Time+Dilation+and+Time+Travel

= Time Dilation =

Time Dilation, according to the theory of relativity, is the inequality of time between two events measured by observers in different reference frames or located differently from gravitational masses. That is to say, a clock moving at a different velocity than another clock will measure time differently, and a clock that is closer to a large body of mass will measure time differently than one floating around near no mass.

Special Time Dilation
According to the special theory of relativity, a clock moving faster in respect to an observer is measured to be running slower than that of the clock at rest in relation to the observer. The faster an object is moving closer to the speed of light, time appears to slow down more. This phenomenon can be represented by the following formula:

math $t^\prime=\frac {t}{\sqrt{1-\dfrac{v^2}{c^2}}}$ math

Where:
 * t' = time as measured by the observer's clock at rest
 * t = time as measured by the moving clock
 * v = the relative velocity between the moving clock and the observer's clock
 * c = speed of light

However, this time dilation is negligible for speeds at even 0.5c.

For example, say a spaceship is travelling between two asteroids moving at a relative velocity of 99% the speed of light. The clock on the spaceship measures the time between the two asteroids as 1 minute. Plugging in 1 as t and .99 as (v/c), we can determine that the time (or t') that passes for an observer at rest relative to the asteroids is approximately 7.09 minutes. So travelling at 99% the speed of light, one experiences time slower by a factor of roughly 7.

From an observer in the spaceship, events that happen on one of the asteroids would appear faster than they actually are. Observers that are on one of the asteroids would view events on the spaceship slower than they are.

Another form of special time dilation is often called special relativistic time dilation. This is known as time 'appearing' to slow down for two clocks moving at uniform motion unaffected by gravity, where the other clock appears to be ticking slower than that of the local clock. An observer at rest with respect to the other clock will observe your local clock to be running slower as well. This effect is magnified the faster the relative velocity. However, this effect is only true for the local perspective, and time does not actually slow down.

Gravitational Time Dilation
Gravitational time dilation, or time dilation according to the general theory of relativity, is the phenomenon of time passing differently in areas of different gravitational influence. For example, clocks running at different altitudes will eventually display different times. However, as with special time dilation, this effect is very small. In spite of this, time dilation has been recorded in objects with less than a 1 meter height difference.

Clocks which are far from large bodies of mass will run faster than clocks close to large bodies of mass. This is due to the fact that in general relativity, gravity can be equivalent to force acquired via acceleration (10 N/kg -> 10 m/s 2 ). Therefore, gravitational force slows down time similar to acceleration would in special time dilation. Calculation of gravitational time dilation involves the use of different formulas depending on what type of gravitational field is involved.

Time Travel
Time travel in the traditional sense (ie.: moving through time itself) is not possible, however manipulating the effects of time dilation to 'travel forward in time' is possible.

For example, say you are travelling at 99.9% the speed of light from Earth to a planet 500 light years away. Not accounting for any gravitational time dilation, you experience time roughly 22 times slower. So you will only age 22 years to travel 500 light years, effectively travelling to the 'future' from your perspective.

Relation to Light and Optics
There is a relationship between time dilation and light/optics. Say light was moving between two mirrors placed vertically from each other in a spaceship moving comparable to the speed of light. When the light moves from one mirror to the other, the light has to move a certain horizontal distance as well as move vertically. This diagonal net movement is a larger distance to travel, therefore light takes a longer time to return to the original mirror than it would if the velocity of the ship was incomparable to the speed of light. This means that it takes longer for 1 second to pass on the spaceship than at a slower velocity.

An observer on the spaceship would view the the light as going straight up and down, as they are in the same frame of reference as the light. This is comparable to tossing a ball up and down in a vehicle; you perceive the ball as moving only vertically, yet to an outside observer, the ball would be moving diagonally.

Videos
Some videos to help understand the concept and derivation are as follows.

media type="youtube" key="SchfetsZysM" height="315" width="420"

media type="youtube" key="q9hqdjDuzGs" height="315" width="420"