Thursday, October 10, 2024

General Relativity for Kids

To understand relativity, we first need to have a brief idea of physics by my friend Newton. In his book Principia, Sir Isaac Newton explained that gravity is a force that pulls two objects toward each other. For example, Earth's gravity pulls everything towards the ground.

On Earth, gravity makes objects fall with a rate of 9.8 meters per second squared (9.8m/s²). It means that if you drop something, its speed will get faster and faster due to gravity.

Newton also thought of a simple way to think about how much force gravity pulls objects:

          		 Force = Mass * gravity
                 	 Force = Mass *  9.8m/s²

So, if you know the mass of an object, which is the matter inside it, and you multiply it with the acceleration provided by Earth, which is 9.8m/s², you will get the force on the body by Earth.

For example, when you step on a scale, it tells you your weight. Let’s say it shows 80 kg. That number comes from the force of gravity acting on your mass. So, your actual mass is how much matter makes up your body, while your weight is how much gravity is pulling you down.

The rate of increase in speed can also be defined as acceleration. For example, when an object falls due to gravity, its speed keeps increasing, which means it’s accelerating. On Earth, the acceleration caused by gravity is 9.8 m/s²—this is why objects fall faster and faster the longer they’re falling.

If there were no gravity, you wouldn’t have any weight! The scale would show zero because there’s nothing pulling you toward the ground. But to be more accurate, there wouldn’t be anything pushing you, like when you are standing on the ground. This is why you will feel weightless—there’s no gravity pulling you down and no surface pushing back up at you. It’s the same feeling astronauts get when they float in space!

Now, let’s do a thought experiment. Imagine you are falling from a great height. What would you feel? You will feel weightless as there isn’t any ground pushing you from beneath. It is the same as what astronauts feel in space stations. Now, let’s imagine you’re inside a rocket ship that’s accelerating upwards at 9.8 m/s² (the same rate as Earth’s gravity). Even though you’re not on Earth anymore, you’ll feel the same force pushing you down as you would if you were standing on the ground! Why? Because the rocket’s acceleration is creating the same sensation as gravity.

This thought experiment shows something very important that my friend Einstein realized: the effects of gravity and acceleration are basically the same. Whether you are standing on Earth or you’re accelerating in a rocket, the force you experience is the same. Einstein realized that gravity and acceleration are two sides of the same coin.

So now, another question arises: how will we know whether we are on Earth or in space? If there isn’t any window to peek through, while you are thinking about it, let’s do another thought experiment. Let’s go back to that rocket and this time let’s imagine the room we are in is very long with the wall really far from where you are standing. You take a torch and flash it towards the wall in front of you. Since the whole room is moving with very high speed, the light won’t follow a straight line; rather, it will take a small curve. But this seems to contradict the idea that light always follows the shortest path. We have observed on Earth that light always moves in a straight line since that is the shortest path. This seems to violate the principle of equivalence, which says that the effects of gravity on Earth should be the same as the effects of acceleration in the rocket. If gravity and acceleration are the same, the behavior of light should be the same in both cases.

My friend Einstein was as confused as you are right now. But then he thought and thought, almost for 10 years. Suddenly, an idea popped into his mind: What if light is following the shortest path, but that path isn’t a straight line? Thinking about it, he realized that Earth isn’t flat; it’s more of a curve. Still, we can see light from far away. If light were to travel straight from the Earth’s surface, it would only go in a tangent, and an observer far away would never see it. But we know for a fact that we can observe light from great distances.

So, what if light is actually bending because of the influence of gravity?

Einstein started to find an answer to this question.

Einstein began to imagine that just like the Earth curves, space itself might be curved too. And if space is curved, then light, which travels through space, could follow a curved path. This was a huge breakthrough! He realized gravity can bend light, just like Earth bends space around it. This is what we call gravitational lensing, when light bends due to the influence of massive objects. He realized that the effects of gravity on light were the same as acceleration. The only difference was that gravity was curving space itself, and acceleration was just pushing things through curved space. Both were doing the same thing: bending the path of light. And that’s why light seemed to bend in an accelerating rocket.

My friend was a genius, but still, it wasn’t possible for him to explain his ideas mathematically. He contacted an old friend of his, Marcel Grossmann. Marcel Grossmann had finished his PhD on the geometry of curved spaces (Riemannian Geometry), which is just a fancy way of saying he knew how to find the area of a circle in curved space! With his help, he figured out the mathematics of curved spacetime. This curved spacetime is really the basis of general relativity.

What is Spacetime?
Spacetime is the idea that space and time are not separate things but are connected as one. Imagine space as a stretchy fabric, and time as the ticking of a clock. When something heavy, like a planet, sits on the fabric, it bends both space and time around it, causing objects to move differently. This bending of space and time is what we feel as gravity

We need to understand that in Newton’s model, gravity is a mysterious force between two objects separated by space. Newton didn’t say that gravity affects spacetime; rather, he based his model on the consideration that space and time are absolute and gravity works within it.

While Einstein said that gravity isn’t a force between two massive objects, but something that emerges from the interaction of objects and massive objects.


“Space-time tells matter how to move; matter tells space-time how to curve.”

Another way to understand it is the trampoline analogy.
Imagine a trampoline with a heavy ball in the center. The ball creates a curve in the trampoline surface. If you roll a smaller ball (like a marble) near it, the marble will move toward the heavy ball because of the curve.

In this analogy:
• The heavy ball is like a massive object (e.g., the Sun).
• The marble is like a smaller object (e.g., Earth).
• The curved trampoline represents curved space-time caused by the mass.

Einstein showed that gravity isn’t a force pulling objects directly, but rather objects move along the curves in space-time caused by mass. This simple model helps explain how objects follow curved paths in space-time due to gravity.

The picture above gives us a brief imagination of the bend, but it isn’t accurate as the bend happens in 3 dimensions.

So, thanks to Einstein, we now understand that gravity isn’t just a force pulling objects together. Instead, gravity is the way mass curves space and time. Just like how a ball can roll towards the curve in a trampoline, planets, stars, and even light bend around massive objects because space itself is curved.
Einstein’s theory of general relativity changed the way we see the universe. It showed us that everything in the universe, from falling apples to distant stars, moves in curved space-time. And even though these ideas might seem strange, they have been proven by experiments and observations, like how light bends around the Sun.

Thanks to this genius, we now have a deeper understanding of how our universe works. And who knows? Maybe one day, these ideas will help us discover even more amazing things about space, time, and gravity. Or who knows, Einstein was wrong all along and someday we will find a better explanation—that is the true beauty of physics.


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General Relativity for Kids

To understand relativity, we first need to have a brief idea of physics by my friend Newton. In his book Principia , Sir Isaac Newton explai...