The revelation of the relative nature of time or the theory of time dilation is the greatest revelation of the early twentieth century. This transformed the whole concept of time as people understood.
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What is time dilation?
The time you observe may not be the same as I do. I may get older faster than you or it may be another way round, irrespective of the day we were born. So, time is a relative quantity and time can run slower or faster according to our velocity or the gravitational force of the heavenly body which we live in. This concept is known as time dilation.
The birth of the concept of time dilation dates back a little before the twentieth century, during the late ninetieth century. But Albert Einstein’s special theory of relativity established it and it became popular. This theory had a concept, velocity of light in a vacuum is constant throughout the Universe. This led to it, the extraordinary revelation about space and time which later formed space-time.
Further, general relativity extended the realm of time dilation from relative motion to the gravitational field. Both of these types of time dilation are completely different from each other.
The theory of time dilation
The theory of time dilation says that time is a relative quantity. This means that measurement of time between two distinct events by two different observers depends on the gravitational field in which they are and velocity with which they are travelling.
This is absurd right! Generally, we think that all of us exist to observe the same time. But this is true because we live on Earth, a common gravitational field and our velocities are very less as compared to the velocity of light. If we travel in space with greater velocities and a place with higher gravitational field, the picture is different. This reminds me of movie Interstellar in which father is in his youth while his daughter is more than 100 years old.
Relative motion dependent time dilation
The theory of time dilation can be mathematically proven by using Lorentz transformation, a mathematical observation of time and space from moving reference points. From it, time is multiplied by a velocity-dependent quantity called a Lorentz factor for a reference frame. This factor is nearly one when the velocity is less, yielding no such difference in observation of time. This is velocity-dependent time dilation.
For example: consider someone older than you. Send him/her to a space flight with speed equal to 90 per cent of the speed of light. If you see him/her return after 365 Earth days in your time, he/she would have spent time equivalent to nearly 160 Earth days mathematically. Both of you may argue about your own individual time being correct but both of you are correct instead. This is how velocity-dependent time dilation works.
Gravitational time dilation
This theory of time dilation corresponding to the gravitational field came a little later. This was one of the major achievement of the general theory of relativity. It shades light upon the ability of the gravitational field to introduce curvature in space-time which can produce a redshift. Redshift is generally seen due to relative motion, a star going away from us appears red. Gravitational field can also produce such effect called gravitational redshift.
So, this ability of gravitation to bring change about space-time as relative velocity resulted in gravitational time dilation. As a result, it can be concluded that the clock runs much slower in a greater gravitational field. This can be mathematically calculated by a formula presented here.
Gravitational time dilation thus suggests that the person living in different planets with different gravitational field will measure time differently. Suppose your friend goes to live on a planet which has acceleration due to gravity and radius 1000 and 10,000 times greater than that of Earth respectively. 365 Earth days would appear to your friend as nearly 210 Earth days.
Of course, the gravitational field must be very large to see effects very distinct, as if observable to us. So, these theories can be proved only by using very highly precise instruments.
Experimental Evidences in the Modern World
Theories need proofs. This theory of time dilation has been proven many times by different experiments. For instance, time dilation due to relative motion can be explained by the muon decay experiment. Muon, an elementary particle, originated from the collision of cosmic rays with atmospheric particles lives longer than their expected life. This is because muon is travelling at high speed so that time slows down for it.
The gravitational time dilation was proved experimentally by observing the time pulse from a rocket falling freely from the height of 10,000 kilometres. The gravitational was observed and calculated. Also, gravitational redshift experiment can provide a proof of a gravitational effect on space-time.
Although the theory of time dilation does not have a vivid significance to a layman, since it is not observed in our daily world, it is the greatest revelation to mankind. It has helped to improve the accuracy of different experiments and made us know the world in a better way. If only we could dilate time as per our will, we can live a lot longer than we are too.