Role of time in the sum-over-histories framework for gravity

I sketch a self-contained framework for quantum mechanics based on its path-integral or sum-over-histories formulation. The framework is very close to that for classical stochastic processes like Brownian motion, and its interpretation requires neither measurement nor state-vector as a basic notion. The rules for forming probabilities are nonclassical in two ways: they use complex amplitudes, and they (apparently unavoidably) require one to truncate the histories at a collapse time, which can be chosen arbitrarily far into the future. Adapting this framework to gravity yields a formulation of quantum gravity with a fully spacetime character, thereby overcoming the frozen nature of the canonical formalism. Within the proposed adaptation, the value of the collapse time is identified with total elapsed spacetime four-volume. Interestingly, this turns the cosmological constant into an essentially classical constant of integration, removing the need for microscopic fine tuning to obtain an experimentally viable value for it. Some implications of the V = T rule for quantum cosmology are also discussed.     

An experiment to test an explanation of a possible violation of quantum theory

An experiment to test a possible explanation of the Schmidt backwards causation results is suggested. The experiment might distinguish between many- and one- world interpretations of quantum theory.     

Axiomatic unsharp quantum theory (From Mackey to Ludwig and Piron)

On the basis of Mackey's axiomatic approach to quantum physics or, equivalently, of a state-event-probability (SEVP) structure, using a quite standard fuzzification procedure, a set of unsharp events (or effects) is constructed and the corresponding state-effect-probability (SEFP) structure is introduced. The introduction of some suitable axioms gives rise to a partially ordered structure of quantum Brouwer-Zadeh (BZ) poset; i.e., a poset endowed with two nonusual orthocomplementation mappings, a fuzzy-like orthocomplementation, and an intuitionistic-like orthocomplementation, whose set of sharp elements is an orthomodular complete lattice. As customary, by these orthocomplementations the two modal-like necessity and possibility operators are introduced, and it is shown that Ludwig's and Jauch-Piron's approaches to quantum physics are interpreted in complete SEFP. As a marginal result, a standard procedure to construct a lot of unsharp realizations starting from any sharp realization of a fixed observable is given, and the relationship among sharp and corresponding unsharp realizations is studied.     

Coherent quantum oscillation trajectories

We discuss coherent oscillations in the quantum potential view of quantum mechanics, giving examples for both a superposition of position states, and a superposition of momentum states.     

THE ORIGIN OF ENTROPY IN THE UNIVERSE

We discuss the entropy generation in quantum tunneling of a relativistic particle under the influence of a time-varying force with the help of squeezing formalism. It is shown that if one associates classical coarse grained entropy to the phase space volume, there is an inevitable entropy growth due to the changes in position and momentum variances. The entropy change can be quantified by a simple expression S=ln cosh 2r, where r, is the squeeze parameter measuring the height and width of the potential barrier. We suggest that the universe could have acquired its initial entropy in a quantum squeeze from nothing and briefly discuss the implications of our proposal.     

Foundation for Quantum Computing

In this paper we introduce a minimal formal intuitionistic propositional Gentzen sequent calculus for handling quantum types, quantum storage being introduced syntactically along the lines of Girard's of course operator !. The intuitionistic fragment of orthologic is found to be translatable into this calculus by means of a quantum version of the Heyting paradigm. When realized in the category of finite dimensional Hilbert spaces, the familiar qubit arises spontaneously as the irreducible storage capable quantum computational unit, and the necessary involvement of quantum entanglement in the quantum duplication process is plainly and explicitly visible. Quantum computation is modelled by a single extra axiom, and reproduces the standard notion when interpreted in a larger category.     

On measurement and irreversible processes

The nature of physical measurements performed on microscopic systems is discussed, and it is suggested that the procedures which are conventionally referred to as measurements fall into at least three different categories. The connection between observation processes and irreversible processes is stressed. The customary quantum mechanical treatment of irreversible processes is discussed, and its deficiencies from the philosophical point of view are criticized. The standpoint that quantum mechanics should not be considered as a basic philosophical system but rather as an immensely useful tool is defended. Some attempts at developing a more basic theory are discussed, and a hypothesis is put forward concerning the role of entropy within some possible future nonlocal hidden-variable theory.     

Particle velocities faster than the speed of light

In connection with another article by the author, we show how it might be possible to travel faster than the speed of light. We show that for clocks and rods moving faster than the speed of light, we get instead of time dilation and Lorentz contraction, respectively, time contraction and Lorentz expansion, respectively. It is shown that this paper is in confirmation with earlier articles dealing with this subject.     

Charge-field formulation of quantum electrodynamics (QEMED)

By expressing classical electron theory in terms of charge-field functional structures, it is shown that a finite formulation of the classical electrodynamics of point charges emerges in a simple and elegant fashion. The classical charge-field form of microscopic electron theory plays the role of a covering theory for renormalized classical electron theory, with the distinct advantage that this is accomplished by adynamic subtraction mechanism, built into the theory. We then generalize this formalism into a hole-theoretic, second-quantized Dirac formulation, in order to construct a charge-field quantum electrodynamic theory, and discuss its basic properties. We find, in addition to the possibility that the finiteness of the classical theory may be propagated into the quantum field theory, that interacting photon states are generated as a secondary manifestation of electron-positron quantization, and do not require the usual free canonical quantization scheme. We discuss the possibility that this approach may lead to a better formulation of quantum electrodynamics in the Heisenberg picture and suggest a crucial experimental test to distinguish this new charge-field quantum electrodynamics QEMED from the standard QED formulation. Specifically QEMED predicts that the Einstein principle of separability should be found to be valid for correlated photon polarization measurements, in which the polarizers are changed more rapidly than a characteristic photon travel time. Such an experiment (Aspect, 1976) can distinguish between QEMED and QED in a complete and clear-cut fashion.     

Lattice theory,quadratic spaces,and quantum proposition systems

A quadratic space is a generalization of a Hilbert space. The geometry of certain kinds of subspaces (closed, splitting, etc.) is approached from the purely lattice theoretic point of view. In particular, theorems of Mackey and Kaplansky are given purely lattice theoretic proofs. Under certain conditions, the lattice of closed elements is a quantum proposition system (i.e., a complete orthomodular atomistic lattice with the covering property).     

Anti-photon

It should be apparent from the title of this article that the author does not like the use of the word photon, which dates from 1926. In his view, there is no such thing as a photon. Only a comedy of errors and historical accidents led to its popularity among physicists and optical scientists. I admit that the word is short and convenient. Its use is also habit forming. Similarly, one might find it convenient to speak of the aether or vacuum to stand for empty space, even if no such thing existed. There are very good substitute words for photon, (e.g., radiation or light), and for photonics (e.g., optics or quantum optics). Similar objections are possible to use of the word phonon, which dates from 1932. Objects like electrons, neutrinos of finite rest mass, or helium atoms can, under suitable conditions, be considered to be particles, since their theories then have viable non-relativistic and non-quantum limits. This paper outlines the main features of the quantum theory of radiation and indicates how they can be used to treat problems in quantum optics.It is a pleasure to join in the 60th birthday celebration of the Director, Herbert Walther, of the Max-Planck-Institute for Quantum Optics at Garching, and wish him much happiness and many more years of his very great scientific creativity.     

On some frequent but controversial statements concerning the Einstein-Podolsky-Rosen correlations

Quite often the compatibility of the EPR correlations with the relativity theory has been questioned; it has been stated that the first in time of two correlated measurements instantaneously collapses the other subsystem; it has been suggested that a causal asymmetry is built into the Feynman propagator. However, the EPR transition amplitude, as derived from the S matrix, is Lorentz andCPT invariant; the correlation formula is symmetric in the two measurements irrespective of their time ordering, so that the link of the correlations is the Feynman zigzag, and that causality isCPT invariant at the microlevel; finally, although the Feynman propagator has theP andCT symmetries, no causal asymmetry follows from that. As for Stapp's views concerning process and becoming, and his Whiteheadean concept of an advancing front, I object that they belong to factlike macrophysics, and are refuted at the microlevel by the EPR phenomenology, which displays direct Fokker-like space-time connections. The reason for this is a radical one. The very blending of a space-time picture and of a probability calculus is a paradox. The only adequate paradigm is one denying objectivity to space-time—but this, of course, is also required by the complementary of the x and the k pictures, which only look compatible at the macrolevel. Therefore, the classical objectivity must yield in favor of intersubjectivity. Only the macroscopic preparing and measuring devices have factlike objectivity; the transition of the quantal system takes place beyond both thex and thek 4-spaces. Then, the intrinsic symmetries between retarded and advanced waves, and statistical prediction and retrodiction, entails that the future has no less (but no more) existence than the past. It is the future that is significant in creative process, the elementary forms of which should be termed precognition or psychokinesis—respectively symmetric to the factlike taboos that we can neither know into the future nor act into the past. It is gratifying that Robert Jahn, at the Engineering School of Princeton University, is conducting (after others) conclusive experiments demonstrating low level psychokinesis—a phenomenon implied by the very symmetry of the negentropy-information transition. So, what pierces the veil of maya is the (rare) occurrence of paranormal phenomena. The essential severance between act and potentia is not a spacelike advancing front, but the out of and the into factlike space-time. Finally, I do not feel that an adequate understanding of the EPR phenomenology requires going beyond the present status of relativistic quantum mechanics. Rather, I believe that the potentialities of this formalism have not yet been fully exploited.     

Can particle creation by a black hole be described in terms of more familiar laboratory processes?

Particle creation by a black hole is described in terms of temperature corrections to the Casimir effect. The results of Levin, Polevoy, and Ritov for spectral and total Poynting vector for a fluctuating electromagnetic field in a plane vacuum gap between two arbitrary media with different temperatures in flat spacetime are applied to clarify the situation that exists between the horizon of a nonrotating black hole and spatial infinity. This helps to reveal the mechanism of particle creation. The Hawking radiation is born inside the bell formed by a potential barrier of a black hole in all the region [2M, ]. Its blackbody spectrum is due to the interaction of field fluctuations with the surface of the bell. The particles between the walls are virtual ones. They can become real after passing through the [3M, ] tail, appearing to an observer at future infinityJ ⁺ as real ones. The arguments for and against the present standpoint are discussed.     

Some Thought-Experiments Involving Macrosystems as Illustrations of Various Interpretations of Quantum Mechanics

I consider various experiments related to the so-called macroscopic quantum coherence experiment, which are probably at present in the class of thought experiment but are likely to become realistic in the next few decades. I explore the way in which outcomes consistent with the predictions of quantum mechanics would be interpreted by an adherent of, respectively, the Copenhagen, statistical, and Bohmian interpretations of the formalism.     

AN EXTENSION OF “POPPER'S EXPERIMENT” CAN TEST INTERPRETATIONS OF QUANTUM MECHANICS

Karl Popper proposed a way to test whether a proposed relation of a quantum-mechanical state to perceived reality in the Copenhagen interpretation (CI) of quantum mechanics—namely that the state of a particle is merely an expression of what is known about the system—is in agreement with all experimental facts. A conceptual flaw in Popper's proposal is identified and an improved version of his experiment (called Extension step 1)—which fully serves its original purpose—is suggested. The main purpose of this paper is to suggest to perform this experiment. The results of this experiment predicted under the alternative assumptions that the CI or the many-worlds interpretation (MWI) is correct are shown to be identical. Only after a further modification (called Extension step 2) (the use of an ion isolated from the macroscopic environment as particle detector) the predictions using the respective interpretations become qualitatively different. This is because what is known by a human observer H can fail as a basis for the prediction of the statistical distribution of measurement results within the MWI in special cases: The temporal evolution of a system un-entangled with H (like the isolated ion) can depend on another system's state components that are entangled with states ortogonal to H. Thus—within the CI—for H they are known not to exist. Yet H can infer their existence by studying the evolution of the ion.     

What makes a theory physically “complete”?

Three claims about what makes a theory physically complete are (1) Shimony's assertion that a complete theory says all there is to say about nature; (2) EPR's requirement that a complete theory describe all elements of reality; and (3) Ballentine and Jarrett's claim that a predictively complete theory must obey a condition used in Bell deviations. After introducing statistical completeness as a partial formalization of (1), we explore the logical and motivational relationships connecting these completeness conditions. We find that statistical completeness motivates but does not imply Jarrett's completeness condition, because Jarrett's condition encodes further intuitions about locality and causality. We also dispute Ballentine and Jarrett's claim that EPR-completeness implies Jarrett's completeness condition.     

Atomic versus ionized states in many-particle systems and the spectra of reduced density matrices: A model study

We study the spectrum of appropriate reduced density matrices for a model consisting of one quantum particle (electron) in a classical fluid (of protons) at thermal equilibrium. The quantum and classical particles interact by a shortrange, attractive potential such that the quantum particle can form atomic bound states with a single classical particle. We consider two models for the classical component: an ideal gas and the cell model of a fluid. We find that when the system is at low density the spectrum of the electron-proton pair density matrix has, in addition to a continuous part, a discrete part that is associated with atomic bound states. In the high-density limit the discrete eigenvalues disappear in the case of the cell model, indicating the existence of pressure ionization or a Mott effect according to a general criterion for characterizing bound and ionized electron-proton pairs in a plasma proposed recently by M. Girardeau. For the ideal gas model, on the other hand, eigenvalues remain even at high density.     

Dark body and black hole horizons

The formula for the horizon of a Newtonian dark body is given and compared to that of a relativistic black hole: a Newtonian dark body has at least one hair.