[MUSIC PLAYING] Isaac Newton said that an apple falls because a gravitational force accelerates it toward the ground, but what if it's really the ground accelerating up to meet the apple?

[THEME MUSIC] Suppose I drop an apple.

According to Isaac Newton, the ground can be considered at rest, Earth applies a gravitational force to the apple, and that force causes the apple to accelerate downward.

But according to Einstein, there's no such thing as a gravitational force.

Instead, it's more appropriate to think of the apple as stationary and the ground-- along with everything on the ground-- as accelerating upward into the apple.

Now what I just said sounds preposterous and maybe even moronic, but it's not sophistry.

There's something substantive here, and today I'm going to clarify what exactly this point of view means, why Einstein came to adopt it, and how it planted the seeds for what would eventually become general relativity.

You ready?

OK, bear with me for a minute because we need to begin with some Physics 101 and Newton's laws of motion.

To analyze motion, you need what's called a frame of reference.

That's just some X-Y-Z axes to label points in space and a clock to track time.

The reason you need a frame of reference is that you can only measure motion relative to other things.

If that concept is not familiar to you, you need to pause me right now and go watch this super awesome 1960s black and white video from MIT all about frames of reference.

It's amazing and I promise you won't be disappointed.

Welcome back.

Now, Newton's laws can't tell you whether a frame of reference is really at rest or really moving at constant velocity because that distinction is meaningless and simply a matter point of view.

However, interestingly, Newton's laws can tell you whether your frame of reference is really accelerating or not.

Here's how that works-- take an object with no forces on it and let go of it.

If it stays right where it is, then your frame of reference is not accelerating and we call it an inertial frame.

Now in Newtonian physics, inertial frames are special because Newton's second law, F equals ma, is only valid in inertial frames.

In other words, the net force on an object will equal that object's mass times its acceleration only if you're measuring that acceleration using an inertial frame.

For example, suppose that you're in a train car that starts accelerating uniformly forward along a flat track.

Relative to the car's interior, you will accelerate backward, even though you can't identify any horizontal forces on you.

So inside the train car, F decidedly does not equal ma and the train car's frame of reference is not inertial.

In contrast, a frame attached to the tracks pretty much is inertial-- at least if you disregard Earth's rotation, because relative to that frame, you don't accelerate at all.

Instead, the train car accelerates forward underneath you.

Now more generally, any frame that accelerates relative to an inertial frame will not be inertial.

You got that?

Inertial frame and non-accelerating frame are synonyms in Newtonian physics.

In fact, you can think of inertial frames as the standard against which you measure true acceleration.

And from the perspective of inertial frames, motion obeys a simple rule-- F equals ma.

All right, let's look at things from the train car's frame of reference though a little more carefully.

Inside that accelerating train car, not only does everything accelerate backward for no apparent reason, everything accelerates backward together.

You, a book, and an elephant will all lurch toward the back of the car with the same acceleration.

Remember, from the preferred point of view of the inertial frame that's attached to the tracks, you, the book, and the elephant are all stationary and it's only the train car that actually accelerates forward to intercept you.

So of course you move in lockstep as viewed in the train car's frame.

But hold on a second.

There's something else familiar that makes people, books, and elephants accelerate in lockstep-- the Newtonian force of gravity.

In fact, in the absence of air resistance, that's the defining feature of gravity.

So in the train car's frame, which is accelerating forward, it's as if there's an additional gravitational field that points backward.

So accelerated frames of reference mimic a gravitational field in the opposite direction of the frames acceleration.

That's interesting.

If you combine that extra fake gravitational field with the actual gravitational field of the Earth, which points down, it looks like there's a net gravitational field inside the car that points at some angle down and back.

Destin at "Smarter Every Day" has a pretty famous video of a helium balloon in an accelerating car that happens to illustrate this point really well.

Destin generously gave us permission to show it, but you should check out the full video by clicking over here or following the link we have down in the description.

Now as you can see, when Destin hits the accelerator, a pendulum hanging from the ceiling tilts back while a balloon that's tied to the floor tilts forward.

Destin explains that air is piling up in the rear of the car and getting slightly denser there, so the balloon is just trying to go toward the less dense air near the front.

All of that is true.

But there's another way to think about this situation.

You can also think that the car's forward acceleration is mimicking some extra gravity pointing backward.

Combine that with Earth's real gravitational field and it's as though the total gravity inside the car points down and back at around a 30-degree angle.

That is the new vertical and the pendulum string and the balloon string are just aligning with the vertical the way they always do.

The pendulum hangs down and the balloon aims up because air is denser on the ground and less dense at higher altitudes.

In fact, the accelerated frame of reference of Destin's car is completely indistinguishable from having that car stationary on the surface of some other planet with slightly bigger gravity than Earth and tilted upward by about 30 degrees.

You see what I mean?

If you blacked out the windows and put perfect shock absorbers in the minivan, then for all Destin and his kids know, they're completely at rest, tilted upward on another planet in a perfectly inertial frame.

Huh.

Now in Newtonian physics, this is just an accounting trick that has no broader significance.

Really, Destin's car is accelerating and this extra backwards gravity is fake.

But Einstein asked, hold on, what if the so-called "real" downward gravity from Earth is also fake, a side effect generated because Earth's surface is really accelerating upward?

Now, you know what Newton would say.

He'd say, that's crazy.

He would remind us that inertial frames are the standard for measuring true acceleration, so you can only say Earth is really accelerating upward if you can identify an inertial frame relative to which Earth's surface accelerates upward, and there's obviously no inertial frame like that, right?

Well, not so fast, says Einstein.

Maybe there is.

What about a frame that's in freefall?

Think about it.

If I put you in a box and drop you off a cliff, then in the frame of the box, everything just floats, weightless.

The falling frame of the box behaves just like a stationary inertial frame that's way out in intergalactic space where there's no gravity.

So why can't the box's frame be inertial?

Well because, Newton says, that frame can't be inertial.

It's really accelerating downward at 9.8 meters per second squared.

The interior just seems like zero G because the downward acceleration acts like a fake extra upward gravitational field that, from the perspective of the box, just happens to exactly cancel the real downward gravitational field of Earth by coincidence.

Really, Newton?

Really?

Einstein says, look buddy, I'm just following your rules.

You established the test for what an inertial frame is-- release a force-free object and it stays put.

Stationary frames in intergalactic space pass that test.

But freely-falling frames here on Earth also pass that test if your so-called gravity is fictitious.

More to the point, Newton, if you're inside the box, there's no way for you to know that you're not in intergalactic space.

This inability to distinguish freefall from lack of gravity has a name, by the way.

Einstein called it the equivalence principle, and if you buy it, then maybe the falling frames really are inertial.

If so, then it's the falling frames that establish the standard of non-acceleration, in which case, it's really the ground that's accelerating upward and what we've always been calling a gravitational force is an artifact of being in an accelerated frame of reference.

It's not different from the weird, backward jolt that you experience on the train that you know perfectly well isn't being caused by anything.

So why are you insisting that the downward jolt we experience every day on Earth has a physical origin?

Maybe gravity, just like that backward jolt on the train, is an illusion.

Doesn't that point of view seem simpler?

Now Newton says, nice try, Einstein, but you forgot something-- Earth is round.

Down isn't really down, it's radially inward, and this creates two problems with thinking about freely-falling frames as inertial or thinking about gravity as an illusion.

First, two objects in a falling box are falling toward Earth on not-quite-parallel radial spokes.

So from the perspective inside the box, they won't actually remain stationary.

They accelerate toward each other slightly, even though there are no forces on them, in seeming violation of F equals ma.

Second, by your criterion, Einstein, orbiting frames of reference-- like on the space station-- should also be considered inertial.

But those frames accelerate relative to frames that are just falling straight down.

And if you recall the beginning of the episode, inertial frames aren't supposed to accelerate relative to each other.

Huh, that's a good point.

So it looks like game over for Einstein, right?

Well, not quite.

It turns out that there's a loophole that makes Einstein's viewpoint self-consistent.

The rule that inertial frames can't accelerate relative to each other turns out only to be true if the world has what's called a flat geometry.

If instead the world is a non-Euclidean and curved spacetime, then straight line at constant speed doesn't mean what you think it means and it turns out that inertial frames in a curved spacetime can do almost anything they want.

It took Einstein about seven years to realize that.

But once he did, a beautiful model of the world emerged called general relativity.

It makes several predictions that Newton's theory of gravity does not, and so far, it has passed all its experimental tests.

And one of the central precepts of general relativity is that we inhabit the curved spacetime.

And in that curved spacetime, the orbit of the ISS is a constant-speed straight line.

The arc of a basketball during a three-point shot?

Constant-speed straight line.

But you, sitting perfectly still in this chair watching this video?

You, my friend, are accelerating, giving you the impression that there's a force of gravity when, in fact, no such thing exists.

Wait a minute-- how can geometry and straight lines possibly work the way I just said?

Patience, grasshopper.

We'll tackle that another time.

For now, just reflect on Einstein's inspired thinking and how he got there, maybe next time you get in a car or a train.

We'll reconvene next time our accelerated paths cross in curved spacetime.