Field and Charge Measurements in Quantum Theory

With L. Rosenfeld, Niels Henrik David Bohr, L. Rosenfeld

Ren Matsuoka

Gauge Probability Charge Theory (GPCT) proposes a physical framework in which quantum probability is treated as physically meaningful and capable of participating in gauge interactions. The central idea of GPCT is that probability density is not merely a mathematical tool for predicting measurement outcomes, but can play an active physical role in interactions. In this framework, the probability density associated with a quantum state is interpreted as a probability charge density, while corresponding probability fields describe its interaction with the gauge sectors of physics. GPCT develops this idea within a field-theoretical framework. It introduces probability-field dynamics, interaction Lagrangians, Hamiltonian formulations, Green's functions, propagators, and gauge-covariant descriptions. The framework is examined in relation to electromagnetic, strong, weak, and gravitational interactions, with the aim of describing these interactions through a common probability-charge coupling principle. A central application of the theory is quantum measurement. GPCT interprets measurement as a physical interaction that compresses and localizes probability density rather than as an instantaneous mathematical projection. The theory proposes a dynamical description of this compression and considers the apparent instantaneous nature of quantum measurement as a limiting behavior of the underlying interaction process. The theory also investigates the relationship between probability-field interactions and quantum uncertainty. It proposes a unified perspective in which uncertainty relations arise from the interaction between physical quantities and their corresponding probability fields. For electromagnetism, GPCT reinterprets electric charge as the coupling strength associated with the interaction between particle probability density and the electromagnetic probability field. Analogous probability-charge descriptions are developed for color and weak interactions, while gravity is considered through a gravitational probability field coupled to matter. The framework further discusses probability-field excitations, probability virtual particles, gauge symmetry, quantum corrections, renormalization-group behavior, and possible connections to established quantum field theory. GPCT proposes several possible experimental avenues for testing deviations or additional effects associated with probability-field interactions. These include precision electromagnetic measurements, atomic spectroscopy, anomalous magnetic moments, collider physics, jet structure, weak-interaction measurements, neutrino physics, and gravitational-wave observations. The purpose of this work is to present a unified theoretical framework in which quantum probability and gauge interactions can be considered from a common physical perspective. The theory is intended as a foundation for further mathematical development, theoretical consistency checks, and experimental investigation.

Craig S. Hamilton

Claus Kiefer

It is shown how the programme of decoherence can be applied in the context of quantum field theory. To illustrate the role of gauge invariance, we first discuss the charge superselection rule in quantum electrodynamics in some detail. We then present an example where macroscopic electromagnetic fields are ``measured" through interaction with charges and thereby rendered classical.

Henry Margenau

Bo-Bo Wei

Conformal invariance powerfully constrains the critical behavior of two-dimensional classical systems with short-range interactions and the critical theories in two-dimensions are parametrized by a dimensional number, termed central charge or conformal anomaly $c$. However, experimental determination of the central charge of a conformal field theory has not been done before. Here we propose to extract the central charge of the conformal field theory corresponding to a critical point of a two-dimensional lattice models from the quantum decoherence measurement of a probe spin which is coupled to the two-dimensional lattice models. Conformal invariance predicts that the leading finite-size correction to the free energy for a two-dimensional system at a conformal invariant critical point is linearly related to the conformal anomaly for various boundary conditions. A recent discovery of thermodynamic holography allows us to obtain the free energy of many-body system from central spin decoherence measurement. Thus the central charge of the conformal field theory could be extracted from central spin decoherence measurement. We have applied the method to the two-dimensional Ising model and extracted the central charge of two-dimensional Ising model with good precision. This work provides a useful approach to extracting the central charge of conformal field theory in various two-dimensional lattice systems.