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  • [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.