Time Dilation

Note: This article is regarding time dilation due to relative velocity (special relativity).

Time dilation is a phenomenon that is exemplified by an apparent disparity in the passage of time within the context of multiple frames of reference.

The Main Idea

Time dilation is best understood to be entirely based on reference frames. All effects or observed effects of time dilation are dependent on the observer's particular frame of reference. For example (as the concept of time dilation relates to special relativity), a pilot travelling in a rocket will observe no change in his own situation, despite the fact that, to an outside observer who is "not moving," the pilot and his instruments will be subject to a great deal of time dilation due to the high velocity disparity between the rocket and the observer.

A Mathematical Model

Time dilation in a special relativistic context can be modeled simply with the formula:

[math]\displaystyle{ \Delta t' = \frac{\Delta t}{\sqrt{1-\frac{v^2}{c^2}}} \, }[/math]

where [math]\displaystyle{ \Delta t }[/math] defines the elapsed time between two events which occur at the same location for one particular observer in his or her frame of reference, [math]\displaystyle{ \Delta t' }[/math] defines a second measured elapsed time between the same two events but by a second particular observer that is moving with a specific velocity of [math]\displaystyle{ v }[/math] with respect to the first observer. In this context, [math]\displaystyle{ c }[/math] refers to the speed of light.

Examples

Simple

Imagine a flight from Cleveland to Atlanta. It would seem obvious that the distance covered by a plane that undertakes this journey is identical to a plane that flies from Atlanta to Cleveland. However, it must be considered which plane is actually moving relative to our frame of reference. In order to understand more complicated aspects of time dilation, simple facts about referential velocities are important to learn.

Difficult

Imagine spaceship one is moving at a uniform speed from point A to point B. Spaceship one has an on-board atomic clock that measures time accurately to the nanosecond. Now, imagine a second, identical spaceship (spaceship two) with an identical atomic clock moving at the same speed but this time heading from point B to point A. At the instance that the spaceships pass by one another on their respective routes, the pilot of spaceship one looks into the cockpit of spaceship two and notices that the atomic clock appears to be ticking slower in comparison to his own atomic clock, which seems to operate normally. Compare this to the viewpoint of the pilot of spaceship two, who sees his clock as operating normally whereas the clock in spaceship one appears to be slower.

The reasoning behind the apparent disparity involves the differing frames of reference of the two pilots. But what happens if the two pilots later decide to meet up at the restaurant at the end of the universe? Which one will be older? To answer this question simply, neither will be "older" than one another, but in comparison to a person who had been standing still on earth during the course of the two pilots' travels, the pilots will have aged somewhat slower.

Connectedness

In regards to my particular major, nuclear engineering, this topic does not have a specific connection. However, the concept of time dilation is one that must be taken into special consideration in the field of aerospace engineering, specifically when designing and engineering methods for deep-space flights. Since the effects of time dilation will result in any extremely high-velocity travel, any human subjects will age at a rate much more slowly than scientists and engineers on earth working on deep-space missions. In the future, this phenomenon indeed presents a unique obstacle for exploration efforts.

History

In 1909, Gilbert Lewis used a model of two "light clocks," each of which moved with relative velocities, to describe a theory of time dilation. The clocks operated by bouncing a "signal light" back and forth between two mirrors; within each clock, the mirrors were parallel to each other as well as to the direction of the clock's motion. It was theorized by Lewis that an observer at the reference frame of the first clock would see the second clock as operating "slower."

See also

• Einstein's Theory of Special Relativity

Provides context for the theories that lead up to time dilation.

• Einstein's Theory of General Relativity

Offers an alternate perspective, specifically in the context of how time dilation affects observable events.

Further reading

Hazla, Miroslav, "Dilation of Time and Space: An Examination of the True Nature of Spacetime."

Pabisch, Roland, "Derivation of the time dilatation effect from fundamental properties of photons."

External links

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References

http://science.howstuffworks.com/science-vs-myth/everyday-myths/relativity10.htm

https://www.fourmilab.ch/cship/timedial.html

http://www.emc2-explained.info/Time-Dilation/#.VmHN4vmrTjY