Wave calculus based upon wave logic

A number operator has been introduced based upon the binary (p-nary) presentation of numbers. This operator acts upon a numerical state vector. Generally the numerical state vector describes numbers that are not precise but smeared in a quantum sense. These states are interpreted in wave logic terms, according to which concepts may exist within the inner language of a phenomenon that in principle cannot be translated into the language of the investigator. In particular, states may exist where mean values of a quantity, continuous in classical limits, take only discrete values. Operators for differentiation and integration of operator functions are defined, which take the usual form in the classical limit.     

Quantum logic approach to wave packet control

We study control of wave packets with a finite accuracy, approaching it as quantum information processing. For a given control resolution, we define the analogs of several quantum bits within the shape of a single wave packet. These bits are based on wave packet symmetries. Analogs of one- and two-bit gates can be implemented using only free wave packet evolution and coordinate-dependent ac Stark shifts applied at the moments of fractional revivals. As in quantum computation, the gates form a logarithmically small set of basis operations which can be used to approximate any unitary transformation desired for quantum control of the wave packet dynamics. Numerical examples show the application of this approach to control vibrational wave packet revivals.     

Physiologic time: A hypothesis

The scaling of respiratory metabolism with body size in animals is considered by many to be a fundamental law of nature. One apparent consequence of this law is the scaling of physiologic time with body size, implying that physiologic time is separate and distinct from clock time. Physiologic time is manifest in allometry relations for lifespans, cardiac cycles, blood volume circulation, respiratory cycle, along with a number of other physiologic phenomena. Herein we present a theory of physiologic time that explains the allometry relation between time and total body mass averages as entailed by the hypothesis that the fluctuations in the total body mass are described by a scaling probability density.     

de Broglie’s wave hypothesis from Fisher information

Seeking the unknown dynamics obeyed by a particle gives rise to the de Broglie wave representation, without the need for physical assumptions specific to quantum mechanics. The only required physical assumption is conservation of momentum μ. The particle, of mass m, moves through free space from an unknown source-plane position a to an unknown coordinate x in an aperture plane of unknown probability density p_X(x), and then to an output plane of observed position y=a+z. There is no prior knowledge of the probability laws or , with the particle momentum at the source. It is desired to (i) optimally estimate a, in the sense of a maximum likelihood (ML) estimate. The estimate is further optimized, by minimizing its error through (ii) maximizing the Fisher information about a that is received at y. Forming the ML estimate requires (iii) estimation of the likelihood law p_Z(z), which (iv) must obey positivity. The relation p_Z(z)≡|u(z)|²≥0 satisfies this. The same u(z) conveniently defines the Fisher channel capacity, a concept central to the principle of Extreme physical information (EPI). Its output u(z) achieves aims (i)-(iv). The output is parametrized by a free parameter K. For a choice K=0, the result is u(z)=δ(z), indicating classical motion. Or, for a finite, empirical choice K=? (Planck’s constant), u(z) obeys the familiar de Broglie representation as the Fourier transform of the particle’s probability amplitude function P(μ) on momentum μ. For a definite momentum μ,u(z) becomes a sinusoid of wavelength λ=h/μ, the de Broglie result.     

The logic of reduction: The case of gravitation

The reduction from Einstein's to Newton's gravitation theories (and intermediate steps) is used to exemplify reduction in physical theories. Both dimensionless and dimensional reduction are presented, and the advantages and disadvantages of each are pointed out. It is concluded that neither a completely reductionist nor a completely antireductionist view can be maintained. Only the mathematical structure is strictly reducible. The interpretation (the model, the central concepts) of the superseded theory T can at best only partially be derived directly from the superseding theory T; it is severely constrained by the mathematical structure, and it can involve qualitatively different central terms that cannot be logically related between T and T.     

Sonoluminescence: A new electrical breakdown hypothesis

We discuss an hypothesis wherein single-bubble sonoluminescence is attributed to electrical breakdown due to large pressure gradients existing for small bubble radii. These large gradients produce large electric fields (the flexoelectric effect) that lead to electrical breakdown, releasing energies up to 10⁻¹⁰ J, which is much larger than the light energy released in each cycle. This hypothesis appears to be consistent with several observations made in studies of the sonoluminescence process. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 12, 849–852 (25 December 1996) Published in English in the original Russian journal. Edited by Steve Torstreit.     

A hierarchy hypothesis

Why attraction and repulsion between likes should not enjoy equal status in nature is considered. By postulating a hierarchy of isolated systems of finite radii whose associated charges form a geometric series with enormous imaginary common ratio, and by identifying a universe (the content of an infinite cosmos within a Hubble radius of an observer), an electron, and a neutrino as three consecutive members of the hierarchy (in fact the only three observable because of the uncertainty principle), it is possible to treat gravitational and electromagnetic phenomena as perfectly analogous and complementary for the overall structure of the cosmos. An isolated system behaves, from an external viewpoint, as an elementary particle, and from an internal viewpoint, as a universe. Remarkable relationships between physical constants emerge.     

The logic of time reversal

Active time reversal in the sense of object reversal and passive time reversal in the sense of a frame reversal of time are discussed separately and then together so as to bring out their dual nature. An understanding of that duality makes it unavoidable to contrast symmetry properties of matter with symmetry properties to be assigned to antimatter. Only frame reversal of time can see all conceivable active time reversals relevant to physical objects. Only frame reversal of time can be used for a meaningful extension of the Neumann principle to the time domain.     

Proof theory for minimal quantum logic: A remark

It is remarked that the inference rule ( ) is superfluous for the sequential system GMQL introduced by H. Nishimura for the minimal quantum logic.     

Energy localization in general relativity: A new hypothesis

A new hypothesis for energy localization in general relativity is introduced which is based upon the fact that the energy-momentum conservation laws are devoid of content in vacuum. The vanishing of pseudotensor components forms the basis of coordinate conditions consistent with the above. The implication is that energy is localized where the energy-momentum tensor is nonvanishing. As a consequence, gravitational waves are not carriers of energy in vacuum. A detailed analysis of a Feynman detector interacting with a plane gravitational wave is consistent with the hypothesis. The fact that there has never been a confirmed direct energy transfer to a detector via gravitational radiation is also consistent with the hypothesis.     

Modeling and analyzing of conformity behavior: A fuzzy logic approach

Modeling students’ classroom behaviors can help educators and researchers better understand these behaviors, and further guide students toward well behaviors. Conformity refers to the tendency to change individual behavior to match group behavior. Through observation and experience, educators have accumulated much linguistic knowledge for describing and understanding students’ conformity behavior and influence. This paper presents a fuzzy logic approach for modeling participants’ classroom behaviors. The simulation results about two observed college classes show that the constructed fuzzy logic system is congruent with the observed participants’ classroom behaviors. Existing findings, as well as new findings, are verified through further simulation and analysis. The proposed fuzzy logic system helps educators quantitatively analyze and understand students’ conformity behavior in classroom.     

The fluctuation hypothesis of hydrogen bonding

To describe the distortion perturbations of the water molecules in solutions the quantum-mechanical method of partial oscillators has been developed. This method allows one to separate in a simple manner two types of influences on vibrations of OH oscillators, viz. the intermolecular perturbations resulting in the different strengths of hydrogen bonds and intramolecular coupling between stretching vibrations. Here the coupling is treated quite strictly, whereas the intermolecular perturbations are introduced phenomenologically. The calculation of the distribution of distortions among molecules in liquid H₂O and D₂O induced by non-equivalency of the two hydrogen bonds of the water molecule has been made on the basis of the method developed, and the parameters of the mean statistical molecule have been found from the experimental spectrum of HOD. The depolarization ratios of vibrations in Raman spectra of the mean statistical molecules H₂O and D₂O have been computed as an illustration of the possibilities of the proposed calculation method. All the estimates show that the stretching oscillators of H₂O and D₂O molecules are significantly coupled in spite of the great distortion of the symmetry of water molecules in the liquid state.     

A new axiomatization of unified quantum logic

Unified quantum logic which is a propositional logic underlying quantum formalism is given a new much simplified axiomatization. A statistical basis for this propositional logical system is given so as to interpret unified quantum logic as a system of deduction. The soundness and completeness of algebraic semantics are proved. Kripkean and probabilistic semantics are discussed.     

How organisms do the right thing: The attractor hypothesis

Neo-Darwinian theory is highly successful at explaining the emergence of adaptive traits over successive generations. However, there are reasons to doubt its efficacy in explaining the observed, impressively detailed adaptive responses of organisms to day-to-day changes in their surroundings. Also, the theory lacks a clear mechanism to account for both plasticity and canalization. In effect, there is a growing sentiment that the neo-Darwinian paradigm is incomplete, that something more than genetic structure, mutation, genetic drift, and the action of natural selection is required to explain organismal behavior. In this paper we extend the view of organisms as complex self-organizing entities by arguing that basic physical laws, coupled with the acquisitive nature of organisms, makes adaptation all but tautological. That is, much adaptation is an unavoidable emergent property of organisms' complexity and, to some a significant degree, occurs quite independently of genomic changes wrought by natural selection. For reasons that will become obvious, we refer to this assertion as the attractor hypothesis. The arguments also clarify the concept of "adaptation." Adaptation across generations, by natural selection, equates to the (game theoretic) maximization of fitness (the success with which one individual produces more individuals), while self-organizing based adaptation, within generations, equates to energetic efficiency and the matching of intake and biosynthesis to need. Finally, we discuss implications of the attractor hypothesis for a wide variety of genetical and physiological phenomena, including genetic architecture, directed mutation, genetic imprinting, paramutation, hormesis, plasticity, optimality theory, genotype-phenotype linkage and puncuated equilibrium, and present suggestions for tests of the hypothesis. (c) 1998 American Institute of Physics.     

Physics and logic: Thales

Thales's protophysics is reconstructed with the help of the Steiner quasigroup. A three-valued logic is proposed, equivalent to it. The discovered connection between physics and logic is used to discuss the natural form of the logic of quantum mechanics.     

Gyrotron travelling wave amplifier: III. A proposed wide-band fast wave amplifier

A simple scheme is proposed for the construction of a wide-band fast wave gyrotron travelling wave amplifier. The key features of this scheme include a contoured waveguide, a tapered magnetic field, and injection of input signals in opposite direction of the streaming electrons. Bandwidths at tens of percents, and gain at tens of decibals, are projected.     

A proof of the cosmic censorship hypothesis

It is shown that in a weakly asymptotically simple and empty space, according to classical general relativity, from nonsingular initial data no strong curvature singularity can arise that is visible from infinity.This essay received the Second Award from the Gravity Research Foundation for the year 1982. Ed. This work is supported by Interdisciplinary Research Project MR-I-7.     

The entropy of observables on quantum logic

The entropy of an abstract observable on quantum logic is defined as an informational property of the corresponding sublogic of a quantum logic associated with the physical system. The main properties of such quantity are stated. It is proved that the entropy is completely characterized by the entropies of the corresponding finite resolutions of the unit (experiments). The connection with the entropy of a state is also mentioned.     

The Leibniz principle in quantum logic

The principle of the identity of indiscernibles (Leibniz Principle) is investigated within the framework of the formal language of quantum physics, which is given by an orthomodular lattice. We show that the validity of this principle is based on very strong preconditions (concerning the existence of convenient predicates) which are given in the language of classical physics but which cannot be fulfilled in orthomodular quantum logic.     

Photon consciousness: Fact or fancy?

An experiment designed to test the highly speculative hypothesis of photon consciousness was executed. It was found that, within the accuracy attainable with the apparatus, there is no empirical justification for the hypothesis.