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arXiv:quant-ph/0307157

Source Field Effects and Wave Function Collapse

Atilla Gürel, Zeynep Gürel

Published Jul 22, 2003• 1 citation
arXivHTMLPDF

Abstract

Detection of a material particle is accompanied by emission of bremsstrahlung. Thus the dynamics of the energy loss of the particle is determined by radiation reaction force. The description of radiation reaction is a difficult problem still being subject of ongoing debates. There are problems of runaway solutions, preacceleration already in classical description of radiation reaction. Additional complications in quantum mechanical description arise because of the infinite source field energy term in hamiltonian for a point charge. There is still no general consensus on an appropriate quantum mechanical description. Neither the achievements of the radiation theory on the subject nor the problems associated with it are sufficiently taken into account in context with measurement problem. Radiation reaction doesn't effect free particle wave packets, but it favors stationary states of the `wave function of the measured particle" in presence of a potential gradient. We suggest therefore that radiation reaction may play a significant role in the dynamics of the wave function collapse. keywords: wave function collapse,interpretation,randomness, Jaynes Cummings dynamics, spontaneous emission, source field effects, radiation reaction, quantum measurement,decoherence

DOI
10.48550/arxiv.quant-ph/0307157

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Detection of a material particle is accompanied by emission of bremsstrahlung. Thus the dynamics of the energy loss of the particle is determined by radiation reaction force. The description of radiation reaction is a difficult problem still being subject of ongoing debates. There are problems of runaway solutions, preacceleration already in classical description of radiation reaction. Additional complications in quantum mechanical description arise because of the infinite source field energy term in hamiltonian for a point charge. There is still no general consensus on an appropriate quantum mechanical description. Neither the achievements of the radiation theory on the subject nor the problems associated with it are sufficiently taken into account in context with measurement problem. Radiation reaction doesn't effect free particle wave packets, but it favors stationary states of the `wave function of the measured particle" in presence of a potential gradient. We suggest therefore that radiation reaction may play a significant role in the dynamics of the wave function collapse. keywords: wave function collapse,interpretation,randomness, Jaynes Cummings dynamics, spontaneous emission, source field effects, radiation reaction, quantum measurement,decoherence
The processes of radiation damping and decoherence in Quantum Electrodynamics are studied from an open system's point of view. Employing functional techniques of field theory, the degrees of freedom of the radiation field are eliminated to obtain the influence phase functional which describes the reduced dynamics of the matter variables. The general theory is applied to the dynamics of a single electron in the radiation field. From a study of the wave packet dynamics a quantitative measure for the degree of decoherence, the decoherence function, is deduced. The latter is shown to describe the emergence of decoherence through the emission of bremsstrahlung caused by the relative motion of interfering wave packets. It is argued that this mechanism is the most fundamental process in Quantum Electrodynamics leading to the destruction of coherence, since it dominates for short times and because it is at work even in the electromagnetic field vacuum at zero temperature. It turns out that decoherence trough bremsstrahlung is very small for single electrons but extremely large for superpositions of many-particle states.
The processes of radiation damping and decoherence in Quantum Electrodynamics are studied from an open system's point of view. Employing functional techniques of field theory, the degrees of freedom of the radiation field are eliminated to obtain the influence phase functional which describes the reduced dynamics of the matter variables. The general theory is applied to the dynamics of a single electron in the radiation field. From a study of the wave packet dynamics a quantitative measure for the degree of decoherence, the decoherence function, is deduced. The latter is shown to describe the emergence of decoherence through the emission of bremsstrahlung caused by the relative motion of interfering wave packets. It is argued that this mechanism is the most fundamental process in Quantum Electrodynamics leading to the destruction of coherence, since it dominates for short times and because it is at work even in the electromagnetic field vacuum at zero temperature. It turns out that decoherence trough bremsstrahlung is very small for single electrons but extremely large for superpositions of many-particle states.
When you follow two separate chains of thought, Watson, you will find some point of intersection which should approximate the truth. —Sir Arthur Conan Doyle, The Disappearance of Lady Frances Carfax ABSTRACT. It is now well established that effects traditionally associated with vacuum electromagnetic field fluctuations can be described equally well in terms of source fields (radiation reaction). This remarkable reconciliation of two previously unconnected points of view, which was stimulated by Jaynes' neoclassical theory, is reviewed and explained in a general and simple way. Background The Jaynes-Cummings paper seems to have been the first to employ dressed states of two-state atoms in fields (Jaynes 1963). One result found in that paper is that semiclassical radiation theory could serve as an excellent approximation even under certain conditions where the average number of photons in the field is small. The accuracy of semiclassical theory paved the way to Jaynes' “neoclassical theory,” where even spontaneous emission was treated without field quantization (Jaynes 1972, Milonni 1976). The neoclassical theory was a subject of much debate and misunderstanding in the 1970s. It turned out not to be so easy to dismiss it on experimental grounds.
Abstract The problem of the wave function collapse (a problem of measurement in quantum mechanics) is considered. It is shown that it can be solved based on quantum mechanics and does not require any additional assumptions or new theories. The particle creation and annihilation processes, which are described based on quantum field theory, play a key role in the measurement processes. Superposition principle is not valid for the system of equations of quantum field theory for particles and fields, because this system is a non-linear. As a result of the creation (annihilation) of a particle, an additional uncertainty arises, which “smears” the interference pattern. The imposition of such a large number of uncertainties in the repetitive measurements leads to the classical behavior of particles. The decoherence theory also implies the creation and annihilation of particles, and this processes are the consequence of non-linearity of quantum mechanics. In this case, the term “collapse of the wave function” becomes a consequence of the other statements of quantum mechanics instead of a separate postulate of quantum mechanics.
The physical mechanism responsible for wave function collapse remains an open question in the foundations of quantum theory. Existing objective reduction models usually rely on gravitational self-energy in the bulk, which makes it difficult to account for the rapid reduction of very light particles and does not naturally address massless quanta such as photons. In this work, a kinematic and mass-independent mechanism for wave function collapse is considered in which radiative emission across a geometric boundary is taken as the operational event associated with reduction. When a single quantum transition is evaluated at a radiative decoupling surface, the governing relation becomes boundary-normalized. Under this formulation both Boltzmann’s constant and Planck’s constant cancel algebraically, and the resulting rate is determined purely by boundary kinematics, Γ ∝ R²ω³ / c². The same structural scaling appears in the standard spontaneous-emission rate derived in quantum electrodynamics, while the fine-structure constant enters only as a dimensionless efficiency factor. Within this framework, quantum states may evolve unitarily in the bulk, whereas any radiative extraction of information into the classical domain must cross a finite decoupling surface. Collapse is therefore interpreted as an objective reduction associated with the finite transmission capacity of a radiative boundary. The Heisenberg cut is consequently assigned a concrete physical location at that boundary.
The quantum theory of radiation, formulated in wave-mechanical language but in terms of running waves, is shown to lead under suitable conditions to the classical theory of emission by a particle as a first approximation. Non-relativistic mechanics is used, and the limitations of the method are brought out in terms of classical theory. The characteristic quantum phenomenon of the Compton effect requires that the Compton recoil shall exceed the spread in momentum of the particle, and so that the wave-packet shall greatly exceed in diameter the wave-length of the incident radiation; this condition is realizable on any scale of magnitude. For quasi-classical motion just the reverse is required; furthermore, if the motion is to last for a number of waveperiods, the wave-length must greatly exceed hmc\frac{h}{\mathrm{mc}}mch​ (m=massoftheparticlem=\mathrm{mass}\mathrm{of}\mathrm{the}\mathrm{particle}m=massoftheparticle). The classical packet-motion arises from combinations between quantum-states of the particle-field system; this fact suggests that the photon is not a fundamental constituent of the field but only one possible aspect of its action. The infinite "zero-energy" associated apparently even with the lowest energy-state of the field implies no electromagnetic field intensities at any point. Whereas for problems on energy or momentum it is customary to represent an incident wave-train by a single typical quantum state, to obtain motional phenomena of classical type a more complete expression such as that given in the paper must be used. The physically empty field likewise corresponds to a mixture of quantum states but without correlation among their amplitudes.