This work attempts a fundamental formulation of physics based on probabilities. The basic assumptions are simple: One world exists. Humans can understand its properties by formulating laws based on probabilities. Our probabilistic setting only employs the notions of a probability distribution, observables and their expectation values, which are computed according to the classical statistical rule. Time is an ordering structure among observables. Understanding the probabilistic laws enables humans to make predictions for future events. Also space, spacetime and geometry emerge as structures among observables.
Within the classical statistical system the time structure induces the concepts of wave functions, density matrices, non-commuting operators and many other aspects of quantum physics. The classical density matrix encodes the probabilistic information of a time-local subsystem. Subsystems are typically correlated with their environment, offering a much richer structure than discussed commonly. We pay particular attention to subsystems with incomplete statistics and probabilistic observables.
Quantum systems are particular time-local subsystems that follow an unitary evolution law. All laws of quantum mechanics are derived from the basic law for expectation values in classical statistics. In particular, we discuss entangled quantum systems in terms of classical probability distributions. In our approach quantum field theories have to be described by an overall probability distribution for the whole Universe for all times. The fundamental functional integral for quantum field theories should define a probability distribution, underlying the functional integral with Minkowski signature.
While this work remains in the context of theoretical physics, the concepts developed here apply to a wide area of science.

C. Wetterich, “The probabilistic world”, Nov. 4, 2020, arXiv:2011.02867 (2020).


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