# The General Relativity Rabbit Hole: Unraveling Space, Time and the Fourth Dimension

Parsing Albert Einstein's theory of our universe -- an idea that's utterly mind-bending, yet seemingly shatterproof.

More than a century ago, Albert Einstein conjured the hypothesis of all hypotheses -- an idea so extraordinary it would relentlessly echo through the vast directory of human thought. It would alter the fundamental tenets of science, inspire the most mind-bending technology, help capture the glory of black holes, motivate authors to write prodigious novels, and stimulate directors to turn deeply metaphysical ideas into film.

It was a concept that would test the limits of our imagination and a puzzle that would force us to rethink the notion of time.

In 1916, Einstein announced his holy grail theory of general relativity.

## The condensed version

Basically, Einstein realized that space is much more than the "space" we live in and that time transcends the clocks we've invented. Rather, he theorized, the two are physically entangled.

Space is like a canvas on which our past, present and future are woven -- and it can fold, twist and ripple like silk. There's no beginning or end to this fabric of space and time, or as he called it, spacetime.

We can't exactly *see* the spacetime continuum because it's part of a realm imperceptible to human eyes: the fourth dimension. But we can deduce its existence, as we can feel its effects. One of those effects you're no doubt familiar with -- gravity. But there are other effects too, like time moving slower depending on where you are in the universe and space-borne magnifying glass phenomena dubbed gravitational lensing.

But I'm getting ahead of myself. It's no problem if pretty much all of that flew over your head.

Regardless of when your indoctrination to general relativity camp was -- even if it was five seconds ago due to my jam-packed intro -- I'd bet you thought it sounded bizarre. I mean, it involves premises like the fourth dimension and an invisible fabric. It projects weird outcomes like wormholes and nonlinearity.

You wouldn't be alone in your skepticism. General relativity was once dismissed as delusion, "totally impractical and absurd." Yet, it remains one of the most elegant theories concerning our universe.

So much so that it's often considered an unbreakable truth.

## Welcome to the fourth dimension

As three-dimensional beings, we tend to think about the universe in intuitive terms.

A one-dimensional object makes sense to us. That's a line. Two dimensions are also easy to understand. Pac-Man. And three dimensions -- tulips, Tic Tacs and iPhones -- are all comprehensible. But when we get to the four-dimensional universe, our intuition disappears.

In 3D, we have an X axis for length, Y for width and Z for depth. In 4D, there's a fourth axis: Time.

But trying to think about 4D space, for us, would be like Pac-Man trying to understand 3D space. That would hurt his brain because there isn't a Z axis for Pac-Man like there isn't a time axis for us. Technically, Pac-Man's view of everything would be a giant line, similar to that of characters in the novel Flatland.

However, Pac-Man's difficulty with perceiving 3D space doesn't mean 3D space can't exist. We're living in it. In fact, *he's living in it. *

Likewise, 4D space exists whether or not our minds can enter it. We even call on the time axis unknowingly when we ask someone to meet us in a coffee shop at 2 p.m., for instance. We give X, Y, Z and time coordinates.

So as you read this, remember that everything we're about to discuss regarding general relativity lives in 4D. Fortunately, even though we can't mentally picture the fourth dimension, we can mathematically calculate it.

## The elevator experiment

You've probably heard the age-old adage that Isaac Newton was sitting underneath an apple tree when a delicious fruit fell onto his head, and voila, he discovered the mysterious force of gravity pulling stuff down to Earth.

Einstein had a (very) different take.

In a nutshell, Einstein realized gravity isn't quite as mysterious as it's chalked up to be. It's a lot like a regular old force we *are* used to. We use it nearly everyday -- driving to work, running around, or perhaps kicking a soccer ball. It's called acceleration.

Einstein's famous elevator thought experiment helps illustrate this connection.

Imagine a nonmoving elevator on Earth and an accelerating one somewhere in space, traveling upward with a force *exactly equivalent *to the force of gravity (9.8 meters/second^2). If there weren't any windows on these elevators, how could you tell if you were in the space one or the Earth one?

Well, Einstein said, you couldn't.

Modifying that a little, what if you had to figure out if you were in a non-windowed elevator that wasn't moving in space and one on Earth that was falling, so you were experiencing weightlessness? Could you then? Nope.

Weightlessness on Earth in the presence of gravity feels just like weightlessness in space in what we'd normally consider zero-gravity.

This is called the equivalence principle.

So, the only plausible explanation for "gravity," Einstein said, is it isn't what we think it is. And, whatever it *really* is, probably has something to do with acceleration.

Then, after a little (no, a lot) more thinking, he concluded that gravity is not a force at all. It's the product of objects interacting, while accelerating in different directions. OK, let's back up a little bit so our brains don't explode.

Here's one way to think of Einstein's conjecture: Things aren't pulling things down; things are holding things up.

## You're falling right now

If a ball were rolling toward a cliff, Newton would say the ball was about to stop moving in a straight line because gravity would pull it down. To Newton, the ball would soon fall off the cliff because of an elusive gravity force.

Einstein, on the other hand, would say the ball has always been falling -- it's just that we only notice such "falling" when it passes the edge of the cliff because that's when nothing will be pushing, or accelerating, *up* on it anymore. Bear with me. Here's an analogy.

Imagine holding a glass of water. The glass, in a way, is constantly stopping the water from falling to the ground. You probably wouldn't say the glass is exerting an invisible force on the water to pull it down, right? It's the same idea. General relativity just takes it a step further.

You're falling right now. You just can't tell because the chair you're sitting in is stopping you from reaching the ground. The floor of your room is stopping you and your chair from reaching the Earth. And the literal Earth is stopping you, your chair and your floor from "falling" through space.

Everything is always in a constant, natural free fall, Einstein realized, yet sometimes that free fall is interrupted. And such interruption, to us, feels like the force of gravity.

It's all... wait for it... relative.

OK, you might still be on that bit about Earth stopping you from falling through space. If Earth weren't there, wouldn't we be floating around like astronauts on the International Space Station?

This brings us to part two of general relativity: The oceanlike fabric of spacetime sort of redefines the notion of falling. Brace yourself, things are about to get trippy. The next thought experiment might seem unrelated to what we've just discussed, but trust me, it'll come together.

## The gravity trampoline

Picture a trampoline.

If we put a bowling ball into this trampoline, it'd roll to the middle and make the stretchy material warp inward. Now imagine putting a marble onto this curved fabric. It'd roll down the curve and stick to one side of the bowling ball. The trampoline is the fabric of spacetime, the bowling ball is Earth, and the marble is you. And once again, I'm scaling the fabric of spacetime down by dimensions because we can't really conceptualize the fourth.

Anyway, according to Einstein, anything in the universe with mass warps spacetime sort of like the bowling ball warps the trampoline. Black holes warp it a whole lot, Earth warps it somewhat, the moon warps it a bit and even you warp it a teeny tiny amount. The more massive the object, the greater the warp. And the greater the warp, the stronger the "gravity."

Now imagine that each grid-line in this image is a cable line that has a car, within which some item is traveling.

This item is always "falling" along the line. If Earth were removed from this picture, the cable line would be straight, so the item would move in the direction we consider "forward." But there's Earth, denting the cable line inward and bringing the object on that line along with it.

So, if space didn't have any objects, Einstein said, a sole item in the cosmos would theoretically continue falling freely along an unwarped trajectory. But the universe is filled with objects. So spacetime is completely warped. And everything "falls" along those warps. Even ISS astronauts are falling freely, because they're following some sort of gravitational warp.

But if you're still scratching your head, American physicist John Wheeler once perfectly explained general relativity in 12 words: "Spacetime tells matter how to move; matter tells spacetime how to curve."

There you have it. That's general relativity. But the madness doesn't stop here.

Consequences of general relativity are arguably even more bizarre than the theory itself. Don't forget, the spacetime grid is made out of, well, time.

## Time is an illusion

In Christopher Nolan's 2014 film Interstellar, something really weird happens when Matthew McConaughey's character, Cooper, visits a planet orbiting close to a black hole.

"Seven years per hour here," he said, before exiting his spacecraft. This simply meant that for every hour on this planet, seven years will pass by on Earth -- and sure enough, when Cooper gets back to Earth after exploring for a couple of hours, decades have gone by.

All that drama was a product of none other than general relativity. Or more specifically, time dilation.

This aspect of general relativity treads into a greater idea Einstein also came up with, called special relativity. We won't go too deeply into special relativity, but what you need to know is that it says light always travels at a constant speed. No matter what.

Light on a train moving at 40 miles per hour will travel at the same speed as light on an airplane moving at 500 miles per hour, and both of those will travel at the same speed as light coming from a star on the other side of the galaxy. As you can imagine, when you take into account the spacetime continuum, this leads to some weird stuff.

Think about the trampoline again. No bowling ball. Say it'd take 10 seconds to roll a marble to the other side. OK, add the bowling ball. The trampoline is now stretched out. Rolling a marble across this warped trampoline would take, maybe, 12 seconds to account for the new area.

With this analogy, you might see how heavier objects create a more massive curve, and therefore greater "area" for an object to travel across. But remember the light rule? Light must always travel at a constant speed, so it can't be affected by the warps.

But obviously, light traveling through a spacetime warp is crossing a longer distance than light traveling through empty space. So, if not speed, what changes? Well, after fiddling with relativity equations, you get the answer to be... time.

Time gets altered to account for the speed of light's constancy.

In short, time moves slower as a gravitational field in spacetime gets stronger. Yes, really. Even though it's an incredibly minuscule difference, we have proof of this. After a six-month journey, astronauts on the ISS aged 0.007 seconds slower than they would've if planted on Earth. This is also why we have atomic clocks that can account for time dilation impacting GPS satellites, for instance.

And with regard to Cooper, someone on Earth would observe time moving slower for him while he's on the black-hole-planet -- such that only one hour passes for every seven years on Earth. There are a few other ways that time dilation occurs due to general relativity, but this one gives you the general gist.

## Wormholes and black holes

Ready for some Star Trek-style thoughts?

What would happen if we folded the trampoline in half, like a piece of paper? Theoretically, you'd be able to punch a hole through the fabric. Hmm. Unfold the trampoline, and you'd see two holes quite far away from each other. Fold it back, and they touch. That's a wormhole.

While the trampoline is folded, a marble wouldn't need to travel from one side to the other. it could potentially just punch through to the other side in less than a second.

Some experts argue that the fabric of spacetime could, theoretically, "fold" like that, especially near a *super* warped area such as regions around black holes. And if that's true, maybe we can travel across the universe in an instant.

OK, before you get excited, though, we have no evidence for such a "fold." This is just speculation. But on the bright side, there are some crazy spacetime-warp consequences we *do* have evidence of.

We've gone over the fact that black holes are a big player in the general relativity game, but let's zoom in to the voids for a moment.

Because these leviathans are among the most gravitationally strong objects in the universe -- some have masses equal to billions of times that of our sun -- they don't just warp spacetime. They twist it and turn it so strongly that the fabric nearly shatters. And around here, time doesn't just slow. It stops.

But even as little 3D humans, we can watch the show.

In 2016, the Laser Interferometer Gravitational Wave Observatory, or LIGO, detected a binary black hole system, or two black holes orbiting each other. The voids' spiral sent actual ripples through the fabric of spacetime, like the way dropping a rock in a pond would send ripples across the water. Exactly as Einstein predicted decades ago. This was the first *direct proof* that spacetime is indeed a moldable sheet.

Since then, scientists have even managed to take two photographs of black holes in the universe, and both of these images show what warped spacetime near these abysses really looks like. There's a ring of photons around each one that literally follow the black hole-induced warp-lines.

## Not so impractical, not so absurd

Even aside from such concrete, visual proof of spacetime, mathematically speaking, experts have tried time and time again to find a flaw in Einstein's general relativity equations. And time and time again, they've failed.

General relativity appears to be so immutable and crucial for our universe that even cosmic phenomena as gravitationally extreme as neutron stars -- so dense that a teaspoon of one would equal the weight of Mount Everest -- seem to abide by its laws.

The idea of gravitational lensing, which is a magnifying effect of warped spacetime near highly massive galaxy clusters, has become practice among astronomers looking at faraway stars and galaxies.

A once "totally impractical and absurd" hypothesis has turned out to be one of the most fundamental truths of our generation.

General relativity states there's a fourth dimension that crochets together space and time, deeming linearity an illusion for our 3D minds, producing the far-fetched possibility of wormholes and creating a foundation for gravitational waves reverberating throughout the cosmos.

And, for now at least, it's airtight.