Nonequilibrium statistical mechanics in the general theory of relativity I. A general formalism

This is the first in a series of papers, the overall objective of which is the formulation of a new covariant approach to nonequilibrium statistical mechanics in classical general relativity. The object here is the development of a tractable theory for self-gravitating systems. It is argued that the “state” of an N-particle system may be characterized by an N-particle distribution function, defined in an 8N-dimensional phase space, which satisfies a collection of N conservation equations. by mapping the true physics onto a fictitious “background” spacetime, which may be chosen to satisfy some “average” field equations, one then obtains a useful covariant notion of “evolution” in response to a fluctuating “gravitational force.” For many cases of practical interest, one may suppose (i) that these fluctuating forces satisfy linear field equations and (ii) that they may be modeled by a direct interaction. In this case, one can use a relativistic projection operator formalism to derive exact closed equations for the evolution of such objects as an appropriately defined reduced one-particle distribution function. By capturing, in a natural way, the notion of a dilute gas, or impulse, approximation, one is then led to a comparatively simple equation for the one-particle distribution. If, furthermore, one treats the effects of the fluctuating forces as “localized” in space and time, one obtains a tractable kinetic equation which reduces, in the newtonian limit, to the standard Landau equation.     

Relativity theory: What is reality?

In classical Newtonian physics there was a clear understanding of “what reality is.? Indeed in this classical view, reality at a certain time is the collection of all what is actual at this time, and this is contained in “the present.? Often it is stated that three-dimensional space and one-dimensional time hare been substituted by four-dimensional space-time in relativity theory, and as a consequence the classical concept of reality, as that which is “present,? cannot be retained. Is reality then the four-dimensional manifold of relativity theory? And if so, what is then the meaning of “change in time?? This problem confronts a geometric view (as the Einsteinian interpretation of relativity theory) with a process view (where reality changes constantly in time). In this paper we investigate this problem, taking into account our insight into the nature of reality as it came by analyzing the problems of quantum mechanics. We show that with an Einsteinian interpretation of relativity theory, reality is indeed four-dimensional, but there is no contradiction with the process view, where this reality changes in time.     

A categorical framework for quantum theory

Underlying any physical theory is a layer of conceptual frames. They connect the mathematical structures used in theoretical models with the phenomena, but they also constitute our fundamental assumptions about reality. Many of the discrepancies between quantum physics and classical physics (including Maxwell's electrodynamics and relativity) can be traced back to these categorical foundations. We argue that classical physics corresponds to the factual aspects of reality and requires a categorical framework which consists of four interdependent components: boolean logic, the linear‐sequential notion of time, the principle of sufficient reason, and the dichotomy between observer and observed. None of these can be dropped without affecting the others. However, quantum theory also addresses the “status nascendi” of facts, i.e., their coming into being. Therefore, quantum physics requires a different conceptual framework which will be elaborated in this article. It is shown that many of its components are already present in the standard formalisms of quantum physics, but in most cases they are highlighted not so much from a conceptual perspective but more from their mathematical structures. The categorical frame underlying quantum physics includes a profoundly different notion of time which encompasses a crucial role for the present. The article introduces the concept of a categorical apparatus (a framework of interdependent categories), explores the appropriate apparatus for classical and quantum theory, and elaborates in particular on the category of non‐sequential time and an extended present which seems to be relevant for a quantum theory of (space)‐time.     

On the Epistemological Status of Cosmology Anthropic Principle,Cosmological Numbers,and the Subject of Cosmology

It is shown that cosmology destroys the fundamental on which it lies as a natural-scientific discipline if it introduces subjectivistic principles as one of them is the so-called Anthropic Principle that superseds the Copernican turn of sciences. Likewise conceptions are proved as conceptions that contradict the physical cosmology which conceive that the “World harmony” or the physical-uniform grasping of the world can be derived from numbers or relations of numbers. This is due to the fact that these conceptions liquadate the advantage of physics to get via measurements statements about reality.     

Towards a separable “empirical reality”?

“To be” or “to be found”? Some contributions relative to this modern variant of Hamlet's question are presented here. They aim at better apprehending the differences between the points of view of the physicists who consider that present-day quantum measurement theories do reach their objective and those who deny they do. It is pointed out that these two groups have different interpretations of the verbs “to be” and “to have” and of the criterion for truth. These differences are made explicit. A notion of “empirical reality” is constructed within the representation of which the physicists of the first named group can consistently uphold their claim. A detailed way of sharpening this definition so as to make empirical reality free of nonlocal actions at a distance is also described.     

Large negative numbers in number theory,thermodynamics, information theory,and human thermodynamics

We show how the abstract analytic number theory of Maier, Postnikov, and others can be extended to include negative numbers and apply this to thermodynamics, information theory, and human thermodynamics. In particular, we introduce a certain large number N ₀ on the “zero level” with a high multiplicity number q _i ? 1 related to the physical concept of gap in the spectrum. We introduce a general notion of “hole,” similar to the Dirac hole in physics, in the theory. We also consider analogs of thermodynamical notions in human thermodynamics, in particular, in connection with the role of the individual in history.     

A gauge model without parity violation in heavy atoms

We address the question: “are weak right-handed non-singlet representations of quarks and leptons necessary?” An extension of the Weinberg-Salam model to SU(2) ? U(1) ? U(1) is found to adequately describe all existing weak interaction data including the lack of parity violation in atomic physics experiments. These data tightly constrain the additional parameters introduced by adding the second weak hypercharge. Although such a model may seem regressive when considered from the standpoint of “simple” unification schemes, we feel that it is aesthetics rather than experiment which leads to non-trivial right-handed multiplet structure. In contrast to most other models, ours predicts a substantial parity-violation effect in atomic experiments on hydrogen. We note that the second weak boson in our model is not constrained to be heavy by existing data and thus might already by accessable in pp → μ⁺μ^?X or possibly in the next generation of colliding beam facilities through e⁺e^? → μ⁺μ^?.     

Sinn und Möglichkeiten der Theoretischen Physik. Zum 300. Jahrestag von Newtons „Philosophiae Naturalis Principia Mathematica”︁

The Meaning and Abilities of Theoretical Physics The Newtonean principles and — derived from them — the congnition of the exixtence of elementary constants according to Planck, Einstein and Bohr increasingly prove to be a strong base not only of physics and its apllication in technology but also of each kind of “exact” sciences in the broadest sense of the word. Since Newton the clarification of concepts with regard so their physical takes place in close connection with the development of mathematical methods. This combination proves to be further productive and ensures the progress of physics an of the “exact” sciences. Most likely all problems which may be of importance in the realm of life can be treated successfully — adequate expenditure taken for granted — with the existing fund of knowledge and methods. The connection between law and accident resting on reality proves to be a relation of complementarity (“there is no absolute accident”). This becomes evident in all branches in all branches of physics, not only in thermodynamics and quantum physics, and can be treated already on the level of the Newtonean principles and elementary constants. Theoretical physics as initiated by newton was designed to comprise all parts of nature. About that there is no contrast between classical physics and quantum physics. It is only a matter of differentiation with regard to the different physical contents and the appropriate mathematical methods, dependent of course on the choice problems. Theoretical physics represents a generally available concentration of the reliable knowledge of physics, which is at the same time the foundation of the “exact” sciences. In this way theoretical physics is the means of communication within the cooperation necessary for the solution of the great complex tasks of science and technology.     

大学物理课程与新式教学方式的融合探究

随着“改革创新,奋发有为”大讨论的深入进行,和“新工科”“新高考”等新形势的发展,大学物理课程改革势在必行.文章分析了大学物理教学改革面临的实际困难,并分析了几种新式教学方式的优缺点.最后针对大学物理课程的特点和现实情况提出了一种兼容多种新式教学方式的课程改革方案.该方案详细描述了在教学环节中如何进行课堂管理、教材选用、课堂构建、平时成绩管理,其间融合了对分易、蓝墨云班、慕课、微课等多种教学方式.该方法已经实践了两年,收到了相当好的教学效果,师生评价良好.     

Why Does Deep and Cheap Learning Work So Well?

We show how the success of deep learning could depend not only on mathematics but also on physics: although well-known mathematical theorems guarantee that neural networks can approximate arbitrary functions well, the class of functions of practical interest can frequently be approximated through “cheap learning” with exponentially fewer parameters than generic ones. We explore how properties frequently encountered in physics such as symmetry, locality, compositionality, and polynomial log-probability translate into exceptionally simple neural networks. We further argue that when the statistical process generating the data is of a certain hierarchical form prevalent in physics and machine learning, a deep neural network can be more efficient than a shallow one. We formalize these claims using information theory and discuss the relation to the renormalization group. We prove various “no-flattening theorems” showing when efficient linear deep networks cannot be accurately approximated by shallow ones without efficiency loss; for example, we show that n variables cannot be multiplied using fewer than \(2^n\) neurons in a single hidden layer.     

On the continuing relevance of Mandelbrot’s non-ergodic fractional renewal models of 1963 to 1967

The problem of “1∕f” noise has been with us for about a century. Because it is so often framed in Fourier spectral language, the most famous solutions have tended to be the stationary long range dependent (LRD) models such as Mandelbrot’s fractional Gaussian noise. In view of the increasing importance to physics of non-ergodic fractional renewal models, and their links to the CTRW, I present preliminary results of my research into the history of Mandelbrot’s very little known work in that area from 1963 to 1967. I speculate about how the lack of awareness of this work in the physics and statistics communities may have affected the development of complexity science, and I discuss the differences between the Hurst effect, “1∕f” noise and LRD, concepts which are often treated as equivalent.     

Nonlinear canonical transformations in the coupling between degenerate high and low energy excitations

In microscopic many-body physics the coupling between the motion of fast particles (electrons) and slow particles (nuclei) is universal. The standard Born-Oppenheimer decoupling procedure breaks down, if the energy separation in the “fast” system is of the same order as the elementary excitation in the “slow” system. In this case “dynamical resonance” effects are to be expected. In the present investigation a model system of a coupling between a doubly degenerate high energy excitation and doubly degenerate low energy oscillator is handled by a non-linear canonical transformation which is shown to be quasi-exact in the sense that it diagonalizes the Hamiltonian in both extremal coupling cases. The transformation has some flexibility, so that the diagonalization regions can be enlarged. It is employed to calculate the “zero-phonon” optical response, which indeed displays aresonance effect. Likewise, another nonlinear transformation is devised, which only in the strong coupling limit yields diagonalization. This latter transformation in a natural way leads to the conventional semi-classical approaches to the dynamical Jahn-Teller problem. The results gotten with it are identical with those from our transformation in the strong coupling limit. On the basis of our results some remarks are made concerning the possible impact of the breakdown of the adiabatic approximation in other regions.     

Quantum-realistic interpretation

1. Realism. Physicists claim rightly to speak about reality. But what does “reality” mean?2. The Copenhagen Interpretation (CI). We consider CI as a minimal semantics for quantum theory, leaving ways open for additional interpretation.3. The Measuring Process. Several interpretations of the process as given in the liteature are discussed.4. Realistic Interpretation. Discussion of the de Broglie-Bohm-Bell interpretation. If well formulated, it is not a necessary consequence of quantum theory but cannot be excluded.