Quantum mechanix plus Newtonian gravity violates the universality of free fall

Classical point particles in Newtonian gravity obey, as they do in general relativity, the universality of free fall. However, classical structured particles, (for instance with a mass quadrupole moment), need not obey the universality of free fall. Quantum mechanically, an elementary “point” particle (in the particle physics sense) can be described by a localized wave packet, for which we can define a probability quadrupole moment. This probability quadrupole can, under plausible hypotheses, affect the universality of free fall. (So point-like elementary particles, in the particle physics sense, can and indeed must nevertheless have structure in the general relativistic sense once wave packet effects are included.) This raises an important issue of principle, as possible quantum violations of the universality of free fall would fundamentally impact on our ideas of what “quantum gravity” might look like. I will present an estimate of the size of the effect, and discuss where if at all it might be measured.

Acceleration-Induced Nonlocality

The locality postulate of the standard relativity theory is exact when dealing with phenomena involving classical point particles and rays of radiation, but breaks down for electromagnetic fields, as field properties cannot be measured instantaneously. Furthermore, Bohr and Rosenfeld pointed out in 1933 that only spacetime averages of the classical electric and magnetic fields have immediate physical significance. This assertion acquires the status of a physical principle when the intrinsic acceleration scales of observers are taken into account. To incorporate acceleration-induced nonlocality into relativity theory, a general integral relation is postulated between the field as measured by an accelerated observer and the instantaneous field measurements of the momentarily comoving inertial observers along the past world line of the observer. This nonlocal ansatz involves an acceleration kernel and leads to nonlocal special relativity once the kernel is determined.

OPERATIONAL GEOMETRY ON DE SITTER SPACETIME

Traditional geometry employs idealized concepts like that of a point or a curve, the operational definition of which relies on the availability of classical point particles as probes. Real, physical objects are quantum in nature though, leading us to consider the implications of using realistic probes in defining an effective spacetime geometry. As an example, we consider de Sitter spacetime and employ the centroid of various composite probes to obtain its effective sectional curvature, which is found to depend on the probe's internal energy, spatial extension, and spin. Possible refinements of our approach are pointed out and remarks are made on the relevance of our results to the quest for a quantum theory of gravity.

Electromagnetic (self-) interactions in relativistic Schrödinger theory

The Relativistic Schrödinger Theory (RST) is applied to a system of N particles with electromagnetic interactions. The gauge group is U(1) × U(1)... × U(1). By exploiting the mathematical structure of fibre bundles, the energy-momentum content of the gauge field can be defined in such a way that no infinite self-energy of point charges can arise. However, the picture of classical point particles becomes insufficient in any case in view of the exchange and overlap effects occurring in RST. The presence of overlap currents seems to be necessary to remedy certain pathological features of the classical point-particle theories. PACS Nos.: 03.65Pm, 03.65Ge, 03.65Ta

Statistical Mechanics of Classical Particles with Gravitational Interactions: Exactly Solvable (for N≤∞) in d=1 and d>2

This paper is concerned with a curious gap in a string of exactly solvable models, a gap that is suggestively related to a completely integrable nonlinear PDE in d=2 known as Liouville's equation. This PDE emerges in a limit N→∞ from the equilibrium statistical mechanics of classical point particles with gravitational interactions (SMGI) in dimension d=2 which, accordingly, is an exactly solvable continuum model in this limit. Interestingly, in d=1 and all d>2, the SMGI can be, and partly has been, exactly evaluated for all N≤∞. This entitles one to suspect that the SMGI for d=2 is likewise exactly solvable for N>∞, but currently this is an unproven hypothesis. If this conjecture can be answered in the affirmative, spin-offs in various areas associated with Liouville's equation, such as vortex gases, superfluidity, random matrices, and string theory can be expected.