Can Black Holes Unify General Relativity & Quantum Mechanics?
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
🌌 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).
🔬 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.
🌐 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
💡Quantum Mechanics
💡Black Hole Information Paradox
💡Black Hole Complementarity
💡Event Horizon
💡Hawking Radiation
💡Quantum Bit (Qubit)
💡Penrose Diagram
💡Unitarity
💡Holographic Principle
💡Unruh Radiation
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
Hey Everyone. Before we get to the episode,
just a heads up we have two new items at the merch store. There’s a link in the description
Black holes are inevitable predictions of general relativity—our best theory of space,
time and gravity. But they clash in multiple ways with quantum mechanics,
our equally successful description of the subatomic world. One such clash is the
black hole information paradox—and a proposed solution—black hole complementarity—may forced
us to radically rethink what it even means for something to exist.
We know that our universe is fundamentally self-consistent—otherwise what are we even
doing trying to science it. But that means when a contradiction appears in our scientific
description of the universe, we know something is wrong with that description. It’s really exciting
when this happens because the nature of the inconsistency can point the way to a better, more
encompassing scientific description. Black holes are one of the favourite tools of the theoretical
physicist because they lead to multiple inconsistencies between general relativity
and quantum mechanics, and so may be our best path to the grander theory that unites the two.
The conflict we looked at recently is the black hole information paradox, and it’s not a bad
idea to watch that episode before this. In it, our intrepid heroes of the gedankenexperiment,
Alice and Bob, discovered that black holes must violate either a fundamental principle of general
relativity or of quantum mechanics. When Alice carries a quantum bit—a qubit—into a black hole,
she witnesses the qubit cross the event horizon. She must, because according to
the equivalence principle—a founding axiom of general relativity—Alice can’t sense anything
unusual when crossing that horizon. Meanwhile, Bob, watching from afar, has to either witness
the qubit escape in the Hawking radiation leaked as the black hole evaporates, or the qubit vanish forever
in that evaporation. In the first case, the qubit is duplicated—it’s both inside
and outside the black hole. In the second it’s annihilated. Either way, a foundational principle
of quantum mechanics—conservation of quantum information or unitarity appears to be violated.
Because both the equivalence principle and unitarity are fundamental to their
respective theories, we know something must be wrong with our understanding of what happens
to quantum information in a black hole. There have been various proposed solutions,
but today I’m going to focus on one of the earliest, and perhaps the least intuitive—and
that’s black hole complementarity, formulated by Leonard Susskind and others in the early 90s.
Black hole complementarity states that there actually is no contradiction. It proposes that
it’s fine for the same quantum information to be inside the black hole as measured by one observer,
and frozen on the surface or radiated away in Hawking radiation according to
another. And according to “BHC” this is fine because no one can ever observe both states,
so no one can prove that unitarity was broken, which means it … wasn’t?
To get our heads around this, let’s start by making the conflict much more precise. To do
that we’re going to use the same black hole map that proper black hole theorists like to use—the
Penrose diagram. Without a black hole, a Penrose diagram looks like this. Up is roughly speaking
the forward time direction, and left and right are roughly one spatial dimension. But space and
time are rescaled so they bend into each other and pile up towards the boundaries. Tick marks
are drawn closer together so that the border of the graph represents infinite distance and infinite past or future. And
all of this is done in just such a way so that light will always travel a 45 degree path. All
sub-lightspeed travel has to take a steeper slope—more time taken to travel less space.
Near an event horizon of a black hole we can think of spacetime as being
infinitely stretched from the point of view of a distant observer. That means we can just say
one of these boundaries is our event horizon, and add the interior of the black hole on the
other side. In these coordinates, the central singularity looks like the top of the Penrose
diagram is cut off—that represents the cessation of space and time inside the black hole. For now
you’ll have to take my word that this is a valid way to draw the spacetime of a universe with a
black hole, but we have other videos on the Penrose diagram if you need more convincing.
Let’s see what Alice’s black hole expedition looks like on the Penrose diagram. Both She
and Bob move up in time, while Alice and the qubit also move closer to the event
horizon. Light from the qubit reaches Alice and then Bob, carrying information about the
qubit’s location—its past location by the time Alice or Bob see it.
Approaching the event horizon, those photons still reach Alice quickly but take longer and
longer to reach Bob. Photons traveling from just above the event horizon only reach Bob
in the far future. No photon emitted below the event horizon can ever reach Bob, so to him
the qubit and Alice are frozen just above the event horizon. Those photons emitted
inside the black hole are doomed to hit the singularity, as is the qubit. As is Alice.
The diagram we’ve been using is for a black hole that’s always been there and always
will be. Real black holes typically form from collapsed stars, and they also leak
Hawking radiation until they disappear. Here’s how we might depict such a black hole. We have
a Penrose diagram for the universe where the black hole forms somewhere in space when a
collapsing star forms an event horizon. Then it evaporates by Hawking radiation. We only
need half of this map because, well, nothing going in one side ever comes out the other.
Let’s look at just the qubit’s path. According to both Alice and Bob it falls and reaches the
event horizon. According to just Alice it enters the black hole and hits the singularity. Bob,
on the other hand, sees it freeze on the horizon and emerge again as Hawking radiation.
It emerges only after the black hole is at least half-evaporated because, according to physicist
Don Page, before that point the information in the emitted radiation is hopelessly scrambled.
From a perspective outside space and time, the quantum bit in some sense exists at all of these
spacetime points, but does it ever exist in two physical locations simultaneously—at the
same instant time? Well there’s no absolute definition of “simultaneous” in Einstein’s
relative universe. But these lines on the Penrose diagram could be considered to describe different
spatial locations at the same moment in time. Therefore, for anything duplicated
on one of these lines, the copies can be thought of as existing at the same time.
So, before it hits the event horizon there’s only one qubit. After the black
hole evaporates there’s only one qubit—the one leaked out in Hawking photons. But
between its entry into the black hole and the black hole’s evaporation we can argue
that the qubit exists simultaneously in two places, violating unitarity.
The key to this is to really dig into what we mean by “existing simultaneously”. Due
to the finite travel time of light, we can only confirm simultaneous existence at two
spacetime points after the light from both reaches us. On our original Penrose diagram,
we only have information about the parts of the universe from which signals traveling at the
speed of light or lower could reach us—that’s our past light-cone. This is the only region in which
we can verify simultaneity—and we can only verify that things existed simultaneously after the fact.
But if we try to do that for our duplicated qubits, we see that there is no past light
cone—no possible observer—who can ever verify that both exist at the same time. Alice sees one,
Bob sees the other, but no one can ever see both. Black hole complementarity argues that
the impossibility of any one observer measuring both qubits means that there’s
no violation of unitarity, so there’s no contradiction. Before we pick that apart,
let’s make sure it’s really impossible for any one observer to see both the Hawking-radiated
and the swallowed versions of the qubit. Physicists Bill Hayden and John Preskill
figured out the best chance of one observer seeing both. The thought experiment goes like this:
Alice jumps into the black hole with the quantum bit just before the black hole is half evaporated
because she knows that only after this so-called Page time can quantum information get back out.
Below the event horizon she tries to send the qubit upwards. She knows it can’t re-cross the
event horizon, but it will slow the qubit’s descent to give Bob more time to catch it.
And now Bob also drops into the black hole. He times the leap exquisitely so that he catches
the Hawking-radiated qubit on its way out, and hopes to also see the swallowed
qubit once inside. And … he misses it. Even with the most perfectly timed experiment,
Hayden and Preskill show that Bob will always barely miss being able to see both qubits.
So it seems that nature is working awfully hard to make it impossible for anyone to
see both versions of the qubit. So maybe the unobservability of the cloned qubits
is telling us something fundamental. That would be the argument of black hole complementarity,
which states that, because it’s impossible for anyone to observe
both qubits, there’s no contradiction—no violation of unitarity—for both to exist.
This sounds like some sort of weird quantum stuff. And complementarity
is indeed fundamental to quantum mechanics. For example, there are complementary quantum
properties like position and momentum that can never be measured perfectly at the same
time. Or complementary descriptions like the wave-like versus particle-like behavior of
a quantum object. The word complementarity implies a connection to quantum mechanics,
but the connection isn’t clear. For black hole complementarity there are different
interpretations, which are still argued over, and which aren’t even necessarily mutually exclusive.
So interpretation 1): If black hole complementarity is right,
it may be telling us that, while unitarity and the conservation of quantum information always hold,
the way they hold is relative to a given observer. Alice will always find that quantum
mechanics works perfectly and that there are never any contradictions. So will Bob,
but for him quantum mechanics might work perfectly in a different way. The key is
that if Alice and Bob can never communicate, no contradiction is ever discovered. If this is
right then it’s telling us something about what the wavefunction and quantum information really
represent and that our description of the world depends quite radically on our reference frame.
Even a concept as basic as the existence of a quantum state may be relative to the observer.
It’s not the only hint at this uncomfortable idea—for example, the existence of a particle can
depend on the acceleration of an observer, as we saw in our Unruh radiation episode. Interestingly,
both Unruh radiation and black hole complementarity involve uncrossable horizons.
So interpretation 2) for black hole complementarity is that the interior and exterior descriptions of
the quantum information are, in a sense, equivalent. Or rather they are different
descriptions of what is fundamentally the one quantum system. There’s no duplication because
the interior and exterior of the black hole are different descriptions of the same abstract
quantum system. This is a form of holography, in which a lower dimensional system can be
equally-well described as a system one dimension higher—a boundary and its interior become
different ways to talk about the same thing. We’ve talked about holographic principle before—it’s an
idea that can be extended well beyond black holes, even suggesting that the interior of
our universe may have a dual and complementary description on its infinitely distant surface.
Black hole complementarity is by no means the accepted solution to the black hole
information paradox. We haven’t talked about black hole firewalls yet—in which
an extreme energy screen just above the event horizon fries anything that tries to enter,
eliminating any duplication of qubits but also violating the equivalence principle. In an episode
coming very soon we’ll see why some physicists think the firewall must exist, and also why the
firewall may not free us from the strangeness of black hole complementarity or vice versa.
So, yeah, black holes are contradictions. They are holes in the universe and in our
understanding of it. But through those holes we’re glimpsing grander visions of what our
universe might really be. For example, that there’s a sort of extreme relativity to our
description of the world, or that the interiors of black holes and of universes may be in a
weird way equivalent to their surfaces—each the warped reflection of a complementary spacetime.
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