Abstract
THE very recent and inspiring work of Prof. E. A. Milne on world structure has led us to investigate whether there exists a law connecting the velocity and distance of a particle from an observer which is invariant for the generalised Lorentz transformation. In the usual notation, the only law of the form f(x1, x2, x3, x4) = 0 which is invariant for the infinitesimal Lorentz transformation is known to be x12 + x2 + x32 + x43 = 0, which gives the propagation of light. Following this, we have investigated whether there exists a law of the form (x1, x2, x3, x4, u, v, w) = 0 which is invariant for the generalised Lorentz transformation; here u = dx1/dx4, v = dx2/dx4, etc. In its generalised form the transformation is and similarly, v, w may be obtained. h, a, b are the constants of the transformation. We have found that the following set of equations is the only invariant set of this type, that is, involving both velocities and co-ordinates: The corresponding equations for u, v, x1, follow immediately from (1).
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NARLIKAR, V. Recession of the Spiral Nebulæ. Nature 135, 149–150 (1935). https://doi.org/10.1038/135149b0
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DOI: https://doi.org/10.1038/135149b0
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