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