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Register a new userThe speed of light under the IST and Lorentz Transformations
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Chandru Iyer
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We expand the IST transformation to three-dimensional Euclidean space and derive the speed of light under the IST transformation. The switch from the direction cosines observed in K to those observed in K-prime is surprisingly smooth. The formulation thus derived maintains the property that the round trip speed is constant. We further show that under the proper synchronization convention of K-prime, the one-way speed of light becomes constant.
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In this paper we develop a framework allowing a natural extension of the Lorentz transformations. To begin, we show that by expanding conventional four-dimensional spacetime to eight-dimensions that a natural generalization is indeed obtained. We then find with these generalized coordinate transformations acting on Maxwells equations that the electromagnetic field transformations are nevertheless unchanged. We find further, that if we assume the absence of magnetic monopoles, in accordance with Maxwells theory, our generalized transformations are then restricted to be the conventional ones. While the conventional Lorentz transformations are indeed recovered from our framework, we nevertheless provide a new perspective into why the Lorentz transformations are constrained to be the conventional ones. Also, this generalized framework may assist in explaining several unresolved questions in electromagnetism as well as to be able to describe quasi magnetic monopoles found in spin-ice systems.
We report the simplest possible form to compute rotations around arbitrary axis and boosts in arbitrary directions for 4-vectors (space-time points, energy-momentum) and bi-vectors (electric and magnetic field vectors) by symplectic similarity transformations. The Lorentz transformations are based exclusively on real $4times 4$-matrices and require neither complex numbers nor special implementations of abstract entities like quaternions or Clifford numbers. No raising or lowering of indices is necessary. It is explained how the Lorentz transformations can be derived from the most simple second order Hamiltonian of general significance. Since this approach exclusively uses the real Clifford algebra $Cl(3,1)$, all calculations are based on real $4times 4$ matrix algebra.
In a recent article [1] we have explored alternative decompositions of the Lorentz transformation by adopting the synchronization convention of the target frame at the end and alternately at the outset. In this note we develop the decomposition by assuming a correct universal synchronization that may be outside the two inertial frames that are involved.
Sometimes it becomes a matter of natural choice for an observer (A) that he prefers a coordinate system of two-dimensional spatial x-y coordinates from which he observes another observer (B) who is moving at a uniform speed along a line of motion, which is not collinear with As chosen x or y axis. It becomes necessary in such cases to develop Lorentz transformations where the line of motion is not aligned with either the x or the y-axis. In this paper we develop these transformations and show that under such transformations, two orthogonal systems (in their respective frames) appear non-orthogonal to each other. We also illustrate the usefulness of the transformation by applying it to three problems including the rod-slot problem. The derivation has been done before using vector algebra. Such derivations assume that the axes of K and K-prime are parallel. Our method uses matrix algebra and shows that the axes of K and K-prime do not remain parallel, and in fact K and K-prime which are properly orthogonal are observed to be non-orthogonal by K-prime and K respectively. http://www.iop.org/EJ/abstract/0143-0807/28/2/004
The relationship between the harmonic mean and special relativity is concisely elucidated. The arguments in favor and against SRT are explored. It is shown that the ratio of the speed of light to the harmonic mean of the onward and return speeds of light in a moving frame under Newtonian mechanics, when equitably distributed between space and time as a correction, leads to the Lorentz transformation. This correction implies an apparent contraction of objects and time dilation. However, the symmetry of the onward and inverse transformations give a different meaning to the gamma factor
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