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

*space*—

*space*contains many, many different “objects.” For instance, where is the Sun in

**? It’s not there! Let’s place it on the trampoline:**

*Figure 2***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 4***, **the photon is not actually being pushed directly towards the center of the Earth.***

The *photon* in ** Figure 6** will enter the “

*space*” that surrounds the Earth (just how the Earth entered the “

*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 space**time***?* *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: http://www.thephysicsmill.com/2015/08/15/general-relativity-is-the-curvature-of-spacetime/*

(featured image: https://media1.britannica.com/eb-media/99/145399-004-D2A75556.jpg)