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arXiv:hep-ph/9609232

Could Spontaneous Transitions be Spontaneous?

Bernd A. Berg

Published Sep 2, 1996• 0 citations
arXivHTMLPDF

Abstract

It is considered to re-formulate quantum theory as it appears: A theory of continuous and causal time evolution, interrupted by discontinuous and stochastic jumps. To develop the (missing) theory of jumps a heuristic-phenomenological approach is suggested. Relying on a global reduction process, a hypothesis is introduced postulating spontaneous collapse of superpositions of states which describe spontaneous absorption or emission. The collapse probability determines a mean collapse time $τ^c = b \hbar / \triangle E$, where $b$ is a dimensionless constant and $\triangle E$ is the difference in energy distribution between alternative branches. Ramsey atomic beam spectroscopy yields a lower bound on $b$ and avalanche photodiodes give an upper bound, such that $1.35\cdot 10^{11} < b < 3.8\cdot 10^{21}$. Ample opportunities for experimental improvements exist.

DOI
10.48550/arxiv.hep-ph/9609232

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It is considered to re-formulate quantum theory as it appears: A theory of continuous and causal time evolution, interrupted by discontinuous and stochastic jumps. To develop the (missing) theory of jumps a heuristic-phenomenological approach is suggested. Relying on a global reduction process, a hypothesis is introduced postulating spontaneous collapse of superpositions of states which describe spontaneous absorption or emission. The collapse probability determines a mean collapse time τc=bℏ/△Eτ^c = b \hbar / \triangle Eτc=bℏ/△E, where bbb is a dimensionless constant and △E\triangle E△E is the difference in energy distribution between alternative branches. Ramsey atomic beam spectroscopy yields a lower bound on bbb and avalanche photodiodes give an upper bound, such that 1.35⋅1011<b<3.8⋅10211.35\cdot 10^{11} < b < 3.8\cdot 10^{21}1.35⋅1011<b<3.8⋅1021. Ample opportunities for experimental improvements exist.
The spontaneous decay of an excited atom by photon emission is one of the most common and elementary physical process present in nature and in laboratories. The decay is random in time with constant probability density, as it can be inferred by the exponential law observed experimentally. Despite the simplicity of the process, in Quantum Mechanics the decay itself is considered a law of nature which is not further analyzed or explained. However it is legitimate to ask for the reason of its randomness and for the dynamics of the atom around the decay. The decay process of an isolated atom is usually assumed to be instantaneous, the so called Quantum jumps. Particular experimental arrangements can widen the duration of the transition from an excited state to the ground state to a finite time. In general this is due to the quantum back action of the detector. The development of Quantum Optics has enormously enriched the possibilities to study in detail the process, and new illuminating insights have been obtained, but the question is still valid and its answer is still elusive. In this paper we analyze the spontaneous decay within the new prospect introduced by a recent model that complete standard Quantum Mechanics in a formalism which is able to describe the dynamics of measurement and of spontaneous decay. Comparison is made with more phenomenological theories, the Quantum Mechanics of open system and the Stochastic wave function model. In the new model the stochastic photon emission by an excited atom is triggered by the vacuum fluctuations. It is suggested how to re-analyze three types of experiments, already realized in many laboratories, in order to reveal the presence and the effect of these fluctuations.
According to the usual quantum description, the time evolution of the quantum state is continuous and deterministic except when a discontinuous and indeterministic collapse of state vector occurs. The collapse has been a central topic since the origin of the theory, although there are remarkable theoretical proposals to understand its nature, such as the Ghirardi–Rimini–Weber. Another possibility could be the assimilation of collapse with the now experimentally well established phenomenon of quantum jump, postulated by Bohr already in 1913. The challenge of nonlocality offers an opportunity to reconsider the quantum jump as a fundamental element of the logic of the physical world, rather than a subsidiary accident. We propose here a simple preliminary model that considers quantum jumps as processes of entry to and exit from the usual temporal domain to a timeless vacuum, without contradicting the quantum relativistic formalism, and we present some potential connections with particle physics. Quanta 2015; 4: 10–26.
In quantum mechanics the state vector evolves in a predictable and continuous way, according to the Schrödinger equation; only if a measurement takes place, the Schrödinger evolution is interrupted. Transitions between stationary states (transitions BSS) are accounted for time dependent perturbation theory (TDPT). It is often ignored that this theory requires measurements. As measurements demand either the intervention of an observer or the interaction between the quantum system with a measuring device, billions of observers and/or measuring devices would be necessary at every small corner of the universe where transitions BSS take place. Nevertheless, there is no evidence of their existence. We are thus led to conclude that transitions BSS are the result of causes different from the measurements required in TDPT. In the spontaneous projection approach, the version of quantum mechanics which we uphold, collapses to the stationary states result from the tendency of the system to jump to the eigenstates of the constants of the motion.
This paper considers the recent description of quantum time evolution in terms of a sequence of discrete quantum jumps. The historical development of continuous time evolution versus sudden jumps is reviewed. A time irreversible master equation is derived heuristically by considering random interruptions of the Schrodinger time development by external interventions characterized by a broad spectrum. The concrete examples we have in mind are atomic collisions and photon counting events. The formulation chosen allows a more general approach to the problem than conventional perturbative treatments. The conserved quantities are considered, and the effects of a dynamical superselection rule is discussed. It is pointed out, that these often break the time reversal symmetry and constitute a counting process which can be regarded as a measurement. Under certain conditions, the intervening process can be decomposed into simple jump processes that allow a simulation in terms of a quantum stochastic process. The significance of the results, their historical origins and the relations to contemporary investigations are all being discussed.
In the paper with the above-noted title, D. T. Gillespie [Phys. Rev. A 49, 1607 (1994)] claims that the theory of Markov stochastic processes cannot provide an adequate mathematical framework for quantum mechanics. In conjunction with the specific quantum dynamics considered there, we give a general analysis of the associated dichotomic jump processes. If we assume that Gillespie's ``measurement probabilities'' are the transition probabilities of a stochastic process, then the process must have an invariant (time independent) probability measure. Alternatively, if we demand the probability measure of the process follow the quantally implemented (via the Born statistical postulate) evolution, then we arrive at the jump process which can be interpreted as a Markov process if restricted to a suitable duration time. However, there is no corresponding Markov process consistent with the Z2{\mathit{Z}}_{2}Z2​ event space assumption, if we require its existence for all times t\ensuremath{\in}R+{\mathbf{R}}_{+}R+​. \textcopyright{} 1996 The American Physical Society.
Introduction The quantum theory of atoms and molecules had its origin in the famous 1913 paper of Bohr [186] in which he suggested that the interaction of radiation and atoms occurred with the transition of an atom from one stationary internal state to another, accompanied by the emission or absorption of radiation of a frequency determined by the energy difference between these states. These transitions came to be known as ‘quantum jumps’. Since all experiments until the late 1970s used to be carried out with large ensembles of atoms and molecules, these jumps were masked and could not be directly observed; they were only inferred from spectroscopic data. In fact, with the advent of quantum mechanics they eventually came to be regarded as artefacts of Bohr's simple-minded semi-classical model. But with the availability of coherent light sources and single ions prepared in ion traps [187], [188], and optically cooled [189], [190], the issue has been reopened with the experimental demonstration of quantum jumps in single ions [191], [192], [193]. These experiments have also opened up the contentious issue of wave function collapse or reduction on measurement, as they can be regarded as making collapse visible on the oscilloscope screen [191]. Evidence of the discrete nature of quantum transitions in a single quantum system had been accumulating from the observation of photon anti-bunching in single-atom resonance fluorescence [194], the tunneling of single electrons in metal–oxide-–semiconductor junctions [195] and spin-flips of individual electrons in a Penning trap [196].