General Relativity IV: The True Nature of Gravity Part 2

Hello, and welcome back to MPC! Last week, we discussed why the bending of light is so strange. Today, we will talk about discoveries (made by Einstein) that make this phenomenon a little more believable. Get ready — things are about to get weird!

We have already discussed the formula that Sir Isaac Newton developed to describe gravity (see last week’s post):


Recall that, in this equation, F is the force of gravity, G is a constant, M is the mass of the “source” of the gravity, m is the mass of the “recipient” of the gravity, and r is the distance between the centers of the “source” and the “recipient” of the gravity (that’s a mouthful!). The impact of Newton’s formulation of gravity cannot be undermined (even considering what we discussed last week and what we will be discussing today). Newton’s work revolutionized physics and was able to sufficiently describe our universe for hundreds of years. Nonetheless, we have already discovered a problem with it: it cannot describe the bending of light!

This is where Einstein comes in. Although Newton’s formula for gravity accurately predicted the phenomena observed in his day, that’s really all it could do: it was nothing more than a formula. For hundreds of years, most people simply discounted gravity as a truth: two objects will attract each other, that’s just how it works! However, when Einstein realized the problems with Newton’s formula, he sought to understand the true nature of gravity: why does gravity work the way it does?

This was no simple feat. In fact, it took Einstein, one of the greatest minds of all time, 10 years to describe what he wanted to describe. 10 years! Regardless, many would argue that it was well worth the effort as it led to one of the most amazing discoveries of the 20th century: spacetime is a trampoline!

Alright, spacetime is not exactly a trampoline. Nonetheless, this analogy sums up Einstein’s discovery very well.

As a side note, some of you may be aware of the limitations/drawbacks of this analogy. Please keep in mind that we are not looking for a rigorous understanding of Einstein’s discovery — we are just looking for a conceptual one, and this analogy is perfect for that.

A few weeks ago, we talked about spacetime. Recall that spacetime is simply the ideas of space (distances, lengths, etc.) and time mixed together. For now, we are going to discuss how space is like a trampoline (we will get to time soon).

Let’s imagine empty space:


Figure 1: Empty space

That was easy enough! We have to be careful though: this picture represents our typical notion of space. According to Einstein, space is a little different (a trampoline):


Figure 2: Space as a trampoline

**Note: This is the side view of a trampoline. In other words, if you were to stand outside of a trampoline and kneel down so the surface of the trampoline was at eye level, this is what you would see.**

Right now, the trampoline in Figure 2 represents empty space (notice that there is nothing on its surface). We know that this is not an accurate representation of spacespace contains many, many different “objects.” For instance, where is the Sun in Figure 2? It’s not there! Let’s place it on the trampoline:


Figure 3: The Sun on a (very strong) trampoline

That’s strange: the trampoline (which represents space itself) has curved. Believe it or not, this is actually what happens in space (and not just outer space: in your house, in the park — anywhere)! Einstein discovered that objects like the Sun completely warp space! It may be hard to believe, but this warping of space is gravity . To phrase it differently, what we think of as gravity is just an illusion for the warping of space.

Why does this matter to us? Well, let’s think about why the Earth orbits the Sun. Of course, we are tempted to say the force of gravity (i.e. the force pulling the Earth towards the Sun) is the cause of Earth’s orbit around the Sun. However, right now, this answer is insufficient. Why? Recall that we are trying to understand gravity at a fundamental level, and, according to Einstein, what we call the force of gravity is just the warping of space in disguise. That begs the question — can we describe the Earth’s orbit just by using the warping of space?

We can! Imagine that we have the Earth on our trampoline, and we push it towards the Sun:


Figure 4: The Earth moving towards the Sun

**Note: The red arrow represents the direction of motion of the Earth. Of course, the Earth did not actually start orbiting the Sun by being rolled towards it. However, as you will soon see, this is an interesting way to think about Earth’s orbit. Additionally, although it cannot be illustrated in this picture, the Earth is not actually being pushed directly towards the center of the Sun in this analogy. This will be illustrated in more detail shortly.**

The Earth will get caught in the pocket created by the Sun and actually start orbiting it! This may be hard to picture, and my drawing abilities are limited, so here is a brief video clip that demonstrates this idea. In the video, the rock at the center of the “trampoline” represents the Sun and the marble represents the Earth. **Note: As is explained in the video, the marble orbiting the rock loses energy rather quickly and eventually hits the rock. Luckily, this does not happen to the Earth!**

That’s pretty amazing! We can take this warping of space even further: we can explain why light bends around the Earth (or any object with mass in space). We can picture just the Earth by itself (for simplicity) on the trampoline:


Figure 5: The Earth on our (very strong) trampoline

Let’s say that a photon of light comes passing by:


Figure 6: Light moving towards the Earth

**Note: The red arrow represents the direction of motion of the photon. As was the case in Figure 4the photon is not actually being pushed directly towards the center of the Earth.**

The photon in Figure 6 will enter the “pocket in space that surrounds the Earth (just how the Earth entered the “pocket in space” that surrounded the Sun in our previous scenario).

Unlike the Earth does with the Sun, the light will not actually start orbiting the Earth. However, the effects of Earth’s warping of space will certainly be felt by the photon and causes it to follow a curved path (you can picture rolling the marble from the previous video very fast so that it curves around the rock at the center a little, but ultimately flys off of the table). This creates the phenomenon that we have been discussing for the past two weeks (in this post and this post):


Figure 7: The Earth “bending light

**Note: Unfortunately, I do not have the tools necessary to draw this phenomenon using the trampoline analogy.**

To summarize, a mass in space completely reshapes space itself. There is no way for an object (such as light) to avoid the warping of space created by, say, the Earth. Why not? Because everything travels through space(time), even light! Imagine a pebble in a body of water approaching a whirlpool:


Figure 8: A pebble moving towards a whirlpool

**Note: The red arrow represents the direction of motion of the pebble.**

The pebble cannot jump over the whirlpool — it is traveling in the water (not in the air)! There is nothing it can do! It will eventually be sucked in by the whirlpool:


Figure 9: A pebble being sucked into a whirlpool

**Note: The black dashed arrows represents a possible path the pebble may follow as it gets sucked in by the whirlpool.**

Just how the pebble will ultimately be influenced by the whirlpool (i.e. sucked into the whirlpool), anything traveling past the Earth (including light) is traveling through space and will, therefore, be influenced by the Earth’s warping of space.

(For some of you with more physics knowledge, you may not like the trampoline analogy: our intuition that an object would follow the curvature created by another object on a trampoline comes from our notion of gravity! Not only that, but the only reason why objects on a trampoline warp the trampoline is because of our notion of gravity! It may seem like we are going in circles. However, do not forget that this is simply an analogy. The real reason why objects in space follow the curvature created by other objects and why objects warp space to begin with can be explained by higher-level geometry and mathematics. If you are interested in this, I would suggest reading the article linked to at the end of this post as a starting point)

So, we now understand how objects can influence the nature of space itself and “create” what we typically call gravity! Didn’t I originally say that objects warp spacetime? How do they affect time?  That will be the topic of next week’s post. See you then!

For more information, be sure to check out this resource:

(featured image:


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