Quantum Probability: New Perspectives for the Laws of Chance

Stanley Gudder

Mounssif Benchekrou

We propose a conceptual analysis of probability within a discrete relational frameworkbased on the additive group (nZ, +). The central claim is that, under the simultaneousassumptions of exact laws, global symmetries, and strict conservation principles, probabilityis more naturally interpreted as epistemic than as the manifestation of ontological chance.In the framework considered here, events are treated as elements of a globally constrainedrelational structure, without introducing fundamental time or a physically postulated wave.We discuss the possible relevance of this perspective for the conceptual relation betweengeneral relativity and quantum mechanics.

Xiaohui Jiang

M.Born's notions on causality are that Quantum World is governed by causality and chance jointly;that quantum particle has the intrinsic property of uncertainty,and the law of chance is the last law of nature;and that the concepts of probability and chance are more elementary than causality.While D.Bohm's notions of potential causality are that there is no last law of nuture at all,and each level manifests unique rules;that causality is just relative necessity and contingency always appears on the cross point of many different factors or probable tendencies;that the potential causality interpretation is some kind of integration of causal determination and probability statistics,which has clear intuitive model in physics,and has definite ontological base in philosophy.

Luigi Accardi

Markus P. Müller

According to our current conception of physics, any valid physical theory is supposed to describe the objective evolution of a unique external world. However, this condition is challenged by quantum theory, which suggests that physical systems should not always be understood as having objective properties which are simply revealed by measurement. Furthermore, as argued below, several other conceptual puzzles in the foundations of physics and related fields point to limitations of our current perspective and motivate the exploration of an alternative: to start with the first-person (the observer) rather than the third-person perspective (the world).In this work, I propose a rigorous approach of this kind on the basis of algorithmic information theory. It is based on a single postulate: that universal induction determines the chances of what any observer sees next. That is, instead of a world or physical laws, it is the local state of the observer alone that determines those probabilities. Surprisingly, despite its solipsistic foundation, I show that the resulting theory recovers many features of our established physical worldview: it predicts that it appears to observers as if there was an external world that evolves according to simple, computable, probabilistic laws. In contrast to the standard view, objective reality is not assumed on this approach but rather provably emerges as an asymptotic statistical phenomenon. The resulting theory dissolves puzzles like cosmology's Boltzmann brain problem, makes concrete predictions for thought experiments like the computer simulation of agents, and suggests novel phenomena such as ``probabilistic zombies'' governed by observer-dependent probabilistic chances. It also suggests that some basic phenomena of quantum theory (Bell inequality violation and no-signalling) might be understood as consequences of this framework.

Stanley Gudder