[MUSIC PLAYING] 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. [THEME MUSIC] 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. OK. 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 know 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.
I have never seen this channel before so that was quite a revelation to me.
So would this mean that from inside a black hole, you would see everything that ever was/will be inside of it at the same time?
I like this idea that a black hole is a set of Event which, from an external point of view, never happen. It seems to me that it gives credit to the idea that black holes are actually alternate universes.
Seeing this for the first time just to find out this is the last video he will make! Argh.
What happens if we get in a generation ship and drop into a supermassive black hole? He was saying a large enough black hole would be relatively calm at the event horizon. I imagine people aboard the generation ship wouldn't really notice any problems up until the event horizon... but then what?
To me, Black Holes will continue being an enigma until our perception expands to the point where we can genuinely comprehend the concept of "singularity". And since, we will never be able to experimentally verify our findings, the best we can do is to make educate guesses. It's one of those mysteries that will never be solved.
Hi, what I dont understand is, if nothing can apparently to us cross the event horizon, how can that black hole grow (increase its events horizon circumference) if it doesnt 'suck' mass?
philosophical questions regarding black holes? Honestly a lot of the stuff in this vid sounds like BS, except some basic things like the redshift and gravitational time dilation.