The Theory of Relativity

Since the days of Newton, the ideas of classical mechanics prevailed in the scientific community. The ideas of absolute velocity and absolute time were accepted phenomenon and were not at all challenged. However, as the nineteenth century drew to a close, new observations were being made, observations which contradicted the current theory of the time.

For instance, throughout the nineteenth century, it was correctly believed that light was a wave. If light were a wave like all other waves, it must have a medium through which to propagate through. This medium was called the ether, a substance which was everywhere throughout the universe. If this hypothesis were true one would be able to calculate the velocity of the Earth through the ether. Many experiments were conducted to determine this velocity the most famous one being the Michelson-Morley experiment.

The results of this experiment were inconclusive. The experiment relied on the fact that the speed of light through the "ether wind" (the speed of the ether as the travels through space) would change according to Galilean transformations (explained in more detail later). Thus the speed of light as it traveled against the direction of the ether should have been the normal speed of light subtracted from the speed of the ether. The speed of light was found to have no change, thus it was concluded that it would be impossible to determine the speed of the Earth through the ether.

However, Einstein later introduced a theory which would account for the unexpected results of the Michelson-Morley experiment and in fact contradict the ether theory all together. The Special Theory of Relativity would then continue to revolutionize the way we thought about space and time.

Specia...

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...cal situation. Let's say we have a system like the one on the right. A stationary observer in the S frame observes an event in the S prime frame. The S prime frame is moving with a velocity v relative to the S frame. Therefore if we had the coordinates of an event in the S frame, we could find out the corresponding coordinates in the S prime frame. The y and z coordinates would translate directly to the other frame, but the time on the axis on which the S prime frame is moving would need be transformed. All that would need to be done is to plug in the S frame x coordinate and the velocity of the S prime frame with the time into the first equation to get the x prime coordinate, and the same to find the time in the S prime frame. To find the coordinates in the S of an event in the S prime frame, simply replace the primed terms with the unprimed terms and vise versa.