Time slowing down: A glance at gravitational time dilation

-“A glance at gravitational time dilation” written by Kananika

The question might arise, what exactly is a black hole? Wald (1984) describes a black hole as a region of spacetime where gravity is so strong that nothing, including particles or even electromagnetic radiation such as light are able to escape from it. The general theory of relativity presented by Einstein predicts that a sufficiently large mass could collapse within itself to deform spacetime, and form a black hole. To give you an estimate, this “sufficiently large mass” is approximately 21 billion times the mass of our sun.

At some point in our lives, all of us have wanted time to slow down. We have wished to cherish the moment a bit longer, feel ecstasy for a bit longer. But we know that is not possible. Ever since the dawn of time, human beings have always understood that time is constant, that everybody has 24 hours in a day. Those who utilize those hours to the fullest, are successful; others perish. Time has always been considered to be the ultimate god. Another fascinating structure, out in the universe, is the black hole. An essence of mystery, curiosity and fear surrounds the word. It is known to be “impending doom” for anybody who gets too close. A black hole is a point of no escape.

Black Hole

To understand the concept of time dilation, that is, time slowing down, we need to understand a few related concepts first. Firstly, “spacetime” refers to the three dimensions of space, length, breadth and height and finally describes the fourth dimension to be time! As described earlier, gravity as strong as near a black hole creates a bend in spacetime. This is not just the case for black holes. In fact, our Earth also creates this bend. The earlier understanding of Newton’s Gravity has now been replaced with Einstein’s Gravity, which describes Gravity to be an after effect of this bend in spacetime. To describe this bend, imagine spacetime to be a stretched sheet. Now, drop a heavy ball into the middle of the sheet. The sheet bends tangentially to the ball. If you drop another small ball near the edge of this sheet, it gravitates to the big ball. This big ball is thus the centre of gravity! All celestial objects are these balls, with numerous sheets of bent spacetime around them.


This concept is important to understand, to understand one simple fact, that is, time is not constant. Just like the other three dimensions, time can be stretched, compressed, or bent at the mercy of the universe. Christopher Nolan, the director of movies like Interstellar, has always been praised for his brilliance in addition to scientific accuracy. In Interstellar, we watch Cooper spend about 2 years in outer-space to come back to see his young daughter Murphy to be an old woman. If you dismissed this incident considering it to be fiction, we are here to tell you that it isn’t entirely fiction. That is exactly what gravitational time dilation means!

To put it into simple words, as you get closer to the gravitational centre, or the “big ball”, slower your time goes in reference to a distant observer who is not under a gravitational influence. The curiosity might arise again, how does this happen? To understand this, we need to look at another concept. We need to understand that if there is truly an universal constant, it is the speed of light. Everything else is relative. To understand this, let us consider another analogy. Consider that you are standing on the road, and you see a car pass by at the speed of 40 kmph. As you are standing, your speed is 0 kmph. Thus, for you, the car’s speed is 40 kmph. Consider another situation where instead of standing on the road, you are in a car going at 30 kmph. A car overtakes you, whose speed is 40 kmph. However, for you, this car’s speed will be 40-30 that is 10 kmph. This is what relativity means. This example explains the fact that speed is relative, that is, it depends on where you are observing it from.

However, the above analogy does not hold true when we consider a photon, a particle of light. A photon is unique, such that it has no mass. Its speed in vacuum, 3,00,000 kmph will stay the same, irrespective of your reference frame, irrespective of where you’re looking at it from. Your speed could be 99% the speed of light, or you could be stationary, but light’s speed stays the same. Moreover, as long as you have mass, you can never achieve the speed of light. This is what it means when we say that the speed of light is constant and it is the universal limit, as no object with mass can go faster than light.

But… that doesn’t seem correct, right? If the speed of light is constant, how does it fit into the General theory of relativity? Well this is because, in such cases, time becomes relative! Speed cannot change according to reference point, so something has to change. In such cases, it is time. This whole discussion has been in an attempt to prove that time is not constant, instead relative. To give you real life examples to discuss this better, I am going to give you two instances where we see time dilation. Firstly, let us consider the Earth to be the gravitational centre. Atomic clocks, known for their definite accuracy, have been experimented upon. Placed at different altitudes, they have shown a difference in the passage of time. By nanoseconds, the one at a lower altitude runs slower than the one at a higher altitude. This is solid proof of gravitational time dilation, as lower altitudes mean that the clock is closer to the Earth, and that is why it is slowing down.

Coming to the second instance, let us go back to the black hole. As you approach a black hole, a brutal fate awaits you. Under such a strong gravitational force and a bend in spacetime, every atom in your body will be pulled and you will undergo “spaghettification”, which is exactly what it sounds like. For you, you will speed into the black hole and never be able to come back. However, here is the paradox. Each nanosecond for you, might be equal to several years for someone observing you at a distance. This is because, as you approach the black hole, your time slows down for a distant observer.

The event horizon is the boundary of the blackhole where we see a curved ray of light. From inside the event horizon, even photons cannot return, thus there is no way to observe what happens beyond the event horizon. The event horizon is the limit to what we know. As you approach the event horizon of the black hole, time further slows down such that for a distant observer, it becomes zero. Thus, paradoxically, while you are speeding into the black hole and undergoing spaghettification, for a distant observer, it will theoretically take you an infinite time to fall into the black hole! In simpler words, your time has slowed down to the extent that the distant observer will not be able to see you move in his entire lifetime. You’ll gradually fade for the observer watching you.

However, it is important to remember that time slows down only relative to a reference point. Irrespective of whether you are in space or on Earth, it will still take you five minutes to shave according to your watch. However, my five minutes might not be equal to your five minutes, because of a difference in our time frames. Gravitational time dilation is a complex concept, and black holes are even more, and in spite of trying my best, I will not be able to explain it all into words here. I do hope that I was able to introduce you to the concept. I also hope that the next time you wish for time to slow down, you smile at the fact that maybe for an observer in space who’s looking at you, it has indeed slowed down.

In the words of Auguste Comte, “Everything is relative, and only that is absolute.”

Please let us know in the comments if you would like to explore a particular concept in this article more, or if you have any questions!

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