Einstein relativity and one-particle Poincaré quantum theory

Léon Brillouin

S. A. Emelyanov

We propose an experiment that allows one to test the Einstein's intuitive objection to Bohr's quantum mechanics (QM), which was that if QM is correct, then there should be a nonlocality related to the collapse of a single-particle macroscopic wavefunction, which by no means is compatible with special relativity. The idea of the experiment is related to the so-called integer quantum Hall (IQH) systems known to have macroscopic quantum orbits often called extended states. The experiment appeared realizable in a modified IQH system and we have found that a single-particle nonlocality does exist precisely as it follows from QM. This fact makes one come back to the Bell-Popper idea to revive the Lorentz-Poincare "dynamic" version of relativity together with the classical concept of space and time. But now, if to add the single-particle nonlocality to the Bohm-Hiley model of undivided universe, one can solve the most formidable problem - to find a preferred reference frame without involving the vague notion "aether". Moreover, now one can adopt a deeper-than-relativistic concept of what we call "reality", which opens the door to a realistic interpretation of QM and, after all, to the awareness of the worldview of this extremely successful theory.

Gleb Wataghin

Christian Bracco

In the absence of any reliable document, from which Einsteins ideas on relativity prior to 1905 could uniquely be drawn, we are forced to make assumptions. If many historians (J. Norton, O. Darrigol, ) have privileged an electromagnetic origin, others like A. Miller have emphasized the role of light quanta. Ill come back on some evidences that the March quanta have played a role in the June and September 1905 relativity papers and reciprocally that the relativity principle may have influenced Einsteins reflexions on free moving quanta. From both a scientific and an historical perspective, the association of quanta and relativity is indeed natural if one has in mind Plancks work on the black body radiation and Poincarés contribution Lorentz theory and the reaction principle to the Lorentz Jubilee, which both occurred in mid-December 1900. As well known, the former introduced fixed energy quanta and the latter (quoted by Einstein in 1906) opened the way to a dynamical and relativistic (at first order in v/c) account of the electromagnetic field behaviour. But unknown, Poincarés paper also exhibited at this order the same transformation law for the energy and the frequency of an electromagnetic plane wave of finite length. If Einstein remarked this before 1906 (which is not proved), it may have encouraged his thinking of moving quanta. We would then meet the point of view expressed by R. Penrose in his preface of J. Stachels book Einsteins miraculous year, that it is virtually inconceivable that [Einstein] would have put forward two papers [March/June] in the same year which depended upon hypothetical views [particle/wave] of Nature that he felt were in contradiction with each other. March, June and September 1905 Einstein's papers would constitute a remarkable synthesis, in a fully original and new epistemological view, of Planck's 1900 work on the interaction between matter and radiation and Poincarés 1900 paper on the relativistic dynamics of charges and the electromagnetic field.

Pei Wang

Abstract In this paper, we develop the quantum theory that has discrete Poincaré symmetry on the one-dimensional Bravais lattice. We review the recently discovered discrete Lorentz symmetry which coexists with the discrete space translational symmetry on a Bravais lattice. The discrete Lorentz transformations and spacetime translations form the discrete Poincaré group, which are represented by unitary operators in a quantum theory. We find the conditions for the existence of representation, which are expressed as the congruence relation between quasi-momentum and quasi-energy. We then build the Lorentz-invariant many-body theory of indistinguishable particles by expressing both the unitary operators and Floquet Hamiltonians in terms of the field operators. Some typical Hamiltonians include the long-range hopping which fluctuates as the distance between sites increases. We calculate the Green’s function of the theory. The spacetime points where the Green’s function is nonzero display a lattice structure. During the propagation, the particle stays localized on a single or a few sites to preserve the Lorentz symmetry.