This episode is supported
by The Great Courses Plus. 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. Thanks to The Great Courses Plus
for sponsoring this episode. The Great Courses Plus is
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lus.com/spacetime and get access to a library of different
video lectures about science, math, history, literature, or
even how to cook, play chess, or become a photographer. New subjects, lectures,
and professors are added every month. For an excellent overview
of basically all physics, I really liked Richard Wolfson's
"Physics and the Universe" course. It even takes you through
the beginnings of Einstein's general relativity. With The Great
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start your one-month trial by clicking the link in
the description or going to thegreatcoursesp
lus.com/spacetime. 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. [MUSIC PLAYING]
I would much rather fall into a black hole, than fall into the Sun or Jupiter.
We have a pretty good idea what's going to happen if we fall into the Sun. Death is definitive. But a black hole, while death is highly probable, it does give you a chance of at least experiencing something amazing, including time dilation, and maybe even surviving and popping out somewhere else.
If I had a choice, I'll take the black hole every time. No contest for me.