Classical mechanics and entropy

This note addresses a problem of nineteenth century applied mathematics—is it possible in the context of Hamiltonian mechanics to define a functionS of the generalized coordinates and momenta which is monotonically increasing along orbits? The question is of interest, because, for a sytem not in thermodynamic equilibrium, entropy should increase strictly monotonically along an orbit, and a negative answer implies that mechanical principles different from those of Hamiltonian mechanics must be introduced to explain thermodynamics. This note answers the question rigorously for Hamiltonian systems confined to an invariant region of finite volume in phase space; it is not possible to define a continuous function which increases monotonically along orbits. An appendix gives a translation of an 1889 paper of Poincaré addressing the same issue.     

On an Approximate Solution of the Cauchy Problem for Systems of Equations of Elliptic Type of the First Order

In this paper, on the basis of the Carleman matrix, we explicitly construct a regularized solution of the Cauchy problem for the matrix factorization of Helmholtz’s equation in an unbounded two-dimensional domain. The focus of this paper is on regularization formulas for solutions to the Cauchy problem. The question of the existence of a solution to the problem is not considered—it is assumed a priori. At the same time, it should be noted that any regularization formula leads to an approximate solution of the Cauchy problem for all data, even if there is no solution in the usual classical sense. Moreover, for explicit regularization formulas, one can indicate in what sense the approximate solution turns out to be optimal.     

普通物理实验教学中的“提出问题”

应用认知心理学中的"问题"概念,依据教育心理学原理,构建了普通物理实验教学中以"提出问题"为主的教学策略.在普通物理实验教学中,教师把提出问题作为一种有效的教学手段,有意识地提出问题,让学生思考和解决.提出问题充分地调动了学生思维的积极性,促进了思维的层层深入,有利于学生对思维的监控及问题意识的形成,推动认知成分中思维的发展.     

On the second law of thermodynamics

The second law of thermodynamics has two distinct aspects to its foundations. The first concerns the question of why entropy goes up in the future, and the second, of why it goes down in the past. Statistical physicists tend to be more concerned with the first question and with careful considerations of definition and mathematical detail. The second question is of quite a different nature; it leads into areas of cosmology and quantum gravity, where the mathematical and physical issues are ill understood.     

On the properties of the four-momentum of an isolated charge + field system

The question of the isolation of a charged particle along with its field such that the four-momentum of an entire system is a four-vector is raised. The relationships between the characteristics of a particle and a field upon such isolation have been obtained. In particular, it has been demonstrated that within the considered nonclassical models the particle mass should be greater than one-third of the field mass.     

On Time Asymmetry and History in an Everett Quantum World

It is usually held that the standard collapse model of a quantum measurement process grounds a kind of fundamental time asymmetry. The question whether and how it should be possible to reconstruct uniquely one's own history in an Everett no-collapse interpretation of quantum theory is investigated. A particular approach to the Everett interpretation, due to John S. Bell, is considered, according to which one of the chief claims of the Everett quantum theory is precisely that it allows us to do without the notion of history.     

The angular momentum controversy: What’s it all about and does it matter?

The general question, crucial to an understanding of the internal structure of the nucleon, of how to split the total angular momentum of a photon or gluon into spin and orbital contributions is one of the most important and interesting challenges faced by gauge theories like Quantum Electrodynamics and Quantum Chromodynamics. This is particularly challenging since all QED textbooks state that such a splitting cannot be done for a photon (and a fortiori for a gluon) in a gauge-invariant way, yet experimentalists around the world are engaged in measuring what they believe is the gluon spin! This question has been a subject of intense debate and controversy, ever since, in 2008, it was claimed that such a gauge-invariant split was, in fact, possible. We explain in what sense this claim is true and how it turns out that one of the main problems is that such a decomposition is not unique and therefore raises the question of what is the most natural or physical choice. The essential requirement of measurability does not solve the ambiguities and leads us to the conclusion that the choice of a particular decomposition is essentially a matter of taste and convenience. In this review, we provide a pedagogical introduction to the question of angular momentum decomposition in a gauge theory, present the main relevant decompositions and discuss in detail several aspects of the controversies regarding the question of gauge invariance, frame dependence, uniqueness and measurability. We stress the physical implications of the recent developments and collect into a separate section all the sum rules and relations which we think experimentally relevant. We hope that such a review will make the matter amenable to a broader community and will help to clarify the present situation.     

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.     

在法拉第效应实验中不同光强点定位检测旋转角灵敏度的研究

通过实验验证马吕斯定律,并分别在消光位置和最大光强位置作检测点,测量介质的费尔德常数.根据实验结果的分析,讨论实验中普遍存在的"在光强极大值和光强最大相对变化率位置"检测灵敏度的问题,得出在消光位置测量线偏振光旋转角最精确的结论.     

Tm3+掺杂材料激光冷却的研究

固体材料的激光制冷又称反斯托克斯荧光制冷,是近年来刚兴起的全光学制冷技术。该技术的核心问题是制冷材料的选择。以Tm^3＋掺杂离子为例,从理论上分析了最小制冷能级间距与激光抽运速率的关系,研究了不同抽运速率下制冷功率与能级间距的关系以及热-光转换效率与能级间距的关系,获得了最佳热-光转换效率与抽运速率的关系。结果表明,最小的制冷能级间距约为4500cm^-1,能级间距在5000～6000cm^-1的宽度是比较合适的。最后探讨了Tm^3＋掺杂材料用于激光冷却的可行性,许讨论了制冷基体材料的合理选择问题。     

红外目标仿真光学机构

论述了目标仿真机构的用途、仿真的光学原理以及实现原理的光学系统。对其中的两个光学问题的研究作了详细地论述 ,即干扰光路 2倍于目标光路的视场角以及如何由摆镜的摆动实现。由于析光镜与光轴成 45°角 ,使像点在子午方向被拉长约为弧矢方向的 10倍。为了减少子午像差 ,将两块析光镜作成略带楔角的楔形镜。结果表明 ,由于该机构的尾焰、尾喷管用的是同一条光路 ,所以使结构大为简化 ,这对降低转动惯量非常有利 ;由于有干扰弹仿真 ,使机构的功能得到了扩大     

Are the quantum rules exact? The case of the imperfect measurements

Should we doubt the exactness of the predictive quantum rules of calculation? Although this question is sometimes raised in connection with the one on how to physically understand quantum mechanics, these two questions should not be mixed up. It is recalled here that even the first one is stil an object of controversy, and it is shown (a) that in one specific case the arguments put forward in support of such doubts are hardly cogent but (b) that, nevertheless, at least in one specific other context, the question is worth attention. This is the problem of repeated imperfect measurements. Relative to it, a theoretical possibility is shown of discriminating between the thesis that the quantum rules are exact and a powerful theory of which it is proved that it cannot be reconciled with the assumption.     

疫情期间线上大学物理教学质量提高方法

针对疫情防控期间线上教学的需求,鉴于高校大学物理课程大班授课特点,结合我校前期大学物理MOOC网络线上课程应用经验和学生学习习惯,实施了基于选择题提问实时反馈的线上教学方法.本文首先对大学物理大班网上教学面临问题进行了分析,然后通过选择题提问时段设计、选择题类型设计和选择题考核方式设计,全面阐述了该方法的实施方案.最后...     

Do metric standards contract?

We address the question: By what class of force-application programs must a meter stick initially at rest in an inertial frame be moved in order to transfer it to a relatively moving inertial frame without altering the internal energy state of the structure in the process? Such stress-free transfer of a metric standard is essential for moving-axis calibration (a neglected art in established relativity theory). In order to deduce the answer by reasonings appropriate to kinematics, it proves necessary to make an extension of the relativity principle to rectilinear (irrotational) accelerated motions, and to enhance the kinematic motion group accordingly. Since the physical motion groups differ, the answers we obtain to this and to the title question differ from those of special relativity. Our alternative kinematics thus leads to discrepancies that should be measurable atO(v ²/c ²).     

Understanding brain networks and brain organization

What is the relationship between brain and behavior? The answer to this question necessitates characterizing the mapping between structure and function. The aim of this paper is to discuss broad issues surrounding the link between structure and function in the brain that will motivate a network perspective to understanding this question. However, as others in the past, I argue that a network perspective should supplant the common strategy of understanding the brain in terms of individual regions. Whereas this perspective is needed for a fuller characterization of the mind-brain, it should not be viewed as panacea. For one, the challenges posed by the many-to-many mapping between regions and functions is not dissolved by the network perspective. Although the problem is ameliorated, one should not anticipate a one-to-one mapping when the network approach is adopted. Furthermore, decomposition of the brain network in terms of meaningful clusters of regions, such as the ones generated by community-finding algorithms, does not by itself reveal “true” subnetworks. Given the hierarchical and multi-relational relationship between regions, multiple decompositions will offer different “slices” of a broader landscape of networks within the brain. Finally, I described how the function of brain regions can be characterized in a multidimensional manner via the idea of diversity profiles. The concept can also be used to describe the way different brain regions participate in networks.     

Possible operation of a 1.5-2-MW, CW conventional cavity gyrotron at 140 GHz

We present a study of the feasibility of continuous wave (CW) operation of a 140-GHz conventional cavity gyrotron at high power levels operating in the TE/sub 31,8/- and TE/sub 25,10/-modes. The question of mode selection is discussed, and a possible design of such a gyrotron with beam energy up to 90 keV and a current of 60-70 A is given. We find that it should be possible to operate a 140-GHz gyrotron at power up to 2 MW if a sufficiently high-order mode is used, although CW power may be somewhat lower.     

高能强子化过程的自旋转移和轻子诱发反应中超子的极化

指出在轻子诱发反应中测量产生超子的极化是研究高能强子化过程自旋转移的理想途径.在总结这些反应产生的初始夸克或反夸克极化的基础上,给出了超子极化的计算方法.作为应用举例,给出了e⁺e^－湮没过程中LEP能量下各种超子的极化及与已有实验的比较.这些结果表明,测量各类超子的极化可作为检验不同的重子自旋结构图像,何者适用于高能碎裂过程的重要手段.     

On adaptation – a secondary concern?

The climate problem has many facets. Whether or not humans are capable of significantly changing climate is no longer a scientific question – they are in fact capable of doing so. However, only partly solved is the question what is happening here and now and how far future anthropogenic climate change will or may possibly go. The most important issue, namely how humankind can or should deal with this change, is a political issue, which needs more debate. Adaptation is a key element in this context. These issues are addressed in a non-technical manner here – from a deliberately broad range of perspectives, from both natural and social sciences. This paper is not a review; it is certainly biased in presenting the author’s views, analyses and conclusions. According to these views, adaptation is not a secondary concern.     

量子力学势垒穿透问题的光学类比

用量子态的线性叠加原理和波函数及其一阶导数的连续性,求解一维方势垒散射问题,得出各区域的波函数,最后求出了反射系数、透射系数以及势垒内部的概率流密度和概率分布,并得到由散射态过渡到束缚态的条件,另外,还将其自然过渡到一维对称方势阱的问题上去。     

Probabilities are single-case or nothing

Physicists have, hitherto, mostly adopted a frequentist conception of probability, according to which probability statements apply only to ensembles. It is argued that we should, instead, adopt an epistemic, or Bayesian, conception, in which probabilities are conceived as logical constructs rather than physical realities and in which probability statements do apply directly to individual events. The question is closely related to the disagreement between the orthodox school of statistical thought and the Bayesian school. It has important technical implications (it makes a difference what statistical methodology one adopts). It may also have important implications for the interpretation of the quantum state.