Gravitational time dilation

Temporary expansions

According to the theory of general relativity, accelerated systems would also experience a time dilation similar to that happening in a gravitational field. Similarly, in systems of reference such as a carousel and a Ferris wheel, will be shown time dilation as an effect of their turns.

Examples of gravitational time dilation

In an accelerated box, the equation with respect to an arbitrary observer would be:

Where $T{_{d}}$ es el tiempo transcurrido medido por el observador acelerado, $g$ It is the acceleration of the box as measured by the observer basis, and $h$ It is the vertical distance between observers.

In a rotating disc when the observer is placed in the center of the disk and rotating with the:

Where $r$ es la distancia al centro del disco, $w$ It is the angular velocity of the disk.

In the framework of the solar system, we would have:

Where $T{_{d}}$ It is time for the events A and B for the observer slow within the gravitational field and ${T_{0}}$ es el tiempo propio del observador rápido, $G$ es la constante gravitacional, $M$ es la masa aparente del objeto que crea el campo gravitacional, $r$ es la coordenada radial del observador, $c$ It is the speed of light and ${r_{0}}=2GM/c^2$

Experimental confirmation

Noteworthy is that temporal dilation is has been measured experimentally using atomic clocks on airplanes, where the clocks on airplanes were slightly ahead with Earth.