a superluminal signal velocity violates Einstein causality implying that cause and effect can be changed and time machines known from science fiction could be constructed. This naive analysis, however, assumes a signal to be a point in the time dimension neglecting its finite duration. A signal is not presented by a point nor by its front, but by its total length. On the other hand a signal energy is finite thus its frequency band is limited, the latter is a fundamental physical property in consequence of field quantization with quantum $h \nu$. All superluminal experiments have been carried out with rather narrow frequency bands. The narrow band width is a condition sine qua non to avoid pulse reshaping of the signal due to the dispersion relation of the tunnelling barrier or of the excited gas, respectively. In consequence of the narrow frequency band width the time duration of the signal is long so that causality is preserved. However, superluminal signal velocity shortens the otherwise luminal time span between cause and effect.Comment: 5 pages, 3 figure

Two-Loop Ultrasoft Running of the O(v^2) QCD Quark Potentials

The two-loop ultrasoft contributions to the next-to-leading logarithmic (NLL) running of the QCD potentials at order v^2 are determined. The results represent an important step towards the next-to-next-to-leading logarithmic (NNLL) description of heavy quark pair production and annihilation close to threshold.Comment: 13 pages, 3 figures; typos corrected, reference added, information on cross checks added on page 7; acknowledgments adde

Teaching the hidden symmetry of the Kepler problem in relativistic quantum mechanics - from Pauli to Dirac electron

Hidden symmetry in Coulomb interaction is one of the mysterious problems of modern physics. Additional conserved quantities associated with extra symmetry govern wide variety of physics problems, from planetary motion till fine and hyperfine structures of atomic spectra. In this paper we present a simple derivation of hidden symmetry operator in relativistic quantum mechanics for the Dirac equation in the Coulomb field. We established that this operator may be reduced to the one introduced by Johnson and Lippmann. It is worthwhile to notice that this operator was discussed in literature very rarely and so is not known well among physicists and was omitted even in the recent textbooks on relativistic quantum mechanics and/or quantum electrodynamics.Comment: 5 page