Geometry of an Accelerated Rotating Disk

We analyze the geometry of a rotating disk with a tangential acceleration in the framework of the theory of Special Relativity, using the kinematic linear differential system that verifies the relative position vector of time-like curves in a Fermi reference. A numerical integration of these equations for a generic initial value problem is made up and the results are compared with those obtained in other works.     

New Perspectives on the Relativistically Rotating Disk and Non-Time-Orthogonal Reference Frames

The rotating disk problem is analyzed on the premise that proper interpretation of experimental evidence leads to the conclusion that the postulates upon which relativity theory is based, particularly the invariance of the speed of light, are not applicable to rotating frames. Different postulates based on the Sagnac experiment are proposed, and from these postulates a new relativistic theory of rotating frames is developed following steps similar to those initially followed by Einstein for rectilinear motion. The resulting theory agrees with all experiments, resolves problems with the traditional approach to the rotating disk, and exhibits both traditionally relativistic and non-relativistic characteristics. Of particular note, no Lorentz contraction exists on the rotating disk circumference, and the disk surface, contrary to the assertions of Einstein and others, is found to be Riemann flat. The variable speed of light found in the Sagnac experiment is then shown to be characteristic of non-time-orthogonal reference frames, of which the rotating frame is one. In addition, the widely accepted postulate for the equivalence of inertial and non-inertial standard rods with zero relative velocity, used liberally in prior rotating disk analyses, is shown to be invalid for such frames. Further, the new theory stands alone in correctly predicting what was heretofore considered a spurious non-null effect on the order of 10^–13 found by Brillet and Hall in the most accurate Michelson-Morley type test to date. The presentation is simple and pedagogic in order to make it accessible to the non-specialist.     

同时性的相对性与经典同时性

比较了相对论同时性与经典同时性并指出了它们的区别。     

玻璃钢转板单重态氧发生器的研究

 研究了作为化学氧碘激光器能源的转板式O₂(¹Δ)发生器非金属化的可行性。实验结果表明, 采用玻璃钢转板代替不锈钢转板是可行的, 有助于COIL小型化和实用化。     

Spacetime without Reference Frames: An Application to Synchronizations on a Rotating Disk

Nonstandard synchronizations of inertial observers in special relativity and synchronizations with respect to a uniformly rotating observer are investigated in a setting which avoids coordinates and transformation rules and so removes some misunderstandings.     

On the Conventionality of Simultaneity

Starting from the experimental fact that light propagates over a closed path at speed c (L/c law), we show to what extent the isotropy of the speed of light can be considered a matter of convention. We prove the consistence of anisotropic and inhomogeneous conventions, limiting the allowed possibilities. All conventions lead to the same physical theory even if its formulation can change in form. The mathematics involved is that of gauge theories and the choice of a simultaneity convention is interpreted as a choice of the gauge. Moreover, we prove that a Euclidean space where the L/c law holds, gives rise to a spacetime with Minkowskian causal structure, and we exploit the consequences for the causal approach to the conventionality of simultaneity.     

Heat Transfer in an Evaporating Liquid Film Flowing Over a Rotating Disk

Heat transfer from a horizontal heated rotating disk to a thin water film flowing over it was investigated. A series of experiments were carried out to determine Nusselt numbers on the disk both with and without evaporation from the liquid film surface. The Nusselt number increased with increasing disk rotation rate, water temperature, and water flow rate, while evaporative cooling from the liquid film surface only had a moderate effect on the Nusselt number magnitude. Functional dependence of the Nusselt number from an accompanying semi-analytical model and experimental data were used to develop semi-empirical correlations for the Nusselt number.     

具有微型沟槽结构旋转圆盘减阻的实验研究

建立了开式旋转圆盘系统减阻实验平台,对圆盘螺线沟槽减阻进行实验研究,并可以结合数值研究手段对微型沟槽减阻的机理进行研究。实验结果表明圆盘开槽面积为7.4%时,螺线微型沟槽使得旋转圆盘的最大减阻率达6.1%,V型沟槽两侧的压力差所产生的正扭矩是其减阻的主要原因。沟槽还能起到提高圆盘内径与外径处的静压差的效果。研究结果还表明,采用和平板减阻相同的无量纲尺寸的沟槽会引起圆盘表面的剪应力较大增加。     

Logic of Simultaneity

A logical model of spatiotemporal structures is pictured as a succession of processes in time. One usual way to formalize time structure is to assume the global existence of time points and then collect some of them to form time intervals of processes. Under this set-theoretic approach, the logic that governs the processes acquires a Boolean structure. However, in a distributed computer system or a relativistic universe where the message-passing time between different locations is not negligible, the logic has no choice but to accept time interval instead of time point as a primitive concept. The resulting logico-algebraic structure matches that of orthologic, which is known as the most simplified version of quantum logic, and the conventionality of simultaneity claim is reduced to the non-distributivity of the logic.     

Relativistic Simultaneity and Causality

We analyzed two types of relativistic simultaneity associated to an observer: the spacelike simultaneity, given by Landau submanifolds, and the lightlike simultaneity given by past-pointing horismos submanifolds. We study some geometrical conditions to ensure that Landau submanifolds are spacelike and we prove that horismos submanifolds are always lightlike. Finally, we establish some conditions to guarantee the existence of foliations in the space-time whose leaves are these submanifolds of simultaneity generated by an observer. These foliation structure allows us to incorporate the simultaneity submanifolds for studying some dynamical systems, for instance free elementary massless particles.     

Boundary Value Problems for the Stationary Axisymmetric Einstein Equations: A Disk Rotating Around a Black Hole

We solve a class of boundary value problems for the stationary axisymmetric Einstein equations involving a disk rotating around a central black hole. The solutions are given explicitly in terms of theta functions on a family of hyperelliptic Riemann surfaces of genus 4. In the absence of a disk, they reduce to the Kerr black hole. In the absence of a black hole, they reduce to the Neugebauer-Meinel disk.     

Simultaneity as an Invariant Equivalence Relation

This paper deals with the concept of simultaneity in classical and relativistic physics as construed in terms of group-invariant equivalence relations. A full examination of Newton, Galilei and Poincaré invariant equivalence relations in ℝ⁴ is presented, which provides alternative proofs, additions and occasionally corrections of results in the literature, including Malament’s theorem and some of its variants. It is argued that the interpretation of simultaneity as an invariant equivalence relation, although interesting for its own sake, does not cut in the debate concerning the conventionality of simultaneity in special relativity.     

On the Conventionality of Simultaneity in Special Relativity

In this paper the classical topic of conventionality in defining the simultaneity (or synchrony) of distant events is tackled again, and the validity of Reichenbach's view is carefully circumscribed. In particular, the role of one-way assumptions in the foundations of special relativity is emphasized. The restriction by the round-trip isotropy condition on the admissible distance functions in inertial frames is studied, and its relevance to several issues (absolute simultaneity, the interpretation of Michelson–Morley type experiments, the self-measured speed of a clock) is shown. Two clock transport synchronizations in an inertial frame, using self-measured speed and proper distance, are presented in detail, and the agreement of the synchronies so established with standard synchrony is proven to be non- circular. By assuming a reasonable concept of convention this result is shown to dissolve several objections by supporters of a strong version of conventionalism. Throughout, a number of common misapprehensions in the literature are pointed out.     

Geometric Simultaneity and the Continuity of Special Relativity

In this note I briefly discuss some aspects of relative geometric simultaneity in special relativity. After saying a few words about the status and nature of Minkowski spacetime in special relativity, I recall a uniqueness result due to David Malament concerning simultaneity relative to an inertial worldline and an extension of it due to Mark Hogarth and I prove an extension of it for simultaneity relative to an inertial frame in time-oriented spacetimes. Then I point out that the uniqueness results do not generalise to definitions of simultaneity relative to the rotating disk. Finally, I evaluate some recent claims of Selleri in the light of the results. Whilst some of his claims are supported by the approach taken here, the conclusion he draws from these claims, that special relativity harbours a discontinuity and so stands in need of replacement, does not follow and is rejected.     

Conventionality of Simultaneity and the Tippe Top Paradox in Relativity

In this paper we critically examine a recently posed paradox (tippe top paradox in relativity) and its suggested resolution. A tippe top when spun on a table, tips over after a few rotations and eventually stands spinning on its stem. The ability of the top to demonstrate this charming feat depends on its geometry (all tops are not tippe tops). To a rocket-bound observer the top geometry should change because of the Lorentz contraction. This gives rise to the possibility that for a sufficiently fast observer the geometry of the top may get altered to such an extent that the top may not tip over! This is certainly paradoxical since a mere change of the observer cannot alter the fact that the top tips over on the table. In an effort to resolve the issue the authors of the paradox compare the equations of motion of the particles of the top from the perspective of the inertial frames of the rocket and the table and observe among other things that (1) the relativity of simultaneity plays an essential role in resolving the paradox and (2) the puzzle in some way is connected with one of the corrolaries of special relativity that the notion of rigidity is inconsistent with the theory. We show here that the question of the incompatibility of the notion of rigidity with special relativity has nothing to do with the current paradox and the role of the lack of synchronization of clocks in the context of the paradox is grossly over-emphasized. The conventionality of simultaneity of special relativity and the notion of the standard (Einstein) synchrony in the Galilean world have been used to throw light on some subtle issues concerning the paradox.     

用大面积立式旋转盘MOVPE反应器生长Ⅲ族氮化物材料

为了降低Ⅲ族氮化物材料和器件的成本,必须开发大尺寸的Ⅲ族氮化物MOVPE生长的反应器.本文报道了EMCORE公司的一种带有旋转盘的立式反应器,其中的衬底片载盘直径为325mm.每次沉积过程中,载盘上可以放置21片2英寸直径的衬底片.反应器的内壁通过水冷,其温度可保持在50～60℃之间.衬底片可用电热丝加热,沉积中衬底载盘的旋转速度可达1 000～1 500rpm.本文给出了用这种325mm GaN生长系统生长的未掺杂GaN,InGaN和p-GaN外延层的相关结果.这些结果表明,这种旋转盘的反应器是一种很适合大尺寸载盘的系统,完全满足Ⅲ族氮化物材料体系生长的要求.与在小反应器中生长的材料相比,用这种大反应器生长的材料具有相同的质量.这种325mm的GaN反应器将使制备蓝光和绿光LED所用的Ⅲ族氮化外延材料的生产成本得到显著的降低.     

Modeling Chemically Reactive Flow of Sutterby Nanofluid by a Rotating Disk in Presence of Heat Generation/Absorption

In this article we investigate the flow of Sutterby liquid due to rotating stretchable disk. Mass and heat transport are analyzed through Brownian diffusion and thermophoresis. Further the effects of magnetic field, chemical reaction and heat source are also accounted. We employ transformation procedure to obtain a system of nonlinear ODE's. This system is numerically solved by Built-in-Shooting method. Impacts of different involved parameter on velocity, temperature and concentration are described. Velocity, concentration and temperature gradients are numerically computed. Obtained results show that velocity is reduced through material parameter. Temperature and concentration are enhanced with thermophoresis parameter.     

Simultaneity in Minkowski Spacetime: From Uniqueness to Arbitrariness

Malament (No?s 11:293–300, 1977) proved a certain uniqueness theorem about standard synchrony, also known as Poincaré-Einstein simultaneity, which has generated many commentaries over the years, some of them contradictory. We think that the situation called for some clarification. After reviewing and discussing some of the literature involved, we prove two results which, hopefully, will help clarifying this debate by filling the gap between the uniquess of Malament’s theorem, which allows the observer to use very few tools, and the complete arbitrariness of a time coordinate in full-fledged Relativity theory. In the spirit of Malament’s theorem, and in opposition to most of its commentators, we emphasize explicit definability of simultaneity relations, and give only constructive proofs. We also explore what happens when we reduce to “purely local” data with respect to an observer.