Quantum Mechanics from Focusing and Symmetry

A foundation of quantum mechanics based on the concepts of focusing and symmetry is proposed. Focusing is connected to c-variables—inaccessible conceptually derived variables; several examples of such variables are given. The focus is then on a maximal accessible parameter, a function of the common c-variable. Symmetry is introduced via a group acting on the c-variable. From this, the Hilbert space is constructed and state vectors and operators are given a definite interpretation. The Born formula is proved from weak assumptions, and from this the usual rules of quantum mechanics are derived. Several paradoxes and other issues of quantum theory are discussed.     

Causal Paradoxes: A Conflict Between Relativity and the Arrow of Time

It is often argued that superluminal velocities and nontrivial space-time topologies, allowed by the theory of relativity, may lead to causal paradoxes. By emphasizing that the notion of causality assumes the existence of a time arrow (TA) that points from the past to the future, the apparent paradoxes appear to be an artefact of the wrong tacit assumption that the relativistic coordinate TA coincides with the physical TA. The latter should be identified with the thermodynamic TA, which, by being absolute and irrotational, does not lead to paradoxes.     

公平性与数学化(III)公平分配

讨论公平分配问题。为三类均分态提供一些有用方法，其中最重要的是有关整分态的四种方法。用一些实例来讨论这些方法的缺陷，并由此讨论了另一个重要的不可能性定理：Ｂａｌｉｎｓｋｉ和Ｙｏｕｎｇ 定理。     

Firewalls as artefacts of inconsistent truncations of quantum geometries

In this paper we argue that a firewall is simply a manifestation of an inconsistent truncation of non‐perturbative effects that unitarize the semiclassical black hole. Namely, we show that a naive truncation of quantum corrections to the Hawking spectrum at order , inexorably leads to a “localised” divergent energy density near the black hole horizon. Nevertheless, in the same approximation, a distant observer only sees a discretised spectrum and concludes that unitarity is achieved by effects. This is due to the fact that instead, the correct quantum corrections to the Hawking spectrum go like . Therefore, while at a distance far away from the horizon, where , quantum corrections are perturbative, they do diverge close to the horizon, where . Nevertheless, these “corrections” nicely re‐sum so that correlations functions are smooth at the would‐be black hole horizon. Thus, we conclude that the appearance of firewalls is just a signal of the breaking of the semiclassical approximation at the Page time, even for large black holes.     

Four-Dimensional Geometric Quantities versus the Usual Three-Dimensional Quantities: The Resolution of Jackson’s Paradox

In this paper we present definitions of different four-dimensional (4D) geometric quantities (Clifford multivectors). New decompositions of the torque N and the angular momentum M (bivectors) into 1-vectors N_s, N_t and M_s, M_t, respectively, are given. The torques N_s, N_t (the angular momentums M_s, M_t), taken together, contain the same physical information as the bivector N (the bivector M). The usual approaches that deal with the 3D quantities etc. and their transformations are objected from the viewpoint of the invariant special relativity (ISR). In the ISR, it is considered that 4D geometric quantities are well-defined both theoretically and experimentally in the 4D spacetime. This is not the case with the usual 3D quantities. It is shown that there is no apparent electrodynamic paradox with the torque, and that the principle of relativity is naturally satisfied, when the 4D geometric quantities are used instead of the 3D quantities.     

Nonparametric universal copula modeling

To handle the ubiquitous problem of “dependence learning,” copulas are quickly becoming a pervasive tool across a wide range of data‐driven disciplines encompassing neuroscience, finance, econometrics, genomics, social science, machine learning, healthcare, and many more. At the same time, despite their practical value, the empirical methods of “learning copula from data” have been unsystematic with full of case‐specific recipes. Taking inspiration from modern LP‐nonparametrics, this paper presents a modest contribution to the need for a more unified and structured approach of copula modeling that is simultaneously valid for arbitrary combinations of continuous and discrete variables.     

Quantum Tunneling of Massive Particles from a Garfinkle-Horowitz-Strominger Dilatonic Black Hole

Hawking radiation is viewed as a process of quantum tunneling. The massive particles＇ tunneling from Garfinkle-I-Iorowitz-Strominger black hole is investigated. Using Jingyi Zhang＇s de Broglie wave method, we get the unthermal spectrum, and the result is consistent with the underlying unitary theory.     

The Lattice Solid Model to Simulate the Physics of Rocks and Earthquakes: Incorporation of Friction

The particle-based lattice solid model developed to study the physics of rocks and the nonlinear dynamics of earthquakes is refined by incorporating intrinsic friction between particles. The model provides a means for studying the causes of seismic wave attenuation, as well as frictional heat generation, fault zone evolution, and localisation phenomena. A modified velocity–Verlat scheme that allows friction to be precisely modelled is developed. This is a difficult computational problem given that a discontinuity must be accurately simulated by the numerical approach (i.e., the transition from static to dynamical frictional behaviour). This is achieved using a half time step integration scheme. At each half time step, a nonlinear system is solved to compute the static frictional forces and states of touching particle-pairs. Improved efficiency is achieved by adaptively adjusting the time step increment, depending on the particle velocities in the system. The total energy is calculated and verified to remain constant to a high precision during simulations. Numerical experiments show that the model can be applied to the study of earthquake dynamics, the stick–slip instability, heat generation, and fault zone evolution. Such experiments may lead to a conclusive resolution of the heat flow paradox and improved understanding of earthquake precursory phenomena and dynamics.     

Lengths on rotating platforms

The paper treats the issue of the length of a rotating circumference as seen from on board the moving disk and from an inertial reference frame. It is shown that, properly defining a measuring process, the result is in both cases 2πR thus dissolving the Ehrenfest paradox. The same holds good when considering that, for the rotating observer, the perceived radius coincides with the curvature radius of a space-time helix and a complete round trip corresponds to an angle which differs from the one seen by the inertial observer. The apparent contradiction with the Lorentz contraction is discussed.     

“Solution” of the EPR Paradox: Negative, or Rather Fuzzy Probabilities?

Negative probabilities were several times proposed in the literature as a way to reconcile violation of Bell-type inequalities with the premise of local realism. It is argued that instead of using negative probabilities that have no physical meaning one can use for this purpose fuzzy probabilities that have sound and unambiguous interpretation.