Coordinate- and Spacetime-Independent Quantum Physics

Wm. Bender

Giovanni Amelino-camelia A, Robert Brandenberger, Chong‐Sun Chu +9 more

Mayeul Arminjon, Frank Reifler

We define and study the probability current and the Hamiltonian operator for a fully general set of Dirac matrices in a flat spacetime with affine coordinates, by using the Bargmann-Pauli hermitizing matrix. We find that with some weak conditions on the affine coordinates, the current, as well as the spectrum of the Dirac Hamiltonian, thus all of quantum mechanics, are independent of that set. These results allow us to show that the tensor Dirac theory, which transforms the wave function as a spacetime vector and the set of Dirac matrices as a third-order affine tensor, is physically equivalent to the genuine Dirac theory, based on the spinor transformation. The tensor Dirac equation extends immediately to general coordinate systems, thus to non-inertial (e.g. rotating) coordinate systems.

James B. Hartle

Mayeul Arminjon, Frank Reifler

We define and study the probability current and the Hamiltonian operator for a fully general set of Dirac matrices in a flat spacetime with affine coordinates, by using the Bargmann-Pauli hermitizing matrix. We find that with some weak conditions on the affine coordinates, the current, as well as the spectrum of the Dirac Hamiltonian, thus all of quantum mechanics, are independent of that set. These results allow us to show that the tensor Dirac theory, which transforms the wave function as a spacetime vector and the set of Dirac matrices as a third-order affine tensor, is physically equivalent to the genuine Dirac theory, based on the spinor transformation. The tensor Dirac equation extends immediately to general coordinate systems, thus to non-inertial (e.g. rotating) coordinate systems.

Marco Pettini

Quantum entanglement is a central resource of quantum information science, yet its correlations are ordinarily treated as properties of the quantum state rather than as the outcome of an underlying physical process. Here we explore the hypothesis that these correlations are mediated dynamically by a field propagating locally at finite velocity through an extension of ordinary spacetime. The model embeds physical $(3,1)$-dimensional spacetime in a warped five-dimensional geometry containing an additional timelike coordinate. Within the adopted geometric ansatz, the form of the extended spacetime metric is determined by the five-dimensional vacuum Einstein equations. A massless field propagating through the resulting five-dimensional bulk can mediate correlations whose projection onto observable four-dimensional spacetime connects arbitrarily distant locations at equal laboratory time, while preserving operational no-signaling. Coupling this field to a Bohm--Bub-inspired collapse scheme provides a possible dynamical realization of entanglement correlations and, under a stated statistical consistency condition, reproduces Born statistics. The framework leads to a concrete experimental test. Two nominally independent Bell pairs are predicted to develop a weak, distance-dependent contextual correlation between particles belonging to different pairs, as a consequence of bulk-field mediation. This cross-pair correlation is absent in standard quantum mechanics for independently prepared systems and is predicted to decrease as the inverse square of their separation. It could therefore be tested by varying the distance between two simultaneous Bell experiments using existing photonic technology. Observation of such a signal would support a dynamical spacetime account of quantum entanglement and could have implications for quantum networks employing multiple independent entangled resources.