By L. P. Hughston
This long-awaited textbook deals a concise one-semester creation to simple basic relativity appropriate for arithmetic and physics undergraduates. Emphasis is put on the student's improvement of either an effective actual take hold of of the topic and a worldly calculational facility. The textual content is supplemented by way of a variety of geometrical diagrams and by way of a wide number of demanding routines and difficulties.
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Extra info for An introduction to general relativity
When making a measurement, it is necessary to compensate for any effect that the quantity being measured has on the scale factors of the instruments which are used. To the author's knowledge, this step has never been included in the measurement of the velocity of light. 19- Consider an attempt to measure the velocity of light in which a measurement is made of the time required for a pulse of light to be sent from the top of one mountain to a retroreflector on the top of an adjacent mountain and returned to its source.
Consider next that the particles in the bullet consist of three springs with identical energies of compression mounted orthogonal to each other with one of each set of springs being parallel to the bullet's projected path. Since, for our thought experiment, the springs themselves are considered to be massless, the only mass the particles in the bullet possess is the energy stored by the compression of the three springs. 28- When the springs acquire a velocity, the acquisition of that velocity causes kinetic energy to be added to the energy of compression which had been stored in them.
From the diagram we may write, for the moving reference frame, Ftm*Lpm=Fpm*Ltm and, since the arms are of equal length in that reference frame, it follows that Ftm=Fpm. We should also be able to write Fts*Lps=Fps*Lts, but, in the stationary reference frame, the length of the parallel arm, Lps, is reduced by the effects of the velocity in accordance with the Lorentz Transformation for Length, Bv. For the net torque to be zero in the stationary reference frame, Fts must equal to Fps/Bv. Minkowski correctly provided the Lorentz Transformation for Parallel Force as equal to unity but the currently accepted Lorentz Transformation for Transverse Force is the reciprocal of its correct value.
An introduction to general relativity by L. P. Hughston