The Emergence of Probability from Fundamental Physical Theories

Angshul Majumdar

Angshul Majumdar

Iker Ibarrola Echeverría

We present an emergent account of quantum theory based on a minimal correlational framework in which no fundamental states, dynamics, or probabilistic axioms are assumed. Quantum behavior arises from admissible decoherent projections that induce equivalence classes of correlational configurations and suppress relational phase information. Effective quantum states are identified with these equivalence classes, while probability emerges as a normalized structural measure over them. The Born rule is recovered as a consistency condition associated with linear representations of equivalence classes, and measurement is reinterpreted as a structural interaction defined by projection rather than as a physical collapse. Decoherence, probability, and classicality are unified as manifestations of restricted access to correlational information stabilized by persistence. Quantum theory is thereby situated as an emergent, regime-dependent description alongside propagation and gravitation, resolving its conceptual puzzles by demoting its formal elements from fundamental postulates to effective constructs.

Gunn Quznetsov

Michał P. Heller

Space, time and probabilities not only form the arena of many physical theories, but also the arena of our everyday life. Therefore, the problem of their ontological status becomes even more interesting. It seems that this problem cannot be solved before we have the final physical theory (theory of everything). However, various methods of looking for such a theory lead to converging results, and are able to elucidate the problem in question. We analyze noncommutative algebraic methods, and show that, when applied to model the fundamental level, they suggest a nonlocal regime in which there is no space and no time, in their usual sense, and which is essentially probabilistic (in a generalized sense). In the noncommutative approach there are many probabilistic measures (not just one as in macroscopic physics), and none of them seems to be distinguished in any way. The tentative conclusion is that space, time and probability are not absolute categories, but rather aspects of the world structure emergent from the fundamental level. One should expect that the ultimate theory will be well off our traditional philosophical categories. This shows that our mind has a peculiar property allowing it to reach far beyond its usual limitations.

Hairong Yin