Can Black Holes Unify General Relativity & Quantum Mechanics?

PBS Space Time
23 May 202415:18

Summary

TLDRThis episode delves into the black hole information paradox and the concept of black hole complementarity, which suggests that quantum information can exist both inside a black hole and as Hawking radiation without violating unitarity. The script explores the Penrose diagram to illustrate the different perspectives of observers, highlighting the impossibility of simultaneous observation of quantum states. It raises questions about the nature of existence and the relativity of quantum states to observers, hinting at a deeper understanding of the universe that unites general relativity and quantum mechanics.

Takeaways

  • 🌌 The script discusses the conflict between general relativity and quantum mechanics, particularly focusing on black holes and the black hole information paradox.
  • 🔍 Black holes are significant in theoretical physics because they present inconsistencies between general relativity and quantum mechanics, potentially leading to a unified theory.
  • 💡 The black hole information paradox suggests that black holes may violate either general relativity or quantum mechanics principles when a quantum bit (qubit) is taken into a black hole.
  • 🌐 Black hole complementarity, proposed by Leonard Susskind, is a solution to the paradox suggesting that no contradiction exists between the two theories when viewed from different observer perspectives.
  • 🕊️ The concept of black hole complementarity implies that quantum information can be both inside a black hole and radiated away as Hawking radiation without violating unitarity, as no observer can witness both states simultaneously.
  • 📈 The Penrose diagram is used to illustrate the spacetime of a black hole and the paths of light and objects near the event horizon.
  • 🕒 The script explains that due to the finite speed of light, the simultaneity of the existence of quantum information in two places cannot be verified by any single observer.
  • 🤔 Black hole complementarity raises questions about the nature of existence and reality, suggesting that our understanding of the universe may be observer-dependent.
  • 🌈 The script touches on the holographic principle, hinting that the interior and exterior of black holes might be different descriptions of the same quantum system.
  • 🔥 Alternative solutions to the black hole information paradox, such as black hole firewalls, are mentioned, indicating ongoing debates in theoretical physics.
  • 🎁 The episode concludes with acknowledgments to supporters and mentions of new merchandise available in the store.

Q & A

  • What is the black hole information paradox?

    -The black hole information paradox is a conflict that arises when considering the fate of information that falls into a black hole. According to general relativity, the information is lost forever as it crosses the event horizon, which contradicts the principle of quantum mechanics that information must be conserved.

  • What is black hole complementarity and who formulated it?

    -Black hole complementarity is a proposed solution to the black hole information paradox. It suggests that there is no contradiction because the same quantum information can be inside the black hole as measured by one observer and frozen on the surface or radiated away in Hawking radiation according to another. It was formulated by Leonard Susskind and others in the early 1990s.

  • How does the Penrose diagram represent spacetime?

    -A Penrose diagram is a graphical representation of spacetime that is used to visualize the structure of a black hole. It compresses space and time so that they bend into each other, with light always traveling at a 45-degree angle. This diagram allows for the visualization of an infinite distance and time at the boundaries, and it is useful for understanding the behavior of objects near the event horizon of a black hole.

  • What is the significance of the event horizon in the context of black holes?

    -The event horizon is the boundary around a black hole beyond which nothing can escape, not even light. It is significant because it marks the point of no return for any matter or radiation that crosses it, leading to the information paradox as the information about what has crossed the event horizon seems to be lost.

  • What is the concept of unitarity in quantum mechanics?

    -Unitarity in quantum mechanics refers to the conservation of quantum information. It is a fundamental principle that states that quantum information cannot be created or destroyed, only transformed. The violation of unitarity in the context of black holes would imply that information can be lost, which challenges the principles of quantum mechanics.

  • What is the role of the equivalence principle in the black hole information paradox?

    -The equivalence principle, a fundamental axiom of general relativity, states that an observer cannot detect anything unusual when crossing the event horizon of a black hole. This principle leads to the paradox because it implies that an observer falling into a black hole would not notice anything out of the ordinary, contradicting the idea that quantum information is lost.

  • How does the concept of Hawking radiation relate to the black hole information paradox?

    -Hawking radiation is a theoretical process by which black holes can lose mass and eventually evaporate. It is related to the black hole information paradox because it is suggested that information about the matter that fell into the black hole could be released back into the universe through this radiation, potentially resolving the paradox.

  • What is the Page time and why is it significant in the context of black hole complementarity?

    -The Page time is the point at which a black hole has evaporated to half its original size. It is significant because, according to physicist Don Page, only after this time can quantum information get back out of the black hole. This is the time when an observer might potentially see both the swallowed and radiated versions of a quantum bit, although black hole complementarity argues that this is still impossible.

  • What is the holographic principle and how does it relate to black hole complementarity?

    -The holographic principle is a concept in theoretical physics suggesting that a lower-dimensional system can be described by a higher-dimensional boundary. It relates to black hole complementarity by proposing that the interior and exterior of a black hole are different descriptions of the same quantum system, with the boundary and its interior being different ways to talk about the same thing.

  • What are the implications of black hole complementarity for our understanding of existence and reality?

    -Black hole complementarity challenges our traditional notions of existence and reality by suggesting that the existence of a quantum state may be relative to the observer. It implies that our description of the world and the fundamental laws of physics may depend on our reference frame, leading to a more relativistic view of the universe.

Outlines

00:00

🌌 Introduction to Black Holes and Theoretical Physics

The script opens with an introduction to the merch store and then delves into the complexities of black holes as predicted by general relativity, which describes space, time, and gravity. It contrasts these with quantum mechanics, which governs the subatomic world. The black hole information paradox is highlighted as a key conflict between these theories. The paradox arises when quantum information (qubits) is carried into a black hole, leading to a potential violation of quantum mechanics' principles. The script suggests that black holes might be the key to unifying these theories. Black hole complementarity, proposed by Leonard Susskind in the 1990s, is introduced as a solution that suggests no contradiction exists between the two states of the qubit as observed by different observers. The Penrose diagram is used to illustrate the spacetime around a black hole and the journey of the qubit as seen by Alice (inside the black hole) and Bob (outside).

05:05

🔬 The Black Hole Information Paradox and Complementarity

This paragraph explores the black hole information paradox in more detail, discussing the Penrose diagram for a black hole that forms from a collapsed star and eventually evaporates through Hawking radiation. It describes the paths of the qubit as seen by Alice and Bob, leading to a potential violation of unitarity if the qubit is considered to exist in two places simultaneously. The script then examines the concept of 'existing simultaneously' and the limitations of verifying such a state due to the finite speed of light and the observer's past light-cone. Black hole complementarity is presented as a solution that argues there's no violation of unitarity because no single observer can measure both states of the qubit. The Hayden-Preskill thought experiment is mentioned, which shows it's impossible for any observer to see both the Hawking-radiated and swallowed versions of the qubit, supporting the idea of black hole complementarity.

10:11

🌐 Interpretations of Black Hole Complementarity and Its Implications

The final paragraph discusses various interpretations of black hole complementarity and its implications for our understanding of quantum mechanics and the nature of existence. The first interpretation suggests that unitarity and the conservation of quantum information are maintained relative to a given observer, implying that the description of the world can be radically dependent on the observer's reference frame. The second interpretation posits that the interior and exterior descriptions of quantum information are equivalent, reflecting a form of holography where a lower-dimensional system can be described as a higher-dimensional one. The script also mentions the concept of black hole firewalls as an alternative to complementarity, which will be explored in an upcoming episode. The paragraph concludes by reflecting on the broader implications of black holes for our understanding of the universe, suggesting that they may reveal a deeper reality where descriptions of the world are relative and interiors of black holes or universes may be equivalent to their surfaces.

Mindmap

Keywords

💡General Relativity

General Relativity is a theory of gravity proposed by Albert Einstein, which describes gravity not as a force, but as a curvature of spacetime caused by mass and energy. In the video, it is mentioned as our best theory of space, time, and gravity and is highlighted as clashing with quantum mechanics, particularly in the context of black holes.

💡Quantum Mechanics

Quantum Mechanics is a fundamental theory in physics that describes the physical properties of nature at the scale of atoms and subatomic particles. The script discusses how quantum mechanics conflicts with general relativity, especially when considering the behavior of matter and information near black holes.

💡Black Hole Information Paradox

The Black Hole Information Paradox refers to a problem in theoretical physics where the predictions of quantum mechanics seem to be violated by the behavior of black holes, specifically the loss of information about physical states that fall into a black hole. The video delves into this paradox, suggesting that black holes might either violate quantum mechanics or general relativity.

💡Black Hole Complementarity

Black Hole Complementarity is a proposed solution to the information paradox, suggesting that an object falling into a black hole appears both inside the black hole and in the Hawking radiation to different observers without any actual contradiction. The concept is central to the video's exploration of how we might reconcile the paradoxes arising from the intersection of general relativity and quantum mechanics.

💡Event Horizon

The Event Horizon is the boundary around a black hole beyond which nothing can escape, not even light. In the script, it is described as the point where Alice, carrying a qubit into a black hole, would cross without sensing anything unusual due to the equivalence principle of general relativity.

💡Hawking Radiation

Hawking Radiation is a theoretical prediction made by physicist Stephen Hawking that black holes are not completely black but emit small amounts of thermal radiation due to quantum effects near the event horizon. The script discusses how this radiation is relevant to the information paradox and the proposed solution of black hole complementarity.

💡Quantum Bit (Qubit)

A Quantum Bit, or Qubit, is the fundamental unit of quantum information, analogous to the classical bit but with the ability to exist in multiple states simultaneously due to quantum superposition. The video uses the example of a qubit being carried into a black hole to illustrate the information paradox.

💡Penrose Diagram

A Penrose Diagram is a graphical representation of the spacetime of a universe, often used to visualize black holes and their event horizons. The script uses the Penrose Diagram to explain the different perspectives of Alice and Bob regarding the fate of a qubit near a black hole.

💡Unitarity

Unitarity in quantum mechanics refers to the property that quantum information is conserved and that the evolution of a quantum system is described by a unitary operator. The script discusses how the black hole information paradox seems to violate unitarity, leading to the proposal of black hole complementarity.

💡Holographic Principle

The Holographic Principle is a concept in theoretical physics suggesting that the information contained within a volume of space can be represented on the boundary to the same space. The video touches on this principle in the context of black hole complementarity, suggesting that the interior and exterior of a black hole might be different descriptions of the same quantum system.

💡Unruh Radiation

Unruh Radiation is a prediction in quantum field theory that an accelerating observer will observe a thermal bath of particles, akin to black body radiation. The script briefly mentions Unruh radiation as an example of how the existence of a particle can depend on the observer's acceleration, which parallels the ideas discussed in black hole complementarity.

Highlights

Black holes are inevitable predictions of general relativity but clash with quantum mechanics.

The black hole information paradox challenges our understanding of quantum mechanics and general relativity.

Black hole complementarity, proposed by Leonard Susskind, suggests no contradiction exists between the two theories.

According to black hole complementarity, quantum information can be both inside and outside a black hole without contradiction.

The Penrose diagram is used to visualize the spacetime of a universe with a black hole.

The concept of 'simultaneous existence' is explored in the context of a black hole's event horizon.

The impossibility of observing both the interior and exterior states of a black hole is a key aspect of black hole complementarity.

The unobservability of duplicated qubits suggests a fundamental principle about the nature of existence in quantum mechanics.

Black hole complementarity implies that the conservation of quantum information holds relative to a given observer.

The concept of holography is related to black hole complementarity, suggesting that lower-dimensional systems can describe higher-dimensional ones.

Black hole complementarity is not the only solution to the black hole information paradox; other theories like firewalls exist.

The idea that our description of the world is relative to our reference frame is a radical implication of black hole complementarity.

The existence of a particle can depend on the acceleration of an observer, as seen in the Unruh radiation episode.

The holographic principle suggests that our universe's interior may have a dual description on its distant surface.

Support for the channel includes Patreon contributions, which help in the production of episodes.

New merchandise items are added to the PBS Spacetime shop, including T-shirts and hoodies.

Transcripts

00:00

Hey Everyone. Before we get to the episode,  

00:01

just a heads up we have two new items at the  merch store. There’s a link in the description

00:07

Black holes are inevitable predictions of  general relativity—our best theory of space,  

00:12

time and gravity. But they clash in  multiple ways with quantum mechanics,  

00:16

our equally successful description of the  subatomic world. One such clash is the  

00:21

black hole information paradox—and a proposed  solution—black hole complementarity—may forced  

00:28

us to radically rethink what it even  means for something to exist.

00:39

We know that our universe is fundamentally  self-consistent—otherwise what are we even  

00:44

doing trying to science it. But that means when a contradiction appears in our scientific  

00:49

description of the universe, we know something is  wrong with that description. It’s really exciting  

00:55

when this happens because the nature of the  inconsistency can point the way to a better, more  

01:01

encompassing scientific description. Black holes  are one of the favourite tools of the theoretical  

01:07

physicist because they lead to multiple  inconsistencies between general relativity  

01:11

and quantum mechanics, and so may be our best  path to the grander theory that unites the two.

01:17

The conflict we looked at recently is the black  hole information paradox, and it’s not a bad  

01:22

idea to watch that episode before this. In it,  our intrepid heroes of the gedankenexperiment,  

01:29

Alice and Bob, discovered that black holes must  violate either a fundamental principle of general  

01:34

relativity or of quantum mechanics. When Alice  carries a quantum bit—a qubit—into a black hole,  

01:41

she witnesses the qubit cross the event  horizon. She must, because according to  

01:46

the equivalence principle—a founding axiom of  general relativity—Alice can’t sense anything  

01:51

unusual when crossing that horizon. Meanwhile,  Bob, watching from afar, has to either witness  

01:58

the qubit escape in the Hawking radiation leaked  as the black hole evaporates, or the qubit vanish forever  

02:05

in that evaporation. In the first case,  the qubit is duplicated—it’s both inside  

02:10

and outside the black hole. In the second it’s  annihilated. Either way, a foundational principle  

02:15

of quantum mechanics—conservation of quantum  information or unitarity appears to be violated.

02:21

Because both the equivalence principle  and unitarity are fundamental to their  

02:26

respective theories, we know something must be  wrong with our understanding of what happens  

02:29

to quantum information in a black hole.  There have been various proposed solutions,  

02:34

but today I’m going to focus on one of the  earliest, and perhaps the least intuitive—and  

02:38

that’s black hole complementarity, formulated  by Leonard Susskind and others in the early 90s.

02:43

Black hole complementarity states that there  actually is no contradiction. It proposes that  

02:49

it’s fine for the same quantum information to be  inside the black hole as measured by one observer,  

02:54

and frozen on the surface or radiated  away in Hawking radiation according to  

02:58

another. And according to “BHC” this is fine  because no one can ever observe both states,  

03:05

so no one can prove that unitarity  was broken, which means it … wasn’t?

03:11

To get our heads around this, let’s start by  making the conflict much more precise. To do  

03:15

that we’re going to use the same black hole map  that proper black hole theorists like to use—the  

03:19

Penrose diagram. Without a black hole, a Penrose  diagram looks like this. Up is roughly speaking  

03:24

the forward time direction, and left and right  are roughly one spatial dimension. But space and  

03:29

time are rescaled so they bend into each other  and pile up towards the boundaries. Tick marks  

03:34

are drawn closer together so that the border of the graph represents infinite distance and infinite past or future. And  

03:41

all of this is done in just such a way so that  light will always travel a 45 degree path. All  

03:45

sub-lightspeed travel has to take a steeper  slope—more time taken to travel less space.

03:52

Near an event horizon of a black hole  we can think of spacetime as being  

03:55

infinitely stretched from the point of view of  a distant observer. That means we can just say  

03:59

one of these boundaries is our event horizon,  and add the interior of the black hole on the  

04:04

other side. In these coordinates, the central  singularity looks like the top of the Penrose  

04:09

diagram is cut off—that represents the cessation  of space and time inside the black hole. For now  

04:14

you’ll have to take my word that this is a valid  way to draw the spacetime of a universe with a  

04:19

black hole, but we have other videos on the  Penrose diagram if you need more convincing.

04:24

Let’s see what Alice’s black hole expedition  looks like on the Penrose diagram. Both She  

04:30

and Bob move up in time, while Alice and  the qubit also move closer to the event  

04:34

horizon. Light from the qubit reaches Alice  and then Bob, carrying information about the  

04:39

qubit’s location—its past location  by the time Alice or Bob see it.

04:44

Approaching the event horizon, those photons  still reach Alice quickly but take longer and  

04:49

longer to reach Bob. Photons traveling from  just above the event horizon only reach Bob  

04:53

in the far future. No photon emitted below the  event horizon can ever reach Bob, so to him  

04:59

the qubit and Alice are frozen just above  the event horizon. Those photons emitted  

05:05

inside the black hole are doomed to hit the  singularity, as is the qubit. As is Alice.

05:11

The diagram we’ve been using is for a black  hole that’s always been there and always  

05:15

will be. Real black holes typically form  from collapsed stars, and they also leak  

05:19

Hawking radiation until they disappear. Here’s  how we might depict such a black hole. We have  

05:24

a Penrose diagram for the universe where the  black hole forms somewhere in space when a  

05:29

collapsing star forms an event horizon. Then  it evaporates by Hawking radiation. We only  

05:35

need half of this map because, well, nothing  going in one side ever comes out the other.

05:42

Let’s look at just the qubit’s path. According  to both Alice and Bob it falls and reaches the  

05:46

event horizon. According to just Alice it enters  the black hole and hits the singularity. Bob,  

05:53

on the other hand, sees it freeze on the  horizon and emerge again as Hawking radiation.  

05:57

It emerges only after the black hole is at least  half-evaporated because, according to physicist  

06:02

Don Page, before that point the information in  the emitted radiation is hopelessly scrambled.

06:08

From a perspective outside space and time, the  quantum bit in some sense exists at all of these  

06:15

spacetime points, but does it ever exist in  two physical locations simultaneously—at the  

06:22

same instant time? Well there’s no absolute  definition of “simultaneous” in Einstein’s  

06:27

relative universe. But these lines on the Penrose  diagram could be considered to describe different  

06:32

spatial locations at the same moment in  time. Therefore, for anything duplicated  

06:37

on one of these lines, the copies can be  thought of as existing at the same time.

06:42

So, before it hits the event horizon  there’s only one qubit. After the black  

06:47

hole evaporates there’s only one qubit—the  one leaked out in Hawking photons. But  

06:52

between its entry into the black hole and  the black hole’s evaporation we can argue  

06:57

that the qubit exists simultaneously  in two places, violating unitarity.

07:04

The key to this is to really dig into what  we mean by “existing simultaneously”. Due  

07:09

to the finite travel time of light, we can  only confirm simultaneous existence at two  

07:15

spacetime points after the light from both  reaches us. On our original Penrose diagram,  

07:21

we only have information about the parts of the  universe from which signals traveling at the  

07:25

speed of light or lower could reach us—that’s our  past light-cone. This is the only region in which  

07:32

we can verify simultaneity—and we can only verify  that things existed simultaneously after the fact.

07:40

But if we try to do that for our duplicated  qubits, we see that there is no past light  

07:44

cone—no possible observer—who can ever verify  that both exist at the same time. Alice sees one,  

07:52

Bob sees the other, but no one can ever see  both. Black hole complementarity argues that  

07:57

the impossibility of any one observer  measuring both qubits means that there’s  

08:02

no violation of unitarity, so there’s no  contradiction. Before we pick that apart,  

08:06

let’s make sure it’s really impossible for any  one observer to see both the Hawking-radiated  

08:13

and the swallowed versions of the qubit. Physicists Bill Hayden and John Preskill  

08:19

figured out the best chance of one observer seeing  both. The thought experiment goes like this:

08:25

Alice jumps into the black hole with the quantum  bit just before the black hole is half evaporated  

08:31

because she knows that only after this so-called  Page time can quantum information get back out.  

08:37

Below the event horizon she tries to send the  qubit upwards. She knows it can’t re-cross the  

08:42

event horizon, but it will slow the qubit’s  descent to give Bob more time to catch it.  

08:47

And now Bob also drops into the black hole. He  times the leap exquisitely so that he catches  

08:53

the Hawking-radiated qubit on its way out, and hopes to also see the swallowed  

08:57

qubit once inside. And … he misses it. Even  with the most perfectly timed experiment,  

09:04

Hayden and Preskill show that Bob will always  barely miss being able to see both qubits.

09:10

So it seems that nature is working awfully  hard to make it impossible for anyone to  

09:14

see both versions of the qubit. So maybe  the unobservability of the cloned qubits  

09:19

is telling us something fundamental. That would  be the argument of black hole complementarity,  

09:24

which states that, because it’s  impossible for anyone to observe  

09:27

both qubits, there’s no contradiction—no  violation of unitarity—for both to exist.

09:34

This sounds like some sort of weird  quantum stuff. And complementarity  

09:38

is indeed fundamental to quantum mechanics.  For example, there are complementary quantum  

09:43

properties like position and momentum that  can never be measured perfectly at the same  

09:48

time. Or complementary descriptions like the  wave-like versus particle-like behavior of  

09:53

a quantum object. The word complementarity  implies a connection to quantum mechanics,  

09:58

but the connection isn’t clear. For black  hole complementarity there are different  

10:03

interpretations, which are still argued over,  and which aren’t even necessarily mutually exclusive.

10:10

So interpretation 1): If black  hole complementarity is right,  

10:14

it may be telling us that, while unitarity and the  conservation of quantum information always hold,  

10:20

the way they hold is relative to a given  observer. Alice will always find that quantum  

10:25

mechanics works perfectly and that there  are never any contradictions. So will Bob,  

10:31

but for him quantum mechanics might work  perfectly in a different way. The key is  

10:37

that if Alice and Bob can never communicate,  no contradiction is ever discovered. If this is  

10:43

right then it’s telling us something about what  the wavefunction and quantum information really  

10:47

represent and that our description of the world  depends quite radically on our reference frame.  

10:55

Even a concept as basic as the existence of a  quantum state may be relative to the observer.  

11:01

It’s not the only hint at this uncomfortable  idea—for example, the existence of a particle can  

11:06

depend on the acceleration of an observer, as we  saw in our Unruh radiation episode. Interestingly,  

11:12

both Unruh radiation and black hole  complementarity involve uncrossable horizons.

11:19

So interpretation 2) for black hole complementarity  is that the interior and exterior descriptions of  

11:25

the quantum information are, in a sense,  equivalent. Or rather they are different  

11:31

descriptions of what is fundamentally the one  quantum system. There’s no duplication because  

11:36

the interior and exterior of the black hole  are different descriptions of the same abstract  

11:42

quantum system. This is a form of holography,  in which a lower dimensional system can be  

11:47

equally-well described as a system one dimension  higher—a boundary and its interior become  

11:53

different ways to talk about the same thing. We’ve  talked about holographic principle before—it’s an  

11:58

idea that can be extended well beyond black  holes, even suggesting that the interior of  

12:02

our universe may have a dual and complementary  description on its infinitely distant surface.

12:09

Black hole complementarity is by no means  the accepted solution to the black hole  

12:13

information paradox. We haven’t talked  about black hole firewalls yet—in which  

12:18

an extreme energy screen just above the event  horizon fries anything that tries to enter,  

12:23

eliminating any duplication of qubits but also  violating the equivalence principle. In an episode  

12:29

coming very soon we’ll see why some physicists  think the firewall must exist, and also why the  

12:35

firewall may not free us from the strangeness  of black hole complementarity or vice versa.

12:42

So, yeah, black holes are contradictions.  They are holes in the universe and in our  

12:47

understanding of it. But through those holes  we’re glimpsing grander visions of what our  

12:50

universe might really be. For example, that  there’s a sort of extreme relativity to our  

12:56

description of the world, or that the interiors  of black holes and of universes may be in a  

13:02

weird way equivalent to their surfaces—each the  warped reflection of a complementary spacetime.

13:09

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Now, today, I want to give an extra special  thank you to John Sronce who supporting us at  

13:38

the Big Bang level. John, we've used some  of your contribution to beat this episode  

13:43

along with this shout out to be included on the  event horizon of the Cygnus X-1 black hole. Now,  

13:49

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13:55

ensuring that even the end of the  universe is reminded of your generosity.

14:01

How do you do fellow simulations? Before we end  the episode, I just wanted to let you know that  

14:06

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Etiquetas relacionadas
Black HolesQuantum MechanicsGeneral RelativityInformation ParadoxHawking RadiationEvent HorizonPenrose DiagramSpacetimeTheoretical PhysicsScientific Exploration
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