Inference in quantum physics

In quantum physics all experimental information is discrete and stochastic. But the values of physical quantities are considered to depict definite properties of the physical world. Thus physical quantities should be identified with mathematical variables which are derived from the experimental data, but which exhibit as little randomness as possible. We look for such variables in two examples by investigating how it is possible to arrive at a value of a physical quantity from intrinsically stochastic data. With the aid of standard probability calculus and elementary information theory, we are necessarily led to the quantum theoretical phases and state vectors as the first candidates for physical quantities.     

A Toss without a Coin: Information,Discontinuity, and Mathematics in Quantum Theory

The article argues that—at least in certain interpretations, such as the one assumed in this article under the heading of “reality without realism”—the quantum-theoretical situation appears as follows: While—in terms of probabilistic predictions—connected to and connecting the information obtained in quantum phenomena, the mathematics of quantum theory (QM or QFT), which is continuous, does not represent and is discontinuous with both the emergence of quantum phenomena and the physics of these phenomena, phenomena that are physically discontinuous with each other as well. These phenomena, and thus this information, are described by classical physics. All actually available information (in the mathematical sense of information theory) is classical: it is composed of units, such as bits, that are—or are contained in—entities described by classical physics. On the other hand, classical physics cannot predict this information when it is created, as manifested in measuring instruments, in quantum experiments, while quantum theory can. In this epistemological sense, this information is quantum. The article designates the discontinuity between quantum theory and the emergence of quantum phenomena the “Heisenberg discontinuity”, because it was introduced by W. Heisenberg along with QM, and the discontinuity between QM or QFT and the classical physics of quantum phenomena, the “Bohr discontinuity”, because it was introduced as part of Bohr’s interpretation of quantum phenomena and QM, under the assumption of Heisenberg discontinuity. Combining both discontinuities precludes QM or QFT from being connected to either physical reality, that ultimately responsible for quantum phenomena or that of these phenomena themselves, other than by means of probabilistic predictions concerning the information, classical in character, contained in quantum phenomena. The nature of quantum information is, in this view, defined by this situation. A major implication, discussed in the Conclusion, is the existence and arguably the necessity of two—classical and quantum—or with relativity, three and possibly more essentially different theories in fundamental physics.     

Nature Has No Elementary Particles and Makes No Measurements or Predictions: Quantum Measurement and Quantum Theory,from Bohr to Bell and from Bell to Bohr

This article reconsiders the concept of physical reality in quantum theory and the concept of quantum measurement, following Bohr, whose analysis of quantum measurement led him to his concept of a (quantum) “phenomenon,” referring to “the observations obtained under the specified circumstances,” in the interaction between quantum objects and measuring instruments. This situation makes the terms “observation” and “measurement,” as conventionally understood, inapplicable. These terms are remnants of classical physics or still earlier history, from which classical physics inherited it. As defined here, a quantum measurement does not measure any preexisting property of the ultimate constitution of the reality responsible for quantum phenomena. An act of measurement establishes a quantum phenomenon by an interaction between the instrument and the quantum object or in the present view the ultimate constitution of the reality responsible for quantum phenomena and, at the time of measurement, also quantum objects. In the view advanced in this article, in contrast to that of Bohr, quantum objects, such as electrons or photons, are assumed to exist only at the time of measurement and not independently, a view that redefines the concept of quantum object as well. This redefinition becomes especially important in high-energy quantum regimes and quantum field theory and allows this article to define a new concept of quantum field. The article also considers, now following Bohr, the quantum measurement as the entanglement between quantum objects and measurement instruments. The argument of the article is grounded in the concept “reality without realism” (RWR), as underlying quantum measurement thus understood, and the view, the RWR view, of quantum theory defined by this concept. The RWR view places a stratum of physical reality thus designated, here the reality ultimately responsible for quantum phenomena, beyond representation or knowledge, or even conception, and defines the corresponding set of interpretations quantum mechanics or quantum field theory, such as the one assumed in this article, in which, again, not only quantum phenomena but also quantum objects are (idealizations) defined by measurement. As such, the article also offers a broadly conceived response to J. Bell’s argument “against ‘measurement’”.     

Laser spectroscopy 9. Prospects and applications

This concluding article in the series discusses the prospects of realizing the ultimate parameters — spectral resolving power and sensitivity — and some fields of application — nuclear physics, chemical kinetics and molecular physics, quantum metrology — of laser spectroscopy.     

Stochastic Gravity

We give a summary of the status of currentresearch in stochastic semiclassical gravity and suggestdirections for further investigations. This theorygeneralizes the semiclassical Einstein equation to an Einstein-Langevin equation with a stochasticsource term arising from the fluctuations of theenergy-momentum tensor of quantum fields. We mentionrecent efforts in applying this theory to the study of black hole fluctuation and backreactionproblems, linear response of hot flat space, andstructure formation in inflationary cosmology. Toexplore the physical meaning and implications of thisstochastic regime in relation to both classical andquantum gravity, we find it useful to take the view thatsemiclassical gravity is mesoscopic physics and thatgeneral relativity is the hydrodynamic limit of certain spacetime quantum substructures. We view theclassical spacetime depicted by general relativity as acollective state and the metric or connection functionsas collective variables. Three basic issues —stochasticity, collectivity, correlations — andthree processes — dissipation, fluctuations,decoherence — underscore the transformation fromquantum microstructure and interaction to the emergenceof classical macrostructure and dynamics. We discuss ways toprobe into the high-energy activity from below and maketwo suggestions: via effective field theory and thecorrelation hierarchy. We discuss how stochastic behavior at low energy in an effective theoryand how correlation noise associated with coarse-grainedhigher correlation functions in an interacting quantumfield could carry nontrivial information about the high-energy sector. Finally, we describeprocesses deemed important at the Planck scale,including tunneling and pair creation, wave scatteringin random geometry, growth of fluctuations and forms, Planck-scale resonance states, and spacetimefoams.     

Accurate correction of arbitrary spin fermion quantum tunneling from non-stationary Kerr-de Sitter black hole based on corrected Lorentz dispersion relation

According to a corrected dispersion relation proposed in the study on the string theory and quantum gravity theory, the Rarita-Schwinger equation was precisely modified, which resulted in the Rarita-Schwinger-Hamilton-Jacobi equation. Using this equation, the characteristics of arbitrary spin fermion quantum tunneling radiation from non-stationary Kerr-de Sitter black holes were determined. A number of accurately corrected physical quantities, such as surface gravity, chemical potential, tunneling probability, and Hawking temperature, which describe the properties of black holes, were derived. This research has enriched the research methods and enabled increased precision in black hole physics research.     

On “Decisions and Revisions Which a Minute Will Reverse”: Consciousness,The Unconscious and Mathematical Modeling of Thinking

This article considers a partly philosophical question: What are the ontological and epistemological reasons for using quantum-like models or theories (models and theories based on the mathematical formalism of quantum theory) vs. classical-like ones (based on the mathematics of classical physics), in considering human thinking and decision making? This question is only partly philosophical because it also concerns the scientific understanding of the phenomena considered by the theories that use mathematical models of either type, just as in physics itself, where this question also arises as a physical question. This is because this question is in effect: What are the physical reasons for using, even if not requiring, these types of theories in considering quantum phenomena, which these theories predict fully in accord with the experiment? This is clearly also a physical, rather than only philosophical, question and so is, accordingly, the question of whether one needs classical-like or quantum-like theories or both (just as in physics we use both classical and quantum theories) in considering human thinking in psychology and related fields, such as decision science. It comes as no surprise that many of these reasons are parallel to those that are responsible for the use of QM and QFT in the case of quantum phenomena. Still, the corresponding situations should be understood and justified in terms of the phenomena considered, phenomena defined by human thinking, because there are important differences between these phenomena and quantum phenomena, which this article aims to address. In order to do so, this article will first consider quantum phenomena and quantum theory, before turning to human thinking and decision making, in addressing which it will also discuss two recent quantum-like approaches to human thinking, that by M. G. D’Ariano and F. Faggin and that by A. Khrennikov. Both approaches are ontological in the sense of offering representations, different in character in each approach, of human thinking by the formalism of quantum theory. Whether such a representation, as opposed to only predicting the outcomes of relevant experiments, is possible either in quantum theory or in quantum-like theories of human thinking is one of the questions addressed in this article. The philosophical position adopted in it is that it may not be possible to make this assumption, which, however, is not the same as saying that it is impossible. I designate this view as the reality-without-realism, RWR, view and in considering strictly mental processes as the ideality-without-idealism, IWI, view, in the second case in part following, but also moving beyond, I. Kant’s philosophy.     

量纲分析在大学物理热力学部分中的教学应用

本文首先简单介绍了量纲分析中的齐次定理和∏定理,然后具体例举了量纲分析在大学物理热力学部分的教学应用.我们的求解过程是:分析例举可能相关的物理量;写出各个物理量的量纲表;分析量纲表,确定相关的物理量和独立量纲;设定无量纲量等式;列出量纲指数方程组并求解.     

Foundations of the Quaternion Quantum Mechanics

We show that quaternion quantum mechanics has well-founded mathematical roots and can be derived from the model of the elastic continuum by French mathematician Augustin Cauchy, i.e., it can be regarded as representing the physical reality of elastic continuum. Starting from the Cauchy theory (classical balance equations for isotropic Cauchy-elastic material) and using the Hamilton quaternion algebra, we present a rigorous derivation of the quaternion form of the non- and relativistic wave equations. The family of the wave equations and the Poisson equation are a straightforward consequence of the quaternion representation of the Cauchy model of the elastic continuum. This is the most general kind of quantum mechanics possessing the same kind of calculus of assertions as conventional quantum mechanics. The problem of the Schrödinger equation, where imaginary ‘i’ should emerge, is solved. This interpretation is a serious attempt to describe the ontology of quantum mechanics, and demonstrates that, besides Bohmian mechanics, the complete ontological interpretations of quantum theory exists. The model can be generalized and falsified. To ensure this theory to be true, we specified problems, allowing exposing its falsity.     

Carl Neumann’s Contributions to Electrodynamics

I examine the publications of Carl Neumann (1832–1925) on electrodynamics, which constitute a major part of his work and which illuminate his approach to mathematical physics. I show how Neumann contributed to physics at an important stage in its development and how his work led to a polemic with Hermann Helmholtz (1821–1894). Neumann advanced and extended the ideas of the Königsberg school of mathematical physics. His investigations were aimed at founding a mathematically exact physical theory of electrodynamics, following the approach of Carl G.J. Jacobi (1804–1851) on the foundation of a physical theory as outlined in Jacobis lectures on analytical mechanics. Neumanns work also shows how he clung to principles that impeded him in appreciating and developing new ideas such as those on field theory that were proposed by Michael Faraday (1791–1867) and James Clerk Maxwell (1831–1879).Karl-Heinz Schlote works as a historian of mathematics in the Arbeitsgruppe für Geschichte der Naturwissenschaften und Mathematik at the Sächsische Akademie der Wissenschaften in Leipzig, Germany.     

Representation of the Universe as a Dendrogramic Hologram Endowed with Relational Interpretation

A proposal for a fundamental theory is described in which classical and quantum physics as a representation of the universe as a gigantic dendrogram are unified. The latter is the explicate order structure corresponding to the purely number-theoretical implicate order structure given by p-adic numbers. This number field was zero-dimensional, totally disconnected, and disordered. Physical systems (such as electrons, photons) are sub-dendrograms of the universal dendrogram. Measurement process is described as interactions among dendrograms; in particular, quantum measurement problems can be resolved using this process. The theory is realistic, but realism is expressed via the the Leibniz principle of the Identity of Indiscernibles. The classical-quantum interplay is based on the degree of indistinguishability between dendrograms (in which the ergodicity assumption is removed). Depending on this degree, some physical quantities behave more or less in a quantum manner (versus classic manner). Conceptually, our theory is very close to Smolin’s dynamics of difference and Rovelli’s relational quantum mechanics. The presence of classical behavior in nature implies a finiteness of the Universe-dendrogram. (Infinite Universe is considered to be purely quantum.) Reconstruction of events in a four-dimensional space type is based on the holographic principle. Our model reproduces Bell-type correlations in the dendrogramic framework. By adjusting dendrogram complexity, violation of the Bell inequality can be made larger or smaller.     

Erzwingt die Quantenmechanik eine drastische Änderung unseres Weltbilds? Gedanken und Experimente nach Einstein,Podolsky und Rosen

Do Quantum Mechanics Force us to Drastically Change our View of the World? Thoughts and Experiments after Einstein, Podolsky and Rosen Since the advent of quantum mechanics there have been attempts of its interpretation in terms of statistical theory concerning individual ‘classical’ systems. The very conditions necessary to consider hidden variable theories describing these individual systems as ‘classical’ had been pointed out by Einstein, Podolsky and Rosen in 1935: 1. Physical systems are in principle separable. 2. If it is possible to predict with certainty the value of a physical quantity without disturbing the system under consideration, then there exists an element of physical reality corresponding to this physical quantity. Together they are, as was shown by Bell in 1964, incompatible in principle with quantum mechanics and no more tenable in view of recent experiments. These experiments once more corroborate quantum theory. In order to understand their results we are forced either to drop the assumption of separability of physical systems (taken for self-evident in classical physics) or to change our concept of physical reality. After investigating the notion of separability and connecting the ‘EPR-correlations’ to the measurement problem we, conclude that a change of the concept of physical reality is indispensable. The revised concept should be compatible with both classical and quantum physics in order to allow a uniform view of the physical world.     

On probability theory and probabilistic physics—Axiomatics and methodology

A new formulation involving fulfillment of all the Kolmogorov axioms is suggested for acomplete probability theory. This proves to be not a purely mathematical discipline. Probability theory deals with abstract objects—images of various classes of concrete objects—whereas experimental statistics deals with concrete objects alone. Both have to be taken into account. Quantum physics and classical statistical physics prove to be different aspects ofone probabilistic physics. The connection of quantum mechanics with classical statistical mechanics is examined and the origin of the Schrödinger equation is elucidated. Attention is given to the true meaning of the wave-corpuscle duality, and the incompleteness of nonrelativistic quantum mechanics is explained.     

A New Book of Numbers: On the Precise Definition of Quantum Variables and the Relationships between Mathematics and Physics in Quantum Theory

Following Asher Peres’s observation that, as in classical physics, in quantum theory, too, a given physical object considered “has a precise position and a precise momentum,” this article examines the question of the definition of quantum variables, and then the new type (as against classical physics) of relationships between mathematics and physics in quantum theory. The article argues that the possibility of the precise definition and determination of quantum variables depends on the particular nature of these relationships.     

A spin-statistics theorem for composites containing both electric and magnetic charges

The present paper states and proves an asymptotic spin-statistics theorem for composites consisting of electrically and magnetically charged particles. We work in the framework of a nonrelativistic theory, taking as the classical configuration space aU(1) bundle over the space of physical configurations, and as the quantum hilbert space the homogeneous square integrable functions on that bundle. The theorems are proved using a formalism we develop here for treating gauge spaces —U(1) bundles with connections; in particular, two products related to tensor products of vector bundles prove to be extremely useful in displaying the structure of the gauge spaces that naturally arise in this theory.Supported in part by the National Science Foundation under grant number PHY 77-07111Supported in part by the National Science Foundation under grant number PHY 78-24275     

The quantum vacuum at the foundations of classical electrodynamics

In the classical theory of electromagnetism, the permittivity ε ₀ and the permeability μ ₀ of free space are constants whose magnitudes do not seem to possess any deeper physical meaning. By replacing the free space of classical physics with the quantum notion of the vacuum, we speculate that the values of the aforementioned constants could arise from the polarization and magnetization of virtual pairs in vacuum. A classical dispersion model with parameters determined by quantum and particle physics is employed to estimate their values. We find the correct orders of magnitude. Additionally, our simple assumptions yield an independent estimate for the number of charged elementary particles based on the known values of ε ₀ and μ ₀ and for the volume of a virtual pair. Such an interpretation would provide an intriguing connection between the celebrated theory of classical electromagnetism and the quantum theory in the weak-field limit.     

Properties of gravitoinertial reference systems

A summary is given of a series of papers of the author on gravitoinertial reference systems (gravito-IRS) in which the following questions are resolved: a) analogues of inertial reference systems — gravito-IRS — are introduced into GTR; b) conserved quantities with a clear physical interpretation are obtained by variational methods using transformations between such reference systems as symmetry transformations; c) using a basis gravito-IRS as a zero reference level of deformations, a theory of elasticity is constructed in GRT, and several of its applications are considered.The results are compared with results of other analogous investigations.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 72–79, April, 1977.     

Nonstandard (non-σ-additive) probabilities in algebraic quantum field theory

Traditionally, physicists deduce the observational (physical) meaning of probabilistic predictions from the implicit assumption that thewell-defined events whose probabilities are 0 never occur. For example, the conclusion that in a potentially infinite sequence of identical experiments with probability 0.5 (like coin tossing) the frequency of heads tends to 0.5 follows from the theorem that sequences for which the frequencies do not tend to 0.5 occur with probability 0. Similarly, the conclusion that in quantum mechanics, measuring a quantity always results in a number from its spectrum is justified by the fact that the probability of getting a number outside the spectrum is 0. In the mid-60s, a consistent formalization of this assumption was proposed by Kolmogorov and Martin-Löf, who defined arandom element of a probability space as an element that does not belong to any definable set of probability 0 (definable in some reasonable sense). This formalization is based on the fact that traditional probability measures are σ-additive, i.e., that the union of countably many sets of probability 0 has measure 0. In quantum mechanics with infinitely many degrees of freedom (e.g., in quantum field theory) and in statistical physics one must often consider non-σ-additive measures, for which the Martin-Löf's definition does not apply. Many such measures can be defined as “limits” of standard probability distributions. In this paper, we formalize the notion of a random element for such finitely-additive probability measures, and thus explain the observational (physical) meaning of such probabilities.     

Quantum mechanics without the projection postulate and its realistic interpretation

It is widely held that quantum mechanics is the first scientific theory to present scientifically internal, fundamental difficulties for a realistic interpretation (in the philosophical sense). The standard (Copenhagen) interpretation of the quantum theory is often described as the inevitable instrumentalistic response. It is the purpose of the present article to argue that quantum theory doesnot present fundamental new problems to a realistic interpretation. The formalism of quantum theory has the same states—it will be argued—as the formalisms of older physical theories and is capable of the same kinds of philosophical interpretation. This result is reached via an analysis of what it means to give a realistic interpretation to a theory. The main point of difference between quantum mechanics and other theories—as far as the possibilities of interpretation are concerned—is the special treatment given tomeasurement by the projection postulate. But it is possible to do without this postulate. Moreover, rejection of the projection postulate does not, in spite of what is often maintained in the literature, automatically lead to the many-worlds interpretation of quantum mechanics. A realistic interpretation is possible in which only the reality ofone (our) world is recognized. It is argued that the Copenhagen interpretation as expounded by Bohr is not in conflict with the here proposed realistic interpretation of quantum theory.     

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.