All you need to know about time dilation!

Theory of relativity series

Posted by Apoorva Patil on Jan 08, 2017

The legendary physicist of all time Albert Einstein changed the landscape of physics forever when he worked out & mathematically proved the Theory of Relativity. He actually did it in two instalments! Namely, The Special Theory of Relativity in 1905 and The General Theory of Relativity in 1915.

You can google about them for definition, formula & stuff ;) Since my intention here is to discuss the implications of TOR. It majorly predicts the behaviour of Space, time, light & gravity and how they interact with each other.

Discovery of Space-time

Time and space! It is finally established that they are inseparable. They together make up the fabric of reality as we perceive it. The biggest discovery of the 20th century was that time is embedded in space itself, that time is integral part of the space & hence the fourth dimension.

Part I: Time Dilation.

Time Dilation can be simply put as the phenomenon of difference in the rate of passage of time for two observers moving relative to each other and located at different points in space-time.

1. Time dilation due to relative velocity.
2. Time dilation due to relative gravity.

1. Time dilation due to relative velocity:

This can be simply put as the phenomenon of slowing down of the passage of time for the observer who is travelling at very high speeds in space-time (Or simply space with time considered as its 4th dimension), compared to the one who is travelling at very low speeds relative to speed of light

The speed of light in vacuum (Read: empty space) is a universal constant, which is 186000 miles/sec or about 3 lakh KM/sec. In other words ‘one second’ can be defines as the duration of time required for the light to travel a distance of 186000 miles.

Now remember, all measurements are relative. You can only measure something with respect to something else. In other words you cannot measure something without a frame of reference.

Since the light speed is a universal physical constant, the space and time bends itself in such a way that the speed of light remains 186000 miles/sec for all observers, in other words light should be able to travel a distance of 186000 miles in one second.

Now let’s say I am standing at a certain point in space. A beam of light emitting from a street light is travelling at 186000 miles/sec with respect to my speed in that same space. Now I start running at a speed of 93000 miles/sec that is at half the light speed. Now for me, the relative speed of light should be 93000 miles/sec. But it is not! It remains unchanged at 186000 miles/sec. It turns out that the passage of time at my location (space-time) is slowed down by 50%!

The light actually took two seconds to make up the relative speed to 186000 miles/sec again, but since the passage of time slowed down at that point in spacetime, those two seconds actually became only one second for me during which light travelled 186000 miles.

So for another stationary observer (Say my younger brother) who is looking at this whole drama from a different point in space time, two full seconds have passed since for him relative speed of light remains 186000 miles/sec

As I approach the speed of light time slows down dramatically for me as observed by my brother & I don’t feel a thing. By the time I spend one day at my time machine travelling near the speed of light, my brother would have aged years!

Theoretically if you reach the speed of light, the time shall stop for you! (How awesome that would be when someone says ‘time waits for none’ & you say LOL in their face!!) For the passage of one second of time at that location in spacetime, light should be able to travel 186000 miles as measured by you. Since you’re already at the speed of 186000 miles/sec and light cannot go any faster, the only option left for the universe is to stop the passage of time itself at your location in space-time so that the time taken by light to travel 186000 miles will be exactly one second as measured by you and that one second will take literally forever to pass!

In practice It is impossible to reach the speed of light due to the limit set by Einstein’s famous E=MC2. As you approach the speed of light the energy required will be infinite to move further.

2. Time dilation due to relative gravity:

Similar to the previous case, here time slows down near objects with heavy gravity compared to other locations with relatively less gravity.

This is because some gravitational pulls such as the gravity of black holes are so strong that even light cannot escape them! Similarly other bodies with considerable gravity slows down the light that it cannot complete 186000 miles sprint in one second. So time again gets slowed down in that location allowing the light to complete 186000 miles in one second as measured by all observers! This is what happened in the climax of interstellar!

Time dilation & GPS:

Relative velocity: Time runs slowly for satellites since they are moving at high velocity compared to GPS devices on earth

Relative gravity: Time runs slowly for the objects in stronger gravitational fields (GPS devices on surface of earth) compared to the ones in weaker gravitational field (GPS satellites in orbit).

For GPS, the effect of relative gravity is much higher than the effect of relative velocity. Hence, time runs faster in GPS satellites compared to GPS devices on earth. It will be continuously adjusted to maintain the accuracy. Without this adjustment the error would be in miles!

There is one more phenomenon called length contraction, which also contributes to maintain the speed of light at the universal constant, which I shall discuss in the Part II.