Time Dilation

What is time dilation?

What is time dilation?

You are probably familiar with the fact that time often chooses to work against us. This is something that all commuters are familiar with. All the attempts to rush to work are futile because of the phenomenon known as velocity time dilation. 

It doesn’t take much intuition to figure out what causes this type of time dilation, the details of which were for the first time ever written down in Albert Einstein’s’ book ’Special Theory of Relativity’, which was published in 1905. This book argued for the first time ever, that it was not only possible to move through time, in the same way you can move through space, but that it was impossible to do one without doing the other.

Specific experiments have been conducted to observe time dilation. One of the most famous experiments designed specifically to test the theory of relativity was the Hafele-Keating experiment. In this experiment, 4 caesium-beam atomic clocks were flown around the world, once eastwards, and once westward. The measured difference between the displayed time of the clocks that had been around the world, and those that had not supported the idea that time dilation did exist.

Despite the fact that this has been observed to happen, we know that you will always perceive your own time to be passing at normal speed, and that time only appears to speed up or slow down relative to an observer (a moving clock slows down relative to a stationary observer).

Fortunately for the commuter, the speeds at which we need to travel in order for time dilation to be noticeable are, and for a very long time will continue to be unattainable. For a person to notice time dilation with the naked eye, they would need to be travelling at a speed close to the speed of light. The equation:

time.gif

shows how time dilation increases exponentially (due to the square sign next to v and the square root sign at the bottom of the fraction). As v gets bigger, the bottom half of the fraction tends towards 0, and t’ tends towards infinity. If v=c, then time for you appears to stop to stationary observers. To give a more visual representation, here is a graph displaying this:

time2.png

As you can see, once you reach speeds around 90% of the speed of light, time dilation rockets upwards and tends towards infinity (which is only reached when you travel at the speed of light). The irony is, for the poor commuter trying to get to work on time, the faster he or she travels, the less time he or she has to get there.


But, fear not, for there is a way around this problem. The solution is gravitational time dilation. This is another phenomenon which is yet again creatively named. You have probably guessed, that this type of time dilation is affected by the strength of the gravitational field that you are in. This is the equation for it (r is the radial coordinate, G is the universal gravitational constant):

This shows that time runs faster outside gravitational fields. It shows that as r tends towards infinity, t (subscript 0) tends towards 0, meaning that a clock an infinite distance away from any gravitational field, would be the fastest clock in the universe.

time3.png

 

For many of you, the physics behind time dilation will be of little interest. However, there are some invaluable lessons which we can take away from it:

1.      Walking is actually a quicker way to work than travelling by vehicle

2.      If you really want to travel by vehicle, travel by spaceship because time passes faster in space (and spaceships are awesome)