Special Relativity

By the late 1800’s, it was becoming obvious that there were some serious problems for Newtonian physics concerning the need for absolute space and time when referring to events or interactions (frames of reference). In particular, the newly formulated theory of electromagnetic waves required that light propagation occur in a medium.
speed_of_lightIn a Newtonian Universe, there should be no difference in space or time regardless of where you are or how fast you are moving. In all places, a meter is a meter and a second is a second. One should be able to travel as fast as you want, with enough acceleration.

In the 1890’s, two physicists (Michelson and Morley) were attempting to measure the Earth’s velocity around the Sun with respect to Newtonian Absolute space and time. This would also test how light waves propagated since all waves must move through a medium. For light, this medium was called the aether.

The results of the Michelson-Morley experiment was that the velocity of light was constant regardless of how the experiment was tilted with respect to the Earth’s motion. This implied that there was no aether and, thus, no absolute space. Thus, objects, or coordinate systems, moving with constant velocity (called inertial frames) were relative only to themselves.

In Newtonian mechanics, quantities such as speed and distance may be transformed from one frame of reference to another, provided that the frames are in uniform motion (i.e. not accelerating)

train_robberyConsidering the results of the Michelson-Morley experiment led Einstein to develop the theory of Special Relativity. The key premise to special relativity is that the speed of light (called c = 186,000 miles per sec) is constant in all frames of reference, regardless of their motion. What this means can be best demonstrated by the aside scenario.

This eliminates the paradox with respect to Newtonian physics and electromagnetism of what does a light ray ‘look like’ when the observer is moving at the speed of light. The solution is that only massless photons can move at the speed of light, and that matter must remain below the speed of light regardless of how much acceleration is applied.

In special relativity, there is a natural upper limit to velocity, the speed of light. And the speed of light is the same in all directions with respect to any frame. A surprising result to the speed of light limit is that clocks can run at different rates, simply when they are traveling a different velocities.

photon_clockThis means that time (and space) vary for frames of reference moving at different velocities with respect to each other. The change in time is called time dilation, whereas frames moving near the speed of light have slow clocks.

time_dilationTime dilation leads to the famous Twins Paradox, which is not a paradox but rather a simple fact of Special Relativity. Since clocks run slower in frames of reference at high velocity, then one can imagine a scenario were twins age at different rates when separated at birth due to a trip to the stars.
lorentz_contractionIt is important to note that all the predictions of special relativity, length contraction, time dilation and the twin paradox, have been confirmed by direct experiments, mostly using sub-atomic particles in high energy accelerators. The effects of relativity are dramatic, but only when speeds approach the speed of light. At normal velocities, the changes to clocks and rulers are too small to be measured.twin_paradox

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