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Time Dilation

Tool to make calculations with time dilation. Time dilation is an effect of the special relativity which states that time is going slower if an object is moving.

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Time Dilation -

Tag(s) : Physics-Chemistry, Date and Time

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# Time Dilation

## Time Dilatation Calculator

### ... According to ...

 An observer moving with the object stationary (e.g. on Earth)

Tool to make calculations with time dilation. Time dilation is an effect of the special relativity which states that time is going slower if an object is moving.

### What is the time dilation?

The dilation of time is a consequence of Einstein's theory of special relativity: the perception of flow of time is different according to the relative speed of movement of an object relative to an observer.

### What is the time dilation formula?

Calculation involves Lorentz factor and is calculated with this formula:

$$\Delta{t} = \frac{\Delta\tau}{\sqrt{1 - \frac{v^2}{c^2}}}\$$

Example: A person (A) voyaging during 1 hour at 99% of the speed of light will appear as a 7 hours-long trip for a stationary person (B).

### How has the dilation of time been proven with atomic clocks?

According to the theory of relativity of Albert Einstein, time is defined in each frame of reference. By associating a clock in each referential, and deduce the time changes (time dilation) for an observer outside of the clock frame of reference, which will see a clock moving with a tick slower than a stationary clock.

An experiment was carried out by installing atomic clocks in planes and returned to earth by comparing the time of the clocks: there was a shift similar to that expected by the theory.

### What is the speed of light?

The speed of light 'in a vacuum' is of 299792458 m/s (an order of magnitude of 300000 km/s) or 1079252848 km/h.

### What is the twin paradox?

The Twin Paradox is a thought experiment presented by Paul Langevin, which is at first sight paradoxical / contradictory.

Take twins, one of them travels at a speed close to that of light, then returns to Earth.

According to the time dilation phenomenon, the twin stayed on Earth lived longer than the one who left in space (which measured less seconds during the trip) and so the traveling twin became younger than his twin on Earth.

However, by changing the frame of reference, the traveling twin may consider that he has remained immobile and that it is his brother who has travel at a speed close to that of light and thus think that it is him who is become younger.

The experience of atomic clocks has clarified the fact that it is the twin traveler who is younger.

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