CHN,QCD, and\overline {SA} (4,R)

CHN≓ (1966)was an algebraic algorithm which reproduced and extended the predictions of the non-interacting≓ quark model in the asymptotic high-energy region. It wus formulated within the conceptual framework of on- mass- shell physics and of the complex angular-momentum plane. Prior to the advent of the standard model, it was reinterpreted in terms of the Melosh transformation relating current≓ to constituent≓ quarks. It is now lied up to the QCD paradigm.Also on leave from Center for Particle Physics, University of Texas, Austin, Texas 78712.     

Continuum and discretum—Unified field theory and elementary constants

Unitary field theories and SUPER-GUT theories work with an universal continuum, the structured spacetime of R. Descartes, B. Spinoza, B. Riemann, and A. Einstein, or a (Machian ^(1–3) ) structured vacuum according the quantum theory of unitary fields (Dirac, ^(4,5) and Heisenberg ^(6–8) ). The atomistic aspect of the substantial world is represented by the fundamental constants which are invariant against all transformations and which depend on nothings (Planck ^(9–11) ). A satisfactory unitary theory has to involve these constants like the mathematical numbers. Today, Planck's conception of the three elementary constants , c, and G may be the key to general relativistic quantum field theory like unitary theory. However, the elementary constants are a question of measurement-theory, also.According to Popper's theory ^(12–16) of induction, such unitary theories are universal explaining theories. The fundamental constants involve the complementarity between the universal statements in unitary theory and the basic statements in the language of classical observables.     

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.     

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.     

A phase cell approach to Yang-Mills theory

Variables are chosen to describe the continuum Yang-Mills fields, a discrete set of group valued variables. These are group elements associated to the sequence of lattice field theory configurations realizing the continuum field. The field is laid down inductively. At each inductive step one of three types of field excitations makes its contribution to the total field. These are either pure modes, averaging correction modes, or chunks. The pure modes are small field excitations, as studied in previous papers in this series [2,3]. The averaging correction modes are small excitations added to make sure the block spin transformation is satisfied at each edge. The chunks, encompassing most of our difficulties, are large field excitations. Topological obstructions in ₃(G) must be dealt with in defining a gauge choice for each chunk. The laying down process is complex, but fiendishly clever, ensuring a principle of gauge invariant coupling. Each group valued variable is either the amplitude of a pure mode or an internal variable in a chunk. The amplitude of an averaging correction mode is a dependent variable, a function of the (independent) variables used to describe the field. The (independent) variables herein defined are those whose mutual interaction will later be inductively decoupled in defining the phase cell cluster expansion (of course treating the variables of each chunk as a unit).This work was supported in part by the National Science Foundation under Grant No. PHY-85-02074     

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.     

Instead of particles and fields: A micro realistic quantum “smearon” theory

A fully micro realistic, propensity version of quantum theory is proposed, according to which fundamental physical entities—neither particles nor fields—have physical characteristics which determine probabilistically how they interact with one another (rather than with measuring instruments). The version of quantum smearon theory proposed here does not modify the equations of orthodox quantum theory: rather it gives a radically new interpretation to these equations. It is argued that (i) there are strong general reasons for preferrring quantum smearon theory to orthodox quantum theory; (ii) the proposed change in physical interpretation leads quantum smearon theory to make experimental predictions subtly different from those of orthodox quantum theory. Some possible crucial experiments are considered.     

Some properties of topological geons

We investigate the Finkelstein-Misner geons for a non-simply-connected space-time manifold (M, g ₀). We use relations between different Lorentzian structures unequivalent tog ₀ and topological properties ofM given by the Morse theory. It implies that to some pieces of geons we have to associate Wheeler's worm-holes. Geons that correspond to time-orientable Lorentz structures are related tog ₀ by Morse functions that describe the attaching of a handle of index one. In the case of geons associated to time-nonorientable Lorentzian structures, appropriate handles are related to loops along which the notion of time reverses. If we assume electromagnetic properties of geons, then only four species, v, e, p, m, of different geons can exist and geon m has to decay according to mv+p+e.     

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.     

The geometry of the quantum correction for topological σ-models

The ring (Frobenius algebra) of local observables for topological -models on ¹ with values in the grassmannianG(s, n) is known to be the same as the quotient of the homology ring of the target space by the (inhomogeneous) ideal generated by the so-called quantum correction. While the need for a quantum correction comes from algebraic motivations in field theory, the aim of this paper is to understand its geometric meaning. The simple examples of ^{1 n} models tell us that the quantum correction comes by restriction on the boundary of the moduli spaces which allows to compute intersections on moduli spaces of lower degrees. We will check this point of view for the case of ¹ G(s,n) models, yielding a proof of the algebraic result from physics in terms of the geometry of the -model itself.Work partially supported by National Project 40% Probabilistic and geometrical methods in Mathematical Physics and by CNR-Gruppo Nazionale di Fisica Matematica.     

Boundary conditions for quantum mechanics on cones and fields around cosmic strings

We study the options for boundary conditions at the conical singularity for quantum mechanics on a two-dimensional cone with deficit angle 2 and for classical and quantum scalar fields propagating with a translationally invariant dynamics in the 1+3 dimensional spacetime around an idealized straight infinitely long, infinitesimally thin cosmic string. The key to our analysis is the observation that minus-the-Laplacian on a cone possesses a one-parameter family of selfadjoint extensions. These may be labeled by a parameterR with the dimensions of length—taking values in [0, ). ForR=0, the extension is positive. WhenR0 there is a bound state. Each of our problems has a range of possible dynamical evolutions corresponding to a range of allowedR-values. They correspond to either finite, forR=0, or logarithmically divergent, forR0, boundary conditions at zero radius. Non-zeroR-values are a satisfactory replacement for the (mathematically ill-defined) notion of -function potentials at the cone's apex.We discuss the relevance of the various idealized dynamics to quantum mechanics on a cone with a rounded-off centre and field theory around a true string of finite thickness. Provided one is interested in effects at sufficiently large length scales, the true dynamics will depend on the details of the interaction of the wave function with the cone's centre (/field with the string etc.) only through a single parameterR (its scattering length) and will be well-approximated by the dynamics for the corresponding idealized problem with the sameR-value. This turns out to be zero if the interaction with the centre is purely gravitational and minimally coupled, but non-zero values can be important to model nongravitational (or non-minimally coupled) interactions. Especially, we point out the relevance of non-zeroR-values to electromagnetic waves around superconducting strings. We also briefly speculate on the relevance of theR-parameter in the application of quantum mechanics on cones to 1+2 dimensional quantum gravity with massive scalars.     

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.     

A model of Piron's preparation-question structures in Ludwig's selection structures

We give a model of the basic Jauch-Piron (JP) approach to quantum physics, i.e., of preparation-question structure (with four basic axioms and without axioms C, P, A), in terms of Ludwig's selection structure; in the latter structure the primitive notion of individual sample of a physical entity is formally described (without making reference to any probability concept). Once we interpret Piron's concept of question in Ludwig's context of a selection structure, we find that there is no difficulty in formalizing notions such as performable together questions; moreover, results such as = or ()= can be formally proved. We develop the theory along the lines of the JP approach; the set of JP propositions is derived and it turns out to be a complete lattice, as happens in Piron's theory, but with a different physical interpretation of the lattice operations. Finally, we study some connections between the standard Ludwig foundation and our approach.     

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.     

The classification of differential structures on quantum 2-spheres

Exterior algebras of differential forms on quantum 2-spheresS _qc ² ,q[–1, 1]/{0},c[0, ] (c=0 forq=±1), are classified. In the definition of exterior algebras we assume the invariance w.r.t. the action of the quantumSU(2) group and dimensionality conditions (which imply that we deal with two-dimensional manifolds). The exterior algebras exist only forc=0 and are unique in that case. The corresponding generalized directional derivatives are provided.     

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.     

Nonstationary quantum mechanics. I. Time-irreversible noninstantaneous self-reduction to a stationary state of some quantal wave packets

It is shown that the formalism of quantum theory needs modification in the case of potential fields swiftly varying with time. The necessity of a time-irreversible master equation for such cases is discussed.The underlying idea is that any (sub)system will undergo a spontaneous transition to a state of definiteenergy in the process of separating spatially from the rest of the universe, assuming the universe is isolated and has a definite energy. This requires what might be termed a pragmatic interpretation of the wave function: If a composite, separated system is represented by a linear superposition of product states, we may say that the actual state of the composite system is represented by some particular component of the superpositionfor the purposes of statistical inferences relevant to each subsystem alone, but the entire superposition—and not the corresponding mixture of the product components—must be used to compute the statistics of correlations. The considerations are illustrated with thought experiments which are real enough to make the application of the usual quantum mechanical formalism possible. Cases of disagreement between conventional theory and experiment in the field of interest are indicated.     

The simplified Fermi accelerator in classical and quantum mechanics

We review the simplified classical Fermi acceleration mechanism and construct a quantum counterpart by imposing time-dependent boundary conditions on solutions of the free Schrödinger equation at the unit interval. We find similiar dynamical features in the sense that limiting KAM curves, respectively purely singular quasienergy spectrum, exist(s) for sufficiently smooth wall oscillations (typically ofC ² type). In addition, we investigate quantum analogs to local approximations of the Fermi map both in its quasiperiodic and irregular phase space regions. In particular, we find pure point q.e. spectrum in the former case and conjecture that random boundary conditions are necessary to model a quantum analog to the chaotic regime of the classical accelerator.     

On a certain method for considering statistical inhomogeneities of a cathode

The paper investigates the effect of the inhomogeneity of the emitting surface of thermionic cathodes on the magnitude of the average value and dispersion of the emission current. A statistical model of an inhomogeneous cathode, according to which the emission of electrons takes place from circular overlapping grains whose centers are distributed along the cathode surface according to the Poisson law, is proposed for performing the corresponding calculations. The parameter d of this distribution has the meaning of the density with which the cathode area is filled with grain centers. There is no emission at all from the cathode sectors that are not covered with grains. The calculations were carried out for the case of an arbitrary low governing the distribution of the emitting grains with respect to the magnitude of their radii.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 15, No. 2, pp. 266–271, February, 1972.