Probabilistic Nature of a Field with Time as a Dynamical Variable

Roger G. Newton

While I very much enjoyed Steven Weinberg’s article “Einstein’s Mistakes,” I am puzzled by the author’s statement about quantum mechanics: “The difficulty is not that quantum mechanics is probabilistic—that is something we apparently have to live with. The real difficulty is that it is also deterministic, or more precisely, that it combines a probabilistic interpretation with deterministic dynamics.” Quantum mechanics is an acausal deterministic theory in the sense that a physical system’s state (mathematically described by a state vector) at a given initial time determines its state at a specified later time, but its state is not in one-to-one correspondence with sharp values of all its dynamical variables; that correspondence is probabilistic. Therefore events, identified by sharp values of those variables at one spacetime point, are not causally connected with other events. That is something we have to live with.Why does the combination of these two attributes—acausality and determinism—constitute a special difficulty? Weinberg asks, “So where do the probabilistic rules of the Copenhagen interpretation come from?” Why do they have to come from anywhere other than from human brains? Nature exists out there, independent of human thought, but its mathematical description surely is a human construction rather than an immutable law given to us on a stone tablet.© 2006 American Institute of Physics.

Hou Y. Yau

Patrick Suppes

Sandeep J Chavan

Quantum mechanics provides extraordinary predictive accuracy yet remains conceptually incomplete regarding wave-function collapse, the role of the observer, and the nature of randomness. Decoherence theory explains the suppression of interference through environmental entanglement but does not complete the transition from probabilistic description to a single resolved outcome for an observer. This paper introduces Alignment Threshold Time (ATT) as a completion principle for quantum description. ATT quantifies the duration over which an observer and a field remain misaligned through a shared, dynamically changing relational variable termed Consequence Deviation (ΔC). The wave function is reframed as an alignment-conditional articulation, valid only while ATT > 0. Collapse is not postulated as a physical discontinuity but arises naturally as the exhaustion of articulation when alignment completes (ΔC → 0). The framework preserves standard quantum dynamics, reclassifies probability as transitional, clarifies the observer–field relationship, and provides a minimal, testable experimental proposal distinguishing decoherence from outcome resolution. This work proposes Alignment Threshold Time (ATT) as a relational completion principle for quantum mechanics, reframing wave-function collapse as exhaustion of articulation rather than a physical discontinuity.

Natalia N. Gorobey, Alexander S. Lukyanenko, Inna Lukyanenko

A probabilistic interpretation of one-particle relativistic quantum mechanics is proposed. Quantum Action Principle formulated earlier is used for to make the dynamics of the Minkowsky time variable of a particle to be classical. After that, quantum dynamics of a particle in the 3D space obtains the ordinary probabilistic interpretation. In addition, the classical dynamics of the Minkowsky time variable may serve as a tool for "observation" of the quantum dynamics of a particle. A relativistic analog of the hydrogen atom energy spectrum is obtained.

Lazar Mayants