When Can Statistical Theories Be Causally Closed?

Trevor W. Marshall

Chandrasekhar Roychoudhuri, Luigi Accardi, Guillaume Adenier +5 more

We use the following epistemology—understanding and visualizing the invisible processes behind all natural phenomena through iterative reconstruction and/or refinement of current working theories towards their limits, constitute our best approach towards discovering actual realities of nature followed by new break‐through theories. We use this epistemology to explore the roots of statistical nature of the real world—classical physics, quantum physics and even our mental constructs. Diversity is a natural and healthy outcome of this statistical nature. First, we use a two‐beam superposition experiment as an illustrative example of the quantum world to visualize the root of fluctuations (or randomness) in the photo electron counting statistics. We recognize that the fluctuating weak background fields make the quantum world inherently random but the fluctuations are still statistically bounded, indicating that the fundamental laws of nature are still causal. Theoreticians will be challenged for ever to construct a causal and closed form theory free of statistical randomness out of incomplete information. We show by analyzing the essential steps behind any experiment that gaps in the information gathered about any phenomenon is inevitable. This lack of information also influences our personal epistemologies to have “statistical spread” due to its molecular origin, albeit bounded and constrained by the causally driven atomic and molecular interactions across the board. While there are clear differences in the root and manifestation of classical and quantum statistical behavior, on a fundamental level they originate in our theories due to lack of complete information about everything that is involved in every interaction in our experiments. Statistical nature of our theories is a product of incomplete information and we should take it as an inevitable paradigm.

Michael J. W. Hall

Son David Bolduc

This sixth volume of Causal Physics 101 completes the operational layer of the CT–United framework by introducing a rigorous theory of measurement, observables, and epistemic access. While Parts I–V established the ontology of natural and reflective causes, will dynamics, attractors, and macro-causal systems, this paper formalizes how causal quantities are accessed, measured, inferred, and compared—without collapsing or confusing ontological structure with epistemic procedure. Causal observables are defined as functionals on the causal field and its derived quantities, and measurement is modeled as a reflective coupling between an observing system and the causal field. Measurement is shown to be a reflective causal act that perturbs the system it probes, yet does not alter the ontological classification of the cause being measured: natural causes remain natural even when accessed reflectively. This clean separation between ontological causation and epistemic access resolves long-standing ambiguities surrounding entities that are fundamental yet indirectly observed, such as neutrinos, black holes, vacuum tension, and the speed of light. The paper further develops measurement noise and resolution limits in terms of coherence alignment, introduces the statistical structure of Causal Physics as an epistemic construct rather than an ontological one, and assigns causal weight to observation itself based on alignment with coherence gradients. By closing the measurement loop, Part VI renders Causal Physics a complete, operationally closed physical theory and prepares the ground for causal thermodynamics and cosmology.

Balázs Gyenis, Miklós Rédei

Guangzhao Zhou, Zhao-Bin Su, Bailin Hao +1 more

A theoretical scheme using closed time-path Green's functions is proposed to describe the quantum statistical properties of the order parameter in terms of a generating functional. The dynamic evolution, is generated by a driving source, while the statistical correlation by a fluctuation source. The statistical causality is shown to hold explicitly and to give rise to a number of important consequences. The problem of determining the quantum statistical properties for the order parameter is reduced to finding a solution of the functional equation for it.