From Information Geometry to Newtonian Dynamics

Abstract

Newtonian dynamics is derived from prior information codified into an appropriate statistical model. The basic assumption is that there is an irreducible uncertainty in the location of particles so that the state of a particle is defined by a probability distribution. The corresponding configuration space is a statistical manifold the geometry of which is defined by the information metric. The trajectory follows from a principle of inference, the method of Maximum Entropy. No additional "physical" postulates such as an equation of motion, or an action principle, nor the concepts of momentum and of phase space, not even the notion of time, need to be postulated. The resulting entropic dynamics reproduces the Newtonian dynamics of any number of particles interacting among themselves and with external fields. Both the mass of the particles and their interactions are explained as a consequence of the underlying statistical manifold.

Newtonian Dynamics from the Principle of Maximum Caliber

“…Newtonian dynamics has been previously derived from information-geometric arguments [8] leading to the idea of entropic dynamics. This idea is based on the assumption of an irreducible uncertainty in the position of a particle, implying an information metric for space from which Newton's second law naturally emerges.…”

Lattice Theory, Measures and Probability

“…It is an important, but subtle distinction. One might go as far as suggesting that the laws of physics are actually laws of inference [8].…”

On Grover’s search algorithm from a quantum information geometry viewpoint

“…Indeed, two classically identical expressions (see (13) and (14), for instance) generally differ when they are extended to a quantum setting. This difference is a manifestation of the non-commutative nature of quantum mechanics and is reminiscent of the idea of quantum discord [29].…”

“…This line of investigation is very stimulating and appealing, especially considering that it is an old dream that of viewing quantum mechanics as rooted in making statistical inferences based on observed experimental data [11,12]. Recent works where information geometry and inference methods are used to investigate the origin of fundamental theories as information geometric inferential theories appear in [13][14][15].…”