A different derivation of the acceleration of a particle in a non-inertial reference frame
Eli Lansey
本文利用复平面上复数的几何关系，导出了一种新的质点在非惯性参考系中加速度的推导方法，其中考虑了科里奥利效应。
A new derivation of the acceleration of a particle in a non-inertial reference frame, including the Coriolis effect, is developed using the geometry of complex numbers in the complex plane.
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Differential aging from acceleration, an explicit formula
我们考虑一个时钟的“悖论”的框架，观察者离开惯性系，被加速后，任意旅行回来。我们讨论了一个简单的方程，给出了，在1+1维的情况下，在惯性系上经过的时间和加速度测量的加速观察员在行程中的一个明确的关系。相对于惯性系的非闭合行程看起来相对于另一个合适的惯性系闭合。利用这一观察，我们定义的微分老化作为一个功能的适当的时间，并表明它是非递减的。重建问题的狭义相对论也进行了讨论，表明其，至少数值，解决方案将允许建设一个“惯性钟”。
This work shows how two simple derivations of the centripetal acceleration are fundamentally related to seminal works of Huygens and Newton. A different, more physically motivated derivation is then given.
It is shown that formulas for the radiative power loss and radiation reaction from a charge can be derived in a heuristic manner from the kinetic power (rate of change of the kinetic energy) of its electric inertial mass. The derivation assumes a non-relativistic but otherwise an arbitrary motion of the charge. We exploit the fact that as the charge velocity changes because of a constant acceleration, there are accompanying modifications in its electromagnetic fields which can remain concurrent with the charge motion because the velocity as well as acceleration information enters into the fiel…
The most general transformation connecting inertial frames is derived from rather general and simple assumptions, without the postulate of constancy of the speed of light in vacuo.
Newton second law of dynamics is a law of motion but also a useful definition of force (F=MA) or inertial mass (M=F/A), assuming a definition of acceleration and parallelism of force and acceleration. In the special theory of relativity, out of these three only the description of force (F=dp/dt) does not raise doubts. The greatest problems are posed by mass, which may be invariant rest mass or relativistic mass or even directional mass like longitudinal mass. This results from breaking the assumption of parallelism of force and standard acceleration. It turns out that these issues disappear if…
A New Kinematical Derivation of the Lorentz Transformation and the Particle Description of Light
洛伦兹变换是从三个简单的假设推导出来的：（i）狭义相对论原理的弱运动学形式，要求两个不同的惯性观测者的相互时空测量是等价的;（ii）唯一性，即洛伦兹变换应该是其参数的单值函数的条件;（iii）空间各向同性。本文还指出，对于两个惯性系中沿平行于相对速度方向的共轴的时空点的洛伦兹变换，只要满足假设（i）和（ii）就足够了。洛伦兹变换的运动学，然后开发，以证明，与经典电动力学的一致性，光必须由无质量（或几乎无质量）的粒子：光子。
An advanced undergraduate derivation of acceleration thermality
研究加速热性质，通过介绍非平衡计算基础，利用精确可解的非均匀加速轨迹，对β衰变光子发射进行光谱分析、时间演化研究，揭示普朗克辐射，适用于高级本科计算。
We present a didactic derivation of the special theory of relativity in which Lorentz transformations are `discovered' as symmetry transformations of the Klein-Gordon equation. The interpretation of Lorentz boosts as transformations to moving inertial reference frames is not assumed at the start, but it naturally appears at a later stage. The relative velocity $\textbf{v}$ of two inertial reference frames is defined in terms of the elements of the pertinent Lorentz matrix, and the bound $|\textbf{v}| <c\;$ is obtained as a simple theorem that follows from the structure of the Lorentz group. Th…
On Nonlinear Inertial Transformations
本文推导了非线性惯性变换的最一般形式，并证明在保持光速条件下仍为仿射线性，同时揭示了Schwarzian微分方程在物理中的应用。
The Minkowski metric in non-inertial observer radar coordinates
本文给出了任意非惯性观测者O在雷达坐标系中的Minkowski（1+1）维度量关于O的固有加速度的封闭表达式。度量的知识允许非惯性观测者在时空中进行实验，而不参考惯性系。为了阐明惯性观测器与非惯性观测器的关系，给出了雷达坐标系与惯性坐标系之间的坐标变换。我们表明，每一个共形平坦的坐标系可以被视为雷达坐标系的一个合适的观察员为一个合适的参数化的观察员世界线。因此，任意移动的观察者之间的坐标变换是共形变换，并且共形不变的（1+1）维理论导致所有观察者的相同物理，而与它们的相对运动无关。
Besides the defining space-time symmetries (homogeneity and isotropy) of inertial frames, the derivation of Lorentz transformation requires postulating the principle of relativity and the existence of a finite speed limit. In this article, we point out that the existence of a finite speed limit can be readily inferred from the nature of allowed inertial frames. We also show that the principle of relativity can be obtained from the defining space-time symmetries of every inertial frame. Therefore, if the conventional definition of inertial frames is augmented properly, the special theory of rel…
Acceleration-dependent self-interaction effects as a possible mechanism of inertia
本文追求两个目标。首先，重新审视经典电磁质量理论，并利用广义相对论的一个推论--光在非惯性参考系中的传播是各向异性的--进一步发展它。第二，表明相同类型的加速度相关的自相互作用的影响，引起的惯性和质量的经典电子出现在量子场论，以及当广义相对论频率移动的虚量子，介导的电磁，弱，和强相互作用之间的非惯性粒子，被考虑在内。这些效应可以解释宏观物体的惯性和质量的起源。
The role of acceleration and locality in the twin paradox
我们研究了加速度在孪生子悖论中的作用。从加速度观测者和惯性观测者的坐标变换中，我们发现，从加速度观测者的观点来看，时间的微分流逝率不仅取决于相对速度，而且还取决于加速度与观测者之间的距离的乘积。然而，该结果不具有直接的操作解释，因为在某个位置处的观察者只能测量在相同位置处定义的物理量。对于局部测量，两个观察者之间的不对称性可以归因于这样的事实，即与惯性坐标系相反，非惯性坐标系只能在局部被正确解释。
Thermal scalar radiation in two spacetime dimensions is treated within relativistic classical physics. Part I involves an inertial frame where are given the analogues both of Boltzmann's derivation of the Stefan-Boltzmann law and also Wien's derivation of the displacement theorem using the scaling of relativitic radiation theory. Next the spectrum of classical scalar zero-point radiation in an inertial frame is derived both from scale invariance and from Lorentz invariance. Part II involves the behavior of thermal radiation in a coordinate frame undergoing (relativistic) constant acceleration,…
We that show two body gravitational orbits may be plotted using a radial reference frame rather than the customary Newtonian rectilinear inertial frame. Infinitesimal calculus cofounder and continental contemporary of Newton, Leibniz claimed that the second radial derivative could be found by taking the difference between an inertial force varying inversely, with the cubed radius and the gravitational force varying with an inversed squared radius. His radial method was severely criticised by Newton and supporters, who preferred the rectilinear inertial frame, also claiming Leibniz failed to sa…
The Planck spectrum of thermal scalar radiation is derived suggestively within classical physics by the use of an accelerating coordinate frame. The derivation has an analogue in Boltzmann's derivation of the Maxwell velocity distribution for thermal particle velocities by considering the thermal equilibrium of noninteracting particles in a uniform gravitational field. For the case of radiation, the gravitational field is provided by the acceleration of a Rindler frame through Minkowski spacetime. Classical zero-point radiation and relativistic physics enter in an essential way in the derivati…
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