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###### Time dilation

Physics (Year 12) - Special Relativity

Dev Lohar

# Equation

The equation for time dilation is as follows:

Sometimes the equation is simplified to:

The time dilation effect becomes important at speeds above 0.1 times the speed of light. Below that speed, the dilated time is nearly the same as the proper time.

# Understanding

It is important to realise that an observer wonâ€™t see time slowing down in their own frame of reference, they will see time slowing down in a moving frame of reference. Imagine an observer A on earth and observer B moving at 0.8 times the speed of light (ie. 0.8c) on a spaceship. The frame of reference for observer A can be considered to be earth and the frame of reference for observer B can be considered as the spaceship. In the frame of reference of observer A, they would see a clock on earth ticking at its â€˜normal paceâ€™, but they would notice a clock on the spaceship ticking slowly. In the frame of reference of observer B, they would notice their clock ticking â€˜normallyâ€™ whilst the clock on earth would be ticking slow. A general rule of thumb to remember is a moving clock runs slower. This may sound confusing and â€˜unrealâ€™ at first but thatâ€™s whole point of relativity. There is no absolute frame of reference and hence no absolute clock ticking at the absolute â€˜correctâ€™ time. The time in your own inertial frame of reference ticks away at one second per second.

Time dilation effect can be used to explain why muons are detected on Earthâ€™s surface even though they have a short lifetime. When muons are produced in the upper atmosphere, they travel at high speeds. Hence in the frame of reference of an observer on Earth, the muonsâ€™ lifetime is dilated enough they end up at the Earthâ€™s surface. In the frame of reference of the muons, there is a different relativistic effect taking place; length contraction, which will be explained separately in the next section.

# Twin paradox | Elucidate Video

In the above video, Dev explains a very common example (the twin paradox) which is used demonstrate the time dilation phenomenon.

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