The Fatal Flaw of Galilean Relativity


Imagine yourself sitting in a car moving at a constant velocity , holding a ball. Then you throw the ball forward with the velocity .

Fig 01.01 Car and Ball

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Obviously, in your frame of reference the ball will be moving forward at the velocity of , and to the people outside the car, it will be moving at the greater velocity of . This is known as Galilean Relativity.

Now imagine a similar scenario, but with the ball replaced by a flashlight.

Fig 01.02 Car and Light

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If we use the same intuition, we will come to the (obviously incorrect) conclusion that the beam of light will be moving at the speed faster than light. Of course this cannot be the case.

History


Since the era of Sir Isaac Newton, it has been commonly agreed upon that light is a kind of wave. However, as opposed to other kinds of wave such as sound waves or ocean waves, light seemed to be able to propagate through space without an apparent medium. Thus, a hypothesis was formed regarding a Luminiferous Aether; a material that extends to all of space and does not interact with anything, merely acting as a medium for light to propagate. An experiment was run to prove the existence of the luminiferous aether by measuring the earth’s velocity relative to it. This experiment was called the Michelson-Morley Experiment. The experiment splits a beam of light into two and directs them in two different directions, hoping that the earth’s motion through the aether will affect the velocity of the two light beams differently, and thus will cause the light beams to have a phase difference, causing an interference in the wave. Spoiler alert: it did not happen. This negative result shows that the aether does not exist. Light moves as it pleases.

The Postulate


From the aforementioned Michelson-Morley Experiment, it shows that the speed of light is constant regardless of the direction or velocity it was shot at, and that there is no absolute frame of reference. So, the primary postulates of special relativity are the following:

  1. The law of physics remains the same in all inertial frames of reference.
  2. The speed of light measured in all frames of reference equals to the constant .

The second postulate may seem counterintuitive when applied to the car-and-flashlight example above. From the car’s frame of reference, the light beam would be in front of the car after amount of time has passed in that frame. However, in the lab frame of reference, the light beam would be in front of the car after has passed.

Fig 01.03 Car and Light 2

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This is due to the fact that time progress at a different rate between the two frames of reference. The phenomenon is called Time Dilation.