Special Relativity

History of Relativity

Relativity theories have been around since Galileo's time and before. Relativity measures the velocity of one object with respect to another. For instance, in Galileo's relativity, if you are in a car traveling at 35 mph and you throw a ball in front of you at 45 mph, to an observer on the road, the ball is traveling at 80 mph.

In 1905 a 26 year old German Scientist named Albert Einstein published a paper on electrodynamics. (Zur Electrodynamik bewegter Körper, Annalen der Physik, 17, 841 (1905)) This paper contained two postulates that would become the basis for the special theory of relativity.

  1. Absolute uniform motion cannot be detected.
  2. The speed of light is independent of the motion of the source.

When taken independently, each postulate seems reasonable enough. However, taken together they comprise Einstein's relativity which is very different from that of Galileo. From the two postulates it is concluded that:

every observer obtains the same value for the speed of light independent of the relative motion of sources and observers.

This means that if you are in a car traveling at 35 mph and you shine a flashlight in front of you, the observer on the road will still measure the light as moving at 1.86 e 5 miles/second, not 1.86 e 5 miles/second + 35 mph. This is very illogical, but the theory is true experimentally, as seen in the Michelson Morely experiment where the speed of light was measured to be the same under various conditions.

One way to think about relativity is that we have typically defined velocity in terms of two constants, space and time. That is v = x/t. However, Einstein's relativity defines space and time in terms of a constant, the velocity of light. That is space and time are relative and variable, while the speed of light is absolute.

The theory of relativity has some very strange consequences.


Time Dilation

Let us imagine a clock consisting of a light emitter and a light detector. Some interval of time Dt is equal to twice the distance from the emitter to the mirror, divided by the speed of the signal, c.

However, if the box which contains our clock is moving, the distance traveled by the signal will be further to an observer outside the box. If its speed stays the same our clock will read a longer time to the observer on the outside of the box, while to someone inside the clock reads the same.

This can be formalized in the following:

where:

The ' indicates the time in the moving reference frame and the sans ' represents the time in the stationary frame, so called proper time.

The largest implication of this is that someone moving at high velocities will live longer than someone at small velocities. For example if someone takes a high c space ship to Alpha Centauri (distance 4.6 LY), it will probably take them about 6 years and in that time, the will have aged 6 years. However, back on Earth, that same person will have aged much more, since more time has passed in their reference frame. When the person got back from Alpha Centauri, the world they knew wouldn't exist anymore.

Does this sound far fetched? Airplanes moving at high velocities have used atomic clocks to prove that the clocks run more slowly. The amount is very small (don't try to live longer by flying often, you'll just waste it looking for your baggage :-)