Black Holes. Explained. For 1.5 Hours.

0:00 Black holes are not just the strangest objects in the universe.

0:03 They're the sharpest tests we have of how reality actually works.

0:07 They form when mass is compressed beyond a critical limit.

0:11 But their importance goes far beyond how they're made.

0:15 Black holes are the most extreme laboratories in the universe,

0:19 forcing general relativity and quantum mechanics into direct confrontation.

0:24 In this longplay episode,

0:25 we're looking back through our 10-year history and giving

0:29 you 90 minutes to explore how black holes form,

0:33 evolve, and ultimately help us test

0:38 and possibly reconcile our deepest theories of reality.

0:46 Black holes are one of the strangest objects in our universe.

0:49 To make one, we need both general relativity and quantum mechanics.

0:53 Today, I'm going to show you how.

0:55 In a previous episode, we discussed the true nature of black holes.

0:59 We talked about them as general relativistic entities,

1:02 as space-time regions whose boundary curvature effectively

1:06 removes the interior from our observable universe.

1:09 Now, it would be a great idea to watch this video first if you haven't already.

1:13 Now these are some abstract ideas and really black

1:16 holes were at first just a strange construction of general

1:20 relativity and just because something exists in the mathematics

1:23 does not mean it has to exist in reality.

1:26 So are black holes real?

1:28 The answer is yes.

1:30 Black holes are astrophysical realities that we have ample evidence for.

1:34 Yet to actually form a black hole,

1:37 Einstein's descriptions of mass, energy, and spaceime are not enough.

1:42 We need quantum mechanics.

1:44 If you're up for it, let's build a black hole.

1:48 First step, find a very massive star and wait.

1:51 Let it cook.

1:52 Not for long, because these guys have very short lives.

1:56 Just wait a few million years for the supernova.

1:58 If you get impatient,

2:00 you can turn up the core temperature by bombarding it with gravitational waves.

2:04 It'll be done quicker.

2:05 The details of the deaths of massive stars are pretty awesome,

2:08 but they can be found in lots of places, so we'll just gloss over them here.

2:12 In the last throws of a very massive stars life,

2:15 increasingly frantic fusion in the interior

2:17 produces one periodic table element after another

2:20 in Russian doll shells of increasingly heavy

2:23 nuclei that finally surround an iron core.

2:26 The formation of that core represents the end of exothermic fusion.

2:31 Fusing two iron nuclei absorbs energy.

2:34 It doesn't release it.

2:36 So, starved of an energy source, the stellar core collapses on itself.

2:41 Electrons are slammed into protons in the iron nuclei, forging a neutron star.

2:46 The collapsing outer shells ricochet off

2:49 this impossibly dense nugget in a supernova explosion,

2:52 enriching the galaxy with juicy new elements.

2:55 The leftover core, the neutron star, is a very weird beast.

2:59 A ball of neutrons the size of a city with the mass

3:04 of at least 1.4 suns and the density of an atomic nucleus.

3:08 We see them when we see them as pulsars.

3:11 Now beneath a thin atmosphere of iron plasma,

3:14 a neutron star is a quantum mechanical entity and it's

3:17 a quantum phenomenon that saves it for the moment from final collapse.

3:22 It's also a different quantum phenomenon that will let

3:25 us push it over the edge creating a black hole.

3:29 To understand how space works for a quantum object like this, we

3:33 need to think not in regular 3D space or even 4D spaceime,

3:38 but rather in sixdimensional quantum phase space.

3:42 For a neutron star, this is the space of both 3D position and 3D momentum.

3:47 And it defines the volume that can be

3:50 occupied by the strange matter in a neutron star.

3:53 Now the exact way that the matter of a neutron star fills

3:57 this 6D quantum phase space depends

3:59 on two important principles of quantum theory.

4:03 The pi exclusion principle and the Heisenberg uncertainty principle.

4:07 These govern the delicate balance between stability and collapse.

4:12 The ply exclusion principle basically just says that two

4:16 things can't occupy the same place at the same time.

4:19 And by thing I mean firm the particle type

4:22 comprising all regular matter for example electrons, protons, neutrons.

4:26 Now by place I mean location in quantum phase space.

4:30 So two firmians can occupy the same physical location just fine

4:35 as long as their momenta or any other quantum property is different.

4:39 Now this rule is what keeps electrons in their separate stable orbits

4:43 and in turn is part of what allows solid matter to have its structure.

4:48 In the case of a neutron star,

4:51 position momentum phase space is completely full of neutrons.

4:55 Every spatial location and every momentum location

4:58 connected to those spatial locations contains a neutron.

5:02 Okay, jargon alert.

5:04 This weird state of matter where phase space is completely full,

5:08 we call it degenerate matter.

5:10 And the degeneracy pressure resulting from particles not

5:14 having anywhere else to collapse into is incredibly strong.

5:18 strong enough to initially resist the insane

5:20 gravitational crush of a neutron star.

5:22 As far as we know, there's no way to overcome par exclusion,

5:27 at least not directly.

5:28 See, it's not a matter of force.

5:31 Two firmians just can't ever occupy the same quantum state, and that's that.

5:36 So, the neutron star is safe.

5:39 But come on, we want to build a black hole.

5:43 Fortunately, there's another quantum phenomenon that lets

5:46 us get around the pi exclusion principle.

5:49 The Heisenberg uncertainty principle tells us that the properties

5:52 of a quantum entity are fundamentally uncertain.

5:55 The details may be a topic for another episode,

5:58 but in short, quantum mechanics describes

6:01 matter as a distribution of possibilities.

6:03 Certain numerical properties that you can assign to a particle

6:07 exist in a wave of varying degrees of maybe.

6:11 Location is one such property.

6:13 A neutron, for instance, is not in any one place,

6:16 but exists as a cloud of possible locations

6:19 that might be tightly constrained or maybe very spread out.

6:24 Location remains a possibility cloud until

6:27 the neutron interacts with another particle,

6:30 at which point its location is resolved.

6:33 This is the weirdest, coolest aspect of quantum mechanics,

6:36 and we'll try to get back to it in another episode.

6:39 But for now, we have a black hole to make.

6:43 The Heisenberg uncertainty principle tells us

6:45 that particular pairs of quantities position and momentum

6:49 or time and energy must when taken

6:52 together contain a minimum degree of uncertainty.

6:54 If one is tightly constrained,

6:56 then the other must be uncertain and span a wide range of potential values.

7:01 So a neutron star is comprised of the densest matter in the universe.

7:06 Its constituent neutrons are about as constrained in position as you can get.

7:11 Therefore, the Heisenberg uncertainty principle tells us

7:14 that they must have highly undefined momenta.

7:17 Very very large neutron velocities become part of the possibility space.

7:22 To put it another way, the neutrons are packed so close together

7:27 in position space that their momentum space becomes gigantic.

7:31 Phase space expands.

7:32 And here's the thing, the denser the neutron star becomes,

7:37 the more momentum space you get.

7:40 So, Heisenberg lets us circumvent that pesky degeneracy pressure.

7:44 If we can somehow add more matter to a neutron star,

7:48 throw another star at it, maybe it won't get spatially larger.

7:52 The extra matter certainly needs somewhere to go.

7:55 The star must expand.

7:57 But it doesn't expand in position space.

8:00 The star expands in momentum space.

8:02 In position space, it actually gets smaller.

8:05 The more mass of the neutron star, the smaller its radius.

8:10 This is a quantum effect even though it's happening on the scale of a star.

8:15 Until now, the neutron star has hovered above a critical size.

8:19 The space-time curvature at the neutron star surface is pretty extreme.

8:23 Clocks run noticeably slower,

8:25 and the densities inside the star produce some very strange states of matter.

8:30 However, despite this, the star is still very much a thing in this universe.

8:35 And yet below the stars surface there lurks the potential event horizon.

8:40 The surface of infinite time dilation.

8:43 Now the event horizon doesn't actually exist as long

8:46 as the neutron star stays larger than the wouldbe horizon.

8:50 However, if we can increase the mass of the neutron star,

8:54 the actual star shrinks and the event horizon expands.

8:57 You can see where I'm going with this.

9:00 There's a mass where the radius

9:01 of the neutron star and the event horizon overlap.

9:04 It's three times the mass of the sun.

9:07 At this point, the event horizon actually comes

9:10 into being and the neutron star submerges beneath it.

9:14 We finally created our black hole.

9:16 But what happens to the star when it slips below its event horizon?

9:20 Everything inside is lost from this universe.

9:24 Spacetime is radically altered inside the star with all

9:28 geodics space-time paths turning inward towards the center.

9:31 When the black hole first forms,

9:33 the material inside must resemble the stuff of the original neutron star.

9:38 But there's no stopping ultimate collapse.

9:41 All paths lead to the central point of infinite curvature, the singularity.

9:46 From the point of view of the star itself, the inward cascade happens.

9:51 All position space collapses towards the singularity while momentum space

9:56 expands accordingly with the corresponding

9:59 enormous velocities all inward pointing.

10:02 Neutrons are certainly shredded into component quarks and gluons.

10:07 But what happens to these as the star

10:09 approaches an infinite decimal point, the plank scale?

10:12 Physics cannot yet tell us.

10:14 From the point of view of an outside observer, so us, this never happens.

10:19 The black hole forms.

10:21 The stellar core goes dark.

10:24 But on our timeline, nothing ever happens beyond the event horizon again.

10:29 We can't meaningfully think about what's

10:31 happening now beneath the event horizon.

10:33 There is no corresponding now.

10:35 The material of the star and all events that happen to it

10:39 are no longer a part of the timeline of the external universe.

10:43 On our clock, the singularity forms infinitely far in the future.

10:48 To us there is only the event horizon.

10:51 So this is how a real astrophysical black hole is made.

10:54 The mass of the stellar core becomes the apparent mass of the black

10:58 hole and very few other properties of the collapsed material are remembered.

11:02 The black hole retains mass,

11:04 electric charge and spin and these continue to influence

11:08 the outside universe sometimes in very important ways.

11:12 Of course, a real black hole is not

11:15 the static creature that we sometimes describe in theory.

11:18 They grow, they leak, they change.

11:21 We'll get to what this means for black holes

11:24 and for the universe in another episode of Spacetime.

11:27 In the very first instant after the Big Bang,

11:31 the density of matter was so great everywhere

11:34 that vast numbers of black holes may have formed.

11:38 These primordial black holes may still be with us.

11:42 There's no longer any question that black holes exist.

11:46 LIGO's recent observation of gravitational waves for emerging

11:49 black holes is a stunning confirmation of this fact.

11:53 Of course, we already thought they must exist as long as a volume

11:57 of space contains a high enough density of mass or energy.

12:01 General relativity tells us that a black hole will form.

12:05 In the modern universe,

12:06 there's only one natural way to get such insane densities.

12:10 That's in the core of the most massive stars when they die.

12:14 The process is awesome and we look at it in a previous video,

12:18 but that's the modern universe.

12:20 Once upon a time, the entire universe had the density of a stellar corpse.

12:26 In fact, soon after the big bang, the density of the universe was vastly higher.

12:31 So why didn't all the matter in the universe become black holes then?

12:35 Well, actually, some of it may have formed what we call primordial black holes,

12:40 and they may still be around today.

12:43 Let's back up a bit.

12:45 In order to make a black hole, extremely high density isn't enough.

12:50 You need a density differential.

12:52 Otherwise, there's no preferred direction for all that gravitational attraction.

12:57 Also, the gravitational pull needs to be strong

13:00 enough to overcome the expansion of the universe.

13:03 Now, matter in the early universe was pretty

13:07 smoothly spread out and the universe was expanding fast.

13:10 That means most of it avoided collapsing into black holes.

13:14 And that's a very good thing, by the way.

13:17 However, it wasn't perfectly smooth.

13:19 There were lumps.

13:20 The oldest light we can see is the cosmic microwave background radiation.

13:25 It reveals tiny differences in the density of matter

13:29 from one point in space to the next.

13:32 The universe was very slightly lumpy at the moment

13:36 the CMBB was created about 400,000 years after the Big Bang.

13:40 These density fluctuations were enough to kickstart the formation of galaxies,

13:44 but certainly not enough to immediately collapse into black holes.

13:50 Yet, if we rewind time, those fluctuations must have been much stronger.

13:55 It's thought that these fluctuations originally formed when

13:58 the entire observable universe was smaller than a single atom.

14:03 Back then, quantum fluctuations caused a sort

14:07 of static fuzz across the minuscule cosmos.

14:11 There are several different stories for the initial size and growth

14:16 of these fluctuations and cosmic inflation certainly plays a role.

14:20 But it's well within the possibility of many models

14:24 that some of these fluctuations were at some point

14:28 in the early expansion intense enough to resist

14:31 the local expansion of the universe and form black holes.

14:36 Some highly speculative big bang physics also predicts primordial black holes.

14:42 For example, the collapse of cosmic string

14:45 loops and the collision of bubble universes.

14:48 Awesome.

14:49 Now, these models can predict a huge

14:52 range of possible masses for primordial black holes.

14:55 PBH's as we like to call them in the biz.

14:59 PBHs could have been formed at a few

15:02 grams to tens of thousands of times the mass

15:05 of the sun depending on which formation model you

15:08 go with, or they might not exist at all.

15:11 That's a big possibility.

15:12 If they do exist, then there's probably a particular

15:15 mass range that most of them formed at.

15:18 Discovering PBH's and learning their masses would tell us

15:22 a huge amount about the earliest moments of our universe.

15:25 We need to hunt for these black holes or their influence in the modern universe.

15:31 First of all, we aren't going to find primordial black holes less

15:35 than around a billion tons or the mass of a small asteroid.

15:40 They would have all evaporated away due to Hawking radiation.

15:44 I'll get back to that.

15:45 Black holes larger than this should still be around,

15:48 but they'd be very difficult to spot being so black and all.

15:52 If PBHs are rare, then it may be

15:55 impossible to confirm or disprove their existence entirely.

15:58 However, there is a question that we can answer with some certainty.

16:03 Could primordial black holes be dark matter?

16:08 This is a slightly terrifying possibility that 80% of the mass

16:13 in the universe is in the form of countless swarming black holes.

16:19 That's a lot of primordial black holes.

16:22 And so we expect them to leave their mark on the universe in different ways.

16:28 For one thing, if these little knots of warped spaceime are everywhere,

16:33 then they should produce obvious gravitational lensing.

16:36 We'd expect them to frequently pass in front of other space stuff.

16:41 Depending on PBH mass, this would cause a twinkling effect.

16:46 microl lensing in stars in our galaxy,

16:49 in distant quazars, even in gammaray bursts.

16:52 And well, we just don't see enough of this twinkling,

16:56 which rules out a lot of possible masses.

16:59 There's also the fact that swarms

17:01 of black holes would mess up their surroundings.

17:04 As the heavier ones buzz around the galaxy,

17:08 they should pull apart loosely bound binary systems

17:10 and have an effect on the structure of star clusters.

17:14 The smallest should fall into neutron stars,

17:17 causing them to either explode or become black holes themselves,

17:21 but we see loosely bound binaries and normal

17:25 star clusters and plenty of neutron stars.

17:28 These arguments let us rule out all but a very narrow set

17:32 of mass ranges for primordial black holes as an explanation for dark matter.

17:37 The options we're left with are either lots of PBH's

17:42 with masses similar to a large asteroid like series,

17:46 so around 10^ of 21 kg, or a much smaller number of really big PBHs,

17:53 around 20 to 100 times the sun's mass.

17:56 Now, this last possibility is sketchy.

17:59 Some scientists think that the voracious feeding of lots of really big

18:03 primordial black holes would have left

18:06 their mark on the cosmic microwave background.

18:09 However, others argue that the recent LIGO detection of the merging of two

18:14 approximately 30 solar mass black holes is evidence in favor of this idea.

18:20 With new observations from both regular telescopes and LIGO,

18:24 we're rapidly closing all of these mass windows.

18:27 Before too long, we'll either spot the signature

18:31 of primordial black holes at these masses

18:34 or discover that PBH's are actually very

18:37 rare and that they're certainly not dark matter.

18:41 This latter is more likely, but we'll see.

18:44 Of course, primordial black holes that have already evaporated

18:48 due to Hawking radiation definitely are not dark matter,

18:51 and that rules out any PBH is lighter than about a billion tons.

18:56 But that last stage of Hawking evaporation is very fast.

19:01 In fact, it's explosive.

19:03 It's possible that certain types of very short gammaray bursts

19:08 are these final flashes from PBH's evaporating in our galaxy.

19:13 Some highly speculative stuff, but also some highly awesome possibilities.

19:19 It wouldn't be right to end a discussion on primordial black holes

19:23 without talking about what would happen if one passed through the solar system.

19:27 Even a close encounter with a black hole as massive

19:31 as the sun or higher would be pretty catastrophic.

19:34 If it passed anywhere near the planetary system,

19:37 the gravitational tug would disrupt the planet's orbits.

19:41 Even if it passed by the outskirts of the solar system,

19:44 it could shake up the orc cloud and send

19:46 a nice rain of comets to pepper the inner solar system.

19:50 Of course, regular black holes from supernova can and perhaps have done that.

19:56 Having highmass primordial black holes just makes it more likely.

20:01 If PBH's are closer to the mass of a large asteroid,

20:05 then they're too low in mass and probably

20:07 moving too fast to do any gravitational damage.

20:10 They'd just zip right through the solar system unnoticed.

20:13 It's a different matter if one hit the Earth traveling at a couple hundred km/s,

20:20 it would punch straight through the planet,

20:22 but certainly leave a narrow column of vaporized rock behind it.

20:26 These sorts of hits would be incredibly rare and may never happen.

20:32 However, if primordial black holes have approximately the minimum

20:36 possible mass to not have evaporated around a billion tons,

20:41 these would be much more abundant than asteroid mass PBH's.

20:45 In fact, they may pass through the planet frequently.

20:48 A billion ton black hole has an event horizon around the size of a proton.

20:53 So, it would pass through the planet as though the Earth were made of air.

20:58 However, it would deposit something like a billion

21:01 jewels of Hawking radiation on its way through.

21:04 This should leave detectable traces in crystalline material in Earth's crust.

21:10 In fact, perhaps geologists will be

21:12 the first to discover primordial black holes.

21:15 If they're out there, someone will figure it out.

21:18 I mean, how long can the universe expect to hide

21:21 vast numbers of holes punched in the fabric of spaceime?

21:26 The singularity, the point of infinite density at the core of a black hole,

21:32 but also so much more.

21:34 In mathematics, singularities come in wild and wonderful varieties.

21:37 The black hole itself contains more than one.

21:41 Isaac Newton's universal law of gravitation was an incredible

21:44 insight when he figured it out in the late 1600s.

21:47 In fact, we still use it to fly spacecraft around the solar system today.

21:53 However, it has its problems.

21:55 Let's look at the math.

21:57 Newton's equation gives you the gravitational force exerted between

22:01 two masses m1 and m2 that are distance r apart.

22:06 Straightforward enough, that r squared in the denominator spells trouble.

22:11 It means the force gets larger the closer the masses are to each other.

22:16 That makes sense.

22:17 But what about when r gets really close to zero?

22:21 Then the result of the equation,

22:23 the force becomes extremely large and is infinite when r becomes equal to zero.

22:30 That doesn't really make a lot of sense.

22:34 Infinite force means infinite acceleration, which means well, physics breaks.

22:39 According to Newton's law,

22:41 in order to feel that infinite gravitational acceleration,

22:44 you need to get zero distance from an object's center of mass.

22:48 That means all of that object's mass

22:50 would need to be concentrated at that center,

22:53 a single point of zero size, which means infinite density,

22:57 and that of course would make it a black hole.

23:01 We often use the word singularity to describe

23:04 the hypothetically infinitely dense core of a black hole.

23:08 But in math, the meaning of this word is much more general.

23:13 You know what?

23:14 Instead of me trying to explain mathematical singularities,

23:16 how about we get a real mathematician to do this properly?

23:20 Guys, meet Kelsey Houston Edwards of the new PBS show, Infinite Series.

23:25 Hey, Kelsey.

23:25 Hey, Matt.

23:26 Thanks for having me on.

23:28 Kelsey, the math for black holes goes

23:30 to infinity for different properties and in different locations.

23:34 What does this mathematical weirdness tell us?

23:37 Well, mathematicians use the word singularity pretty broadly.

23:41 It's really just any point that causes problems.

23:45 Commonly, these problematic points are

23:47 where quantities become bigger and bigger,

23:50 approaching infinity, as they do near a black hole.

23:53 Some singularities come about from your choice

23:55 of reference frame or coordinate system.

23:57 An example of a frame dependent singularity that might be familiar

24:02 to space-time viewers is the event horizon of the black hole.

24:06 I'll leave that to you to explain.

24:08 Here on Earth, the north and south

24:10 pole are examples of coordinate singularities.

24:12 It's possible to pass through time zones infinitely quickly,

24:16 but only because of your choice of spherical coordinates.

24:19 All right, that makes sense.

24:21 But the gravitational singularity at the center

24:23 of a black hole is a so-called real singularity, right?

24:27 I mean, the curvature and the density

24:30 are infinite from any frame of reference, right?

24:33 And there's no way to avoid a horrible

24:36 crushing death just by switching coordinate systems.

24:38 But the reality of the black hole singularity may give

24:42 reason to doubt the theory that predicts such a thing.

24:45 In fact, it's happened many times before.

24:47 From models of the movement of water to human population growth.

24:52 Mathematics predicts a physical singularity and we've

24:55 been forced to reject the corresponding theory.

24:58 So you're saying Einstein is wrong?

25:01 blasphemy.

25:02 Actually, Einstein himself agreed on this point.

25:05 Guys, you should check out Kelty's show, Infinite Series,

25:09 where she goes into much more depth on the nature of singularities.

25:13 It's a math show, by the way, so it's sometimes about real stuff.

25:18 Mathematicians are lucky.

25:19 Being limited by reality is so boring.

25:22 So, does the fact that it includes a singularity

25:26 mean there's something fundamentally wrong with Newton's law of gravitation?

25:30 Well, we already know the law isn't really so universal.

25:34 When the gravitational field is too strong,

25:36 say near a star or a black hole, Newton's law gives the wrong answers,

25:41 and we need Einstein's general theory of relativity,

25:45 which is the far more complete theory of gravity.

25:48 So, does general relativity rid us of Newton's pesky singularity?

25:52 Uh, no.

25:53 In fact, it gives us even more singularities.

25:57 To understand this, we need to look at something called the Swatshield metric.

26:03 It's what you get when you

26:05 solve the delightfully complicated Einstein field equations

26:08 for the simple case of a spherically

26:11 symmetric mass in an otherwise empty universe.

26:14 We're going to simplify it to only allow

26:16 movement directly towards or away from our massive object.

26:20 In that case, it looks like this.

26:23 Okay, that sure is some math.

26:25 Hey, this is spacetime.

26:26 we can deal.

26:27 Actually, it's really easy to see the singularities in this equation.

26:31 But let me first walk you through what it tells us.

26:35 The swast shield metric allows us to compare two points or events

26:39 in spaceime around a massive object from the perspective of different observers.

26:44 For example, a short space-time path of some object, so its world line,

26:50 might move an object a distance deltar over a short time step delta t.

26:55 That motion is towards or away from the mass

26:59 of object which is a distance r away.

27:02 That delta s squ thing is the space-time interval.

27:06 And it's a strange and interesting quantity.

27:10 Every inertial so non-acelerating observer will agree on the same space-time

27:14 interval for every pair of events and for every world line.

27:18 We talk about this in a lot more detail in our relativity playlist.

27:23 Today, we're going to keep it simple.

27:26 As long as our object's world line doesn't require faster than light motion,

27:31 then the square root of the space-time interval is equal

27:34 to the amount of time that the object itself feels over that interval.

27:39 We call that the object's proper time.

27:42 Oh, and r subscript s is a measure of the mass of the mass of object.

27:48 In fact, it's 2 times the gravitational constant times the mass.

27:52 There would have been some speed of lights through the equation,

27:55 but we set them equal to one because we're that cool.

27:59 Now, the first thing to notice is that the singularity

28:02 is still present in the SWAT shield metric.

28:05 R the distance to the center of mass remains

28:08 in the denominator just as it was in Newton's law.

28:11 When you use the swast shield metric to calculate

28:14 the curvature at r equals0 that curvature is infinite.

28:18 This gives us the same infinite gravitational pull as Newtonian singularity.

28:22 And just as with the Newtonian case this gravitational

28:27 singularity can only exist if infinite densities are possible.

28:32 But unlike Newton's law of gravity the swast shield metric

28:36 actually tells us whether or not that infinite density is expected.

28:40 To see how we need to look at the second singularity in this equation,

28:46 a singularity that Newton's law does not contain.

28:49 See, when distance to the center of mass is exactly equal to this RS thing,

28:55 then RS over R is equal to 1,

28:59 at that point the entire equation starts behaving very badly.

29:04 It's as much a mathematical singularity as the one

29:07 in the center of the black hole.

29:09 If you haven't guessed, this bad behavior corresponds to the event

29:14 horizon and RS is the SWAT shield radius.

29:19 Imagine an object sitting at the event horizon but not moving.

29:23 So it's delta R would be zero.

29:26 But this bracket is zero also because 1 minus one.

29:31 The entire space-time interval for a non-moving

29:33 point at the event horizon is zero.

29:37 But remember for sub lighteed world lines the space-time

29:41 interval tells us the rate of flow of proper time.

29:45 So does that mean time doesn't pass for an object hovering at the event horizon?

29:50 Not quite.

29:51 Time certainly doesn't pass at the event horizon.

29:55 No clock ticks can ever happen there.

29:59 But the prohibition against objects experiencing time at the event horizon

30:04 is actually a prohibition against objects spending time at the event horizon.

30:10 No temporal thing, nothing that normally experiences the passage

30:14 of time can have a space-time interval of zero.

30:17 At the event horizon,

30:19 the only way to get a nonzero space-time interval is to have a nonzero delta r.

30:26 An object at the event horizon has to change its

30:29 distance from the black hole to keep its clock ticking.

30:32 That means falling below the event horizon.

30:36 And once inside, inward spatial movement continues to be the only

30:40 way to fuel the ticking of an object's proper time clock.

30:44 We'll come back to that bit of awesome weirdness in a future episode.

30:48 There is one thing that can have a space-time interval of zero.

30:53 Light.

30:54 Actually, anything capable of traveling at light speed

30:57 can only have a space-time interval of zero.

31:01 From its perspective, a photon exists in a single instant,

31:05 and so it can hang out at the event horizon,

31:09 which also only exists at one infinitely stretched out instant.

31:12 The act of crossing the event horizon is

31:15 where this singularity really starts to behave badly.

31:18 At the moment of crossing, the denominator here in the swar metric is zero.

31:24 and the whole equation blows up to infinity.

31:28 But what is actually infinite here?

31:30 It's nothing physical.

31:32 It's the fact that even an outgoing light

31:34 ray takes infinite time to move any distance.

31:37 So using boring old time and distance, delta t and delta r,

31:41 doesn't let us trace a world line smoothly across the event horizon.

31:46 That horizon is a coordinate singularity, just like Kelsey talked about.

31:52 But that means we can fix it.

31:54 There are ways to construct our space-time axes.

31:56 So this singularity just evaporates.

31:59 For example, Edington Finkelstein taught us coordinates,

32:04 the compactify with the stretching of spaceime to cancel out the infinities.

32:09 That's a bit much for right now, but Google away, my friends.

32:13 Anyway, the upshot is that it's really

32:16 a breeze to drop through the event horizon, both physically and mathematically.

32:21 Of course, once inside the event horizon,

32:24 we still have that central singularity to deal with.

32:28 Unfortunately, that one can't be done away

32:30 with by a simple change in coordinates.

32:33 But can that point of infinite density really exist?

32:37 Actually, Einstein's theory and the swaste solution

32:41 that is derived from it suggests it must exist.

32:45 The apparent inevitability of this singularity may

32:49 be evidence that general relativity is incomplete.

32:53 But to better understand why the central

32:57 infinity is unavoidable in Einstein's theory,

33:00 we have to go back to that coordinate shift at the event horizon there.

33:05 The causal roles of space and time switch places,

33:08 and the central singularity becomes not so much a location in space,

33:13 but an inevitable future.

33:15 Actually, to really get this, we're going to need another entire episode.

33:21 Stand by to explore what happens when you switch

33:27 the causal roles of time versus space to space time.

33:33 The special theory of relativity tells us

33:36 that one person's past may be another's future.

33:39 When time is relative, paradoxes threaten.

33:41 Today, we peer deeper into Einstein's theory to find that the immutable ordering

33:48 of cause and effect emerges when we discover the causal geography of spacetime.

33:54 Recently, we've been talking about the weirdness of spacetime

33:57 in the vicinity of a black hole's event horizon.

34:00 Very soon, we'll be dropping below that horizon

34:02 to peer at the interior of the black hole.

34:05 There, space and time switch roles.

34:08 But to truly understand that bizarre statement,

34:11 we need to think a little bit more about

34:14 how the flow of time is described in relativity.

34:17 Today, we're going to look at the amazing geometric structure that time,

34:22 or more accurately, causality, imprints on the fabric of spacetime.

34:26 First, let's recap a little bit of Einstein's special theory of relativity.

34:31 There are two previous episodes in particular that will

34:35 be useful here if you find you need more background.

34:38 Special relativity tells us that our experience

34:41 of both distance and time are well relative.

34:44 If I accelerate my rocket ship to half the speed of light,

34:47 the distance I need to travel to a neighboring

34:50 star shrinks dramatically from my point of view.

34:53 An observer I leave behind with an amazing

34:56 telescope observes me traveling the entire original distance,

35:00 but will perceive my clock as having slowed.

35:03 The combination of this length contraction

35:05 and time dilation allows both moving and stationary

35:08 observers to agree on how much older everyone looks at the end of the journey.

35:13 Everyone agrees on the number of ticks that occurred on everyone else's clock.

35:19 They just don't agree on the duration of all of those ticks.

35:23 Reminder, time measured by a moving observer

35:25 on their own clock is called proper time.

35:28 But counting those clock ticks isn't the best

35:31 way for everyone to agree on space-time relationships.

35:35 There's this thing called the space-time

35:37 interval that relates observer dependent perspectives

35:40 on the length and duration of any journey that all observers will agree on.

35:47 even if they don't agree on the delta x and deltat t of that journey.

35:52 We've talked about it before,

35:54 but it's a tricky concept to understand intuitively.

35:57 But we want that intuition because more than proper time,

36:01 the space-time interval defines the flow of causality.

36:04 In relativity, 3D space and 1D time become a single 4D entity called spacetime.

36:11 To preserve our sanity, we represent this on a space-time diagram,

36:15 plotting time and only one dimension of space.

36:19 We'll see our causal geometry emerge plain as day.

36:23 Even in this simplified picture,

36:25 there is no standing still on a space-time diagram.

36:28 If I don't move through space,

36:30 I still travel forward in time at a speed of exactly 1 second per second.

36:36 According to my proper time clock,

36:38 motion at a constant velocity appears as a sloped line and the time

36:42 axis is scaled so that the speed of light is a 45° line.

36:47 Now, let's say we have a group of space-time travelers.

36:50 They start at the origin where x and t equal zero.

36:54 They race away to the left and the right

36:57 for 5 seconds according to their own watches.

37:00 They all travel at different speeds,

37:02 some close to the speed of light, but never faster.

37:05 The path they cut through spaceime is called their world line.

37:10 My world line is only through time.

37:13 And the tick marks on the time axis

37:15 correspond to my own proper time clock ticks.

37:18 The faster a traveler moves, the longer their world line.

37:22 That's not just because of their speed, though.

37:25 To me, their clocks tick slow.

37:27 They time their journey on these slow clocks.

37:30 So I perceive them traveling for longer.

37:33 Accounting for this, we find that our space-time travelers

37:36 are arranged on a curve that looks like this.

37:40 This shape is a hyperola.

37:42 Drawing a connecting line at the tick of every traveler's

37:46 proper time clock gives us a set of nested hyperbole.

37:49 But these aren't just a pretty pattern.

37:51 These curves are kind of the contours defining the gradient of causality down

37:56 which time flows and etched into spaceime

37:59 by the equations of special relativity.

38:02 But to understand why, we need to see how these proper

38:06 time contours appear to other space-time travelers.

38:08 Instead of doing that with equations, we can see it with geometry.

38:14 First, we need to draw the space-time diagram

38:17 from the perspective of one of the other travelers.

38:20 To transform the diagram,

38:21 we need to figure out what they see as their space and time axes.

38:27 Time is easy.

38:28 They see themselves as stationary.

38:30 So, their time axis is just their own constant velocity world line.

38:35 and their x-axis.

38:36 Well, from my stationary point of view,

38:40 I define my x-axis as a long string of space-time events at different distances,

38:45 but that all occur simultaneously at time t=0.

38:49 To observe those points,

38:50 I just wait around until their light has had time to reach me.

38:56 At every future tick of my clock, a signal arrives from the left and the right,

38:59 and I use that to build up a set of simultaneous events,

39:04 defining my tals 0 xaxis.

39:06 Our traveler does the same thing, but from my point of view,

39:11 their clock is slow, so I see them register signals at a different rate.

39:15 At the same time, they're moving away from the signals coming

39:18 from the left and towards the ones originating on the right,

39:22 affecting which signals are seen at a given instant.

39:26 The traveler infers a set of simultaneous

39:29 events that to me are not simultaneous,

39:32 but there is no preferred reference frame.

39:35 Their sloped xaxis is right for them.

39:39 Even just doing this graphically, we see that the traveler's x-axis is rotated

39:45 by the same angle as their time axis.

39:48 That comes from insisting that we all see the same speed of light,

39:54 45° on the spac-time diagram.

39:56 Moving between these reference frames is now

39:59 a simple matter of squaring up our traveler's axes.

40:02 In fact, we grid up the diagram with a set of lines parallel

40:06 to these new axes and square

40:08 up everything while maintaining our intersection points.

40:11 My world line is now speeding off to the left while our traveler is motionless.

40:18 We just performed a Lorent transformation but using geometry rather than math.

40:25 This transformation allows you to calculate how properties like distance,

40:28 time, velocity, even mass and energy shift between reference frames.

40:32 But check out what happens if I attach pens to all of the intersections.

40:38 When I transform between frames, they trace out our hyperbole.

40:43 Those intersections represent locations of space-time

40:46 events relative to the origin.

40:49 They will always land on the same hyperola,

40:52 no matter the observer's reference frame.

40:54 I told you that these contours show where clocks

40:58 moving from the origin reach the same proper time count.

41:02 But more generally, each represents a single value for the space-time interval.

41:07 The delta x and delta t of the event

41:10 at the end point of a traveler's world line might

41:13 change depending on who is watching but the hyperbolic

41:17 contour that they landed on the space-time interval will not.

41:21 This is because the space-time interval

41:24 itself comes directly from the lorren transformation

41:27 as the only measurement of space-time separation

41:31 that is unchanging or invariant under that transformation.

41:35 Now we can finally get to why this thing

41:39 is so important and what it really represents.

41:42 It may seem counterintuitive that an event very close

41:45 to the origin in both space and time can be separated

41:50 from that origin by the same space-time interval as an event

41:54 that is very distant in both space and time.

41:57 The hyperbolic shape seems to demand that.

42:00 But remember, it takes the same amount of proper time to travel from the origin

42:05 to a nearby near future event compared

42:08 to a distant far future event on the same contour.

42:12 From the point of view of a particle communicating some causal influence,

42:18 those points are equivalent.

42:21 The space-time interval tracks this causal proximity.

42:25 We can think of these lines as contours on a sort of causal geography.

42:29 The way I define the space-time interval,

42:31 it becomes increasingly negative in the forward time direction.

42:35 So we can represent this as a valley dropping away from me here at the origin.

42:40 I naturally slide through time by the steepest path straight down.

42:44 I can change that path by expending energy to change my velocity.

42:49 Although doing so realines the contours,

42:51 so I always slide down the steepest path.

42:55 There's no point anywhere downhill that I can't reach as long

42:58 as I can get close enough to the speed of light.

43:02 In fact, the nearest downhill contour defines the forward

43:06 light cone for anyone anywhere on the space-time diagram.

43:11 But uphill is impossible as long as the cosmic speed limit is maintained.

43:17 Breaking that speed limit and sliding uphill are equivalent.

43:21 To reverse the direction of your changing space-time

43:24 interval is to reverse the direction of causality.

43:27 To travel backwards in time,

43:29 the space-time diagram we looked at today was for a flat or manowski space

43:34 in which faster than light travel is

43:37 the only way to flip your spac-time interval.

43:39 But in the crazy curved space within a black hole, it gets flipped for you.

43:46 We'll soon see how this requirement of a forward causal evolution leads to some

43:53 incredible predictions when we try to calculate

43:57 the subevent horizon interval of spaceime.

44:01 Today on spacetime, we're going to talk about time

44:05 space or the strange switching in the roles of space

44:08 and time that occurs in the mathematics when we

44:11 drop below the event horizon of a black hole.

44:14 What does this bizarre statement space and time switching roles even mean?

44:20 Is this space-time dyslexia purely a mathematical quirk

44:24 or does it correspond to real tiny wimy weirdness?

44:29 We've been working up to this one, so you might want to hit pause and check out

44:33 these episodes if you think you need some more background.

44:36 Okay, let's get started.

44:38 First, we'll think about what the flow of time

44:41 looks like without black holes or even space-time curvature.

44:44 When we talked about the geometry of causality,

44:47 we saw that this quantity that we called

44:50 the space-time interval governs the flow of cause and effect.

44:55 The only reliable ordering of events in a relative universe.

44:59 I'm going to show you the math one more time,

45:02 and then we'll get back to doing all of this graphically.

45:05 The spac-time interval is defined like

45:08 this for boring old flat or Minkovsky space.

45:11 Different observers may report that two events are separated by different

45:16 distances delta x and by different amounts of time delta t.

45:20 However, all observers record the same space-time interval.

45:24 If one event causes a second event,

45:27 the space-time interval must be zero or negative.

45:30 That just means that a light speeded causal link may have traveled between them.

45:35 You could say that an object at a given space-time instant

45:40 is caused by whatever version of itself existed an instant earlier.

45:45 So, world lines of objects have decreasing space-time intervals.

45:49 In fact, forward temporal evolution requires a negative space-time interval.

45:54 In flat spacetime, that negative sign in front

45:57 of the delta t drives that forward evolution.

46:01 This makes t the timelike coordinate while x is the space-like coordinate.

46:07 For causality to be maintained, the timelike coordinate must always increase.

46:12 Reversing causality means flipping the sign of the space-time interval.

46:17 In our episode on super luminal time travel, we saw that in flat space,

46:23 this means traveling faster than light, which is of course impossible.

46:27 But if we introduce a black hole,

46:29 we now have a second way to flip the sign of the space-time interval.

46:34 We're going to see how this changes the behavior of time in very strange ways.

46:39 Add a non-rotating uncharged black hole

46:42 and the space-time interval becomes this.

46:46 This comes from Carl Schwartzshield's solution to the Einstein field equations,

46:51 the very first accurate description of a black hole.

46:54 I've left out a few terms.

46:56 This equation assumes no orbital motion,

46:58 only motion towards or away from the center of the black hole,

47:01 which is a distance r away.

47:04 That RS is the swast shield radius, the radius of the event horizon.

47:09 Very far from the event horizon,

47:11 the swast shield interval becomes the good old Minkovsky interval.

47:15 and time and space are nicely separated.

47:18 But if an object gets close to the event horizon,

47:22 so are just a little bit bigger than RS,

47:26 that stuff in the two brackets describes extreme warping of spaceime.

47:31 But as long as you're outside the event horizon, time behaves itself mostly,

47:37 a negative space-time interval still means causal movement.

47:40 And the only way to break causality is still with faster than light travel.

47:45 Things change radically below the event horizon.

47:48 When R gets smaller than RS, then both of these brackets become negative.

47:54 The entire deltar stuff is now negative and the delta t stuff is positive.

47:59 Below the event horizon, there is only one way to maintain the respectable

48:04 causal progression expected of a well-mannered temporal entity.

48:08 That's to fall inwards to have a nonzero delta r.

48:13 As it happens, you don't have a choice.

48:16 Space itself is falling inwards faster than

48:18 the speed of light towards the central singularity.

48:21 It carries you with it and drives your personal clock forward as it does so.

48:26 In the mathematics, the coordinate r which once represents a distance

48:30 now grants the negative sign needed to maintain your causal flow.

48:36 It becomes timelike.

48:37 It's unidirectional.

48:38 Meanwhile, the coordinate previously known as time

48:42 t lost its negative sign and become space-like.

48:46 So, it can be traversed in any direction or not traversed at all.

48:51 But what does all of this time space switching actually look like?

48:56 Let's fall into the black hole one

48:58 more time now graphically instead of mathematically.

49:01 Back out here in the regular universe,

49:05 it's pretty obvious where the past and the future are.

49:09 On our ever popular space-time diagram, we see a sharp division between the two.

49:14 Our past light cone encompasses all of spaceime that could have influenced us.

49:19 While our future light cone shows us the parts

49:22 of the universe that we might ever hope to encounter or influence.

49:26 Which direction is the future?

49:29 ahead along our time axis and at right angles to all of our space axes.

49:36 Our future light cone stares fixedly forwards,

49:39 encompassing all spatial directions equally.

49:41 This is no longer true if we introduce gravity.

49:45 Close to a massive object, your future is no longer at right angles to space.

49:50 It becomes slightly tilted in the direction of that mass.

49:53 send out a burst of future defining light rays and they

49:56 won't spread out evenly because they bend towards the gravitational field.

50:00 As you approach the event horizon of a black hole,

50:03 more and more light rays are turned towards the event horizon.

50:07 Your future light cone and your time axis begin to blur

50:11 together with the inward radial axis of the black hole.

50:15 At this point, it's time we switch diagrams.

50:18 Close to and within the black hole.

50:20 The Penrose diagram is much more useful.

50:23 It deals with the extreme stretching of space and time

50:27 by compactifying lines of constant space or time close to its boundaries.

50:31 We talked about these diagrams previously,

50:33 but an important thing to remember is that the lines

50:37 of constant space and time are curved so

50:39 that light cones remain upright and light always travels

50:43 at a 45° angle even inside the black hole.

50:47 This entire diagonal line represents the event horizon.

50:50 Watch what happens to our view of the universe as we approach it.

50:55 Our entire future light cone encompasses more and more of the event horizon.

51:01 That last tiny sliver is a narrowing window directly above

51:05 that you could escape to at close to the speed of light.

51:10 Meanwhile, our past light cone now encompasses light that has been struggling

51:14 to escape from just above the event horizon since the distant past.

51:19 But we still see nothing from below the horizon.

51:23 Yet, as soon as we pass the horizon, everything changes.

51:27 The outside universe exits our future light cone,

51:31 which now just contains the singularity.

51:34 We also begin to encounter a new set of photons from the past.

51:38 At the moment of crossing,

51:39 light rays from the event horizon itself are suddenly visible.

51:42 In fact, we plummet through a sea of light

51:46 that is eternally climbing outwards but getting nowhere.

51:49 After that, we have access to the history of the interior of the black hole.

51:54 As we fall with the faster than light flow of spaceime,

51:58 we overtake light that is outward pointing.

52:01 That light isn't actually making headway outwards.

52:03 It's trying to swim upstream and failing

52:06 against the faster than light cascade of spaceime.

52:10 Some of this light might be from the collapsing

52:13 surface of the star that first formed the black hole,

52:16 emitted long before we entered the event horizon.

52:19 It appears to come from below us because it's trying to climb upwards.

52:24 In fact, though, it was emitted at larger radi than wherever we encounter it.

52:28 Also, in our past light cone are light rays that are pointed inwards.

52:33 some of them coming from the outside universe.

52:36 This light overtakes us as we fall.

52:38 This is light that entered the event horizon after

52:41 we did and appears to reach us from above.

52:44 We can try to move towards either source of light,

52:47 down towards light from the black holes past

52:49 or up towards light from the black hole's future.

52:52 Those directions, those spatial freedoms are now

52:55 described by what was once the time coordinate, but it's no longer timelike.

53:00 You can traverse it in either direction, making it space-like.

53:04 Doing so isn't actually traveling in time,

53:07 even though there's a sense of past events in one direction,

53:11 the collapsing star, and future events in the other,

53:13 everything that fell into the black hole after us.

53:16 But remember that our future light

53:18 cone actually just points towards the singularity.

53:21 If we try to accelerate in either direction,

53:24 up or down, we just quicken our demise.

53:27 Best just to fall.

53:29 It's the last mercy granted by the black hole.

53:32 It transports us to our doom by the slowest path unless we resist.

53:37 Below the event horizon, there's still a sense of spatial upness and downness.

53:42 However, the old radial dimension isn't space-like.

53:45 It's timelike.

53:46 Every photon that reaches us was emitted

53:49 at some larger radius than wherever we encounter it.

53:53 Even if it's old light struggling outwards, the past is radially outwards.

53:58 and all possible future directions lead radially inwards in the same way

54:03 that all world lines move towards the future in the outside universe.

54:08 Time is layered radially and r is timelike unidirectional.

54:12 The singularity becomes a future time not a central place.

54:17 In fact, the swast shield metric really gives

54:21 two separate space-time maps in a single equation.

54:25 One for above and one for below the event horizon.

54:28 The coordinates R and T play different roles in those regions.

54:32 There are other coordinate systems in which that switch never happens.

54:36 But this mysterious dimensional flip does give

54:40 us some fascinating insight into how time and space blend together in what is

54:47 perhaps the strangest place in all of spaceime.

54:51 Lurking in the depths of the mathematics of Einstein's general

54:55 relativity is an object even stranger than the mysterious black hole.

54:59 In fact, it's the black holes mirror twin, the white hole.

55:04 Some even think that these could be the origin of our universe.

55:08 The astrophysical phenomenon of the black hole has captured

55:12 the imagination of scientists and science enthusiasts alike for many decades.

55:17 When the idea first emerged from Einstein's general theory of relativity,

55:22 physicists wondered how seriously to take this mathematical

55:26 description of an inescapable region of spaceime.

55:29 Astronomers have since demonstrated that black holes

55:33 are very real with convincing evidence that quazars,

55:37 x-ray binaries, even the center of our own

55:40 Milky Way galaxy harbor these gravitational monstrosities.

55:43 But the mathematics that predicts the existence of the black hole also describes

55:51 entities that are even stranger but whose

55:54 relationship with reality is still unclear.

55:58 One such entity is the white hole.

56:00 A white hole is the opposite of a black

56:04 hole in a very literal mathematical sense.

56:07 In fact, it's a time reversed black hole.

56:09 A black hole is defined as a region of inward flowing spaceime with a one-way

56:15 boundary called the event horizon from inside of which nothing can ever escape.

56:21 That makes a white hole a region of outward flowing spaceime.

56:25 It also has an event horizon, but that horizon prohibits entry, not exit.

56:30 Nothing outside a white hole can ever enter,

56:33 and everything inside must be ejected.

56:36 Not even light can leave a black hole, hence the whole black thing.

56:41 But light can only leave a white hole.

56:44 So, these might be expected to radiate like crazy,

56:48 and white would be an understatement.

56:51 Now, before everyone gets too excited,

56:54 white holes are probably a figment of mathematical imagination,

56:58 but they're a fascinating one,

57:00 and the idea may help us understand the origin of the universe.

57:05 White holes first emerged in the very

57:08 earliest mathematical description of black holes.

57:10 Only a few months after Einstein published his general theory of relativity,

57:15 Carl Schwartzshield solved its equations for a very particular case.

57:20 a single point of mass in an otherwise empty spaceime.

57:25 The resulting SWAT shield metric actually describes a black hole,

57:30 the simplest black hole possible,

57:32 one without spin, without charge, or without change.

57:36 An eternal black hole that doesn't grow or shrink and has always existed.

57:43 We've talked quite a bit about the bizarre behavior of space

57:47 and especially time at and below the event horizon of a black hole.

57:52 Here's a little playlist if you want a refresher.

57:54 But here's the lowdown.

57:56 The time that happens inside a black hole is not

58:00 part of the past or future history of the outside universe.

58:04 From the perspective of an outside observer,

58:06 any events occurring at the event horizon,

58:09 including falling into it, happen infinitely far in the future.

58:13 Once you fall into the black hole,

58:16 the swath shield metric tells us that space and time switch their roles.

58:21 The singularity no longer occupies a central location.

58:25 It now occupies an inevitable future time.

58:29 Now, a real black hole forms

58:31 from the gravitational collapse of a massive stars core.

58:35 After the collapse, the future singularity comes into being.

58:39 And in the past, well, there's just a star.

58:43 But what does this idealized eternal black hole look like in the past?

58:48 If we follow the Swatshield metric back in time, we find something very strange.

58:55 We find the singularity again lurking infinitely far in the past.

59:00 From the point of view of the outside universe,

59:02 the eternal black hole singularity exists both

59:05 in the infinite future and in the infinite past.

59:10 That may sound strange, but it gets stranger.

59:13 To really understand what this eternal black hole looks like,

59:17 we're going to need to use a tool

59:19 that we've already played with the Pinrose diagram.

59:22 To refresh your memory, in a Penrose diagram,

59:25 the X and Y axes are redefined from space

59:28 and time to merge space and time into new coordinates.

59:32 They compactify spaceime so that time bunches up towards

59:37 the edges and the borders correspond to infinite past and future.

59:43 Also, lines of constant distance and time curve

59:48 so that light paths always travel on 45° paths.

59:51 We are hanging out here and now at the center of the diagram.

59:56 If we place an eternal black hole far to the left,

1:00:01 then the future left boundary represents the black holes event horizon.

1:00:05 Any movement to the left brings you closer to that event horizon.

1:00:10 The event horizon itself is a 45° line.

1:00:13 In our weird Penrose coordinates,

1:00:15 this represents a constant distance from the center of the black hole.

1:00:19 Light traveling at that 45 degree angle

1:00:22 takes infinite time to escape the event horizon.

1:00:25 And the region beyond that line represents the interior of the black hole.

1:00:30 There the dimensions of space and time switch roles.

1:00:34 The once vertical contours of space are now

1:00:38 timelike and flow inexorably towards the future singularity.

1:00:43 These two regions, our universe and the black hole interior,

1:00:48 are just the swast shield metric mapped out using Penrose coordinates.

1:00:52 But our map isn't complete.

1:00:55 Remember, this is an eternal black hole.

1:00:58 So, it must exist in the past.

1:01:01 Map into the past and we see a time reflected version of our future black hole.

1:01:07 Everything about it is time reversed.

1:01:10 The singularity is a past event.

1:01:12 Space within is timelike.

1:01:14 But instead of flowing towards the singularity, it flows away.

1:01:18 And the event horizon is now a barrier to entry, not to exit.

1:01:23 We can make some sense of the behavior

1:01:27 of this strange region by using the Penrose diagram.

1:01:30 Imagine that something in our past was traveling at the speed

1:01:34 of light and trying to reach the past event horizon.

1:01:38 There's no way it can get there unless it goes faster than light.

1:01:43 Oh, it'll reach an event horizon, but only the event horizon of our future

1:01:49 where it plunges into a regular old black hole.

1:01:53 Remember that all of this is from our perspective, far from the event horizon.

1:01:57 We can never see anything cross the horizon.

1:01:59 The light rays from any crossing reach us infinitely far in the future.

1:02:05 Even if the black hole plunge began far in the past.

1:02:09 So the past region of the eternal black hole

1:02:13 has an event horizon that's a barrier to entry.

1:02:17 But also light rays within that region must move up

1:02:21 on the diagram that suggests they must exit into the outside universe.

1:02:26 Anything inside the past eternal black hole must be ejected.

1:02:31 So far, this region fits perfectly the description of a white hole.

1:02:36 The eternal black hole of the past technically is a white hole.

1:02:42 However, it's not one that we can ever observe for two reasons.

1:02:46 One, light rays exiting that past white hole can never reach us.

1:02:51 The past singularity and past event horizon are infinitely

1:02:55 far in the past from our point of view.

1:02:59 light has to traverse infinite time to reach our location.

1:03:03 And two, there's no such thing as an eternal black hole.

1:03:07 The universe hasn't existed for eternity.

1:03:09 And it didn't even begin with black holes in place.

1:03:13 Even though this type of white hole isn't observable,

1:03:17 some physicists have taken the description very seriously.

1:03:20 The math describing the white hole is

1:03:23 a perfectly good use of the swat geometric.

1:03:26 It obeys general relativity.

1:03:28 It really is just a black hole but viewed backwards in time.

1:03:33 Yet general relativity is time reversal symmetric.

1:03:36 Something that can happen forwards in time

1:03:39 should also be able to happen in reverse.

1:03:42 So can new white holes actually form?

1:03:45 Well, theoretically yes.

1:03:47 But to make one, you need to reverse entropy.

1:03:52 See, although it's possible to build a white hole in general relativity,

1:03:56 there are other laws of physics that the universe needs to obey.

1:04:00 For example, the second law of thermodynamics.

1:04:04 It demands that entropy, a measure of disorder, always increase.

1:04:08 This law defines the direction of the flow of time.

1:04:13 To reverse time, you need to break the law.

1:04:16 You need to decrease entropy.

1:04:18 Now, this is technically possible because entropy is a statistical phenomenon.

1:04:23 Very rare reductions in entropy do happen.

1:04:26 As long as globally entropy increases on average,

1:04:30 it's conceivable that an incredibly rare entropy dip could lead

1:04:34 to an effective reversal of time and a white hole could form.

1:04:38 However, it would immediately explode in a burst of energy as soon

1:04:43 as entropy and time resumed their normal flow upwards and forwards.

1:04:47 We actually did talk about a case where a random drop in entropy

1:04:53 led to something very much like a white hole in this episode.

1:04:57 It's been speculated that the Big Bang itself

1:05:01 came from such a profoundly improbable entropy dip.

1:05:05 And as it happens, the Big Bang looks

1:05:08 mathematically at least much like a white hole.

1:05:12 It's an expanding outpouring of spaceime containing a vast amount of energy.

1:05:18 And the bang itself can never be entered.

1:05:21 After all, it's in the past.

1:05:23 The difference between the Big Bang and a white

1:05:26 hole is that the former possesses no singularity.

1:05:29 It happened everywhere at the same time.

1:05:32 Still, that hasn't stopped physicists from having fun with the idea.

1:05:37 It's been proposed that when a black hole forms,

1:05:40 a white hole forms on the opposite side.

1:05:43 Energy entering the black hole exits the white hole.

1:05:48 Physicist Lee Smolen takes it a step further

1:05:52 to suggest that the resulting white hole is the big bang of a new baby universe

1:05:58 and that in fact our universe formed that way.

1:06:02 More on that another time.

1:06:04 But speaking of other universes,

1:06:07 it turns out that we haven't finished building our Penrose diagram yet.

1:06:12 The past white hole was revealed when we

1:06:15 traced the eternal black hole backwards in time.

1:06:17 In fact, what we did was to maximally extend spaceime.

1:06:22 We required that all paths be traceable through infinite past and future space,

1:06:28 provided they don't hit the singularity.

1:06:30 But what about light rays entering or leaving

1:06:33 our eternal black hole from the opposite side?

1:06:36 The mathematics of the swast shield metric describes

1:06:39 an entirely independent region of spaceime parallel to our own.

1:06:45 It looks like an identical alternate universe on the other side

1:06:50 of the black hole accessible through what we call an Einstein Rosen bridge,

1:06:55 better known as a wormhole.

1:06:58 In the not too distant future,

1:07:01 we'll investigate the reality of this mysterious parallel patch of spaceime.

1:07:07 He was perhaps the greatest genius of our time.

1:07:11 Steven Hawking peered behind the curtain of reality

1:07:14 and glimpsed the true workings of the universe.

1:07:17 He inspired all of us to pursue our curiosity no matter the obstacles.

1:07:23 However, his true legacy is his work.

1:07:25 He made profound contributions across physics from quantum theory to cosmology.

1:07:30 Our tribute is to bring you Steven Hawkings most famous discovery.

1:07:34 I'm Matt Odow.

1:07:35 This is spaceime and it's time for Hawking radiation.

1:07:39 Soon after Einstein revealed his great general theory of relativity in 1915,

1:07:45 physicists realized that it allowed

1:07:47 for the possibility of catastrophic gravitational collapse

1:07:49 in places of extreme density like the dead core of a massive star.

1:07:54 Space and time could be dragged inwards to create a hole in the universe,

1:08:00 a boundary in spaceime called an event horizon that could

1:08:04 be entered but from beyond which nothing could return.

1:08:07 Once formed, there was nothing in theory or imagination

1:08:11 that could bring material consumed back to the outside universe.

1:08:16 These black holes should exist forever, only growing, never shrinking.

1:08:21 Or so we thought, until 1974 when a young physicist named

1:08:25 Steven Hawking published a paper in Nature entitled Black Hole Explosions.

1:08:30 In this and in a follow-up 1975 paper,

1:08:34 he attempted a new union of quantum mechanics and general relativity

1:08:38 to show that black holes should not be so black after all.

1:08:42 They should leak.

1:08:43 They should emit what we now know as Hawking radiation.

1:08:47 There's a popular description of how Hawking radiation works.

1:08:50 It goes something like this.

1:08:51 Empty space seas with activity as pairs

1:08:55 of virtual particles matter and antimatter

1:08:57 spontaneously appear and then annihilate each other

1:09:00 briefly borrowing energy from the vacuum itself.

1:09:03 But when this happens near a black hole,

1:09:06 sometimes one of the pair will be swallowed by the event horizon,

1:09:10 leaving the other free to escape and taking its stolen energy with it.

1:09:14 That energy can't come from nothing,

1:09:16 and so the black hole itself pays the debt by slowly leaking away its mass.

1:09:21 This is a nice picture, but how accurate is it?

1:09:24 In fact, if we follow the narrative of Hawkings original calculation,

1:09:27 the story sounds rather different.

1:09:29 We've come a long way over the past few months,

1:09:32 building up the knowledge we'll need to follow that calculation.

1:09:36 Re-watching some of those episodes either now

1:09:38 or after this video will be helpful.

1:09:40 But if you think you're ready,

1:09:41 let's take a deep dive into the quantum field theory

1:09:45 of curved spaceime to glimpse the true nature of Hawking radiation.

1:09:49 Actually, a quick QFT refresher can't hurt.

1:09:52 Space is filled with quantum fields.

1:09:55 They can oscillate with different frequencies,

1:09:57 much like the many possible vibrational modes on a guitar string.

1:10:01 A particle is like a note on the string.

1:10:03 And just like a real guitar note,

1:10:06 real particles tend to be comprised of many vibrational modes.

1:10:10 Those underlying vibrational modes are still

1:10:12 present in the absence of real particles.

1:10:14 They fluctuate in energy due to quantum uncertainty.

1:10:16 And those fluctuations give us what we think of as virtual particles.

1:10:21 Now, don't take the existence of virtual particles too seriously.

1:10:25 They're really just a tool for calculating the infinite

1:10:28 ways in which a fluctuating quantum field can behave.

1:10:32 One way that quantum fields are very different to guitar

1:10:35 strings is that they can have both positive and negative frequencies.

1:10:39 A negative frequency can be thought of as a mode that travels

1:10:43 backwards in time and can be interpreted as corresponding to antimatter.

1:10:46 Now, that's a whole level of weird all on its own.

1:10:50 And we talk about it here.

1:10:51 When a quantum field is in a vacuum state,

1:10:54 there's a balance between positive and negative frequency modes,

1:10:57 which you can crudely think of as a balance

1:11:00 between virtual matter and antimatter particles.

1:11:03 These all virtually annihilate or cancel out so that no real particles exist.

1:11:08 This is all fine in flat space, but spatial curvature can mess with the balance

1:11:14 of the underlying quantum field modes by introducing horizons.

1:11:18 Horizons cut off access to certain modes of the quantum fields,

1:11:23 disturbing the balance that defines the vacuum.

1:11:25 Steven Hawking knew that black holes with their insane space-time

1:11:29 curvature would wreak havoc on quantum fields in their vicinity.

1:11:33 But what would the effect be?

1:11:35 To answer that properly,

1:11:36 he would need a full union of general relativity and quantum mechanics,

1:11:40 a theory of quantum gravity, a theory of everything.

1:11:45 It didn't exist then and it doesn't exist yet.

1:11:48 Not to be deterred by the impossible,

1:11:51 Hawing came up with an ingenious workaround.

1:11:54 The narrative of Hawings mathematics goes something like this.

1:11:59 He imagined a single space-time path,

1:12:01 a light speeded trajectory called a null geodisic.

1:12:04 It extends from far in the past to far in the future.

1:12:08 This is a perilous path.

1:12:10 It passes through the location of a black hole in the instant before it forms.

1:12:14 In fact, it is the very last trajectory to do so.

1:12:17 It emerges barely ahead of the forming event horizon.

1:12:20 Hawking imagined a simple quantum field tracing this path.

1:12:23 a field that is in a perfect vacuum

1:12:26 state before the formation of the black hole.

1:12:29 But he found that the close shave with the black hole

1:12:32 disturbs the fundamental vibrational modes

1:12:34 that define the fluctuations of the vacuum.

1:12:37 By the time this trajectory has found its way back out into flat space again,

1:12:42 those fluctuations look like real particles.

1:12:44 A distant future observer sees radiation coming from the black hole.

1:12:49 Hawkings imaginary path from the distant

1:12:51 past to the distant future was brilliant.

1:12:54 It allowed him to compare the state of the vacuum

1:12:57 in two regions of flat space far from the black hole.

1:13:00 Regions where the nature of vacuums,

1:13:02 quantum fields, and particles are perfectly well understood.

1:13:06 But to understand the effect of the close encounter with the black hole,

1:13:10 he required an uneasy marriage of quantum mechanics and general relativity.

1:13:13 In the absence of a theory of quantum gravity, Hawking needed a hack.

1:13:18 That hack was the Boliv transformations.

1:13:21 Say that three times fast.

1:13:24 These can be used to approximate the effect of curved

1:13:27 spacetime on quantum fields by smoothly connecting regions of flat space.

1:13:30 They describe a sort of mixing of the positive and negative

1:13:34 frequency vibrational modes that are caused by that curved space.

1:13:38 The physical interpretation of this mixing

1:13:40 via the Bolivia transformations is tricky.

1:13:43 In fact, there isn't just one valid interpretation.

1:13:45 Hawings calculation talks about scattering.

1:13:48 Certain modes of the quantum field are scattered or deflected

1:13:52 by the gravitational field of the forming black hole.

1:13:55 They are nudged off their narrow escape path

1:13:58 and so are lost behind the forming event horizon.

1:14:01 Meanwhile, other modes avoid scattering and continue unscathed.

1:14:04 With the loss of certain fundamental modes,

1:14:06 the vacuum state must be constructed from the remaining modes.

1:14:10 That distorted vacuum looks like it's full of particles.

1:14:14 The nature of the lost modes tells us what Hawking radiation should look like.

1:14:19 Black holes tend to scatter modes with wavelengths similar to their own sizes.

1:14:23 The quantum field that emerges is distorted in the same wavelength range.

1:14:27 And so it produces wave packets.

1:14:29 It produces particles that also have wavelengths

1:14:31 about as large as the event horizon.

1:14:34 So the more massive the black hole, the longer the wavelength of its radiation.

1:14:39 Hawking calculated the frequency distribution

1:14:41 of this radiation and found something incredible.

1:14:44 It should look exactly like thermal radiation.

1:14:47 Black holes should have a heat glow

1:14:49 with an apparent temperature that depends on their mass.

1:14:53 More directly, it's proportional to the surface area of the event horizon.

1:14:57 Large black holes should appear cold, radiating excruciatingly slowly,

1:15:01 but small black holes should appear

1:15:03 hot and the smallest should radiate explosively.

1:15:06 Okay, so what about the whole picture of particle

1:15:09 antiparticle pairs being pulled apart by the event horizon?

1:15:13 So, Hawings math describes splitting or mixing

1:15:16 of these pure positive and negative frequency modes.

1:15:19 It's fair to interpret this mixing as the promotion

1:15:23 of what were once virtual particles into reality.

1:15:26 And for the escaping modes, there exist a corresponding set of modes linked

1:15:31 by quantum entanglement that are trapped behind the event horizon.

1:15:35 We can interpret those as corresponding to the swallowed antiparticle partner.

1:15:39 So the split matter antimatter part of the picture is reasonable.

1:15:44 But there are reasons to dismiss aspects of this picture.

1:15:48 Firstly, this radiation is not localized.

1:15:51 Remember the Hawking radiation has wavelengths the size of the event horizon,

1:15:55 the size of the entire black hole.

1:15:57 Well, these are the deu wavelengths of created particles and they tell us

1:16:01 that there is an enormous quantum

1:16:03 uncertainty in the location of these particles.

1:16:06 Hawking radiation must appear to come from the global black hole,

1:16:10 not from specific points on the event horizon.

1:16:13 In fact, an observer in freef fall through the horizon sees nothing.

1:16:17 To them, space is locally flat.

1:16:19 The vacuum should look like a vacuum.

1:16:22 This radiation is visible only to distant observers.

1:16:26 Well, there is one exception.

1:16:28 When you turn on your jetpack and hover a fixed distance above the horizon,

1:16:32 then you do see particles.

1:16:34 you see unrew radiation.

1:16:36 We'll look at its relationship to Hawking radiation in the future.

1:16:39 By the way, Hawking radiation is mostly

1:16:42 going to be photons and other massless particles.

1:16:44 To produce particles with mass, the energy of the radiation has to be high

1:16:49 enough to cover the rest mass of the particle.

1:16:52 So, it's okay to interpret the narrative of Hawkings

1:16:55 calculation as the splitting of entangled matter and antimatter pairs.

1:16:58 Even if it really is just a huristic interpretation,

1:17:01 it's the cause of the splitting that's hard to pin down.

1:17:05 We can think about positive and negative

1:17:07 frequency modes being mixed due to scattering,

1:17:10 perhaps by the as yet undiscovered graviton.

1:17:13 Other physicists have derived Hawkings

1:17:15 result with very different seeming narratives.

1:17:17 For example, in 2001,

1:17:19 Periq and Wilchek got the same thermal spectrum for Hawking radiation

1:17:23 by thinking about particles escaping from beneath

1:17:26 the event horizon through quantum tunneling.

1:17:29 The common thread is quantum uncertainty.

1:17:32 For example, uncertainty in positional momentum can lead

1:17:35 to particle pairs that were once in the same

1:17:38 location or modes that were once on the same

1:17:41 world line becoming separated by the event horizon.

1:17:44 Alternatively, uncertainty in energy can lead to particle creation.

1:17:48 Whichever way you interpret it,

1:17:50 it's hard to avoid the conclusion that black holes emit particles.

1:17:53 The fact that different derivations lead to exactly the same

1:17:57 result or that the radiation looks thermal can't be by chance.

1:18:00 It's hard to make Hawking radiation go away in the math.

1:18:04 And believe me, Steven Hawking himself tried.

1:18:07 Ultimately, however, these calculations are all hacks,

1:18:12 albeit utterly brilliant ones.

1:18:14 Without a full quantum theory of gravity,

1:18:16 the origin of Hawking radiation will remain mysterious.

1:18:19 And there are other mysteries that we haven't touched on.

1:18:23 For example, what happens to the particles or modes trapped by the black hole?

1:18:28 How do they end up reducing the black hole's mass instead of increasing it?

1:18:32 And then there's the famous information paradox in which Hawking

1:18:36 radiation appears to destroy what should be a conserved quantity,

1:18:41 quantum information.

1:18:42 We'll tackle all of these in future episodes.

1:18:44 For now, we must conclude that black holes radiate and in doing so evaporate.

1:18:49 The scariest monsters of general relativity

1:18:52 are ultimately unraveled by the brilliant

1:18:55 mind of Steven Hawking and a mysterious quirk of quantum spacetime.

1:19:03 Black holes seem like they should have no entropy,

1:19:05 but in fact, they hold most of the entropy in the universe.

1:19:09 Let's figure this out.

1:19:10 At first, it seemed that black holes were so simple they should have no entropy.

1:19:15 Well, it turns out they contain most of the entropy in the universe.

1:19:19 Let's see why.

1:19:20 Because this fact may force us to conclude that the universe is a hologram.

1:19:25 Black holes are a problem.

1:19:27 They are the inevitable result of extreme gravitational collapse.

1:19:31 At least they are inevitable according

1:19:33 to the equations of Einstein's general theory of relativity.

1:19:37 That theory is one of the most thoroughly tested in all of physics,

1:19:40 which means we should probably believe in black holes.

1:19:43 Also, we've seen them in their gravitational effects on their surrounding

1:19:47 space and in the gravitational waves caused when they merge.

1:19:51 And yet, if black holes exist, which apparently they do,

1:19:55 they contradict other theories in physics

1:19:57 that are as sacred as general relativity.

1:19:59 They cause all sorts of problems with quantum theory,

1:20:02 which we've talked about before and we'll review in a sec.

1:20:06 But they also present an apparent conflict with the notion

1:20:09 of entropy and the second law of thermodynamics.

1:20:12 It was while pondering that conflict that Jacob Beckenstein

1:20:16 realized an incredible connection between black holes and thermodynamics.

1:20:20 His insight launched an entire new way of thinking about the universe

1:20:25 in terms of information theory and ultimately led to the holographic principle,

1:20:29 which I promise we're getting to and are almost there.

1:20:32 But first, you are going to need to know more

1:20:35 about why black holes contain most of the universe's entropy.

1:20:38 Okay, I'm getting way ahead of myself.

1:20:41 Let's actually rewind back to those episodes where we laid out the black

1:20:45 hole information paradox because they're going

1:20:46 to be critical to a proper understanding.

1:20:48 We're also rewinding to the late '60s,

1:20:51 early '7s when physicists realized something odd about black holes.

1:20:55 What they realized is that it doesn't matter what material goes into one.

1:20:59 From the point of view of the outside universe,

1:21:02 black holes can only have three properties: mass, spin, and electric charge.

1:21:06 This is the so-called no hair theorem.

1:21:08 And it suggests that most of the information about anything

1:21:11 that falls into a black hole is lost to the outside universe.

1:21:15 But a fundamental tenant of quantum mechanics

1:21:18 is that quantum information can never be destroyed.

1:21:21 So if black holes evaporate, as Hawking discovered and we also covered,

1:21:25 this evaporation should destroy a black hole's internal quantum information,

1:21:29 giving us the black hole information paradox.

1:21:33 Eventually, a possible resolution to this paradox was found by Gerard.

1:21:37 He described a mechanism by which the information contained by infalling

1:21:41 particles could be preserved on the event horizon of the black hole.

1:21:46 From there, it could be imprinted on the outgoing Hawking radiation,

1:21:50 allowing the information to escape back into the universe.

1:21:53 Okay, problem solved.

1:21:54 But in our previous episodes,

1:21:56 we skipped the key insight that started all of this.

1:22:00 It all began with Jacob Beckinstein thinking about black hole entropy.

1:22:04 Okay, first entropy.

1:22:06 Yeah, we talked about that a lot recently.

1:22:09 Also, you know, it's almost like all

1:22:12 of those episodes are starting to come together.

1:22:14 Almost like we planned this.

1:22:16 Go and watch that background stuff if you're behind.

1:22:19 But of course, for now, I'll give you a quick TLDW on entropy.

1:22:23 So, we can think of entropy in two ways.

1:22:26 One, it's a measure of how evenly energy is spread out.

1:22:30 High entropy means thermal equilibrium.

1:22:32 So energy is very evenly distributed and can't be extracted in a useful way.

1:22:37 And two, entry measures the amount of unknown information that you would need

1:22:41 to perfectly describe the systems internal state

1:22:43 like all the particle positions, velocities, etc.

1:22:46 The higher the entropy, the more randomly distributed its particles and the more

1:22:50 possible configurations lead to the same macroscopic state.

1:22:53 The higher the entropy, the less you can guess about the properties

1:22:57 of individual particles based on the global properties like temperature,

1:23:01 volume, pressure, etc.

1:23:02 Okay, so the second law of thermodynamics states

1:23:05 that entropy of an isolated system must always increase which

1:23:09 means energy tends to spread out evenly and particles

1:23:13 tend to randomize reducing our information about their microscopic states.

1:23:17 How does this relate to black holes?

1:23:19 Let's make a black hole and see what happens to entropy.

1:23:23 We start as usual by collapsing the core of a dead star.

1:23:27 Now that's a high entropy beast,

1:23:29 super hot and full of randomly moving particles.

1:23:32 We have almost no information about the individual particles,

1:23:35 but that information still exists in the universe,

1:23:38 like I guess the particles know where they are.

1:23:40 At the instant the star collapses far enough to form an event horizon,

1:23:44 it becomes a black hole.

1:23:45 We go from knowing next to nothing about the object to knowing everything.

1:23:49 We can easily measure its mass, spin, and electric charge.

1:23:53 And according to the no hair theorem, that's all there is to know.

1:23:57 The region of space in which the black hole formed appears

1:24:01 to have gone from high entropy to zero entropy in an instant,

1:24:04 shattering the second law in the process, which to put it mildly is a problem.

1:24:09 But if you paid attention to the whole information paradox bit,

1:24:12 you might be able to think of a solution.

1:24:15 If quantum information is stored on the surface of the black hole,

1:24:19 can't we store entropy there also?

1:24:21 And then why not radiate the entropy

1:24:24 back into the universe as Hawking radiation?

1:24:26 Actually, yeah.

1:24:27 The resolution to the information paradox

1:24:30 also saves the second law of thermodynamics.

1:24:32 That was easy.

1:24:33 I thought physics was supposed to be hard.

1:24:36 Okay, hang on.

1:24:37 Let's think about this a little bit more.

1:24:40 It was this seeming violation of the second law that got Jacob Beckinstein

1:24:44 thinking about the connection between black

1:24:46 holes and information in the first place.

1:24:49 The breakthrough insight was this simple observation.

1:24:52 The surface area of a black hole event horizon

1:24:56 can never decrease at least not according to general relativity.

1:24:59 So you know how nothing can escape

1:25:01 black holes ignoring corking radiation for the moment.

1:25:04 That should mean that black holes can only grow.

1:25:07 They can never shrink in mass or radius.

1:25:10 Well, that's not quite true.

1:25:12 If you merge two black holes, some of their mass gets converted

1:25:17 to the energy radiated away in gravitational waves.

1:25:20 There's also the Penrose process in which you

1:25:22 can extract rotational energy of a spinning black hole.

1:25:25 And by you, I mean not you, I mean super advanced far future civilizations.

1:25:31 Gravitational radiation and the Penrose process reduce black hole mass

1:25:35 and radius or the sum of masses and radio merging black holes.

1:25:39 But there's one property of black holes

1:25:41 that no process other than Hawking radiation can decrease.

1:25:44 That's the surface area of the event horizon.

1:25:47 Do anything to black holes and their total

1:25:50 surface area can only grow or stay constant.

1:25:53 Beckenstein saw a close correspondence between the always increasing event

1:25:56 horizon surface area and the always increasing nature of entropy.

1:26:00 He also realized that the equation relating

1:26:03 the change in black hole surface area to the change in its mass closely

1:26:08 resembles the original definition of thermodynamic entropy.

1:26:11 Just replace change in entropy and internal thermal energy with change

1:26:15 in black hole surface area and black hole mass respectively.

1:26:18 You can also add the work done when you extract energy from the black hole

1:26:23 and it looks the same as the equation

1:26:26 for the work extracted from a thermodynamic system.

1:26:28 Beckinstein had just discovered black hole thermodynamics,

1:26:31 but that didn't give him the exact definition for black hole entropy.

1:26:37 For that, he turned to Ludvig Boltzman'sformational definition for entropy.

1:26:41 So entropy can be defined as the information hidden

1:26:45 in a systems microscopic configuration times the Boltzman constant.

1:26:49 Beckenstein estimated the amount of information that would

1:26:53 be lost into a black hole as it grew.

1:26:56 Essentially, he built a black hole out of idealized

1:26:59 elementary particles that each contained a single bit of information.

1:27:03 And guess what?

1:27:04 The information content of a black hole is

1:27:07 proportional not to its mass or radius or volume,

1:27:10 is proportional to its surface area.

1:27:13 In fact, the information content is very close

1:27:16 to that surface area divided by the number of plunk areas.

1:27:20 It's as though each of these minimum possible quant

1:27:24 of area each contain a single bit of information.

1:27:28 Now just multiply that information content by the Boltzman

1:27:31 constant and you have the entropy of a black

1:27:34 hole which is going to be directly proportional

1:27:36 to the surface area of the event horizon.

1:27:39 Beckenstein's connection between surface area

1:27:41 and entropy could have been a coincidence.

1:27:44 At least until Steven Hawking came along.

1:27:47 In 1974, a year after Beckenstein's first paper on black hole thermodynamics,

1:27:52 Hawking published his first Hawking radiation paper.

1:27:54 He showed that black holes radiate random particles exactly as though they

1:27:59 have a heat glow of a particular temperature that depends on their mass.

1:28:03 So if black holes have a temperature, then they also have entropy.

1:28:08 Good old-fashioned thermodynamic entropy tells us that change in entropy

1:28:13 is change in internal thermal energy divided by temperature.

1:28:16 So Hawking just plugged his Hawking temperature

1:28:19 into that equation along with black hole

1:28:21 mass for internal energy and figured out

1:28:24 the total entropy contained in a black hole.

1:28:27 He got an expression almost identical to Beckenstein's

1:28:30 but just a slightly different constant of proportionality.

1:28:32 So you get the same result for black hole

1:28:35 entropy whether you figure it out from the amount

1:28:37 of information that gets trapped building a black hole

1:28:40 or the amount of heat that leaks as it evaporates.

1:28:44 And it's proportional to the surface area.

1:28:47 How bizarrely consistent.

1:28:49 I'd say that means it's right.

1:28:52 The second law of thermodynamics is saved because black holes do have entropy.

1:28:56 In fact, they have enormous entropies, the maximum possible.

1:29:00 So much that black holes are now believed

1:29:03 to contain most of the entropy in the universe.

1:29:06 But the real importance of this work

1:29:09 wasn't the solution to some obscure conundrum.

1:29:12 It changed our thinking about the informationational content of the universe.

1:29:16 Beckinstein's formula was derived for black holes,

1:29:19 but it also gives the maximum amount of information

1:29:22 that can be fit into any volume of space.

1:29:25 In this respect, it's called the Beckenstein bound

1:29:28 and it's proportional to the surface area of that space.

1:29:32 This is unexpected.

1:29:33 Surely, the maximum amount of information you can fit into some

1:29:37 patch of space depends on the volume of that space,

1:29:41 as in one bit per tiny volume element inside that space.

1:29:45 But in fact, the rule is one bit per

1:29:48 tiny area element on the surface of that space.

1:29:51 That also means that the information needed to describe any volume of space,

1:29:56 no matter its contents, is proportional to the area bounding that space.

1:30:00 I've hinted once or twice that this simple

1:30:03 idea led to the holographic principle.

1:30:05 The idea that the entire 3D volume of the universe is just

1:30:09 a projection of information encoded on a 2D surface surrounding the universe.

1:30:13 You just need to add a little bit of string theory.

1:30:17 It's a hell of a conceptual leap given it started

1:30:20 with Jacob Beckenstein noticing a peculiar similarity between some formula.

1:30:24 It might also be true and obviously we'll be back before too

1:30:30 long to talk about string theory and the holographic nature of spaceime.

1:30:37 These black stones are volcanic rock and this is

1:30:40 one of the youngest patches of land on planet Earth.

1:30:43 But that same geological event that built this land has provided another window.

1:30:48 It allows us to observe a time when the universe

1:30:52 was still cooling from the fire of its own formation.

1:30:55 And to see this, all we have to do is travel

1:30:58 to a telescope on top of the tallest volcano in the world.

1:31:02 So we're driving up to the summit of Monaco on the big island of Hawaii.

1:31:06 This is the tallest volcano on the planet that 4200 m.

1:31:10 The oxygen up here is 60% sea level, but astronomers deal with it because it is

1:31:16 the premier astronomical observing site in the northern hemisphere.

1:31:21 To Hawaiians, it is a sacred site.

1:31:26 And to astronomers, it's where the Earth meets the universe.

1:31:34 Wow, it's amazing up here.

1:31:36 It's like being on another planet.

1:31:38 I can already feel the effect of the thinner atmosphere.

1:31:42 My natural impulse, bizarrely, is to hold my breath.

1:31:46 Must remember to keep breathing.

1:31:48 Here we have 13 of the greatest telescopes

1:31:51 in the world operated by 11 different countries.

1:31:54 We have the Japanese Subaru telescope, the Twin Kemes.

1:31:57 Over here we have the Canada, France, Hawaii telescope, and this is Gemini.

1:32:03 That's where we're going.

1:32:05 We're here to talk about a very special observation.

1:32:09 In the spring of 2017, astronomers turned Gemini's great mirror towards

1:32:14 the constellation of Buotis, the plowman.

1:32:17 They were looking for a faint speck of light that had

1:32:21 been noticed in one of our great surveys of the sky.

1:32:24 Astronomers guessed the speck was a quazar,

1:32:27 a vortex of radiant matter falling into a giant black hole.

1:32:33 Now quazars are the most luminous objects in the universe.

1:32:36 What was strange about this one was its distance.

1:32:39 Its light was so red that astronomers realized

1:32:43 that that light must have been stretched out,

1:32:46 redshifted by traveling many billions of years through our expanding universe.

1:32:50 The quazar appeared to be more distant than any we had ever seen.

1:32:55 But that doesn't mean we can't unravel their mysteries.

1:32:59 And Gemini did exactly that.

1:33:02 To find out how, we're going to need to go inside.

1:33:07 You've got to see this.

1:33:09 It's incredible.

1:33:10 Meet the Gemini telescope.

1:33:12 This is what a worldass telescope looks like these days.

1:33:16 It is enormous.

1:33:17 I still remember the first time I came to a telescope like this.

1:33:21 It blew me away.

1:33:22 Look at the size of this thing.

1:33:24 This is our window to the universe.

1:33:27 It's cold in here.

1:33:29 They keep the dome at the temperature of the upcoming night so

1:33:32 that giant structure doesn't warp and twist with the change in temperature.

1:33:36 That's a little below freezing right now.

1:33:38 And you hear that sound?

1:33:40 That's the cryogenics.

1:33:41 They keep the sensitive infrared cameras at 15 above absolute zero.

1:33:45 Let's actually talk about light for a second.

1:33:49 Light is a wave and the wavelength

1:33:51 of that wave determines the properties of light.

1:33:54 For example, visible light, the wavelength range that our eyes are sensitive

1:33:58 to, spans only a tiny fraction of the spectrum.

1:34:01 That's why we create telescopes.

1:34:03 The universe looks very, very different at different wavelengths.

1:34:07 For example, viewed in visible light,

1:34:09 the Andromeda galaxy shows us newborn stars.

1:34:12 Our atmosphere is transparent to visible light.

1:34:15 So, a groundbased telescope can see a visible universe as can we.

1:34:21 Gemini is built to be sensitive to the infrared.

1:34:25 The infrared andrometer is a swirl of star forming clouds and gas.

1:34:29 Some infrared light also makes it through the atmosphere,

1:34:31 though it helps to be up here on a mountaintop.

1:34:35 Although the air above the observatory is crystal clear,

1:34:38 it still blurs distant light somewhat.

1:34:40 Turbulence in the atmosphere causes incoming wave fronts of light to be warped,

1:34:45 and it blurs our view.

1:34:47 To correct this, Gemini uses adaptive optics.

1:34:50 It has a deformable mirror that flexes and bends

1:34:54 to match and correct the warping of incoming light.

1:34:58 To do this in real time,

1:35:00 Gemini creates its own artificial guide star by shooting

1:35:03 lasers to twinkle off sodium atoms at 90 km height, right off the edge of space.

1:35:13 This is the instrument used to analyze the most distant quazar.

1:35:17 It's the Gemini North infrared spectrograph.

1:35:19 Genius.

1:35:20 A spectrograph takes incoming light and breaks it

1:35:23 into its component wavelengths similar to a prism.

1:35:26 And it records how much energy is received at each wavelength.

1:35:30 We call that a spectrum.

1:35:33 When the light analyzed by this machine left its quazar, it was ultraviolet.

1:35:40 But traveling through the expanding universe

1:35:42 sapped energy and stretched the wavelength

1:35:44 of that light so that it was infrared by the time it reached the earth.

1:35:49 And this spectrograph the red shift tells

1:35:52 us how long that light has been traveling.

1:35:56 13.1 billion years, meaning the quazar lived when

1:35:59 the universe was only 5% its current age.

1:36:03 There's a broad blank patch in the quazar spectrum.

1:36:06 It's a stretch of nothing that tells us a ton.

1:36:10 Shortly after the Big Bang, when things had cooled down a bit,

1:36:14 the universe was filled with hydrogen gas.

1:36:17 It was murky, especially for ultraviolet light.

1:36:20 Now, that gas collapsed into the very first stars.

1:36:24 Then the very first galaxies.

1:36:26 Those stars eventually melted away the remaining

1:36:29 hydrogen in a process called reionization, leaving a crystal clearar universe.

1:36:34 But this quazar shines out from the era

1:36:38 of those first stars before they'd finished the job of reionization.

1:36:42 Much of the quazar's once ultraviolet light was

1:36:45 sucked up before it escaped the early universe.

1:36:48 And what about the super massive black hole at the center of the quazar?

1:36:52 The same signature wavelengths used to measure red shift are also broadened

1:36:56 due to the extreme speeds of matter moving near the black hole.

1:37:00 That allows us to estimate the mass of the black hole.

1:37:05 800 million suns.

1:37:06 If it replaced our sun, it would easily swallow Saturn's orbit.

1:37:10 Scientists struggle to figure out how it could grow to that insane

1:37:14 size in a tiny fraction of the age of the universe.

1:37:19 We are expanding our understanding of physics to figure this one out.

1:37:24 That tiny speck is both a revelation and a mystery.

1:37:28 It literally shines a light on the earliest epochs of our universe,

1:37:32 teaching us about our most fundamental origins.

1:37:35 But it also opens new questions.

1:37:37 And our great telescopes, our portals to the universe,

1:37:41 past and present, will tackle those questions,

1:37:44 too, and ultimately bring us closer to understanding this mysterious,

1:37:52 this magnificent spaceime.