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I'm sure you've read, seen, and heard a lot about black holes.
Well, today, I'm going to try to make you rethink all of it,
down to what the term "black hole"
even means.
Today's episode, we'll only talk about black holes
from the perspective of classical general relativity.
That means no Hawking radiation, no string theory,
and no quantum anything-- baby steps.
Trust me, if I do this right, it'll be mind blowing enough.
Now, it's a lot harder to say what
I want to say about black holes if I
make this video self-contained.
To treat gravity Einsteinially rather than Newtonianially
from the outset, it will help a lot
if I can rely on technical terms like "geodesic" or "flat
spacetime" and if I can draw a spacetime diagram or two.
We all need to be on the same page with this vocabulary.
So if you need a refresher, go watch our relativity playlist.
And finally, to minimize miscommunication,
I need a favor from you.
I need you to put your preconceptions
about black holes aside and for the next few minutes,
become "tabula rasa" and let me tell you a story about me,
a pony, and a very acrobatic monkey.
Suppose that I'm very far from a black hole
and there's a pony orbiting the black hole.
She's close, but not that close to the hole.
Don't worry.
Fact-- events that happen at a normal rate,
as far as the pony is concerned, will happen in slow motion
according to me.
A day for her might be months for me.
This is called gravitational time dilation
and the same thing happens around Earth, just
to a lesser degree.
Atomic clocks in high-altitude orbit
will get ahead of clocks on the ground
by a few microseconds each day, which is tiny,
but GPS doesn't function properly
if you don't take this into account.
Now suppose that I send a tumbling monkey
falling radially toward the black hole.
As he tumbles on, I see his rotation rate
become more slow motion, but I also
see him pick up translational speed,
just as I would if he were falling toward Earth.
That is, until he gets really close to the black hole-- see,
eventually, the monkey will cross the black hole's edge
without him noticing anything unusual.
But that's not what I see.
I see him weirdly slow down his progress
until he's floating right outside the black hole's edge.
At a certain point, I see him in suspended animation,
not rotating, not progressing, just frozen.
And the pony agrees with me.
So does another pony that's using powerful rockets
to hover much closer to the black hole's edge.
In fact, so would any observer, inertial or otherwise,
who is always outside the black hole's edge.
Even if the ponies and I were immortal, all of us
would agree that the monkey's life just doesn't progress
past this frozen moment.
The monkey knows he crosses the edge.
I mean, he was there.
But everyone else insisted he never
does, even after an infinite amount
of time on any of our clocks.
Do you get how freaky this is?
The monkey is saying that certain events happen,
but everyone else outside the black hole
says that those events never happen, ever.
In other words, there are apparently events that
according to us out here cannot consistently be assigned
a "when."
From our frame of reference outside the black hole,
those events just don't occur, even if we wait
an infinite amount of time.
OK, you got all that?
Here's the thing-- a black hole is that set of events.
According to observers like the monkey who are at those events,
those events take place at spatial locations
inside that black blob we see in the sky.
But the blob, the black hole, is not just a set of locations.
It's all the events that have ever or will ever
take place there, according to observers
who are physically there.
The black hole is not a region of concurrent happenings
with the outside world that the pony and I are just
unable to see.
It's not a visibility issue.
Instead, the black hole is the collection of happenings
that we say don't happen at all.
And that black blob you see in the sky
is just what it ends up looking like in ordinary spatial
and temporal terms when you delete entire occurrences
from every external observer's self-consistent record
of the history of the universe.
By the way, for every particle that enters the black hole,
some event on its world line is always
the last event that makes it into my movie
of the history of the world out at time infinity.
OK, this final batch of events for all objects that
enter that black void taken together
is called the event horizon of the black hole.
The horizon is not just a spherical surface in space.
It's not a shroud.
It's a surface in spacetime.
It represents the last events to which
you can even assign a "when."
So if a black hole is a bunch of events,
then why do we talk about it as if it's an object?
Here's why.
For simplicity of presentation, let's
pretend that the Sun is a perfect sphere.
It determines the spacetime geometry in its neighborhood,
the resulting geodesics of which correspond
to things like radial freefall, orbits, et cetera.
Now, if I replace the Sun with a spherical black hole
that's around six kilometers across--
and I'll tell you later how I got that number--
the geodesics beyond where the Sun's edge used
to be remain unchanged.
Earth will freeze, of course, but its orbit
won't be any different.
So as far as Earth is concerned, that black hole
generates the same spacetime geometry out here
that the Sun does.
In that respect, the black hole certainly
behaves like an object, an object with the Sun's mass.
So we associate one solar mass with the black hole itself.
In fact, if I give you a spherical object of any mass M,
a spherical black hole with this special radius,
called the Schwarzschild radius, will
leave the spacetime that's originally external to that
object unchanged.
A black hole that mimics the Sun has a Schwarzschild radius
of 3 kilometers.
One with the mass of Earth would have a radius
of just under 1 centimeter.
But hold on a second.
A black hole is a bunch of events.
So is that collection of events somehow mimicking mass
or does it actually have mass?
Is there even a difference?
Hold that thought, because first, I
want to debunk a few black hole misconceptions
and then we'll come back to this question.
Misconception one, that black holes suck stuff in-- they
don't do that.
They're not vacuum cleaners.
You can orbit them just fine.
I think this idea of suckage is rooted
in a misunderstanding of the region that
used to be inside the Sun but is still outside the black hole.
See, spacetime geometry in this region is very foreign.
For example, that is an allowed planetary orbit in that region.
That region also has a cutoff radius inside
of which there are no circular geodesics anymore.
So a freefalling observer inside that cutoff, like the monkey,
will go radially inwards.
But it's not because he's being sucked in
any more than the Earth sucks in a falling apple.
He's just falling.
As long as he stays outside the horizon,
he can use rockets to hover or move radially outward
just like on Earth.
Misconception two-- black holes are
black because not even light can escape
their gravitational pull.
That's not the reason, but here's
my guess about how this unfortunate metaphor started.
In Newtonian gravity, a projectile
on the surface of a planet or a star
needs a minimum speed called the escape velocity in order
to get really far and not turn back as it's
pulled by the planet's gravity.
If a planet's radius equals the Schwarzschild radius
of the equivalent-mass black hole,
it turns out that the escape velocity is the speed of light.
But that's just a numerical coincidence.
In general relativity, remember, gravity is not a force at all.
So even though it's true that everything inside a black hole,
including a photon, will always move radially inward,
it's not being "pulled."
Instead, the insane curvature there
has made geometry so weird that radially out
is simply not an available direction.
Loosely speaking, it's like being
in an episode of "The Twilight Zone," in which no matter which
way you turn, you're always facing inwards.
Now, that's really freaky, but it's not the reason
black holes are black.
Remember, from our point of view,
there are no photons inside.
A laser pointer carried by the monkey
never enters the black hole, as far as we're concerned.
Because of time dilation, we would detect any laser pulse
that the monkey sends with a lower frequency, i.e.
a redder color, than whatever the monkey emits.
So just before the monkey freezes from our perspective,
the time dilation is so severe that any light he emits
gets redshifted to undetectably low frequencies.
That means that to external observers,
black holes are black because light that gets emitted just
outside the horizon is redshifted into invisibility.
So even though my story about the monkey is correct,
I shouldn't really have used the verb "see,"
because the infinite redshift keeps me
from seeing him at all.
Misconception three, that all black holes
are super dense-- this kind of depends
on what you mean by "density."
If you mean that it's the black hole
mass divided by the volume inside the horizon, then no.
More massive black holes can have very low density.
For instance, the 4 million solar mass black hole
at the center of the Milky Way is about as dense as water.
Strangely, the Schwarzschild radius criterion
is based on circumference, not on volume.
By the way, bigger black holes also
have smaller tidal effects near their horizons.
So even though a solar mass black hole
would spaghettify you from pretty far away,
you could enter a billion solar mass black hole
completely unscathed.
But maybe that's not what you mean by "density."
Maybe you mean that all black holes
are infinitely dense because all the stuff that
goes into the black hole collapses
to an infinitely dense point called the singularity
at the center, right?
Again, we have to be careful.
Misconception number three actually brings us full circle
back to the mass question that I raised earlier.
Astrophysically, a black hole can
form when a sufficiently massive object, typically
a very heavy star, collapses and becomes
more compact than its own Schwarzschild radius.
In this situation, the mass of the precursor star
and the associated mass of the black hole
will indeed be the same.
However, the horizon forms first in the interior of the star
and then expands.
So to external observers, most of the matter
never crosses the horizon.
Remember, it's all frozen.
So in this scenario, we can kind of
sidestep the whole mass issue.
To us, it's not inside the black hole.
But here's the problem.
The Einstein equations also allow for an empty universe
that has an eternal black hole that didn't form from anything,
a spacetime that has an event horizon
even though there's no stuff anywhere,
including behind the horizon.
This is the prototypical Schwarzschild black hole
and I've always felt that whatever
we're going to say a black hole's mass is the mass of,
it should apply equally well to astrophysical black holes
and to these idealized black holes.
And in this circumstance, what are we
supposed to assign the black hole's mass to?
Remember, there's no stuff anywhere.
So is the mass a property of the singularity?
Personally, I don't think that works.
You see, the singularity also isn't
a thing or a place or an event.
It's like a hole that's been punched out of spacetime.
So the geodesics terminate because there's
no way for them to continue.
So where's the mass?
Is it associated with the curvature of spacetime,
with all of spacetime?
I'm not sure what the right answer is to interpretational
questions like this or even if there is a right answer
in vanilla general relativity.
But this may just be my ignorance.
My goal today was just to correct
some common misconceptions and to highlight
some of the philosophical subtleties associated
with thinking about black holes as "things."
Of course, I've only scratched the surface of black holes.
There's tons more to learn about them.
There's rotating black holes, charged black holes, black hole
evaporation, what goes on around black holes, how you form
supermassive black holes, tons of stuff, some of which
you might hear about, but from someone else.
I didn't realize how much of an impact I and this show
were having on you until I read some
of the lovely things you guys said after I announced
that I was leaving.
I haven't responded to those comments
because I don't really know how, but I have read them all
and I want to say that I was really touched by them.
Nevertheless, I have other places I need to go.
So even though I will be back next week with the answer
to the challenge questions, this is officially my final episode
of "Space Time."
Our last full episode dealt with misconceptions about what
causes ocean tides on Earth.
You guys had a lot to say.
hauslerful and Andrew Brown said that I should tone things down,
take myself less seriously, and not fixate so much
on one versus another metaphor.
I can be accused of many things, but taking myself seriously
is not one of them.
And in case there was any confusion,
I'm not claiming to be the harbinger of some new insight
into the mechanism of tides.
This is how tides have been known
to work since the early 18th century, when Euler and Laplace
worked out the details.
But it doesn't change the fact that a lot of people,
including physicists and physics teachers, as you've
seen in our comments, and me had this mechanism
wrong in our heads for a variety of reasons.
And I just wanted to make sure that a correct representation
of the mechanism was out there in video form.
Ivan or Ivan Chagas, ErgoCogita, and Arthur Withheld
all asked how contemporary students
of physics and teachers of physics
could get this information so wrong.
All I can say is it happens and it happened to me.
Science Asylum actually gave a really good answer
to this question.
He's a physics teacher and he said, look,
there are some things that we just
don't focus on in our training because they
seem kind of trivial.
And unless we have a specific reason to look at them in more
depth, we just don't.
He, for example, never thought about why cups of coffee
don't have tides because no one ever asked him.
It happens.
Romesh Srivastava-- I hope I pronounced
that right-- and shoofle both asked whether there
are some more mathematical resources or papers that I
could give you explaining the same thing.
There are.
I dug some up.
And remember, this has been known
since the early 18th century, but I gave you a few more
contemporary resources.
I added them into the Description area
under the tides video.
You can check them out.
Madhu Sujan Paudel-- hope I pronounced that right--
and gottabweird both asked whether Earth's atmosphere then
has tides.
It does.
There are gravitational effects from the Sun and Moon
that do the same thing, but they're highly, highly masked
by the much more dominant effect of temperature variations
and pressure variations on the atmospheric distribution
around the Earth.
Finally, Tim VanBuren and Dox both insisted that the Great
Lakes do have tides.
No, they don't.
Well, they do, but they're only a few centimeters
between high and low tide, like I said in the episode.
What you are mistaking for tides is
seiching in those bodies of water,
namely resonant oscillations of the water
due to the shape of the lakes.
It's easily mistaken for tides and sometimes
even has approximately the same period, but it's not tides.
And I've added a link in the description of the tides
episode from Noah explaining the distinction.