Video Infoblog: Space-Time: The Biggest Problem in Physics

26 Sept 2024

What is the deepest level of reality? In this Quanta explainer, Vijay Balasubramanian, a physicist at the University of Pennsylvania, takes us on a journey through space-time to investigate what it’s made of, why it’s failing us, and where physics can go next.Explore black holes, holograms, “alien algebra,” and more space-time geometry: https://www.quantamagazine.org/the-un... 00:00 - The Planck length, an intro to space-time 1:23 - Descartes and Newton investigate space and time 2:04 - Einstein's special relativity 2:32 - The geometry of space-time and the manifold 3:16 - Einstein's general relativity: space-time in four dimensions 3:35 - The mathematical curvature of space-time 4:57 - Einstein's field equation 6:04 - Singularities: where general relativity fails 6:50 - Quantum mechanics (amplitudes, entanglement, Schrödinger equation) 8:32 - The problem of quantum gravity 9:38 - Applying quantum mechanics to our manifold 10:36 - Why particle accelerators can't test quantum gravity 11:28 - Is there something deeper than space-time? 11:45 - Hawking and Bekenstein discover black holes have entropy 13:54 - The holographic principle 14:49 - AdS/CFT duality 16:06 - Space-time may emerge from entanglement 17:44 - The path to quantum gravity --------

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The Planck length, an intro to space-time

0:01

This is the Planck length.

0:02

It’s a trillion trillion times smaller than an atom.

0:07

It’s also the biggest problem in  physics.

0:10

Because when we try to ponder what's happening near 10 to the minus 33 centimeters,

0:18

the laws of nature break down.

0:21

The stage of our universe – space-time – seems to dissolve,

0:26

and we can't make sense of the awful chaos underneath.

0:30

Decades of investigations have converged on a haunting conclusion:

0:35

Our best descriptions of nature, quantum mechanics and general relativity,  

0:40

are failing us. To dig into the deepest layers of reality,

0:43

we’re going to need new physics.

0:46

In this video, we’ll build the stage of space-time from the ground up.

0:52

And then we’ll see how we have no choice but to tear it all down again.

0:56

And in the wreckage, we’ll look for clues to paths forward – towards a quantum theory of gravity.

1:04

During our journey, we’ll be forced to  challenge our basic assumptions.

1:08

Is space-time real, or simply a large-scale illusion?

1:12

At the fundamental level of nature, do questions like “where?”

1:17

and “when?” even have answers?

Descartes and Newton investigate space and time

1:23

In 1637, the French mathematician Rene Descartes imagined a hidden  mathematical framework for space.

1:33

He invented the Cartesian grid, which  labels points in space using x-, y-,  

1:39

and z- coordinates.

1:41

He thought of this grid  as the backdrop of our stag e of reality.

1:46

A few decades later, Isaac Newton described time  in a similar way,

1:52

as an absolute and rigid part of the stage.

1:56

But for Descartes and Newton, space  and time existed independently of each other.

2:03

Then, in 1905, Albert Einstein entered the  scene with his theory of special relativity.

Einstein's special relativity

2:12

Einstein’s first revelation  was that time is relative:

2:15

an observer’s measurement of the time between  events depends on their motion in space.

2:22

This was a clue that we should think of space and time as a single entity:

2:27

the physical fabric of our universe, with three  dimensions of space and a fourth of time.

The geometry of space-time and the manifold

2:33

With this picture of space-time  as a unified continuum, Einstein began to wonder about its shape.

2:42

To get a sense for the mathematical model of  space-time, let’s begin with one flat grid.

2:48

Now, let’s take another one,  and another, and another.

2:53

When we stitch them together, we create  a mathematical object called a manifold.

3:00

Let’s imagine we’re a cat walking on the surface  of this manifold. Locally, the grid looks flat,  

3:06

with straight-line coordinate axes everywhere.

3:09

But if we zoom out, the manifold turns out  to be made up of curved coordinate axes.

Einstein's general relativity: space-time in four dimensions

3:16

Einstein’s big revelation, in  his general theory of relativity,  

3:20

is that space-time is a manifold that bends  and curves in the presence of matter or energy.

3:27

The effects of this curvature produce  what we experience as gravity.

The mathematical curvature of space-time

3:36

To measure this curvature,  let’s return to our flat space.

3:41

Thanks to Pythagoras, we know that if you have  

3:43

a triangle with sides x and y and  diagonal s, then s^2 = x^2 + y^2.

3:54

Now, suppose you make the triangle really  small, and call the displacements in the x and y  

3:59

directions along the two sides dx and dy.  Then the diagonal ds satisfies this formula.  

4:09

But this is also simply the distance  between the endpoints of the diagonal.

4:13

So we can think of this formula  as giving us a ruler for 2D space.

4:20

What happens when we put these coordinates on  a rubber sheet and stretch it? They’re still  

4:26

separated by the same number of grid spacings,  but their physical distances have changed.

4:31

Now, we need a new ruler that tells us how  much stretching and skewing is happening  

4:38

on our manifold. This is the metric: our  modified ruler for curved 2D space-time.

4:47

Einstein expanded on this ruler,  

4:49

creating a metric for how space-time  curves in a 4D universe like ours.

Einstein's field equation

4:58

To describe the geometry of space-time,  

5:01

you have to calculate where and by how  much matter tells our manifold to curve,  

5:08

producing the effects of gravity. This brings  us to the crown jewel of general relativity:  

5:13

Einstein’s field equation for how the distribution  of matter and energy curves space-time.

5:22

This is the Einstein tensor, which describes the  

5:26

curvature of space-time. It’s a function  of the metric – our ruler for 4D space-time.

5:33

This next part accounts for the cosmological  constant, which is the energy intrinsic in space.

5:40

This part is the stress-energy tensor. It  describes the energy density, momentum density,  

5:46

and pressures of matter and energy at  each location in space. In other words,  

5:52

it tells us where stuff is  and how much there is of it.

5:56

You can think of this equation as matter  and energy telling space-time how to bend.

Singularities: where general relativity fails

6:04

In a simpler world, this  would be the end of physics:  

6:08

an elegant theory of distances in space and  time, described geometrically by the manifold.

6:14

But buried in Einstein’s blueprints are places  where the theory describes its own demise.

6:20

In places called singularities,  such as at the moment of the Big  

6:24

Bang and at the center of black  holes, matter becomes so dense  

6:29

that it squeezes infinitely – forcing  space-time to curve infinitely, too.

6:36

In physics, when you encounter infinities in your  equations, it’s a signal they’ve broken down.  

6:42

So we have to conclude that general relativity  fails to describe physics at these singularities. 

Quantum mechanics (amplitudes, entanglement, Schrödinger equation)

6:50

Einstein’s theory is also ignorant  of physics at the subatomic level,  

6:54

where particles are too light to noticeably curve  space-time and physics is quantum mechanical.

7:00

To investigate space-time at the fundamental  level – to really start to ask questions about  

7:05

what it’s made of – we need to look  at it from a quantum point of view.

7:12

This is the quantum stage. In this probabilistic  universe, subatomic particles don’t have  

7:18

fixed positions in space. Instead, they  have “amplitudes."

7:25

Amplitudes are like probabilities. But unlike  probabilities, they can be complex numbers,  

7:31

which means that amplitudes can cancel each other  out.

7:36

Quantum mechanics says that  to go from here to there,  

7:39

a particle can take many different  paths, each with an amplitude. These  

7:44

amplitudes must be summed up to find  the total amplitude of that transition.

7:50

So, on our quantum stage, physics  is not described by saying where  

7:54

things are and how they move, but how  amplitudes for different possibilities  

7:59

change over time. This evolution is  described by the famous Schrodinger equation.

8:08

And then there’s quantum entanglement.

8:11

When two particles are entangled,  their amplitudes become contingent.

8:16

If you measure either particle,  the outcome is uncertain, but,  

8:20

if you measure one, it appears to  collapse the state of the other,  

8:25

so that the outcome of the second measurement  is suddenly completely determined.

The problem of quantum gravity

8:32

Ever since physicists realized that quantum  mechanics is the underlying language of our  

8:37

universe, we’ve been trying to fit everything  we know about nature into its strange laws.

8:44

The result of these efforts is Quantum  Field Theory, a more sophisticated version  

8:49

of quantum mechanics. It’s the framework  that allows us to apply quantum principles,  

8:53

or “quantize,” all of the matter and force fields  that fill the universe – except one – gravity.

9:02

That’s because in all quantum field theories, the  matter and force fields are described as lying on  

9:10

top of a smooth, fixed, continuous grid of  space-time – the special relativity stage. 

9:16

But to describe gravity, we have  to quantize the space-time stage  

9:21

itself. How are we supposed to do  this, without a stage to stand on?

9:27

This is the problem of quantum  gravity. It brings us to the edge  

9:31

of our understanding of physical reality  – to the end of space-time as we know it.

Applying quantum mechanics to our manifold

9:39

Let’s see what happens when we apply  quantum mechanics directly to our manifold.

9:45

Just like particles, the manifold should  behave quantumly. This means it can’t be  

9:50

fixed. It must have a probability  of being in many different states.

9:56

There is even some probability for space-time  to start shredding itself, resulting in an awful  

10:02

soup of quantum uncertainty, where bits  of spacetime pop in and out of existence.

10:09

All of this happens at the Planck  length, because here, gravity is quantum.

10:15

At these short distances, the notions  of “here” and “there” become murky.  

10:21

If we try to place coordinates on  our manifold, they quickly lose  

10:26

meaning. Our metric dissolves in  the chaos of quantum uncertainty.

Why particle accelerators can't test quantum gravity

10:37

In the quest to understand what  happens at very small distances,  

10:41

experimental physicists have built  powerful particle accelerators. 

10:46

Today, the Large Hadron Collider at  CERN can probe physics at 10-17 cm.

10:53

But to see what’s happening at the Planck  length, you'd need a particle collider  

10:58

1,000-trillion-times more powerful – one  about as big as our entire Milky Way galaxy.

11:05

And even if we could build one, the collisions  it would produce would put so much energy  

11:10

into such a tiny region of space that the  region would collapse into a black hole.

11:16

There's simply no operational way of  probing space-time below this length.  

11:21

That suggests that space-time below  the Planck length doesn't have meaning.

Is there something deeper than space-time?

11:28

Something deeper is happening  here. We might be tempted to ask:  

11:32

What if space-time isn’t the base  layer of reality? What if there is  

11:38

a more fundamental description of physics  that produces what looks like space-time?

Hawking and Bekenstein discover black holes have entropy

11:46

In the 1970s, Jacob Bekenstein  and Stephen Hawking stumbled on  

11:51

a compelling clue about the  nature of quantum gravity. 

11:55

To appreciate the profound  implications of what they discovered,  

11:59

we need to first review the laws of thermodynamics  and their origin in statistical physics.

12:07

Suppose you have a system  with large numbers of atoms  

12:11

or molecules and macroscopic  properties, like temperature.

12:15

The entropy of such a system measures the  number of different possible molecular  

12:20

arrangements, or microstates, that produce  a macroscopic system at this temperature.

12:29

While using the equations of general  relativity to explore black holes,  

12:33

Bekenstein and Hawking discovered that black holes  act as if they have an entropy, and that quantum  

12:39

mechanics causes them to radiate particles in  a particular way that gives them a temperature. 

12:45

But black holes, like everything else, need  to comply with the laws of thermodynamics.

12:51

So if black holes have an entropy, they  must be made of more primitive parts:  

12:56

quantum micro-states that can be  thought of as the “atoms” of space-time.

13:04

Usually, the entropy of a  system is related to its volume,  

13:08

because it depends on how many ways you  can arrange all the microstates inside.

13:15

But Bekenstein and Hawking  showed that with black holes,  

13:19

something surprising happens:a black  hole’s entropy is proportional to its  

13:23

area – more specifically, the area  of its event horizon, or boundary.

13:30

It’s as if we can know all of  the possible microstates of a  

13:34

black hole’s interior structure just by  counting the ways of arranging things on  

13:38

its surface. But how could a surface know  everything about an interior volume? This  

13:45

strange finding is the best clue we have  about the quantum nature of space-time.

The holographic principle

13:54

If a 3D object like a black hole is best  understood using only two dimensions,  

14:00

could the same be true for the entire universe? 

14:03

In the 1990s, these questions coalesced into a  compelling idea called the holographic principle. 

14:11

The holographic principle says that space-time is  like a hologram “projected” from the information  

14:18

available on some lower-dimensional  surface like the boundary of the universe.

14:24

On the holographic stage, the  fabric of our reality – space-time  

14:28

and gravity – actually emerges from a  quantum description in a lower dimension.

14:36

If the holographic principle is true, the math  describing gravity and the geometry of spacetime  

14:43

should be equivalent to the math of quantum  physics in a space of one fewer dimension. 

AdS/CFT duality

14:51

In the last few decades, physicists  have searched for these mathematical  

14:55

equivalences with the goal of creating  a dictionary of physics that bridges the  

14:59

dual descriptions. The best example so far  is something called the AdS/CFT duality. 

15:10

This (CFT) is a well-understood quantum  theory known as a conformal field theory,  

15:15

or CFT. It has no gravity in it. Let’s consider a  CFT in two spatial dimensions, and of course time.

15:25

This is a kind of space-time permitted in  general relativity known as anti–de Sitter space,  

15:32

or AdS. It has gravity. Let’s consider an AdS  space with three spatial dimensions, and time.

15:41

The AdS/CFT duality is a dictionary that  relates the math of the two theories.  

15:47

You can use it to calculate anything in  one theory in the language of the other.

15:53

We might describe this situation by saying that  the AdS spacetime is “emergent” from the CFT,  

16:00

because some of its dimensions appear out of  the dynamics of the lower-dimensional CFT.

Space-time may emerge from entanglement

16:06

But if space-time is emergent, what are  the quantum processes that produce it? 

16:15

Here, AdS/CFT gives us a compelling  hint. The AdS space-time geometry,  

16:21

along with Einstein’s equations of general  relativity, emerge from entanglement – a  

16:27

sort of quantum inseparability between  the states of the particles of the CFT.

16:35

The idea is that if two things  are entangled in one description,  

16:40

they become physically connected in the other.

16:46

So, at the deepest level of reality, it’s possible  that quantum entanglement is knitting space-time  

16:52

together in this way, giving rise to the geometry  of the space-time manifold – and our universe. 

17:05

If space-time is emergent in this way, entanglement doesn't happen in space-time--

17:11

entanglement CREATES space-time.

17:15

Below the Planck length, it’s entirely  possible that the quantum entanglement  

17:19

knitting spacetime fluctuates wildly. This  would mean that things are connecting and  

17:24

disconnecting all the time in such a  way that distance as we understand it  

17:29

may cease to exist. Maybe this is why we can’t  measure distances below the Planck length.

The path to quantum gravity

17:44

The holographic principle is one place where we’ve  made lots of progress toward a theory of quantum  

17:51

gravity. There’s a catch, though. The AdS universe  has a different space-time geometry than our own.

17:58

So while the AdS/CFT duality  is remarkable in its own right,  

18:04

it’s not proof that we live on  a holographic stage. Instead,  

18:09

you can think of it as a toy model of how  space-time can emerge from entanglement.

18:19

To make further progress, we have to find a  way to extend these ideas to a model describing  

18:25

our universe with its particular geometry,  particles, and peculiarities, like dark energy.

18:33

Ideally, we should also find a way  to test the holographic principle  

18:37

experimentally. That’s going  to require creative new ideas.

18:43

To me, space and time are the two of  the most fundamental concepts in all  

18:48

of science. The very language we use to  describe nature depends on them.  

18:52

So if space and time  are emergent -- in some sense

18:57

"not really there," we have to  figure out what replaces these concepts.

19:03

This is the exciting quest for  the next generation. There is  

19:06

hardly anything deeper and more  inspiring to work on than that.

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