Time Dilation Explained

Albert Einstein delivered two major blows to the established order of physics, through his presentation of the theories of special and general theory of relativity published in 1905 and 1915. While special theory of relativity unified, space and time into a single entity, general theory of relativity showed gravity to be an effect of the curvature of space time. Albert Einstein first destroyed Newton's idea of an absolute time and then, went on to show the flaws in Newton's theory of gravitation, by presenting the general theory of relativity in 1915. This theory showed that matter bends or warps the space time around it, and motion of objects is affected by this curvature. Special and general theory of relativity are two separate theories. One described the motion according to inertial frames of reference, while the other deals with the equivalence of accelerated frames and gravity. One phenomenon that is commonly predicted by both theories is time dilation.

Special Relativity Based Time Dilation

Special theory of relativity is based and derived from two very basic postulates. One states that the speed of light is constant in vacuum and unattainable, while the other postulate states that the laws of physics should remain exactly the same in all inertial frame. An inertial frame is any frame that is moving at a constant velocity with respect to a fixed frame or is at rest with respect to it.

Now consider a guy sitting in a space ship, which is moving at a constant velocity in a specific direction with respect to a fixed frame, with no other forces acting on it other than the space ship's own propulsive force.

Then the time dilation principle states that time will slow down for the space ship, with respect to the time associated with the fixed frame. The larger the velocity of the space ship, more will be the dilation of time and slower will be the time for the space ship. This effect is quantified by the following equation:

Δt' = Δt / √(1 - v² / c²)

In this physics formula, Δt' is the time interval for a person on the space ship, while Δt is the time interval for the rest frame of reference. Here v is the constant velocity of the space ship and c is the speed of light (3 x 10⁸). Thus the above equation states that the faster space ship moves, slower will be its clocks running. This is a consequence of the fact that time is relative and local in nature and not absolute for all! To know how this effect is derived, you must study special theory of relativity in greater detail.

Gravitational Time Dilation

The phenomenon of time dilation due to gravitation is a bit more difficult to grasp and a full understanding will require that you study general relativity. So here, I purely explain the phenomenon but to know why it happens so, you will have to go deep into general theory of relativity.

The basic idea is the following. Time slows down in presence of a gravitational potential. The closer an object is to a gravitational potential, slower will time be for it. Thus, for a satellite moving in orbit around the Earth, a clock will be faster, compared to a clock on the Earth's surface!

The gravitational time dilation equation will vary according to the space time geometry and therefore the degree of dilation will entirely depend on the degree of bending of space time caused by a massive object. The space time around a black hole is supposed to be so extremely warped, that time virtually comes to a standstill for an object observed falling into it!

To know these things in more details, you have to deeply explore and understand the special and general theory of relativity. One of the best introductions to special relativity is the book 'Spacetime Physics' by Taylor and Wheeler, which is highly recommended reading, if you want to explore the beautiful and astounding theory of special relativity. For understanding the general theory of relativity, you will need some mathematical expertise in differential geometry and tensors. A good place to learn it from is 'Spacetime and Geometry: An Introduction to General Relativity' by Sean Carroll. However, know that this is an advanced physics text and will take some hard work to understand. I can assure you that it will be all worth it!