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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?
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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.
Last week, we debunked media coverage of so-called habitable
exoplanets like Kepler-186f.
Let's dive right into your, as usual, great comments
and questions.
Many of you asked about the upcoming James Webb Space
Telescope or JWST.
When it launches in 2018, will it
be able to characterize exoplanetary atmospheres?
Yes and no.
Primarily, JWST is an infrared telescope
that will see exoplanets because,
contrary to Earthenfist's comment,
planets do glow, in the infrared.
But the caveat that I gave in the episode
still applies-- JWST will see super-Earths maybe
that are very close to red dwarfs
because only those planets will heat up enough to be
bright in the infrared.
Earth analogs in Earth-like orbits around Sun-like stars
are not going to be visible.
Now, JWST could see dimmer planets
if it had enough continuous observation,
but that probably won't happen because JWST,
just like the Hubble telescope, has
to be shared with lots of other astronomers
who aren't looking at exoplanets.
BukueOner and dulez ninjaman asked, so why
the focus on habitable exoplanets when we're never
going to go there and we still haven't
explored our own solar system?
But remember, astronomers have other reasons
for studying exoplanets-- just basic science.
They want better understandings of how planetary systems form,
of how proximity to different kinds of stars
affects the atmospheres of planets,
and so forth-- the prospect for life, whatever.
We can't reposition the planets here,
so other star systems are the laboratories for these kinds
of investigations.
Lutranereis points out that one problem with media reporting
might be that the reporters lack adequate science background,
and that's a good point.
I'm a trained astrophysicist and I
have a pretty tough time just getting some facts straight
for the show.
I try not to make mistakes, but sometimes I do.
Reporters also have deadlines, which doesn't always help.
Lukos0036 suggested that maybe interest
in space without sensationalist headlines
won't happen until space travel becomes
more accessible and immediate in people's lives.
It's an interesting idea.
You might be right.
And finally, Pikminiman give us some really nice feedback
about the show which I and the rest of the team at Kornhaber
Brown really appreciate.
For those who are curious, I write
the scripts, which then go through revisions
and great group editing with Andrew Kornhaber, who produces,
and Kyle Kukshtel, who also directs.
Some topics come from me, some are
brainstormed with Andrew, Kyle, and the other producer, Eric
Brown.
BJ Klophaus does the film and sound editing and sound effects
and Michael Leng does the animation and graphics.
It's a big effort by a team of people
every week to bring what we think
is clear thinking to interesting science topics
and it means a lot to us and me that you guys find it valuable.
And Pikminiman is right-- I think our comments section is
among the best on YouTube, so you guys also
make this channel great and I really want to thank you.
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