Probability, geometry, and irreversibility in quantum mechanics

Daniel Burnstein

The fundamental laws of classical mechanics, quantum mechanics, and general relativity are time-symmetric, yet macroscopic experience is irreversible without exception. Standard physics bridges this gap with statistical argument: reversal is treated as merely improbable, not physically inadmissible. This paper argues that the gap is an artifact of treating space as a continuum, and that it closes once space is treated as discrete, as in Quantum-Geometry Dynamics (QGD). Two independent grounds are identified for the categorical, non-statistical irreversibility of every elementary interaction in discrete space: a local ground, the loss of individual addressability when one particle's constituent preon(+)s merge into another upon absorption; and a global ground, the irreducible universal gravitational trace left by any positional change, given that gravity in QGD is instantaneous and universal in scope. Applied across four domains, this single result dissolves the arrow-of-time problem, grounds the second law of thermodynamics in dynamics rather than probability, dissolves the apparent asymmetry between unitary evolution and measurement collapse, and shows the reversible/irreversible distinction in quantum gate theory to be a feature of the abstract computational model rather than of physical mechanism. The result is shown to be compatible with, and silent on, whether a finite deterministic system's forward dynamics eventually revisit an earlier configuration by a non-retracing causal path. No new axiom or free parameter is introduced: the result follows from elements of QGD already established for independent reasons.

G. C. Ghirardi

Boris B. Kadomtsev

Emile Van Der Merwe

Quantum mechanics provides unparalleled predictive accuracy yet remains conceptually unsettled regarding the ontological status of particles, waves, and measurement. Many apparent paradoxes arise from object-centred interpretations inherited from classical mechanics. This paper offers a structural clarification in which space is treated not as an empty container but as a continuous, relational constraint system whose geometry and boundary conditions permit only certain self-consistent excitation patterns. Within this framework, quantisation arises as a consequence of discrete boundary lock-in rather than as a fundamental postulate, and measurement is interpreted as irreversible pattern resolution under material constraints. The approach does not modify quantum formalism, but clarifies its interpretation by relocating discreteness, localisation, probability, and entanglement within geometry and topology.

Kalyan B. Sinha, Debashish Goswami

The classical theory of stochastic processes has important applications arising from the need to describe irreversible evolutions in classical mechanics; analogously quantum stochastic processes can be used to model the dynamics of irreversible quantum systems. Noncommutative, i.e. quantum, geometry provides a framework in which quantum stochastic structures can be explored. This book is the first to describe how these two mathematical constructions are related. In particular, key ideas of semigroups and complete positivity are combined to yield quantum dynamical semigroups (QDS). Sinha and Goswami also develop a general theory of Evans-Hudson dilation for both bounded and unbounded coefficients. The unique features of the book, including the interaction of QDS and quantum stochastic calculus with noncommutative geometry and a thorough discussion of this calculus with unbounded coefficients, will make it of interest to graduate students and researchers in functional analysis, probability and mathematical physics.

N. V. Lunin, Vladimir I Kogan