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Special Relativity

by

James Adrian

Introduction

Light (and all other electromagnetic radiations) travel at 299,792,458 meters per second in a vacuum, but even a mere 458 meters per second is over 1024 miles per hour. Our daily experience with time and distance, and even the vast majority of our manufacturing and tool-making pursuits do not involve speeds that are an appreciable fraction of the speed of light or the speed of radio waves. As a result, time dilation, length contraction, mass changes due to speed, and twins aging at different rates are effects of high speed that are absent from our daily lives. These effects are, however, becoming increasingly relevant to our wellbeing and happiness.

      This article explains what special relativity is.


The Michelson-Morley Experiment


Strange as it may seem, the speed of light in a vacuum, as measured by the receiver of that light, is the same, regardless of the speed or direction of travel of the source of that light. This was first shown by the The Michelson-Morley Experiment.

      This result does not depend on the accuracy of our standard for time or our standard for distance. A speed equals a distance traveled divided by the time elapsed. If we arbitrarily choose a distance to be a meter, and arbitrarily choose a duration to be a second, and we use those meanings for distance and time, the receiver of the light will always observe the same speed, regardless of the frame of motion of the source of that light.

      You can change the length that you are calling a meter and do another thousand calculations of the speed of light. In that event, you will find that each of those thousand calculations give you the same result, whatever it may be. You can change what a second is and calculate a different speed result, but if you measure the speed of light another thousand times with this new unit of time, all one thousand of those results will be the same.

      As long as we define speed as being distance divided by time, the speed of light is constant. Here is how that remarkable result was discovered:


The Interferometer

      The experiment performed by Albert A. Michelson and Edward W. Morley took place between April and July of 1887 and made its measurements by means of the interferometer. An understanding of the workings of this instrument is crucial to the understanding of the experiement and its results.

      In the six pictures below, there are two mirrors, labeled A and B. The diagonal line in the middle of each picture represents a half-mirrored sheet of glass serving as a beam splitter. A light source marked S and and light detector marked D are also present in each of the pictures.

      In the first time interval of interest, the light from source, S, is reflected to mirror A and simultaneously transmitted to mirror B, because the glass of the bean splitter is half mirrored. This is illustrated in pictures A - t1 and B - t1.

      In the second time interval of interest, the light reflected from mirror A is transmitted through the beam splitter to the detector, while at the same time, the light reflected from mirror B is reflected by the beam splitter to the detector. This is illustrated in pictures A - t2 and B - t2.


                A - t1                                       A - t2                                         A - t2a



       



                  B - t1                                       B - t2                                         B - t2a


      The second time interval of interest also includes two light paths that do not affect the operation of the interferometer, and do not affect the results of the experiment. Pictures A - t2a and B - t2a each show a beam of light returning to the source, S. The beam splitter reflects light from mirror A to source, S, and also transmits light form mirror B to source, S. Neither has any influence on source, S, or the experiment.


 



 Refraction A - t2             Refraction B - t1


      The two pictures above illustrate refraction as light is being transmitted through the beam splitter. This does not alter the direction of the light beam, but it slightly offsets its path to one that is parallel to what it would follow if the beam splitter was not in its path.

      This link fully explains this effects of this refraction.

      When the light from mirror B is reflected by the beam splitter, the direction and placement of the light moving toward the detector is identical to that in picture named Refraction A - t2. Both refractive delays are also identical. (The speed of light in glass is less that the speed of light in air or in a vacuum.)


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