Thursday, 9 July 2009

Special Theory of Relativity

Special Theory of 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 (the waves had to be waves on something).
In 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. And you
should be able to travel as fast as you want, with enough acceleration (i.e. force).
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
hypothetical 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).

Considering 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 following 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 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.

This 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, where frames moving
near the speed of light have slow clocks.

Likewise, space is shorten in in high velocity frames, which is called Lorentz contraction.

Time 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.

It 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.
Special relativity demonstrated that there is a relationship between spatial coordinates and
temporal coordinates. That we can no longer reference where without some reference to
when. Although time remains physically distinct from space, time and the three dimensional
space coordinates are so intimately bound together in their properties that it only makes sense
to describe them jointly as a four dimensional continuum.
Einstein introduced a new concept, that there is an inherent connection between geometry of
the Universe and its temporal properties. The result is a four dimensional (three of space, one
of time) continuum called spacetime which can best be demonstrated through the use of
Minkowski diagrams and world lines.

Spacetime makes sense from special relativity since it was shown that spatial coordinates
(Lorentz contraction) and temporal coordinates (time dilation) vary between frames of
reference. Notice that under spacetime, time does not `happen' as perceived by humans, but
rather all time exists, stretched out like space in its entirety. Time is simply `there'.

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