The principle of relativity and the special relativity triple

Based on the principle of relativity and the postulate on universal invariant constants (c,l) as well as Einstein's isotropy conditions, three kinds of special relativity form a triple with a common Lorentz group as isotropy group under full Umov–Weyl–Fock–Lorentz transformations among inertial motions.     

Cosmological special relativity

Recently we presented a new special relativity theory for cosmology in which it was assumed that gravitation can be neglected and thus the bubble constant can be taken as a constant. The theory was presented in a six-dimensional hvperspace. three for the ordinary space and three for the velocities. In this paper we reduce our hyperspace to four dimensions by assuming that the three-dimensional space expands only radially, thus one is left with the three dimensions of ordinary space and one dimension of the radial velocity.     

The momentum conservation law in special relativity

The derivation of the functional form of the relativistic momentum of a particle has a history going back to Lewis and Tolman's paper of 1909, yet satisfactory presentations seem to be few in number. Careful examination of the several types of derivation shows that their shortcomings are avoidable and allows the presentation of exact and improved analyses.     

The electromagnetic two-body problem in special relativity

A system of two point charged particles is considered. Each particle moves in the electromagnetic field created by the other particle according to Maxwell's equations. A scheme of successive approximations is developed to study the field and the motion of the charges. The field (potentials and intensities) are exapanded in powers of c^?1 using a retarded time coordinate. The variables of the motion (position vectors, velocities, etc) are expanded in powers of c^?1 with coefficients depending on t only. The field is evaluated in the first three approximations. The equations of motion are derived in the same approximations and the corresponding conserved quantities are explicitly given. Thus, the usual assumption of an action-at-a-distance principle is avoided and the original nonlinear integrodifferential equations are reduced to a sequence of linear equations.     

Conventionalism in special relativity

Reichenbach, Grünbaum, and others have argued that special relativity is based on arbitrary conventions concerning clock synchronizations. Here we present a mathematical framework which shows that this conventionality is almost equivalent to the arbitrariness in the choice of coordinates in an inertial system. Since preferred systems of coordinates can uniquely be defined by means of the Lorentz invariance of physical laws irrespective of the properties of light signals, a special clock synchronization—Einstein's standard synchrony—is selected by this principle. No further restrictions conerning light signal synchronization, as proposed, e.g., by Ellis and Bowman, are required in order to refute conventionalism in special relativity.     

Transformations in special relativity

By using the principle of relativity alone (no assumptions about signals or light) it is shown that a relativisitic group of linear transformations of a spacetime plane is, if infinite, either Galilean, Lorentzian or rotational. The largest such finite group is a Klein 4-group, generated by space-reversal and time-reversal. In the infinite case an invariant of the group, denotedc, appears. Whenc is real, nonzero, noninfinite, then the group is a Lorentz group andc is identified with the speed of light. Lorentz transformations are represented through an algebra ofiterants that provides a link among Clifford algebras, the Pauli algebra and Herman Bondi'sK-calculus.     

The consistency of the postulates of special relativity

In a recent article in this journal, Kingsley has tried to show that the postulates of special relativity contradict each other. Here we show that the arguments of Kingsley are invalid because of an erroneous appeal to symmetry in a non-symmetric situation. The consistency of the postulates of special relativity and the relativistic kinematics deduced from them is restated.     

Cosmological relativity: A special relativity for cosmology

Under the assumption that Hubble's constant H₀ is constant in cosmic time, there is an analogy between the equation of propagation of light and that of expansion of the universe. Using this analogy, and assuming that the laws of physics are the same at all cosmic times, a new special relativity, a cosmological relativity, is developed. As a result, a transformation is obtained that relates physical quantities at different cosmic times. In a one-dimensional motion, the new transformation is given by

Test theories of special relativity

We review the Edwards transformation, and investigate the Robertson transformation and the Mansouri-Sexl (ms) transformation. It is shown that thems transformation is a generalization of the Robertson transformation, just as the Edwards transformation is a generalization of the Lorentz transformation. In other words, thems transformation differs from the Robertson transformation by a directional parameterq, just as is the case for the Edwards and Lorentz transformations. So thems transformation predicts the same observable effects as the Robertson transformation, just as the Edwards transformation does with the Lorentz transformation. This is to say that the directional parameterq representing the anisotropy of the one-way speed of light is not observable in any physical experiment. The observable difference between thems (Robertson) transformation(s) and the Lorentz transformation is caused by the anisotropy of the two-way speed of light. Therefore a physical test of thems transformation is a test of the two-way speed of light, but not of the one-way speed of light.     

The axiomatic foundations of the theory of special relativity

In this paper it is shown that (1) linear transformations more general than the Lorentz transformation—containing the Palacios and the Lorentz transformation as special cases—(2) and the principle of the constancy of the velocity of light (taken originally by Einstein together with the supposition of the linearity of transformation as fundamental hypotheses of the theory of special relativity)—can be deduced from Maxwell's equations for the electromagnetic fieldin vacuo (A ₁), the principle of relativity (A ₂) and the two following axioms (which do not contain explicitly the hypothesis of the isotropy of space!): (A ₃) to every event in the Galilean reference systemS there corresponds one and only one event in the systemS so that these two systems are connected by reversible single-valued functions, continuously differentiable as their inverse transformations, (A ₄) the constant relative velocitiesv _ss andv _ss betweenS andS are each other equal in magnitude and opposite in signv _ss =–v _ss To obtain uniquely the Lorentz transformation the following axiom has to be added: (A ₅) the distanceD of any two points at rest inS, situated in a plane orthogonal to the relative velocity betweenS andS is measuredS as independent of the sense of the velocity, i.e. if one changesv _ss into –v _ss the distanceD does not vary for an observer inS. Results of our theory are the ideas that (a) the fact that the Lorentz transformation is not the unique transformation leaving Maxwell's equations for the electromagnetic field in all Galilean systems of reference invariant but that there exists a more general transformation (containing these two transformations as special cases) leaving Maxwell's equations invariant; (b) that the Michelson-Morley as well as the Fizeau experiment does not represent an experimental proof in favour of the theory of special relativity. At the end of the paper the mutual relations between the principle of relativity (the axiomA ₁ together with the axiomA ₂), the axiomA ₅ and the possibility of the discernibility as well as the indiscernibility of right and left at the macrocosmic level is discussed.     

Rotating frames in special relativity

A uniformly rotating frame is defined as the rest frame of a particle revolving with constant velocityω in a circle about theZ-axis of an inertial frame Σ⁰. Under the conditionz=Z,r=R, theoretical constraints are established for the solution of the transformation problem Σ⁰→Σ^ω r,Σ^ω r being the cylindrical subframe of Σ^ω. The unique solution of the problem in cylindrical coordinates is isomorphic to the special Lorentz transformationL _x, withβ=v/c replaced byβ _r=ωr/c. Hence the intrinsic geometry on the surface of a rotating cylinder is Euclidean. Though there exists no complete intrinsic geometry on the surface of a rotating disk, the geodesics on it are straight lines while the circumference of a concentric circle isK _r2πr as predicted by Einstein.     

Quantum entropy and special relativity

We consider a single free spin- 1 / 2 particle. The reduced density matrix for its spin is not covariant under Lorentz transformations. The spin entropy is not a relativistic scalar and has no invariant meaning.     

The application of special relativity to the right-angled lever

The Lorentz transformation relates the Einstein-defined measures, associated with two inertial frames, of the space and time coordinates of a body or event. From such information relative velocities and accelerations may be deduced, and their appropriate transformations derived. All other transformations of special relativity are derived from the Lorentz transformation and hence depend on the coordinate measures related by the transformation. In particular, the transformation of forces depends on that for accelerations; hence it may not be appropriately applicable to equilibrium phenomena involving null-acceleration. It is suggested that this is the root of the apparent paradox which arises when the conventional force transformation is applied to the consideration of a right-angled lever in equilibrium in its proper inertial frame. It is shown that this paradox is resolved by the employment of a nonconventional but appropriate special relativistic transformation for forces not associated with corresponding accelerations.     

Projective geometry and special relativity

Some concepts of real and complex projective geometry are applied to the fundamental physical notions that relate to Minkowski space and the Lorentz group. In particular, it is shown that the transition from an infinite speed of propagation for light waves to a finite one entails the replacement of a hyperplane at infinity with a light cone and the replacement of an affine hyperplane – or rest space – with a proper time hyperboloid. The transition from the metric theory of electromagnetism to the pre‐metric theory is discussed in the context of complex projective geometry, and ultimately, it is proposed that the geometrical issues are more general than electromagnetism, namely, they pertain to the transition from point mechanics to wave mechanics.     

牛顿力学中的惯性质量与狭义相对论中的惯性质量

分别详细说明了在牛顿力学中和在狭义相对论中,惯性和惯性质量的概念是如何引入的.明确地阐述了狭义相对论同牛顿力学相类似,物体(可视为质点或粒子)的固有质量(或静止质量)就是其惯性质量.通过分析,指出并强调了运动质量只是个规定,并非物体惯性的大小真的随运动发生了改变.最后还对静止质量为零、速度为光速的粒子只遵从狭义相对论而...     

狭义相对论中运动物体的视觉形象分析

我们在点观察模型的基础上,考虑小孔成像的方法,给出了一个研究运动物体视觉形象更细致化的模型,并得到了理论计算的表达式.以正方体为例,展示了它在某一观察方向上低速、高速运动时的视觉形象,并揭示了物体靠近、远离观察者时视觉形象的不同,以及棱边弯曲的现象.     

The homogeneity of the ball inR 3 and special relativity

Einstein's velocity addition formula ofspecial relativity (SR) defines a transformation _v of the ballB _c of radiusc inR ³, representing all possible velocities in an inertial systemK, onto identical ballB _c , which represents the velocities in another systemK, moving with velocity v relative toK. Since _v maps the zero velocity ofB _c into arbitrary vector v ofB _c ,B _c is homogeneous under all possible _v.A similar homogeneity of the unit ballB inL(G, H) under a set of maps _a, a B, arises also in theLine Transmission Theory (TLT) for a lossless line. HereL(G, H) is the space of all linear operators between Hilbert spacesG,H, representing the signals on the line in the two directions. The explicit form of _a is obtained naturally in TLT.     

Deformed special relativity in position space

We investigate how deformations of special relativity in momentum space can be extended to position space in a consistent way, such that the dimensionless contraction between wave-vector and coordinate-vector remains invariant. By using a parametrization in terms of an energy dependent speed of light, and an energy dependent Planck's constant, we are able to formulate simple requirements that completely determine the active transformations in position space. These deviate from the standard transformations for large velocities of the observed object. Some examples are discussed, and it is shown how the relativistic mass gain of a massive particle is affected. We finally study the construction of passive Lorentz-transformations.