Equivalence principle for antiparticles and its limitations

Abstract

We investigate the particle-antiparticle symmetry of the gravitationally coupled Dirac equation, both on the basis of the gravitational central-field problem and in general curved space-time backgrounds. First, we investigate the central-field problem with the help of a Foldy-Wouthuysen transformation. This disentangles the particle from the antiparticle solutions, and leads to a "matching relation" of the inertial and the gravitational mass, which is valid for both particles as well as antiparticles. Second, we supplement this derivation by a general investigation of the behavior of the gravitationally coupled Dirac equation under the discrete symmetry of charge conjugation, which is tantamount to a particle→antiparticle transformation. Limitations of the Einstein equivalence principle due to quantum fluctuations are discussed. In quantum mechanics, the question of where and when in the Universe an experiment is being performed, can only be answered up to the limitations implied by Heisenberg's Uncertainty Principle, questioning an assumption made in the original formulation of the Einstein equivalence principle. Furthermore, at some level of accuracy, it becomes impossible to separate non-gravitational from gravitational experiments, leading to further limitations.

Antimatter Gravity: Second Quantization and Lagrangian Formalism

“…Equipped with an appropriate form of the Dirac adjoint in curved space-time, we start from the well-known Lagrangian density [13,32,[34][35][36][37][38][39][40][41][42][43][44][45]…”

“…Corresponding investigations have been initiated in a series of recent publications [10][11][12][13]. One may ask whether the dynamics of particles and antiparticles differ in a central, static, gravitational field, but also, if there are any small higher-order effects breaking the particle-antiparticle symmetry under the gravitational interaction.…”

“…A preliminary result has recently been published in [13,32], where a relationship was established between the positive-energy and negative-energy solutions of the Dirac equation in an arbitrary dynamics curved-space-time-background. However, the derivation in [13,32] is based on a first-quantized formalism, which lacks the unified description in terms of the field operator. The field operator comprises all (as opposed to any) solution of the gravitationally (and electromagnetically) coupled Dirac equation.…”

“…In general, a satisfactory description of antiparticles, in the field-theoretical context, necessitates a description in terms of particle-and antiparticle creation and annihilation processes, and therefore, the introduction of a field operator. In consequence, the investigation [13,32] is augmented here on the basis of a transformation of the entire Lagrangian density, which can be expressed in terms of the charge-conjugated (antiparticle) bispinor wave function, and generalized to the level of second quantization. The origin [13] of a rather disturbing minus sign which otherwise appears in the Lagrangian formalism upon charge conjugation in first quantization will be addressed.…”

“…In consequence, the investigation [13,32] is augmented here on the basis of a transformation of the entire Lagrangian density, which can be expressed in terms of the charge-conjugated (antiparticle) bispinor wave function, and generalized to the level of second quantization. The origin [13] of a rather disturbing minus sign which otherwise appears in the Lagrangian formalism upon charge conjugation in first quantization will be addressed. The use of the Lagrangian formalism necessitates a definition of the Dirac adjoint in curved space-times.…”