Simultaneity-Time Simultaneity-Time

Simultaneity-Time Simultaneity-Time

by T L Hurst

Introduction

Einstein's Train Einstein's Train

The idea that the speed of light, in empty space, is the same in all frames of reference is fundamental to Einstein's Special and General Theories of Relativity. Hence in the version of the Einstein's Train thought experiment given by Wikipedia it is stated that the light approaching the ends of the carriage is travelling at c with respect to both the observer on the train, and the observer on the platform.

This means that, for the observer on the train, the light flashes reach the ends of the carriage simultaneously, but for the observer on the platform, the light flashes reach the rear of the carriage first and the front later. This difference in simultaneity leads directly to the Lorentz transformation, and the time dilation and spatial contraction that describes.

However, the evidence provided by the Michelson's Interferometer experiment, and others like it, only show that measurements of the speed of light are constant in the rest frame of the equipment used to measure it. That says nothing about the speed that the light is travelling at with respect to other objects in different rest frames.

Hence the claim that the light is travelling at c with respect to the observer on the train follows from the empirical evidence, but the claim that it is the same with respect to the observer on the platform does not. Furthermore, the differences in simultaneity predicted by this have never actually been empirically observed. Hence this site explores the implications of taking the speed of light to be constant in the rest frame of the target, i.e. without making any assumption as to its value in other frames of reference. First we consider a simple thought experiment...

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