Conventional Quantum Theory Research Articles

Positive and Negative Mixtures in Relativistic Schrödinger Theory

The general formalism of relativistic Schrodinger theory (RST) is specialized to a scalar two-particle system with electromagnetic interactions (scalar helium atom). The set of dynamically allowed field configurations splits up into positive and negative mixtures and pure states. The static and spherically symmetric solutions are constructed by means of first-order perturbation theory for the case of an attractive Coulomb potential. The corresponding energy levels for the positive and negative mixtures resemble the emergence of ortho and para states in the conventional quantum theory. The associated energy eigenvalues predicted by the RST seem to undergo a certain kind of mixture degeneracy as the RST analog of the conventional exchange degeneracy. The charge densities of the positive mixtures assimilate, whereas the densities of the negative mixtures recede from one another. Thus, positive (negative) mixtures strongly resemble the bosonic (fermionic) matter of the conventional theory when the Pauli principle is applied.

Quantum theory of excess noise

We analyze the excess noise in the framework of the conventional quantum theory of laserlike systems. Our calculation is conceptually simple and our result also shows a correction to the semiclassical result derived earlier.

Timing quantum particles from the perspective of Bohmian mechanics

According to Bohm's causal alternative to conventional quantum mechanics a quantum ‘particle’ such as an electron is at all times a point-like particleandan accompanying wave that guides the particle along a well-defined continuous trajectory. This paper focuses on the Bohm trajectory approach to the determination of various characteristic times associated with the motion of the particle component of a quantum ‘particle’. An attempt is made to relate this approach to those based on conventional quantum theory with its very different concept of wave/particle duality.

Temporally-quantized theory of exponential radioactive decay: Resolution of Zeno's paradox of quantum theory

As characterized experimentally by Rutherford, an essential feature of radioactive decompositions is their being constituted of randomly occurring events in terms of which the decomposing systems exhibit exponential temporal decay behavior with associated characteristic half-lives. This feature is rigorously accounted for generally by the recent temporally-quantized dynamical theory of strictly-irreversible evolution of isolated and localized non-relativistic quantum systems, which theory also obviates the celebrated Zeno's paradox of conventional quantum theory.

On the general covariance and strong equivalence principles in quantum general relativity

The various physical aspects of the general relativistic principles of covariance and strong equivalence are discussed, and their mathematical formulations are analyzed. All these aspects are shown to be present in classical general relativity, although no contemporary formulation of canonical or covariant quantum gravity has succeeded to incorporate them all. This has, in part, motivated the recent introduction of a geometro-stochastic framework for quantum general relativity, in which the classical frame bundles that underlie the formulation of parallel transport in classical general relativity are replaced by quantum frame bundles. It is shown that quantum frames can take over the role played by complete sets of observables in conventional quantum theory, so that they can mediate the natural transference of the general covariance and the strong equivalence principles from the classical to the quantum general relativistic regime. This results in a geometrostochastic mode of quantum propagation in general relativistic quantum bundles, which is mathematically implemented by path integration methods based on parallel transport along horizontal lifts of geodesics for the vacuum expectation values of a quantum gravitational field in a quantum spacetime supermanifold. The covariance features of this field are embedded in a quantum gravitational supergroup, which incorporates Poincare as well as diffeomorphism invariance, and resolves the issue of time in quantum gravity.

Quantum chaos, complex spectral representations and time-symmetry breaking

As has been shown in recent publications, classical chaos leads to complex irreducible representation of the evolution operator (such as the Perron-Frobenius operator for chaotic maps). Complex means that time symmetry is broken (appearance of semi-groups) and irreducible that the representation can only be implemented by distribution functions (and not by trajectories). A somewhat similar situation occurs in Hamiltonian nonintegrable systems with continuous spectrum (“Large Poincaré Systems” LPS), both in classical and quantum mechanics. The elimination of Poincarés divergences requires an extended formulationof dynamics on the level of distribution functions (or density matrices). This applies already to simple situations such as potential scattering in the case of persistent interactions. There appear characteristic delta-function singularities in the density matrices in momentum representation. Our theory predicts then dissipative processes corresponding to the destruction of invariants of motion throuh Poincaré resonances. This prediction is quantitative agreement with extensive numerical simulations presented here. We concentrate in this paper on potential scattering. We discuss also briefly a simple model of a many-body system (the so called “perfect Lorentz gas”). In both cases we obtain irreducible spectral representations which we consider as the signature of “chaos”. We solve the eigenvalue problem for the Liouville-von Neumann operator for the class of singular density matrices corresponding to persistent scattering. This leads to a complex spectral representation in which cross sections appear as eigenvalues. Our previous results [see our previous paper in Chaos, Solitons & Fractals (1991)] obtained by “subdynamics theory” are now derived through the solution of the eigenvalue problem for singular distributions. Our results can be tested by numerical simulations. Again the agreement is excellent. Note that our results cannotbe derived from conventional quantum theory for probability amplitudes. We have therefore here a simple example of a quantum theory which goes beyond the traditional Schrödinger formulation. As already mentioned, our theory is formulated on the level of density matrices. Wave functions corresponding to persistent scattering (and therefore to singular density matrices) “collapse” as the result of Poincaré divergences. We obtain therefore a unified formulation of quantum theory without any appeal to extra dynamical concepts (such as many worlds, influence of environment,…). The appearance of chaos for LPS through the formulation of complex irreducible representations on the level of density matrices solves therefore not only the “time paradox” as it introduces time symmetry breaking on the microscopic level, but eliminates also the old standing epistemological problems of quantum theory associated to measurement and to decoherence.

The stretched horizon and black hole complementarity.

Three postulates asserting the validity of conventional quantum theory, semi-classical general relativity and the statistical basis for thermodynamics are introduced as a foundation for the study of black hole evolution. We explain how these postulates may be implemented in a ``stretched horizon'' or membrane description of the black hole, appropriate to a distant observer. The technical analysis is illustrated in the simplified context of 1+1 dimensional dilaton gravity. Our postulates imply that the dissipative properties of the stretched horizon arise from a course graining of microphysical degrees of freedom that the horizon must possess. A principle of black hole complementarity is advocated. The overall viewpoint is similar to that pioneered by 't~Hooft but the detailed implementation is different.

Probing space with the two-slit experiment

The two-slit experiment is one of the most important in quantum physics. The particle-wave duality of particles is purportedly established on the basis of this experiment and others similar to it. Conventional quantum theory attributes the observed wavelike properties to the particles themselves, and not to the space through which they travel. Recently the wavelike properties of particles in the two-slit experiment have been modelled using a random map dynamical system. This model requires only particle attributes and the interference effects can be explained by postulating the existence of a complicated underlying space. Based on this model, a simple experiment is suggested which could produce results different from what is predicted by quantum mechanics. This would provide evidence that (1) particles behave as particles and that (2) the complex nature of the space through which the particles travel plays a role in the observed interference effects of the two-slit experiment.

Interpretation of the curious results of the new quantum formalism of pre- and post-selected systems

The analysis, with the use of two state vectors, of a quantum system, during the time interval between two measurements, leads to some amazing results, which seem to contradict our usual “quantum common sense.” We explore the questions of compatibility with the conventional quantum theory, uniqueness of pre- and post-selected ensembles, commutativity, simultaneity and reality of strong and weak values in the intermediate time, and the meaning of the weak value. Common criticisms are shown to be unfounded.

Quantization of discrete deterministic theories by Hilbert space extension

Quantization of a theory usually implies that it is being replaced by a physically different system. In this paper it is pointed out that if a deterministic theory is completely discrete, such as a classical gauge theory on a lattice, with discrete gauge group, then there is an essentially trivial procedure to quantize it. The equations for the evolution of the physical variables are kept unchanged, but are reformulated in terms of the evolution of the transition turns a system into a conventional quantum theory, which may have more symmetries that can be seen in the original classical theory. This is illustrated in a cellular automaton, of which only the quantum version is time-reversal symmetric. Another automation shows self-duality only after Hilbert space extension. We discuss the importance of such observations for physics. The procedure can also be used to construct a completely finite and soluble quantum gravity model in 2 + 1 dimensions.

Non-Hermitian quantum dynamics.

An algorithm previously obtained for complex-energy modal probabilities in non-Hermitian quantum dynamics is generalized to determine expectation values for arbitrary observables. When cast in conventional form, the formalism including the generalized algorithms appears as a natural generalization of conventional quantum theory, in that conventional quantum theory obtains in the continuous Hermitian limit.

Quantum physics without time

A formulation of quantum physics which does not rely upon a time parameter is proposed. Conventional quantum theory is recovered in the limit of infinite energies but finite energy systems exhibit unconventional features. The no-time formulation appears as the natural one if gravity is considered at the quantum level in a logically consistent way; it indicates the possible incompleteness of quantum physics.

Normalization and Probability Densities for Wavefunctions of Quantum Fieldtheoretic Energy Equations

Abstract Quantum fields can be characterized by the set of transition amplitudes {〈0|π(A)|a〉V̶|a,〉∈V} where π(A) is a representation of the field operator algebra in V. This set has to satisfy renormalized energy equations and the elements of this set are called wavefunctions. However, these wavefunctions are not identical with wavefunctions of conventional quantum theory in Fockspace. Thus a theoret­ical interpretation is needed. In the present paper, by means of some theorems a method of normalization and construction of probability densities for these wavefunctions is given, which differs from the method of derivation of the normalization condition for Bethe-Salpeter amplitudes. The method can be applied both to nonrelativistic and relativistic fields with positive definite or indefinite state spaces, provided the renormalized energy equations possess finite solutions.

A quantized approach to space-time

Some consequences are traced of a simple approach to the concept of a quantized relativistic space-time. It is assumed that the basic unit of space-time s 0 depends on the rest-mass of the individual particle m 0 and that the location in space-time of the particle cannot be defined more closely than s 0, where s 0 equals h/ m 0 ic in space coordinates or h/ m 0 c 2 in time coordinates. This leads to the same expressions for the uncertainty in space and time, the de Broglie wavelength, basic frequency and energy levels, and phase velocity as in conventional quantum theory but without the need to introduce a physically significant wave function. This avoids the difficulty in accepting a probability explanation for the wave function and the apparently contradictory wave and particle concepts when dealing with interference and detection from large volumes at very low intensities as well as a possible inversion of cause and effect. Interference appears as the segregation of beams into different units of space-time, each with its own selection of quantum numbers n i of units s 0 along the four axes but with the same total Σ n i . The different beams correspond merely to a (quantized) change of axes. This approach is compared with that involved in the Schrodinger equation, which leads to an extensive wave function, and this must then be “reduced” by an observation or measurement to establish a localized particle. Prior to such a measurement, the nature of the particle, spread in some sense over the wave function raises questions of reality in unobserved objects. No such problems of reality need arise with the concept of quantized space-time, and the observer intervenes only by choosing the framework axes.

Measurement in Bohm's versus Everett's quantum theory

The interpretations of measurements in Bohm's and Everett's quantum theories are compared. Since both theories are based on the assumption of a universally valid Schrodinger equation, they face the common problem of how to explain that arrow of time, which in conventional quantum theory is represented by the collapse of the wave function. Its solution requires, in a statistical sense, a very improbable initial condition for thetotal wave function of the universe. The historical importance of Bohm's quantum theory is pointed out.

The nonrelativistic Schr�dinger equation in ?quasi-classical? theory

The author has recently proposed a “quasi-classical” theory of particles and interactions in which particles are pictured as extended periodic disturbances in a universal field χ(x, t), interacting with each other via nonlinearity in the equation of motion for χ. The present paper explores the relationship of this theory to nonrelativistic quantum mechanics; as a first step, it is shown how it is possible to construct from χ a configuration-space wave function Ψ(x1,x2,t), and that the theory requires that Ψ satisfy the two-particle Schrodinger equation in the case where the two particles are well separated from each other. This suggests that the multiparticle Schrodinger equation can be obtained as a direct consequence of the quasi-classical theory without any use of the usual formalism (Hilbert space, quantization rules, etc.) of conventional quantum theory and in particular without using the classical canonical treatment of a system as a “crutch” theory which has subsequently to be “quantized.” The quasi-classical theory also suggests the existence of a preferred “absolute” gauge for the electromagnetic potentials.

Irreversibility, time, and fluctuations in quantum statistical theory of dissipative molecular systems. II. Application to fluorescence spectroscopy

AbstractSome basic concepts of the Prigogine quantum statistical theory of irreversible processes are discussed in connection with a previous paper by Chatzidimitriou‐Dreismann and Lippert. The removal of the “dual role” that the Hamiltonian plays within conventional quantum theory corresponds to the introduction of a star‐unitary operator 𝒯 called “intrinsic time.” The formalism of the previous paper is extended to systems that interact with external fields. A formal specification of 𝒯, furthermore, follows from the Lt invariance of the basic equations of motion and its connection with the intrinsic time. As an application to fluorescence spectroscopy, a photon counting experiment is presented. It allows us to detect certain predicted “dynamical” fluctuations in emission spectra. Some current experimental results are reported concerning the resolution of the broad fluorescence band of fluoranthene (dissolved in ethanol) through detection of the underlying finer vibrational structure.

On the theory of accommodation and adsorption of atoms on solid surfaces at low energies

The present theory of accommodation and adsorption of atoms on solid surfaces is re-examined, and the consequences of a more exact quantum treatment are explored. Using the system He-W as an illustrative example, it is shown that the disturbing qualitative features of the quantum results, that is the well-known qualitative disagreement of the results with both intuition and experimental trends at low energies, are still present. The precise physical reasons for the qualitative behavior of the theoretical results are examined in detail, and are made clear. With these reasons clarified and understood, it is concluded that there is no hope of bringing the conventional quantum theory into agreement with the expected trends, and that further theoretical progress will be difficult without results of certain future experiments. Effects of dimensionality of the (continuum) solid model are examined: it is shown that the situation is improved slightly if a two-dimensional model (surface modes?), as opposed to the conventional three-dimensional model (bulk modes) is used; use of a one-dimensional model considerably improves the situation, but this is presumably irrelevant to the real processes involved.

Collapse postulate for observables with continuous spectra

In order to provide a mathematical framework for discussing the statistical correlations between the outcomes, when an arbitrary sequence of observables are measured, it is necessary to generalize the conventional von Neumann-Luders collapse postulate to observables with a continuous spectrum. It is shown that the standard prescription in conventional quantum theory for the joint probabilities of compatible observables is sufficient to characterize, more or less completely, the appropriate “generalized collapse postulate” which associates with each observable a unique “finitely additive expectation valued measure”. An interesting feature of the collapse associated with observables with continuous spectra, which again follows from the basic principles of conventional quantum theory, is that it must be formulated in terms of the so-called non-normal conditional expectations, which implies that the joint probabilities associated with successive observations of such observables are not in general σ-additive. The implications of this non-σ-additivity on the determination of expectation values, correlation functions etc., are also investigated. It is demonstrated that the basic prescriptions introduced in this paper constitute a natural completion of the framework of conventional quantum theory for discussing the statistics of an arbitrary sequence of observations.

Operator formulation of classical mechanics

An operator formulation of classical mechanics is given. Rather than being concerned with Lie algebraic or abstract Hilbert space properties of classical mechanics, the present formulation is directly concerned with wave packets in configuration space and is thus more similar to that of conventional quantum theory than other extant operator formulations of classical mechanics. Among other things, the following items are discussed for classical systems: Ehrenfest’s theorem, the uncertainty principle, dissipative systems, and field theory.