TIME DILATION due to Gravity

Time dilation is an interesting phenomenon that was introduced by special relativity. Time dilation, as the name suggests, is the effect of slowing down of time. Time dilation introduces possibility of actual time travel into the future. It may sound science fiction for some, but it’s a well tested and practical phenomenon.

Time dilation has two independent causes- gravity and relative velocity. In this article we will see what's time dilation due to gravity and how it is caused.

When light moves against a gravitational field caused by any massive body, its energy decreases. We know that energy of an electromagnetic wave of frequency 'µ' is given by E=hµ where ‘h’ is the plank's constant. So, from this equation we get that energy of an electromagnetic wave is directly proportional to its frequency. This means as the light moves up in a gravitational field, it energy goes down causing its frequency to go down as well.

You must be familiar with the equation v=λf. It gives us the relation between the velocity of a wave ‘v’, its frequency ’f’ and wavelength ‘λ’. Now here comes the role of special relativity. Special relativity states that the speed of light just like any other electromagnetic wave is constant or absolute for all observers no matter where they are or in what speed they are moving. So, in the equation stated above, the velocity 'v' becomes constant. As a result we get that the frequency 'f' is inversely proportional to the wavelength 'λ'. So, as the frequency of the light moving against gravity decreases, it wavelength increases.

We know that f=1/t, where 't' is the time period of oscillation of the wave. So the above equation can be rewritten as v=λ/t. Now, as 'v' is constant (as proved earlier), we get that wavelength is directly proportional to the time period. So, as the wavelength of the light wave moving against gravity decreases, the time period of oscillation of the light wave increases.

So, when a light wave (coming from an event near the source of gravity) with lower time period reaches an observer who is far away from the source of gravity, it would appear to him that the event is taking more time to happen. In other words, it will appear to him that the time has slowed down at the place and everything is taking longer to happen.

This strange effect he would be observing is nothing but time dilation which, in this case, is caused by difference in gravitational field intensity for the observer and the event.