The Misapplication of Probability Theory in Quantum Mechanics

L. E. Ballentine

Andrei Yu. Khrennikov

We start with the discussion on misapplication of classical probability theory by Feynman in his analysis of the two slit experiment (by following the critical argumentation of Koopman, Ballentine, and the author of this paper). The seed of Feynman's conclusion on the impossibility to apply the classical probabilistic description for the two slit experiment is treatment of conditional probabilities corresponding to different experimental contexts as unconditional ones. Then we move to the Bell type inequalities. Bell applied classical probability theory in the same manner as Feynman and, as can be expected, he also obtained the impossibility statement. In contrast to Feynman, he formulated his no-go statement not in the probabilistic terms, but by appealing to nonlocality. This note can be considered as a part of the author's attempts for getting rid off nonlocality from quantum physics.

Li Huo

The incompatibility between quantum mechanics and relativity is not a lack of technical details, but a fundamental one—they are each built on distinct local invariants: quantum mechanics relies on gauge invariance, while relativity is based on Lorentz invariance. Starting from different mountain feet, they naturally cannot converge at the summit. What physicists are truly seeking is a global, absolute, and simple invariant—one that can govern all physical phenomena and serve as the common source of all physical laws.This paper proposes the Axiom of Cosmic Uniqueness: all events, physical states, particle configurations, and interaction relationships in the universe are strictly unique, and there are no two identical forms of existence. From the perspective of group theory, this axiom is the ultimate invariant that physicists have long pursued—because the attribute of "everything is unique" remains unchanged regardless of any transformation applied (temporal evolution, spatial translation, rotation, gauge transformation, etc.).Based on this single axiom, this paper argues that:· The essence of time is the sequential unfolding of unique states, and the unidirectionality of the arrow of time is a direct inference of uniqueness;· The essence of space is the topological structure of causal correlations between unique events;· Causality possesses absolute necessity, and the "randomness" in quantum mechanics is a cognitive limitation rather than physical reality;· Probability has no physical reality and is purely an instrumental approximation under cognitive limitations—because the definition of probability relies on "repeatable experiments", a premise negated by the Axiom of Cosmic Uniqueness;· The paradox of the origin of life is thus resolved: the origin of life has already occurred, and no probabilistic explanation is needed under the Axiom of Cosmic Uniqueness—the so-called "extremely low probability" is a pseudo-problem arising from the misapplication of the concept of probability to unique historical events.This axiom requires no presupposition of any physical laws, particle properties, or spacetime frameworks, and achieves self-consistency solely through ontological logic. It is a more fundamental global invariant than Lorentz invariance and gauge invariance, and can govern the core laws of classical physics, quantum mechanics, relativity, and cosmic evolution—for all of them are branches growing from this common source.

Patrick Suppes

Martin Strauss

Huo Li

The incompatibility between quantum mechanics and relativity is not a lack of technical details, but a fundamental one—they are each built on distinct local invariants: quantum mechanics relies on gauge invariance, while relativity is based on Lorentz invariance. Starting from different mountain feet, they naturally cannot converge at the summit. What physicists are truly seeking is a global, absolute, and simple invariant—one that can govern all physical phenomena and serve as the common source of all physical laws. This paper proposes the Axiom of Cosmic Uniqueness: all events, physical states, particle configurations, and interaction relationships in the universe are strictly unique, and there are no two identical forms of existence. From the perspective of group theory, this axiom is the ultimate invariant that physicists have long pursued—because the attribute of "everything is unique" remains unchanged regardless of any transformation applied (temporal evolution, spatial translation, rotation, gauge transformation, etc.). Based on this single axiom, this paper argues that: · The essence of time is the sequential unfolding of unique states, and the unidirectionality of the arrow of time is a direct inference of uniqueness; · The essence of space is the topological structure of causal correlations between unique events; · Causality possesses absolute necessity, and the "randomness" in quantum mechanics is a cognitive limitation rather than physical reality; · Probability has no physical reality and is purely an instrumental approximation under cognitive limitations—because the definition of probability relies on "repeatable experiments", a premise negated by the Axiom of Cosmic Uniqueness; · The paradox of the origin of life is thus resolved: the origin of life has already occurred, and no probabilistic explanation is needed under the Axiom of Cosmic Uniqueness—the so-called "extremely low probability" is a pseudo-problem arising from the misapplication of the concept of probability to unique historical events. This axiom requires no presupposition of any physical laws, particle properties, or spacetime frameworks, and achieves self-consistency solely through ontological logic. It is a more fundamental global invariant than Lorentz invariance and gauge invariance, and can govern the core laws of classical physics, quantum mechanics, relativity, and cosmic evolution—for all of them are branches growing from this common source.