Transcript of YouTube Video: Something Strange Happens When You Follow Einstein's Math

Transcript of YouTube Video: Something Strange Happens When You Follow Einstein's Math

The following is a summary and article by AI based on a transcript of the video "Something Strange Happens When You Follow Einstein's Math". Due to the limitations of AI, please be careful to distinguish the correctness of the content.

Article By AIVideo Transcript
00:00

- You can never see anything enter a black hole.

00:03

(bell dings)

00:04

Imagine you trap your nemesis in a rocket ship

00:07

and blast him off towards a black hole.

00:10

He looks back at you shaking his fist at a constant rate.

00:14

As he zooms in, gravity gets stronger,

00:17

so you would expect him to speed up,

00:19

but that is not what you see.

00:21

Instead, the rocket ship appears to be slowing down.

00:25

Not only that, he also appears

00:27

to be shaking his fist slower and slower.

00:30

That's because from your perspective,

00:32

his time is slowing down

00:35

at the very instant when he should cross the event horizon,

00:38

the point beyond which not even light can escape,

00:41

he and his rocket ship do not disappear,

00:45

instead, they seem to stop frozen in time.

00:51

The light from the spaceship gets dimmer and redder

00:54

until it completely fades from view.

00:57

This is how any object would look

00:59

crossing the event horizon.

01:01

Light is still coming from the point where he crossed,

01:04

it's just too redshifted to see,

01:08

but if you could see that light,

01:10

then in theory you would see everything

01:12

that has ever fallen into the black hole

01:14

frozen on its horizon, including the star that formed it,

01:19

but in practice, photons are emitted at discreet intervals,

01:22

so there will be a last photon emitted outside the horizon,

01:26

and therefore these images will fade after some time.

01:29

- This is just one of the strange results

01:32

that comes outta the general theory of relativity,

01:34

our current best theory of gravity.

01:36

The first solution of Einstein's equations

01:38

predicted not only black holes,

01:40

but also their opposite, white holes.

01:43

It also implied the existence of parallel universes

01:46

and even possibly a way to travel between them.

01:50

This is a video about the real science of black holes,

01:53

white holes, and wormholes.

01:56

- The general theory of relativity

01:58

arose at least in part due to a fundamental flaw

02:00

in Newtonian gravity.

02:02

In the 1600s Isaac Newton

02:04

contemplated how an apple falls to the ground,

02:06

how the moon orbits the earth and earth orbits the sun

02:09

and he concluded that every object with mass

02:12

must attract every other,

02:14

but Newton was troubled by his own theory.

02:17

How could masses separated by such vast distances

02:20

apply a force on each other?

02:22

He wrote, "That one body may act upon another at a distance

02:26

through a vacuum without the mediation of anything else

02:29

is to me, so great and absurdity that I believe no man

02:33

who has a competent faculty of thinking

02:34

could ever fall into it."

02:38

One man who definitely had a competent faculty of thinking,

02:42

was Albert Einstein and over 200 years later,

02:45

he figured out how gravity is mediated.

02:48

Bodies do not exert forces on each other directly.

02:52

Instead, a mass like the sun curves the spacetime

02:55

in its immediate vicinity.

02:58

This, then curves the spacetime around it

03:00

and so on all the way to the earth.

03:03

So the earth orbits the sun, because the spacetime

03:06

earth is passing through is curved.

03:09

Masses are affected by the local curvature

03:12

of spacetime, so no action at a distance is required.

03:16

Mathematically, this is described

03:18

by Einstein's field equations.

03:20

Can you write down the Einstein field equation?

03:23

- This was the the result of Einstein's decade of hard work

03:26

after special relativity

03:28

and essentially what we've got in the field equations

03:30

on one side it says,

03:32

tell me about the distribution of matter and energy.

03:34

The other side tells you what the resultant curvature

03:37

of spacetime is from that distribution

03:40

of matter and energy and it's a single line.

03:43

It looks like, oh, this is a simple equation, right?

03:46

But it's not really one equation.

03:47

It's a family of equations and to make life more difficult,

03:51

they're coupled equations, so they depend upon each other

03:54

and they are differential equations,

03:56

so it means that there are integrals

03:58

that have to be done, da, da da.

04:00

So there's a whole bunch of steps that you need to do

04:02

to solve the field equations.

04:04

To see what a solution to these equations would look like,

04:07

we need a tool to understand spacetime.

04:11

So imagine your floating around in empty space.

04:14

A flash of light goes off above your head

04:16

and spreads out in all directions.

04:19

Now your entire future, anything that can

04:22

and will ever happen to you will occur within this bubble

04:27

because the only way to get out of it

04:29

would be to travel faster than light.

04:31

In two dimensions, this bubble is just a growing circle.

04:35

If we allow time to run up the screen

04:37

and take snapshots at regular intervals,

04:39

then this light bubble traces out a cone,

04:41

your future light cone.

04:43

By convention, the axes are scaled so that light rays

04:46

always travel at 45 degrees.

04:48

This cone reveals the only region of spacetime

04:51

that you can ever hope to explore and influence.

04:55

Now imagine that instead of a flash of light

04:57

above your head, those photons were actually traveling in

05:00

from all corners of the universe

05:02

and they met at that instant

05:03

and then continued traveling on

05:05

in their separate directions.

05:08

Well, in that case then into the past,

05:10

these photons also reveal a light cone,

05:13

your past light cone.

05:15

Only events that happened inside this cone

05:17

could have affected you up to the present moment.

05:21

We can simplify this diagram even further

05:23

by plotting just one spatial and one time dimension.

05:26

This is the spacetime diagram of empty space.

05:29

If you want to measure how far apart

05:31

two events are in spacetime, you use something called

05:34

the spacetime interval.

05:36

The interval squared is equal to minus dt squared,

05:39

plus dx squared, since spacetime is flat,

05:43

the geometry is the same everywhere

05:45

and so this formula holds throughout the entire diagram,

05:48

which makes it really easy to measure the separation

05:50

between any two events, but around a mass,

05:54

spacetime is curved and therefore you need to modify

05:57

the equation to take into account the geometry.

06:00

This is what solutions to Einstein's equations are like.

06:04

They tell you how spacetime curves

06:06

and how to measure the separation between two events

06:09

in that curved geometry.

06:12

Einstein published his equations in 1915

06:15

during the First World War,

06:16

but he couldn't find an exact solution.

06:19

Luckily, a copy of his paper made its way

06:22

to the eastern front where Germany was fighting Russia,

06:25

stationed there was one of the best astrophysicists

06:27

of the time, Karl Schwarzschild.

06:30

Despite being 41 years old, he had volunteered

06:33

to calculate artillery trajectories for the German army.

06:36

At least until a greater challenge caught his attention,

06:40

how to solve Einstein's field equations.

06:45

Schwarzschild did the standard physicist thing

06:47

and imagined the simplest possible scenario,

06:49

an eternal static universe with nothing in it

06:52

except a single spherically symmetric point mass.

06:55

This mass was electrically neutral and not rotating.

06:59

Since this was the only feature of his universe,

07:01

he measured everything using spherical coordinates

07:04

relative to this center of this mass.

07:06

So r is the radius and theta and phi give the angles.

07:10

For his time coordinate, he chose time as being measured

07:13

by someone far away from the mass,

07:15

where spacetime is essentially flat.

07:18

Using this approach, Schwarzschild found the first

07:20

non-trivial solution to Einstein's equations,

07:23

which nowadays we write like this.

07:26

This Schwarzschild metric describes how spacetime curves

07:30

outside of the mass.

07:32

It's pretty simple and makes intuitive sense,

07:34

far away from the mass spacetime is nearly flat,

07:37

but as you get closer and closer to it,

07:39

spacetime becomes more and more curved,

07:41

it attracts objects in and time runs slower.

07:45

(gunshots firing)

07:47

Schwarzschild sent his solution to Einstein,

07:49

concluding with, "The war treated me kindly enough

07:52

in spite of the heavy gunfire

07:54

to allow me to get away from it all

07:55

and take this walk in the land of your ideas."

08:00

Einstein replied, "I have read your paper

08:02

with the utmost interest, I had not expected

08:04

that one could formulate the exact solution to the problem

08:06

in such a simple way."

08:12

But what seemed at first quite simple,

08:15

soon became more complicated.

08:17

Shortly after Schwarzschild solution was published,

08:19

people noticed two problem spots.

08:22

At the center of the mass, at r equals zero,

08:25

this term is divided by zero, so it blows up to infinity

08:30

and therefore this equation breaks down

08:32

and it can no longer describe what's physically happening.

08:35

This is what's called a singularity.

08:38

Maybe that point could be excused,

08:40

because it's in the middle of the mass,

08:42

but there's another problem spot outside of it

08:45

at a special distance from the center

08:47

known as the Schwarzschild radius, this term blows up.

08:50

So there is a second singularity. What is going on here?

08:57

Well, at the Schwarzschild radius,

09:00

the spacetime curvature becomes so steep

09:02

that the escape velocity, the speed that anything would need

09:06

to leave there is the speed of light

09:10

and that would mean that inside the Schwarzschild radius,

09:13

nothing, not even light would be able to escape.

09:17

So you'd have this dark object

09:18

that swallows up matter and light,

09:22

a black hole, if you will,

09:26

but most scientists doubted that such an object could exist,

09:29

because it would require a lot of mass

09:31

to collapse down into a tiny space.

09:35

How could that possibly ever happen?

09:39

(thrilling music)

09:40

Astronomers at the time were studying

09:42

what happens at the end of a star's life.

09:44

During its lifetime the inward force of gravity is balanced

09:47

by the outward radiation pressure

09:49

created by the energy released through nuclear fusion,

09:52

but when the fuel runs out, the radiation pressure drops.

09:55

So gravity pulls all the star material inwards, but how far?

10:01

Most astronomers believed some physical process

10:04

would hold it up and in 1926,

10:07

Ralph Fowler came up with a possible mechanism.

10:10

Pauli's exclusion principles states that,

10:11

"Fermions like electrons cannot occupy the same state,

10:15

so as matter gets pushed closer and closer together,

10:18

the electrons each occupy their own tiny volumes,"

10:21

but Heisenberg's uncertainty principle says that,

10:23

"You can't know the position and momentum of a particle

10:26

with absolute certainty, so as the particles become

10:29

more and more constrained in space,

10:32

the uncertainty in their momentum,

10:34

and hence their velocity must go up."

10:37

So the more a star is compressed,

10:39

the faster electrons will wiggle around

10:41

and that creates an outward pressure.

10:44

This electron degeneracy pressure would prevent the star

10:47

from collapsing completely.

10:49

Instead, it would form a white dwarf

10:51

with the density much higher than a normal star

10:54

and remarkably enough astronomers had observed stars

10:57

that fit this description.

10:58

One of them was Sirius B.

11:04

But the relief from this discovery was short-lived.

11:06

Four years later, 19-year-old Subrahmanyan Chandrasekhar

11:09

traveled by boat to England to study with Fowler

11:12

and Arthur Eddington, one of the most revered scientists

11:15

of the time.

11:17

During his voyage, Chandrasekhar realized

11:19

that electron degeneracy pressure has its limits.

11:22

Electrons can wiggle faster and faster,

11:24

but only up to the speed of light.

11:27

That means this effect can only support stars

11:30

up to a certain mass, the Chandrasekhar limit.

11:33

Beyond this, Chandrasekhar believed,

11:35

not even electron de degeneracy pressure

11:37

could prevent a star from collapsing,

11:40

but Eddington was not impressed.

11:42

He publicly blasted Chandrasekhar saying,

11:45

"There should be a law of nature

11:47

to prevent a star from behaving in this absurd way"

11:51

and indeed scientists did discover a way

11:53

that stars heavier than the Chandrasekhar limit

11:55

could support themselves.

11:58

When a star collapses beyond a white dwarf,

12:00

electrons and protons fuse together

12:02

to form neutrinos and neutrons.

12:05

These neutrons are also fermions,

12:07

but with nearly 2000 times the mass an electron,

12:10

their degeneracy pressure is even stronger.

12:13

So this is what holds up neutron stars.

12:16

There was this conviction among scientists

12:19

that even if we didn't know the mechanism,

12:21

something would prevent a star from collapsing

12:23

into a single point and forming a black hole,

12:28

because black holes were just too preposterous to be real.

12:34

The big blow to this belief came in the late 1930s

12:38

when Jay Robert Oppenheimer and George Volkoff

12:40

found that neutron stars also have a maximum mass.

12:44

Shortly after Oppenheimer and Hartland Snyder

12:47

showed that for the heaviest stars,

12:49

there is nothing left to save them when their fuel runs out,

12:53

they wrote, "This contraction will continue indefinitely,"

12:58

but Einstein still couldn't believe it.

13:00

Oppenheimer was saying that stars can collapse indefinitely,

13:03

but when Einstein looked at the math,

13:05

he found that time freezes on the horizon.

13:08

So it seemed like nothing could ever enter,

13:11

which suggested that either

13:12

there's something we don't understand

13:14

or that black holes can't exist,

13:17

(star explodes)

13:21

but Oppenheimer offered a solution to the problem.

13:23

He said to an outside observer,

13:26

you could never see anything go in,

13:27

but if you were traveling across the event horizon,

13:31

you wouldn't notice anything unusual

13:33

and you'd go right past it without even knowing it.

13:37

So how is this possible?

13:39

We need a spacetime diagram of a black hole.

13:43

On the left is the singularity at r equals zero.

13:46

The dotted line at r equals 2M is the event horizon.

13:49

Since the black hole doesn't move,

13:51

these lines go straight up in time.

13:55

Now let's see how ingoing and outgoing light ray travel

13:58

in this curved geometry.

14:01

When you're really far away,

14:02

the future light cones are at the usual 45 degrees,

14:06

but as you get closer to the horizon,

14:07

the light cones get narrower and narrower,

14:11

until right at the event horizon,

14:13

they're so narrow that they point straight up

14:16

and inside the horizon, the light cones tip to the left,

14:22

but something strange happens with ingoing light rays.

14:26

- They fall in, but they don't get to r equals 2M,

14:29

they actually asymptote to that value

14:32

as time goes to infinity,

14:34

but they don't end at infinity, right?

14:36

Mathematically they are connected and come back in

14:41

and they're traveling in this direction

14:44

and this bothered a lot of people,

14:46

this bothered people like Einstein,

14:48

because he looked at these equations and went,

14:50

"well, if nothing can cross this sort of boundary,

14:55

then how could there be black holes?

14:57

How could black holes even form?"

15:00

- So what is going on here?

15:02

Well, what's important to recognize

15:04

is that this diagram is a projection.

15:06

It's basically a 2D map

15:08

of four dimensional curved spacetime.

15:12

It's just like projecting the 3D Earth onto a 2D map.

15:15

When you do that, you always get distortions.

15:18

There is no perfectly accurate way

15:20

to map the earth onto a 2D surface,

15:22

but different maps can be useful for different purposes.

15:25

For example, if you wanna keep angles and shapes the same,

15:28

like if you're sailing across the ocean

15:30

and you need to find your bearings,

15:31

you can use the Mercator projection,

15:33

that's the one Google Maps uses.

15:35

A downside is that it misrepresent sizes.

15:39

Africa and Greenland look about the same size,

15:42

but Africa is actually around 14 times larger.

15:46

The Gall-Peters projection keeps relative sizes accurate,

15:49

but as a result, angles and shapes are distorted.

15:53

In a similar way, we can make different projections

15:56

of 4D spacetime to study different properties of it.

16:00

Physical reality doesn't change,

16:01

but the way the map describes it does.

16:05

- He had chosen to put a particular coordinate system

16:07

of a space and have a time coordinate, and off you go.

16:11

It's the most sensible thing to do, right?

16:14

- [Derek] People realize that if you choose

16:15

a different coordinate system

16:17

by doing a coordinate substitution, then the singularity

16:20

at the event horizon disappears.

16:23

- It goes away.

16:24

That problem goes away and things can actually cross

16:27

into the black hole.

16:30

- What this tells us is that there is

16:32

no real physical singularity at the event horizon.

16:36

It just resulted from a poor choice of coordinate system.

16:41

Another way to visualize what's going on

16:44

is by describing space as flowing in towards the black hole,

16:48

like a waterfall.

16:49

As you get closer, space starts flowing in

16:52

faster and faster.

16:54

Photons emitted by the spaceship have to swim

16:56

against this flow, and this becomes harder and harder

17:00

the closer you get.

17:02

Photons emitted just outside the horizon

17:04

can barely make it out, but it takes longer and longer.

17:09

At the horizon, space falls in

17:11

as fast as the photons are swimming.

17:13

So if the horizon had a finite width,

17:16

then photons would get stuck here,

17:18

photons from everything that ever fell in,

17:21

but the horizon is infinitely thin.

17:23

So in reality, photons either eventually escape or fall in.

17:29

Inside the horizon, space falls faster

17:31

than the speed of light,

17:33

and so everything falls into the singularity.

17:36

So Oppenheimer was right.

17:38

Someone outside a black hole can never see anything enter

17:42

because the last photons they can see

17:44

will always be from just outside the horizon,

17:48

but if you yourself go,

17:50

you will fall right across the event horizon

17:52

and into the singularity.

17:55

Now you can extend the waterfall model

17:57

to cover all three spatial dimensions,

17:59

and that gives you this, a real simulation

18:02

of space flowing into a static black hole

18:05

made by my friend Alessandro from ScienceClic.

18:08

Later we'll use this model to see what it's like

18:10

falling into a rotating black hole.

18:16

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18:18

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18:20

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18:22

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18:25

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20:19

and now back to spacetime maps.

20:22

If you take this map and transform it

20:25

so that incoming and outgoing light ray

20:27

all travel at 45 degrees like we're used to,

20:30

then something fascinating happens.

20:33

The black hole singularity on the left

20:35

transforms into a curved line at the top

20:40

and since the future always points up in this map,

20:44

it tells us that the singularity is not actually

20:47

a place in space, instead, it's a moment in time,

20:52

the very last moment in time for anything

20:55

that enters a black hole.

20:58

The map we've just created is a Kruskal-Szekers diagram,

21:02

but this only represents a portion of the universe,

21:04

the part inside the black holes event horizon

21:07

and the part of the universe closest to it,

21:10

but what we can do is contract the whole universe,

21:13

the infinite past, infinite distance, and infinite future,

21:17

and morph it into a single map.

21:20

It's like using the universe's best fish eye lens.

21:24

That gives us this penrose diagram.

21:28

Again, light rays still always go at 45 degrees.

21:31

So the future always points up.

21:33

The infinite past is in the bottom of the diagram.

21:36

The infinite future at the top

21:39

and the sides on the right are infinitely far away.

21:42

The black hole singularity is now a straight line

21:44

at the top, a final moment in time.

21:49

These lines are all at the same distance

21:51

from the black hole.

21:52

So the singularity is at r equals zero,

21:55

the horizon is at r equals 2M,

21:57

this line is at r equals 4M,

21:59

and this is infinitely far away.

22:02

All of these lines are at the same time.

22:05

What's great about this map is that it's very easy to see

22:09

where you can still go and what could have affected you.

22:12

For example, when you're here, you've got a lot of freedom.

22:15

You can enter the black hole or fly off to infinity,

22:19

and you can see and receive information from this area,

22:23

but if you go beyond the horizon,

22:25

your only possible future is to meet the singularity.

22:29

You can still, however, see and receive information

22:32

from the universe.

22:33

You just can't send any back out.

22:36

Now think about being at this point in the map.

22:39

This is at the event horizon,

22:41

and now your entire future is within the black hole,

22:45

but what is the past of this moment?

22:48

Well, you can draw the past light cone

22:51

and it reveals this new region.

22:54

If you're inside this region,

22:56

you can send signals to the universe,

22:58

but no matter where you are in the universe,

23:00

nothing can ever enter this region

23:02

because it will never be inside your light comb.

23:06

So things can come out, but never go in.

23:09

This is the opposite of a black hole, a white hole.

23:15

What color is a white hole?

23:18

(Geraint exhales)

23:19

(Derek laughs)

23:20

- I mean, it's gonna be the,

23:22

it's not gonna have a color, right?

23:24

It's gonna be whatever's being spat out of it.

23:27

It depends what's in there and gets thrown out,

23:31

that's what you are going to see.

23:33

So if it's got light in there, it's got mass in there,

23:35

it's all gonna be ejected.

23:36

So the white hole kind of picture

23:39

is the time reverse picture of a black hole,

23:42

instead of things falling in, things get expelled outwards

23:46

and so whilst a black hole has a membrane,

23:51

the Schwarzschild horizon, which once you cross,

23:53

you can't get back out, the white hole has the opposite.

23:56

If you're inside the event horizon, you have to be ejected,

23:59

so it kicks you out kind of thing, right?

24:01

Relativity doesn't tell you which way time flows.

24:04

There's nothing in there that says that, that is the future

24:08

and that is the past.

24:10

When you are doing your mathematics

24:12

and you're working out the behavior of objects,

24:15

you make a choice about which direction is the future,

24:19

but mathematically, you could have chosen

24:21

the other way, right?

24:22

You could have had time point in the opposite direction.

24:25

Any solution that you find in relativity,

24:28

mathematically, you can just flip it

24:30

and get a time reverse solution

24:32

and that's also a solution to the equations.

24:36

- [Derek] Now, we've been showing things

24:37

being ejected to the right, but they could just as well

24:40

be ejected to the left.

24:42

So what's over there?

24:44

This line is not at infinity,

24:46

so there should be something beyond it.

24:49

If we eject things in this direction,

24:51

you find that they enter a whole new universe,

24:55

one parallel to our own.

25:01

- [Geraint] We can fall into this black hole,

25:03

and somebody in this universe here

25:05

could fall into this black hole in their universe,

25:08

and we would find ourselves in the same black hole.

25:11

(Derek chuckles)

25:12

- The only downside is that

25:14

we'd both soon end up in the singularity.

25:18

I guess I'm just trying to understand

25:20

where that universe appears

25:22

in the mathematical part of the solution.

25:24

Like, can you point to the part of the equation and be like,

25:27

so that's our universe, and then these terms here,

25:30

that's the other universe, or do you know what I mean?

25:32

Like- - Yeah,

25:33

well, it's coordinates, right?

25:35

Imagine somebody, right, came up with a coordinate system

25:40

for the earth, but only the northern hemisphere

25:43

and you looked at that coordinate system, right?

25:45

And you looked at it and you said,

25:47

"Ah, I can see the coordinate system, it looks fine,

25:50

but mathematically latitudes can be negative, right?

25:55

You've only got positive latitudes in your solution.

25:58

What about the negative ones?"

25:59

And they said to you, (scoffs) "Negative ones?

26:02

No southern hemisphere, right?"

26:05

And you've gotta go, "Well, the mathematics says that

26:08

you can have negative latitudes.

26:09

Maybe we should go and look over the equator

26:12

to see if there is something down there"

26:13

and I know that's a kind of extreme example,

26:16

because we know we live on a globe,

26:17

but we don't know the full geometry

26:20

of what's going on here in the sense that

26:22

Schwarzschild laid down coordinates

26:24

over part of the solution.

26:26

It was like him only laying down coordinates

26:28

on the northern hemisphere

26:30

and other people have come along and said,

26:32

"Hey, there's a southern hemisphere"

26:34

and more than that, there's two earths.

26:36

That's why it's called maximal extension.

26:39

It's like, if I have this mathematical structure,

26:43

then what is the extent of the coordinates

26:47

that I can consider?

26:49

And with the Schwarzschild black hole,

26:51

you get a second universe

26:52

that has its own independent set of coordinates

26:56

from our universe.

26:57

I want to emphasize right, this is the simplest solution

27:00

to the Einstein field equations,

27:02

and it already contains a black hole,

27:03

white hole and two universes.

27:05

- [Derek] That's what you get

27:07

when you push this map to its limits

27:09

so that every edge ends at a singularity or infinity.

27:13

- And in fact, there's another little feature in here,

27:16

which is that, that little point there where they cross,

27:19

that is an Einstein Rosen Bridge.

27:24

- To see it, we need to change coordinates.

27:27

Now this line is at constant crustal time

27:30

and it connects the space of both universes.

27:33

You can see what the spacetime is like

27:35

by following this line from right to left.

27:38

Far away from the event horizon,

27:39

spacetime is basically flat,

27:41

but as you get closer to the event horizon,

27:43

spacetime starts to curve more and more.

27:46

At this cross, you are at the event horizon,

27:49

and if you go beyond it, you end up in the parallel universe

27:53

that gives you a wormhole that looks like this.

27:59

- So that is hypothetically how we could use a black hole

28:04

to travel from one universe to another.

28:06

- Hypothetically, because these wormholes

28:08

aren't actually stable in time.

28:11

- It's a bit like a bridge, but it's a bridge that is long

28:14

and then becomes shorter and then becomes long again

28:17

and if you try to traverse this bridge,

28:19

at some point, the bridge is only very short, right?

28:21

And you say, "Oh, well, let me just cross this bridge."

28:23

But as you start crossing the bridge and start running,

28:25

your speed is finite, right?

28:27

The speed of light roughly and then the bridge starts,

28:30

becoming stretching and you never come out the other side.

28:35

- [Derek] This pinching off always happens too fast

28:38

for anything to travel through.

28:40

You can also see this if you look at the Penrose diagram,

28:43

because when you're inside one universe,

28:45

there isn't a light cone that can take you

28:47

to the other universe.

28:49

The only way to do that

28:50

would be to travel faster than light,

28:54

but there might be another way.

28:57

Schwarzschild solution describes a black hole

28:59

that doesn't rotate.

29:00

Yet, every star does rotate

29:02

and since angular momentum must be conserved,

29:04

every black hole must also be rotating.

29:08

While Schwarzschild found his solution within weeks

29:10

after Einstein published his equations,

29:12

solving them for a spinning mass

29:14

turned out to be much harder.

29:15

Physicists tried, but 10 years after Schwarzschild solution,

29:19

they still hadn't solved it.

29:21

10 years turned into 20, which turned into 40

29:24

and then in 1963, Roy Kerr found the solution

29:28

to Einstein's equations for a spinning black hole,

29:32

which is far more complicated than Schwarzschild solution

29:35

and this comes with a few dramatic changes.

29:40

The first is that the structure is completely different.

29:43

The black hole now consists of several layers.

29:47

It's also not spherically symmetric anymore.

29:50

This happens because the rotation

29:52

causes it to bulge around the equator.

29:54

So it's only symmetric about its axis of spin.

29:59

Alessandro from science click simulated what happens

30:02

around this spinning black hole.

30:07

Space gets dragged around with the black hole

30:10

taking you and the particles along with it.

30:13

When you get closer, space gets dragged around

30:15

faster and faster until it goes around faster

30:19

than the speed of light,

30:20

you've now entered into the first new region,

30:24

the ergosphere.

30:26

No matter how hard you fire your rockets here,

30:29

it's impossible to stay still relative to distance stars,

30:33

but because space doesn't flow directly inward,

30:36

you can still escape the black hole.

30:39

When you travel in further, you go through the next layer,

30:42

the outer horizon, the point of no return.

30:46

Here you can only go inwards,

30:49

but as you get dragged in deeper and deeper,

30:52

something crazy happens, you enter another region,

30:57

one where you can move around freely again,

31:00

so you're not doomed to the singularity.

31:03

You're now inside the inner event horizon.

31:07

Here you can actually see the singularity

31:12

- In a normal black hole, it's a point,

31:13

but it in a rotating black hole,

31:14

it actually expands out to be a ring

31:17

and there are weird things happened

31:19

with spacetime inside the center of a black hole,

31:22

a rotating black hole,

31:23

but it's thought that you can actually

31:24

fly through the singularity.

31:29

- [Derek] We need a Penrose diagram

31:31

of a spinning black hole, where before the singularity

31:35

was a horizontal line at the top

31:37

here, the singularity lifts up and moves to the sides,

31:40

revealing this new region inside the inner horizon.

31:45

Here we can move around freely and avoid the singularity,

31:49

but these edges aren't at infinity or a singularity,

31:53

so there must be something beyond them.

31:55

Well, when you venture further,

31:57

you could find yourself in a white hole,

32:00

which would push you out into a whole nother universe.

32:05

- You can have these pictures whereby

32:08

you're in one universe, you fall into a rotating black hole,

32:12

you fly through the singularity,

32:14

and you pop out into a new universe from a white hole,

32:18

and then you can just continue playing this game.

32:21

- Extending this diagram infinitely far.

32:25

but there is still one thing we haven't done,

32:27

brave the singularity.

32:30

So you aim straight towards the center of the ring

32:33

and head off towards it, but rather than time ending,

32:37

you now find yourself in universe, a strange universe,

32:40

one where gravity pushes instead of pulls.

32:44

This is known as an anti-verse.

32:48

If that's too weird, you can always jump back

32:50

across the singularity and return to a universe

32:53

with normal gravity.

32:55

- And I know this is basically science fiction, right?

32:57

But if you take the solutions of relativity at,

33:02

you know, essentially at face value and add on a little bit,

33:05

which is what Penrose does here, he says this,

33:07

"oh look, these shapes are very similar,

33:10

I can just stick these together."

33:12

Then this is the conclusion that you get.

33:14

Now we have effectively an infinite number

33:17

of universes all connected with black hole, white holes

33:20

all the way through and you, of you go to explore,

33:25

but it'll be a very brave person who's the first one

33:28

who's gonna leap into a rotating black hole

33:30

to find out if this is correct?

33:31

(Derek chuckles)

33:33

- Yeah, I would not sign up for that.

33:35

So could these maximally extended Schwarzschild

33:38

and Kerr solutions actually exist in nature?

33:41

Well, there are some issues.

33:43

Both the extended Schwarzschild and Kerr solutions

33:46

are solutions of eternal black holes in an empty universe.

33:50

- As you say, it's an eternal solution.

33:52

So it stretches infinitely far into the past

33:55

and infinitely far into the future

33:57

and so there's no formation mechanism in there,

33:59

it's just a static solution

34:02

and I think that is part of the,

34:07

part of the reason why black holes

34:10

are realized in our universe and white holes aren't-

34:15

- Or might not be.

34:16

- Or might not be,

34:16

or I'm reasonably I,

34:18

personally, I'm reasonably confident

34:20

that they don't exist, right?

34:22

- [Derek] For the maximally extended Kerr solution,

34:24

there's also another problem.

34:26

If you're an immortal astronaut inside the universe,

34:28

you can send light into the black hole,

34:31

but because there's infinite time compressed

34:34

in this top corner, you can pile up light along this edge,

34:37

which creates an infinite flux of energy

34:40

along the inner horizon.

34:42

This concentration of energy

34:43

then creates its own singularity,

34:46

sealing off the ring singularity and beyond.

34:50

- My suspicion and the suspicion

34:51

of some other people in the field is that

34:55

this inner horizon will become singular

34:56

and you will not be able to go through these second copies.

34:59

- So all the white holes, wormholes, other universes

35:03

and anti universes disappear.

35:06

Does that mean that real wormholes are impossible?

35:10

In 1987, Michael Morris and Kip Thorne looked at wormholes

35:13

that an advanced civilization could use

35:15

for interstellar travel, ones that have no horizons,

35:18

so you can travel back and forth, are stable in time,

35:20

and have some other properties like

35:22

being able to construct them.

35:24

They found several geometries that are allowed

35:26

by Einstein's general relativity.

35:28

In theory, these could connect different parts

35:31

of the universe, making a sort of interstellar highway.

35:34

They might even be able to connect to different universes.

35:39

The only problem is that all these geometries

35:42

require an exotic kind of matter

35:44

with a negative energy density

35:45

to prevent the wormhole from collapsing.

35:48

- This exotic kind of matter,

35:50

is really against the loss of physics, so it's,

35:54

I have the prejudice that it will not exist.

35:56

I'm bothered by the fact that we say that

35:58

the science fiction wormholes are mathematically possible.

36:01

It's true, it's mathematically possible

36:03

in the sense that there's some geometry that can exist,

36:05

but Einstein's theory is not just geometries,

36:09

it's geometries plus field equations.

36:12

If you use the kinds of properties of matter

36:14

that matter actually has, then they're not possible.

36:17

So I feel that the reason they're not possible

36:20

is very strong.

36:22

- So according to our current best understanding,

36:25

it seems likely that white holes, traversable wormholes,

36:28

and these parallel universes don't exist,

36:32

but we also used to think that black holes didn't exist.

36:35

So maybe we'll be surprised again.

36:38

- I mean, we have one universe, right?

36:41

Good, why can't we have two.

36:46

(whimsical music)