A Probabilistic Formulation of the Special Theory of Relativity.

Frank Blume

Fabrice PFAFF

This paper uncovers a surprising connection between special relativity and probability theory through simple competitive games. By modeling contests—first as draws from an urn and then as races between exponentially distributed events—we derive expectation values that mirror the relativistic velocity addition formula. Remarkably, these probabilistic outcomes obey Einstein’s rule for combining velocities, suggesting a structural analogy between relativistic kinematics and probabilistic competition. This finding blurs the traditional divide between the deterministic framework of relativity and the stochastic nature of quantum mechanics, hinting that probabilistic principles may underpin aspects of special relativity. We provide rigorous derivations and explore implications for interdisciplinary studies in physics and probability.

Ryusho Nemoto

Norberto Sainz

The theory of special relativity (TSR) exhibits an unquestionable success, at the expense of an unresolved axiomatic conflict with functional analysis and operator theory, as this paper demonstrates. These mathematical disciplines —amongst the newest developments in the field— could not possibly be incorporated into the original formulation of the TSR because they were in an incipient state at the turn of the 20th century when the TSR was being formulated, maturing only decades later.

Ryusho Nemoto

Lucién Hardy

In this paper we develop an operational formulation of General Relativity similar in spirit to existing operational formulations of Quantum Theory. To do this we introduce an operational space (or op-space) built out of scalar fields. A point in op-space corresponds to some nominated set of scalar fields taking some given values in coincidence. We assert that op-space is the space in which we observe the world. We introduce also a notion of agency (this corresponds to the ability to set knob settings just like in Operational Quantum Theory). The effects of agents' actions should only be felt to the future so we introduce also a time direction field. Agency and time direction can be understood as effective notions. We show how to formulate General Relativity as a possibilistic theory and as a probabilistic theory. In the possibilistic case we provide a compositional framework for calculating whether some operationally described situation is possible or not. In the probabilistic version we introduce probabilities and provide a compositional framework for calculating the probability of some operationally described situation. Finally we look at the quantum case. We review the operator tensor formulation of Quantum Theory and use it to set up an approach to Quantum Field Theory that is both operational and compositional. Then we consider strategies for solving the problem of Quantum Gravity. By referring only to operational quantities we are able to provide formulations for the possibilistic, probabilistic, and (the nascent) quantum cases that are manifestly invariant under diffeomorphisms.