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arXiv:quant-ph/0303067

Timing of the Penrose R-Process

Richard A. Mould

Published Mar 11, 2003• 2 citations
arXivHTMLPDF

Abstract

The Penrose reduction theory is applied to a particle/detector interaction where the time that it takes for a particle capture (and reduction of the original state) is constrained by the Heisenberg uncertainty between time and energy . The usual interpretation of this equation is found to conflict with the Hamiltonian dynamics of the interaction. Another interpretation of this equation seems to solve that problem, but then another difficulty arises. We conclude that the Penrose theory cannot reflect the timing implicit in the Hamiltonian dynamics unless it can be amended to take account of the probability current flow between competing states. Key Words: decoherence, probability current, stochastic choice, wave collapse.

DOI
10.48550/arxiv.quant-ph/0303067

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The Penrose reduction theory is applied to a particle/detector interaction where the time that it takes for a particle capture (and reduction of the original state) is constrained by the Heisenberg uncertainty between time and energy . The usual interpretation of this equation is found to conflict with the Hamiltonian dynamics of the interaction. Another interpretation of this equation seems to solve that problem, but then another difficulty arises. We conclude that the Penrose theory cannot reflect the timing implicit in the Hamiltonian dynamics unless it can be amended to take account of the probability current flow between competing states. Key Words: decoherence, probability current, stochastic choice, wave collapse.
A model of state reduction in relativistic quantum field theory involving a nonlinear stochastic extension of Schrödinger's equation is outlined. The eigenstates of the annihilation operator are chosen as the preferred basis onto which reduction occurs. These are the coherent states which saturate the bound of the Heisenberg uncertainty relation, exhibiting classical-like behaviour. The quantum harmonic oscillator is studied in detail before generalizing to relativistic scalar quantum field theory. The infinite rates of increase in energy density which have plagued recent relativistic proposals of dynamical state reduction are absent in this model. This is because the state evolution equation does not drive particle creation from the vacuum. The model requires the specification of a preferred sequence of space-like hyper-surfaces supporting the time-like state evolution. However, it is shown that the choice of preferred surfaces has no effect on perturbative results to second order in the coupling parameter. It is demonstrated how state reduction to a charge density basis can be induced in fermionic matter via an appropriate coupling to a bosonic field undergoing this mechanism.
We study the construction of probability densities for time-of-arrival in quantum mechanics. Our treatment is based upon the facts that (i) time appears in quantum theory as an external parameter to the system, and (ii) propositions about the time-of-arrival appear naturally when one considers histories. The definition of time-of-arrival probabilities is straightforward in stochastic processes. The difficulties that arise in quantum theory are due to the fact that the time parameter of Schrödinger’s equation does not naturally define a probability density at the continuum limit, but also because the procedure one follows is sensitive on the interpretation of the reduction procedure. We consider the issue in Copenhagen quantum mechanics and in history-based schemes like consistent histories. The benefit of the latter is that it allows a proper passage to the continuous limit–there are however problems related to the quantum Zeno effect and decoherence. We finally employ the histories-based description to construct Positive-Operator-Valued-Measures (POVMs) for the timeof-arrival, which are valid for a general Hamiltonian. These POVMs typically depend on the resolution of the measurement device; for a free particle, however, this dependence cancels in the physically relevant regime and the POVM coincides with that of Kijowski. 1
Abstract The problem of time in quantum mechanics (QM) concerns the fact that in the Schrödinger equation time is a parameter, not an operator. Pauli's objection to a time–energy uncertainty relation analogue to the position–momentum one, conjectured by Heisenberg early on, seemed to exclude the existence of such an operator. However Dirac's formulation of an electron's relativistic QM does allow the introduction of a dynamical time operator that is self-adjoint. Consequently, it can be considered as the generator of a unitary transformation of the system, as well as an additional system observable subject to uncertainty. In the present paper these aspects are examined within the standard framework of relativistic QM.
We consider two straightforward rules that govern the stochastic choice in a single quantum mechanical event. They are shown to lead to absurd results if an objective state reduction is allowed to compete with an observer state reduction. Since the latter collapse is empirically verifiable, the existence of the former is thrown into question. Key Words: Born Interpretation, brain states, continuous observation, conscious observer, objective measurement, observer measurement, probability current, state reduction, wave collapse.
This preprint develops a physical mechanism for quantum state reduction within the Relativistic Coherent Vacuum Gravity Theory (rCVGT). Building on Penrose’s gravitational collapse proposal, it formulates a generalized self-energy functional that includes not only mass–energy differences but also vacuum coherence and physical time-rate structure. Quantum superpositions are interpreted as competing vacuum configurations, and collapse arises as a finite-time instability of the physical time-rate field. The framework identifies vacuum dynamics, rather than stochastic noise or measurement postulates, as the driver of state reduction. In appropriate limits, the model reproduces Penrose-type collapse while extending it to coherence-dominated and mesoscopic regimes. The work offers a physically grounded, testable approach to the quantum measurement problem rooted in vacuum structure and emergent time. Companion paper to: “Quantum Phenomena as Vacuum-Coherence Dynamics in rCVGT” (Nielsen, 2025), 10.5281/zenodo.17950974.