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Hey Crazies.
About 6 months ago, I got a comment asking about how falling works in general relativity.
Bob, I know, 6 months is a long time,
but this whole series of quantum videos happened
and, when the crazy train calls, you’ve just got to ride it.
Wooo! Wooo!
Stop making excuses, Nick.
Anyway, I’m ready now.
Let’s kick this pig!
We’re going to start with the classical version of gravity
or the “Old-School” version as we say on the hip side of physics.
No one says that.
I say that!
I want to make sure everyone is on the same page.
Example Time!
Say a squirrel falls from a tree.
There’s a force of gravity pulling it down and a bit of air drag resisting the fall,
but we’ll be ignoring that air drag for simplicity.
Physicsland! Ah!
As the squirrel falls, the gravity stays very steady.
Eventually, the squirrel impacts the ground, which exerts an upward force on the squirrel,
resisting gravity.
The squirrel slows down and stops.
This all makes perfect sense.
It’s just an interplay of forces.
But, in a previous video, we took a look at the history of relativity.
We did a couple thought experiments
Gedanken Versuch!
that made Einstein’s relativity completely unavoidable.
The ultimate conclusion was: Gravity isn’t a real force.
And, Prat, that doesn’t mean gravity doesn’t exist.
It’s just not a force.
There’s a difference.
The truth is gravity is just curvature in space-time,
a process governed by Einstein’s Equation.
That equation looks like this,
but, put more simply, like this.
A physicist once explained this equation by saying:
“Energy tells space-time how to curve.
Space-time tells energy how to move.”
which I can’t say any better myself.
That equation looks pretty interesting, but it... it might leave you asking:
What the [BEEP] does that mean?
Well, that’s what this video is for.
I should start by leveling with you though.
Einstein’s equation outlines the fundamental principle of curved space-time
and it’s used in a few math steps when working with general relativity.
But it’s not actually very useful beyond that.
We’re going to get a much better understanding of how things like squirrels
move in curved space-time by talking about geodesics.
You mean that guy that’s dating Sofia Richie?
What?
No, that’s Scott Disick.
I said geodesic!
Let’s… let’s just get back to the squirrel.
In old-school physics, gravity is a force pulling down objects
until another force stops them.
But if we trust general relativity, gravity isn’t a force.
So why on Earth would the squirrel even bother falling?!
The answer: It’s following a geodesic, a straight line in curved space-time.
But there’s a lot of stuff in that statement we need to unpack.
First, anything that’s under the influence of only gravity
is following one of these geodesic paths.
That makes sense for the squirrel because its path looks straight.
But a satellite orbiting the Earth is also traveling along a geodesic.
No one is really saying that an orbit is straight.
We’re just saying that now we talk about geodesic paths,
where we used to talk about straight ones.
It’s a replacement concept.
A geodesic is the new straight line.
Second, it’s not curved space.
It’s curved space-time!
And that time part is what matters most for the falling squirrel.
This is why it’s important to avoid visuals like ribbons wrapped around shapes
and definitions about minimizing or maximizing distance or time.
They’re not necessarily wrong, but they’re probably going to mislead you.
So then what’s a Geodesic?
Let’s start with Newton’s laws and go from there.
Newton’s second law says acceleration is caused by an unbalanced force
or net force equals mass times acceleration.
In old-school physics, the squirrel accelerates toward the ground
because gravity is an unbalanced force pulling it down.
When the ground finally pushes up, the gravity is balanced and the acceleration
drops to zero.
But in general relativity, there is no gravity force,
so Newton’s second law no longer makes sense.
That’s where curvature comes in and, by far, the biggest curvature for the
squirrel is time curvature.
The squirrel doesn’t fall because there’s a force.
It falls simply because its future is on the ground.
That’s what a Geodesic is.
It’s just a path you take when there aren’t any unbalanced forces on you,
which is exactly what a straight line used to be.
In fact, that equation is called the Geodesic Equation.
It’s usually written as a differential equation, but, conceptually, those are the same thing.
At the Earth’s surface, that curvature actually equals 9.8 meters per second squared,
the free fall acceleration we’ve observed for centuries.
The squirrel will travel along that geodesic until a force tells it not to
like one from the ground.
None of you are on a geodesic path right now because you all have a force underneath
holding you up.
Unless, of course, you’re watching from the International Space Station.
In which case, wow!
Thanks for watching the show!
Anyway, things don’t really fall because of a force of gravity.
They fall because time curvature puts their future at different place in space.
From our point of view, that just happens to look like a force.
Because we can’t see space-time as it really is.
So, got any questions about general relativity?
Please ask in the comments.
Thanks for liking and sharing this video.
Don’t forget to subscribe if you’d like to keep up with us.
And until next time, remember, it’s OK to be a little crazy.
For those of you who don’t follow me on social media or the community tab,
I have a PO Box!
No pressure or anything.
But, if you’re into the whole snail-mail thing, it is now possible to do that.
Just thought I’d let you know.
Anyway, thanks for watching!