运动轨迹真是这样吗?

高中物理第三册（选修）教学参考书（以下简称教参），在论述“机械能守恒定理不解决物体做什么运动”的问题时，例举了如图1情形下摆球的运动，即让绳的一端栓-11,球，另一端悬挂在O点，悬点O的正下方距离为摆长一半处有一个钉子P，让小球从与O点处于同一高度的A点释放．则小球经过8点后，先沿以P为圆心的圆弧运动，     

Beautiful Gauge Field Equations in Clifforms

By combining the tetrads of unholonomic frames of spacetime with the Dirac matrices to a one-form , we can reformulate not only the Dirac equation, but also the Einstein equations and supergravity in a very concise form. These Clifforms also shed some light on the chiral decomposition à la Ashtekar, the role of the axion as a dynamical degree of freedom dual to the torsion of the Einstein—Cartan theory, and the role of the Seiberg—Witten equation for S-duality.     

The World Is Not a Theorem

The evolution of the biosphere unfolds as a luxuriant generative process of new living forms and functions. Organisms adapt to their environment, exploit novel opportunities that are created in this continuous blooming dynamics. Affordances play a fundamental role in the evolution of the biosphere, for organisms can exploit them for new morphological and behavioral adaptations achieved by heritable variations and selection. This way, the opportunities offered by affordances are then actualized as ever novel adaptations. In this paper, we maintain that affordances elude a formalization that relies on set theory: we argue that it is not possible to apply set theory to affordances; therefore, we cannot devise a set-based mathematical theory to deduce the diachronic evolution of the biosphere.     

Is CuO a spin fluid?

We present the results of the Electron Spin Resonance (ESR) experiments on cupric oxide (CuO), which establishes the existence of a highly correlated state of mutually interacting spins, above the Néel temperature (T_N ≈ 230 K) and extending up to T_s ≈ 630 K.     

Is a horizon-free cosmology possible?

In a space of FRLW models, filled with a single fluid such that its energy-momentum tensor satisfies standard energy conditions and the dynamics of the universe is described by a second order differential equation,the existence of particle horizons is a generic property. To remove particle horizons one must invest nearly as much as to remove them together with the initial singularity.     

What a Classical r-Matrix Really Is

Abstract

To my friend and colleague K.C. Reddy on occasion of his retirement.

The notion of classical r-matrix is re-examined, and a definition suitable to differential (-difference) Lie algebras, – where the standard definitions are shown to be deficient, – is proposed, the notion of an O-operator. This notion has all the natural properties one would expect form it, but lacks those which are artifacts of finite-dimensional isomorpisms such as not true in differential generality relation End (V ) V ^? ? V for a vector space V . Examples considered include a quadratic Poisson bracket on the dual space to a Lie algebra; generalized symplectic-quadratic models of such brackets (aka Clebsch representations); and Drinfel’d’s 2-cocycle interpretation of nondegenate classical r-matrices.     

Is Empty Spacetime a Physical Thing?

This article deals with empty spacetime and the question of its physical reality. By “empty spacetime” we mean a collection of bare spacetime points, the remains of ridding spacetime of all matter and fields. We ask whether these geometric objects—themselves intrinsic to the concept of field—might be observable through some physical test. By taking quantum-mechanical notions into account, we challenge the negative conclusion drawn from the diffeomorphism invariance postulate of general relativity, and we propose new foundational ideas regarding the possible observation—as well as conceptual overthrow—of this geometric ether.     

这是一幅不受光控的示意图

非农机专业适用的“全国中等农业学校教材《物理》”是目前全国中等农校正在使用的课本,该书第221页图12-7是一幅利用光电效应控制电动机工作的示意图，如图1所示．按照课本第221和222页所述，该图表示的控制过程是：“当光照在光电管上时，光电管电路中产生微弱电流。