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At the event horizon of the black hole,

space and time are fundamentally changed.

Even professional physicists disagree on what

we expect to happen there.

But there is a powerful tool in physics

that can give us real intuition into the true nature

of the event horizon.

Its time you learned it.

Black holes, objects with densities

so high that there's this region, the event

horizon, where the escape velocity reaches

the speed of light.

Nothing that falls below the event horizon

can never escape and is lost to the universe

forever while we see falling objects freeze as time

stands still at the horizon.

And anything that happens below the event horizon

stays below the event horizon.

That's the official sanitized public version.

It's not entirely inaccurate, but the reality

is, of course, a good deal more complex and interesting.

Even ignoring the complications of Hawking radiation

or black hole rotational growth, the simplest black hole

of Einstein's general theory of relativity-- purely

gravitational, static, and eternal--

is a subtle and misunderstood beast.

But we can come to a powerful and intuitive understanding

of the beast.

Today I want to teach you how to use the same tool

that physicists use.

It's a tool that will let us easily

and so the most common questions about black holes.

For example, are objects falling through the event horizon

really physically frozen there from the point of view

of the outside universe?

Would you see the entire future history

of the universe playing fast forward at the instant

that you crossed the event horizon?

And do you see anything at all once you're

inside the black hole?

The tool that will answer these questions

is called the Penrose diagram, sometimes also

the Carter Penrose diagram.

It's a special type of space-time diagram designed

to clarify the nature of horizons.

But first, a quick refresher on basic space-time diagrams.

By graphing time versus just one dimension in space,

we can look at the limits of our access

to the universe due to its absolute speed

limit, the speed of light.

With the right choice of space and time units,

the speed of light becomes a diagonal line

on the space-time diagram.

The area encompassed by the so-called light-like paths

defines all future events or space-time locations

that we could potentially travel to or influence constrained

by the cosmic speed limit.

That's our forward light cone.

Our past light cone defines the region

of the past universe that could potentially have influenced us.

Let's drop a black hole onto our space-time diagram.

It lives at x=0 on the space axis,

but exists through all the times on the graph.

It has a point of infinite density, the singularity,

and an event horizon a bit further out.

The mass of the black hole stretches space and time

so that light rays appear to crawl out

of the vicinity of the event horizon

before escaping to flat space-time,

no longer following 45 degree paths.

Now let's throw a monkey into the black hole.

As it approaches the event horizon,

its future light cone bends towards the black hole

as fewer and fewer of its possible trajectories

lead away.

Below the event horizon, all possible trajectories

lead towards the singularity.

The problem with the regular space-time diagram

is that the path of light and the shape of the light cone

changes as space-time becomes warped.

That makes it difficult to figure out

what parts of the past and future universe

the monkey can witness or escape to.

And this is where the Penrose diagram comes in.

It looks like this.

It transforms the regular space-time diagram

to give it two powerful features.

It crunches together, or compactifies,

the grid lines to fit infinite space-time on one graph-- very

useful for black holes.

It also curves the lines of constant time

and constant space in what we call a conformal transformation

so that light always follows a 45 degree path.

That means light cones always have the same orientation

everywhere.

Super handy for understanding monkey trajectories.

This is the Penrose diagram for flat space-time

with no black holes.

Same as with a regular space-time diagram,

blue verticalish lines represent fixed locations

in one dimension of space and red horizontalish lines

are fixed moments in time.

Now, those lines get closer and closer together

towards the edge of the plot to encompass

more and more space-time.

They're extremely finely separated at the edges

so that any tiny stretch on the graph

represents vast distances and/or times.

The lines also converge together towards the corners

so that light travels a 45 degree path everywhere

on the diagram.

So a light ray starting from really, really far away

and coming towards us hugs the edge of the diagram

and crosses an enormous number of time and space steps,

only reaching us in our very distant future.

OK.

Let's drop a black hole into this space-time.

Nice and safely far off to the left.

And because we only have one dimension of space,

and any motion to the left brings

us closer to the black hole.

Its event horizon becomes the end

of the line in that direction.

The future cosmic horizon on the Penrose diagram

is replaced with a plunge into a black hole.

The compactified grid lines there

now represent the stretched space-time

near the event horizon.

An entirely new Penrose region represents the interior

of the black hole.

Weirdly, the lines of constant position and constant time

switch.

Space flows at greater than the speed of light inwards,

towards the central singularity.

It becomes uni-directional, flowing inexorably downwards,

just as time flowed inexorably forward

in the outside universe.

All paths lead to the inevitable singularity.

Once you're beneath the horizon, your future light cone

still represents all possible paths that you could take.

All of them end up at that singularity.

The only way to escape back to the outside universe

would be to widen your light cone

by traveling faster than light.

So you're out of luck.

Now that we've nailed the Penrose diagram,

we can use it to do some serious black hole monkey physics.

Our space-faring simian begins its journey

and emits a regular light signal that we

observe from a safe distance.

As it approaches the black hole, these light rays

have further and further to travel through increasingly

curved space-time and so the interval

between receiving signals also increases.

The progress of the monkey appears

to slow to a halt very close to the event horizon,

and the final signal at the moment of crossing never

reaches us.

It's trying to travel at the speed of light

against light speed cascade of space-time.

With this picture, we can start to answer

some very serious questions.

First, what would happen if the monkey remembered

to fire its jet pack at the last instant

before reaching the event horizon?

Well, it could still escape.

Its future light cone still includes a tiny sliver

of the outside universe.

It had better be a good jet pack because it's

going need to follow a very long near light speed path away.

It will, nonetheless, have experienced far less time

than us when it emerges into flat space-time

in our far future.

Assuming no jet packs, the monkey

is probably doomed to a graceful reverse swan dive

through the event horizon, watching

the entire future history of the universe

play out above it at that last instant.

Yet actually, no.

It doesn't see that at all.

The monkey's last view of the outside universe

is defined by its past light cone

that encompasses all of the light that will catch up to it

and that light is stuck following these diagonal lines

because it has to contend with the same stretched space-time

as the monkey.

There's no future universe spoiler promo.

If it could instead hover above the event horizon,

then it would see the universe in fast forward,

although that view would be compressed into a small circle

directly overhead.

Watching the monkey frozen on the event horizon

is going to make us feel a bit guilty, after a while.

Could we change our minds and launch a daring monkey rescue

mission?

Sadly, no.

Even if we do travel at the speed of light,

after a certain point there's no catching the monkey.

We would see it suspended above the horizon

as we're racing to meet it, but it will always

appear to be just a little further ahead

no matter how close to that horizon we dare to go.

Remember, the monkey isn't actually

above the horizon for infinite time,

it only appears that way to us because as long

as we're outside the event horizon, no times

that we can witness correspond to the monkey crossing

that horizon.

In order to see that crossing, we

would have to cross the event horizon ourselves.

Once inside the black hole, we could potentially

see the monkey below us.

All space-time within the black hole

is flowing toward the singularity faster

than the speed of light.

The two neighboring radial layers

aren't traveling faster than light relative to each other.

That means that the monkey's signal can still reach us,

although it might be more accurate to say

that we catch up to the monkey's outgoing signal.

But even that so-called outgoing light is still

moving downwards, doomed to hit the singularity along

with the monkey and our rescue mission.

All of this describes a non-rotating, uncharged black

hole, a Schwarzschild black hole.

Even this simple case is a good deal more complicated

than I let on.

For example, I only showed you half of the Penrose diagram.

The complete mathematical solution

for a Schwarzschild black hole has two additional regions,

one corresponding to a parallel universe

on the other side of untraversable wormhole,

the Einstein-Rosen Bridge.

And down here we have what we call a white hole.

These are strange mathematical entities

and probably aren't real, but we'll certainly

come back to them.

We'll also come back to what happens

if we set the black hole spinning

or add some electric charge.

Then our Penrose diagram blooms outwards

to include potentially infinite parallel regions of space-time.

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Hey, guys.

A couple of quick shout-outs.

First, a huge thank you to our first Patreon supporter

at the Big Bang level.

Antonio Park, you rock and I'm really looking forward

to our hangouts.

Your support is going to make a big difference, as is

the support at all levels.

So thanks again to everyone who's contributed on Patreon.

And a quick announcement of a couple of events

I'll be at early next year.

First, South by Southwest, March 10 to 19 in Austin, Texas.

A few months ago I asked you guys

to head to the South by Southwest panel picker

to vote for myself, Astrophysicist Katie Mack,

and It's OK to be Smart's Joe Hanson to be

picked for a panel titled, "We are All Scientists."

Well, thanks to you guys, we're scheduled.

We're going to talk about the value of and the threat

to critical thinking and scientific reasoning

and why these skills need to be seen

as accessible and important to everyone

and how we can act on this idea.

Also, for those of you thinking of attending grad school

in physics, I'll be talking about studying physics

at a professional level at the City University of New York's

Student Research Day, April 7 at the CUNY Graduate

Center in New York City.

More details closer to then, but for now I'll

put a link in the description and feel free to reach out

to me if you're interested.

OK.

Onto the comments from last week's episode

on De Broglie-Bohm theory.

Wow.

This is the closest I've seen a YouTube comment section come

to looking like a Q&A session after a professional physics

seminar.

Now, a lot of you wondered why I never mentioned the EM drive

when talking about pilot wave theory.

The answer is simple, there was nothing

useful to say on that connection.

In the recent paper out of Eagle Works Labs,

Herald White and collaborators present some results

on the thrust produced by their EM drive

and then go on to talk about how pilot wave theory might

explain the apparent conservation

of momentum-breaking results.

I might get into the details in an upcoming episode,

but for the sake of explaining pilot wave theory

this paper isn't relevant.

The connection is extremely speculative,

and honestly I wondered whether pilot wave theory was

chosen partly because the internet happens

to love it at the moment.

DinosaurFromtheFuture asks how it

can be that pilot wave theory predicts different particle

trajectories, given that the particles supposedly all start

at exactly the same point.

Well, the simple answer is that the particles don't start

at exactly the same points.

We just can't know exactly their location at the beginning.

See, pilot wave theory states that the particle riding

the wave does have a definite position at all times

and that position defines its future directory.

So if you know the position perfectly

and you know the wave function, you can perfectly

predict future locations.

However, you can't perfectly measure a particle position

without changing it slightly in ways

that themselves aren't perfectly predictable.

As a result, you never know exactly where a particle is.

This uncertainty leads to the range

of potential future trajectories,

including trajectories through one slit or the other.

More generally, it allows pilot wave theory

to agree with Heisenberg's uncertainty principle.

In the Copenhagen interpretation,

the uncertainty principle describes

the intrinsic randomness of the quantum world.

De Broglie-Bohm pilot wave theory

states that this uncertainty just

arises from our imperfect knowledge

and that the universe itself knows exactly

where all these particles are.

Vacuum Diagrams correctly points out

that to know the future trajectory of a particle,

you only need position, not velocity, as I had stated.

That velocity information is in the guiding wave.

Thanks for the correction and thanks also

for pointing out those extremely interesting papers that

detail certain failings of the pilot wave interpretation.

I'll link those and a couple of others

that take different sides in the description of this video,

as well as in the pilot wave episode.

In fact, there was some really heated and fascinating

discussion both for and against the pilot wave interpretation

and some of it was from people who

know a good deal more than I do, like Vacuum Diagrams.

Something I took from this is that Bohmian mechanics

is, on its own, very unlikely to be the full picture, even

ignoring the whole relativity issue.

That doesn't necessarily mean, though, that it's not useful.

I'll get back to why.

But first, as was pointed out to me in a nice email by physicist

and science writer Adam Becker, I wasn't entirely accurate

when I said that De Broglie, the founder of pilot wave theory,

remained convinced by Niels Bohr and his Copenhagen camp,

even after Bohm's work.

More accurately, De Broglie remained convinced

of the objections raised against his idea,

even after some of them were addressed in Bohmian mechanics.

To quote De Broglie from his 1956 book,

he, Bohm, assumes that the [INAUDIBLE] wave

is a physical reality, even the [INAUDIBLE]

wave in configuration space.

I have already stated why such a hypothesis appeared

absolutely untenable to me.

In fact, De Broglie was never a huge fan

even of his own simplistic particle

carried by a wave idea.

That formulation was a simplified version

of what was to be a much more intricate double solution

theory in which the so-called particle was actually a matter

wave itself embedded in and carried by the sine

wave, represented by the wave function.

He was unable to pull the math together

in time for the fated Solvay Conference,

and so derived the simpler description in which

the particle is point-like.

De Broglie never completed his full double solution theory,

but did work on it intermittently

throughout his life and was inspired

to return to it by Bohm's publication,

even if he didn't buy Bohmian mechanics.

The fact is we just don't know whether the reality that

drives the strange results of quantum experiments

is actually deterministic in the way

that we understand determinism.

But De Broglie-Bohm pilot wave theory

is a great example of how a deterministic theory can

at least go some way towards predicting the results

of quantum experiments.

Personally, I'm agnostic towards the relative truth

behind the Copenhagen, many-worlds,

pilot wave, or the other interpretations of quantum

mechanics.

I like the idea of a deterministic theory,

but the universe has often demonstrated

that it couldn't care less about our pet theories.

However, it's also shown itself to be

vulnerable to experimentation even for questions

that we previously thought untestable.

We'll figure this out, and until then it's

OK to like one theory over another

but belief should wait on the evidence.

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