What Happens If You Jump Into A Black Hole?
Summary
TLDRThe video script narrates a thought experiment involving Alice and Bob, two intrepid explorers, who embark on a journey to explore the enigmatic depths of a black hole. Alice, the more adventurous of the two, dives into Sagittarius A*, the supermassive black hole at the center of the Milky Way, while Bob observes from a safe distance. Alice carries a clock and a box containing a single electron, serving as a quantum bit of information. As she approaches the event horizon, Bob witnesses time dilation effects and the scrambling of information across the horizon. From Alice's perspective, she experiences no significant tidal forces and continues to fall towards the black hole's singularity. The crux of the narrative revolves around the paradox of quantum informationβwhether it is preserved within the black hole or emitted as Hawking radiation. Bob, in a monumental effort, constructs a detector to capture all future Hawking radiation, eventually recovering the quantum bit and Alice's information. The script delves into complex concepts such as the holographic principle, entanglement, and the conservation of quantum information, posing profound questions about the nature of spacetime and the fate of information within black holes.
Takeaways
- π **Alice and Bob's Mission**: The thought experiment involves Alice and Bob, famous explorers, jumping into a black hole to determine the fundamental structure of spacetime and its connection to quantum entanglement.
- β«οΈ **Black Hole Exploration**: The script discusses the concept of black holes and their role in theoretical physics, including the holographic principle and the idea that spacetime may be 'knitted' from entanglement.
- β **Time Dilation**: Bob observes Alice's time dilation as she approaches the event horizon, which slows her descent and eventually makes her appear to merge with the black hole's event horizon.
- 𧲠**Gravitational Redshift**: As Alice falls, the photons emitted by her and the box are gravitationally redshifted, stretching to longer wavelengths and becoming fainter.
- π¬ **Quantum Information**: Alice carries a box with a single electron, representing a quantum bit of information, to test the fate of quantum information inside a black hole.
- π **Observer Perspectives**: The script contrasts the perspectives of Alice (falling into the black hole) and Bob (observing from a distance), highlighting the differences in their experiences.
- π **Hawking Radiation**: Bob constructs a detector to collect Hawking radiation, hoping to find the quantum bit and thus prove that black holes do not destroy quantum information.
- β³ **Time and Patience**: Bob waits for an incredibly long time (10^87 years), uploading his mind to a computer and building massive computers to analyze the data from the black hole.
- π **Entanglement's Role**: The script suggests that entanglement plays a crucial role in the structure of spacetime, possibly being the underlying fabric from which spacetime emerges.
- π‘ **Unitarity and No-Cloning**: The script touches on the principles of quantum mechanics, including unitarity and the no-cloning theorem, which are challenged by the paradox of quantum information inside a black hole.
- π **Merchandise**: The script ends with an announcement of limited edition merchandise available for sale, including a black hole enamel pin and a Star Wars-inspired t-shirt.
Q & A
Who are Alice and Bob in the context of the script?
-Alice and Bob are famous explorers of the abstract landscapes of theoretical physics. They are heroes of the thought experiment whose life mission is to find contradictions in the deepest layers of scientific theories.
What is the significance of Alice and Bob jumping into a black hole?
-Alice and Bob are jumping into a black hole to determine the fundamental structure of spacetime and its connection to quantum entanglement, which is a key aspect of understanding the fabric of the universe.
What is the holographic principle mentioned in the script?
-The holographic principle is a concept in theoretical physics suggesting that all the information contained in a volume of space can be represented on the boundary to the same space.
How does quantum entanglement relate to the structure of space?
-Quantum entanglement is thought to be a fundamental aspect of the structure of space. It is suggested that space may be 'knit together' from a network of mutual information of its contents, implying that entanglement plays a key role in the fabric of spacetime.
What is the ER=EPR conjecture?
-The ER=EPR conjecture is a proposal in theoretical physics that connects entanglement (EPR) with wormholes (ER), suggesting a deep relationship between quantum entanglement and the structure of spacetime.
What is the black hole information paradox?
-The black hole information paradox is a conflict between quantum mechanics and general relativity. It questions what happens to the information about physical states when it enters a black hole, as quantum mechanics states that information cannot be lost, while general relativity suggests that information is not retrievable from a black hole.
What is the concept of Hawking radiation?
-Hawking radiation is a theoretical prediction by physicist Stephen Hawking that black holes emit radiation due to quantum effects near the event horizon. This radiation is faint and is named after Hawking for its theoretical discovery.
Why does Bob construct a detector to surround the black hole?
-Bob constructs a detector to surround the black hole to collect all future Hawking radiation emitted by the black hole. This is in an attempt to not lose track of the experimental Cubit and potentially, signs of Alice.
What is the significance of the no-cloning theorem in quantum mechanics?
-The no-cloning theorem states that it is impossible to create an identical copy of an arbitrary unknown quantum state. This is significant because it protects the integrity of quantum information and is a fundamental principle in quantum computing and quantum information theory.
What is the concept of unitarity in quantum mechanics?
-Unitarity in quantum mechanics is the principle that the total probability of all possible outcomes of a quantum system must add up to one. It is a fundamental concept that ensures the conservation of probability in quantum processes.
What is the contradiction identified by the thought experiment involving Alice and Bob?
-The contradiction identified is that two different observers, Alice and Bob, have irreconcilably different answers to the question of where the Cubit is. This challenges the principles of quantum mechanics, specifically unitarity and the equivalence principle, and is a key point of discussion in the script.
What is the significance of the limited edition merch mentioned at the end of the script?
-The limited edition merch, including a black hole enamel pin and a Star Wars inspired SpaceTime t-shirt and sweatshirt, is a promotional item for the SpaceTime series. It serves to engage the audience and provide a tangible connection to the content they are consuming.
Outlines
π Introduction to the Black Hole Experiment
The video introduces Alice and Bob, famous explorers of theoretical physics, who embark on a mission to explore the structure of spacetime and its connection to quantum entanglement. They plan to jump into a black hole to test these theories. Alice, the more adventurous, prepares to jump into Sagittarius A*, the supermassive black hole at the center of the Milky Way, while Bob watches from a safe distance. Alice carries a clock and a box containing a single electron to track time and quantum information. As Alice descends, Bob observes her through a gamma ray telescope, noticing gravitational time dilation and redshift. However, Alice appears to quickly merge with the event horizon, contrary to expectations of time dilation slowing her approach.
π Bob's Observations of Alice's Descent
From Bob's perspective, Alice experiences gravitational time dilation, but as a free-falling observer, she moves quickly and doesn't experience the extreme dilation expected near the event horizon. Alice's body appears to flatten due to the gravitational forces, and Bob loses sight of her as her photons become indistinguishable from the black hole's Hawking radiation. Bob decides to construct a detector to collect all future Hawking radiation, hoping to find the quantum information carried by Alice. He also uploads his mind to the ship's computer to outlive the black hole and begins a long wait.
π Alice's Perspective Inside the Black Hole
Alice, in freefall, experiences no significant tidal forces or acceleration effects as she approaches the event horizon. She observes the black hole as a vast black surface that appears to move away from her. As she crosses the event horizon, she doesn't notice any unusual phenomena, which aligns with the equivalence principle of general relativity. Alice continues to fall, believing the experiment to be a success as she confirms that black holes can contain quantum bits. Meanwhile, Bob, outside the black hole, dedicates eons to collecting and analyzing Hawking radiation, eventually detecting a pattern that suggests the presence of the quantum bit, proving that black holes do not erase quantum information.
π§ The Quantum Information Paradox
The video concludes with a paradox: Bob and Alice have different observations regarding the fate of the quantum bit, or 'Cubit'. Bob sees the Cubit freeze on the horizon and later recovers it from the Hawking radiation, while Alice sees it fall into the black hole. This contradiction challenges the principles of quantum mechanics, specifically unitarity, which states that quantum probabilities must sum to one, and the no-cloning theorem, which prohibits the duplication of quantum bits. The resolution to this paradox is promised in an upcoming video, which will explore concepts like black hole complementarity and the idea of a firewall at the event horizon.
ποΈ Merchandise Announcement
The video script concludes with an announcement about new limited edition merchandise available for sale. The items include a black hole enamel pin designed by the SpaceTime graphics team and a Star Wars-inspired SpaceTime t-shirt and sweatshirt designed by the director. The enamel pins are available for pre-sale with shipping expected in June, and the Star Wars-inspired items are available until May the 4th.
Mindmap
Keywords
π‘Black Hole
π‘Quantum Entanglement
π‘Hawking Radiation
π‘Event Horizon
π‘Quantum Information
π‘Unitarity
π‘Equivalence Principle
π‘Spaghettification
π‘Dion Sphere
π‘Black Hole Complementarity
π‘No Cloning Theorem
Highlights
New limited edition merchandise available at the merch store featuring Alice and Bob, famous explorers of theoretical physics.
Alice and Bob embark on a mission to explore the abstract landscapes of theoretical physics by jumping into a black hole.
The thought experiment aims to determine the fundamental structure of spacetime and its connection to quantum entanglement.
Previous episodes discussed the holographic principle and the idea that space could be encoded on its boundary.
Quantum entanglement is proposed as a method to encode the emergent dimension on the boundary of a black hole.
The fabric of space may be emerging from entanglement, with space being knit together by mutual information of its contents.
The ER=EPR conjecture suggests a deep connection between entanglement and wormholes.
Black hole complementarity challenges our intuition about where information exists within a black hole.
Alice carries a clock and a box containing a single electron to track her position and the flow of time as she descends into the black hole.
From Bob's perspective, Alice appears to slow down, speed up, and then merge with the black hole's event horizon.
Alice's and the box's descent seem to freeze only very close to the event horizon, with Alice appearing to flatten from Bob's viewpoint.
Alice experiences no spaghettification due to the scale of the black hole and her position relative to the event horizon.
Bob loses sight of Alice and the box as their photons become indistinguishable from the black hole's Hawking radiation.
Bob constructs a detector to surround the black hole to collect all future Hawking radiation in an attempt to preserve quantum information.
Alice, in freefall, experiences no significant gravitational forces and observes the black hole as a vast black surface moving away from her.
Upon crossing the event horizon, Alice does not experience any unusual phenomena, consistent with the equivalence principle.
The experiment reveals a contradiction in the perspective of Alice and Bob regarding the fate of the quantum bit, challenging the principles of quantum mechanics.
Bob, after an immense wait, detects a pattern in the Hawking radiation, suggesting that black holes do not swallow quantum information.
Bob uses advanced technology to reconstruct Alice's consciousness, providing a potential resolution to the paradox.
The paradox identified in the experiment may lead to new insights in theoretical physics, including the concept of a firewall at the event horizon.
Limited edition merch items include a black hole enamel pin and a Star Wars inspired SpaceTime t-shirt and sweatshirt.
Transcripts
before we get started I want to let you
know that there's some new limited
edition merch for sale at the merch
store meet Alis and Bob famous explorers
of the abstract Landscapes of
theoretical physics Heroes of the dunkan
experiment the thought experiment whose
life mission is to find contradiction in
the deepest layers of our theories and
so lead us deeper today our intrepret
pair are jumping into a black hole again
why well to determine the fundamental
structure of SpaceTime and its
connection to quantum entanglement of
[Music]
course in recent as well as less recent
episodes we've seen how thinking about
black holes leads to weird ideas like
the fact that there's a minimum
meaningful distance in space or that all
the information of a volume of space
fits on its boundary we also saw a
simplistic manner in which an entire new
spatial Dimension can actually be
encoded on that boundary leading to the
notion of the holographic Universe we
even saw one idea for how gravity could
emerge from the thermodynamics on that
boundary in a couple of the recent
episodes we talked about how the
emergent Dimension could be encoded in
the scale of patterns on the boundary
but these days most physicists working
in that area think there's a better way
to do that encoding and that's with
quantum entanglement the subtle
correlations between the bits of
information that define the properties
of part articles in fact as we'll see in
upcoming episodes it's starting to look
like the entire fabric of space may be
emerging from entanglement that space is
sort of knit together from the network
of mutual information of its
contents this idea of the role of
entanglement came from thinking about
black holes in parallel to the stuff
that led to this minimal plank length
and the holographic principle in
particular in thinking about what
happens to Quantum information in a
black hole this is ultimately going to
lead to a deep connection between
entanglement and wormholes in the ER
equals epr conjecture and the same line
of reasoning is going to completely mess
with our intuition about where
information exists leading to black hole
complimentarity we'll get to these in
upcoming episodes but today we want to
set up the contradiction that drives all
of these and for that we need Alice and
Bob to jump into a black hole well just
Alice actually she's always been a bit
more adventurous than Bob so Alice and
Bob head to Sagittarius AAR the super
massive black hole at the center of the
Milky Way Alice suits up and prepares to
jump Bob prepares to watch from a safe
distance Alice carries a clock that
emits pulses of high energy Gamay with a
regular period so that Bob can track her
position and also how her flow of time
changes Alice also carries a box in
which there's a single electron with its
spin Frozen this is our Cubit our bit of
quantum information in this case the
information is about whether that
electron spin is pointing up or down the
box also emits regular pulses of Gamay
so it can be tracked
independently excited to be the first
human to see below an event horizon
Alice high-fives Bob and leaps head
first towards sag a star and as she
begins her descent she throws the Cubit
box to fall just ahead of her let's
start with Bob's perspective he watches
Alice and the Box fall training his
Gamay telescope on them to monitor their
flow of time those Gamay photons arrive
with increasing separation due to
gravitational time dilation and at the
same time the photons are
gravitationally red shifted stretched to
longer wavelengths Bob has also switched
on detector sensitive to all wavelengths
from x-ray to visible to radio he
settles in expecting to watch Alice slow
down as she approaches the event Horizon
to witness her seconds stretch to hours
years
Millennia but that doesn't happen
instead he observes Alice fall quickly
speed up and then suddenly slow down and
merge with the black holes Event Horizon
so what happened to the time dilation
approaching Infinity at the Event
Horizon well it's true that for any
black hole you can find a distance from
The Event Horizon with any ridiculously
high time dilation that you want on like
a millisecond stretching to 100 trillion
years but the thing is a Free Falling
Observer like Alice is moving very very
fast by the time she reaches these
points she's approaching the speed of
light the time dilation increases but
the amount of time spent at each point
decreases now ultimately the formal
winds and both Alice's and the Box's
descent seem to slow down and freeze but
really only very close to the event
horizon
Bob sees the Box slow down and freeze
first which means Alice appears to catch
up to the box and then Alice's head
slows down before her feet so from Bob's
perspective she appears to flatten now
Bob had been worried about the opposite
effect that Alice might get
spaghettified elongated by the tidal
forces pulling on her head harder than
her feet but that doesn't happen here
because human scale tidal forces for a
black hole this massive are only deep
inside the black hole instead by the
time the top of Alice's head is just
above the Event Horizon her entire body
is also just above the Event Horizon now
this effect doesn't have a term but Bob
wonders if pancake ification might be
appropriate at this point Alice's
photons are much fainter than the
ambient glow of the universe the cosmic
microwave background and the wavelengths
of those photons are are much longer
than the CMB those photons are barely
detectable even by Bob's giant radio
antenna and then Bob loses sight
altogether the last thing he sees is
that all of Alice's cubits along with
the experimental Cubit get scrambled
over the entire event horizon now any
light from Alice is indistinguishable
from the black hole's own Hawking
radiation and may actually be equivalent
to it Hawking radiation is the faint
glow that every black hole produces due
to its non-zero temperature for sadj
star that temperature is 10 to the power
of -4 Kelvin resulting in Hawking
photons with wavelengths over 100
million km long but Bob is desperate to
not lose track of the experimental Cupid
the only way is to collect all future
Hawking radiation emitted by the black
hole he begins the construction of a
detector that will surround the entire
black hole a type of Dion sphere he also
goes ahead and uploads his mind to the
ship's computer so that he can outlift
the black hole and he settles in for the
long game in the meantime let's look at
what happened to Alice from her own
perspective plummeting towards sjar take
some hours but most of that time is
spent far from The Event Horizon she
rapidly accelerates and by the latter
part of the journey whizzers
exponentially quickly there's no GeForce
from that acceleration and no tidal
forces from the black Hall Alice is in
freeall towards an event horizon vastly
larger than she is so she feels like
she's floating this is a consequence of
Einstein's equivalent principle which
tells us that for an observer in
freefall their local patch of SpaceTime
behaves exactly like space in the
absence of a gravitational
field Alice sees the black hole beneath
her as a vast black surface oddly though
that surface appears to move away from
her as she approaches see the true Event
Horizon looks black from a great
distance due to the infinite gravity
ational red shift of photon struggling
to depart it that red shift results from
the full trajectory out of a black
hole's gravitational well but Alice can
still encounter photons that were
emitted a hair above the Event Horizon
because she's deep in that gravitational
well effectively she's coming to them
rather than waiting for them to reach
her also as Alice approaches The Event
Horizon her own Extreme Velocity sort of
D redshifts the outward pointing photons
that she passes through she sees the
record of objects that fell ahead of her
including the Cubit
box now comes the critical part of the
experiment from Alice's perspective at
some point the cubid Box crosses the
true Event Horizon ahead of her even if
she sees no marker of that Horizon in
her reference frame does she still see
the Box well yes but the Box she sees is
the box as it was just before crossing
the horizon she could only catch photons
emitted by the box from below the
Horizon if she crosses that Horizon
herself she is first and foremost a
scientist so turns her mind back to the
experiment and plummets through the
Event Horizon and nothing weird happens
remember the equivalence principle that
tells us that there's no experiment you
can do or observation you can make on
the local patch of space that
distinguishes whether that patch is Free
Falling or free floating this principle
is the Bedrock of relativity and
physicists are very uncomfortable by
anything that appears to violate it now
remember this because we may have to
break the equivalence principle later
and that should make you uncomfortable
also but assuming the equivalence
principle holds Alice can't see things
freeze at the Event Horizon not the
Cubit not herself nor does she catch up
to the Cubit so now Beneath The Horizon
the Cubit is still below her and still
gaining ground towards the dark surface
that also always appears below
but now that dark surface is growing and
stretching around behind her also the
outside universe is a shrinking fisheye
view above Alice's sense of up iris's
closed and all directions become an
enveloping down all directions lead to a
Terminus of space and time Alice can't
ever leave to tell Bob the result of the
experiment but from her perspective it's
a huge success she she now knows with
short that black holes can swallow
Quantum bits let's go back to Bob
remember he's now in the business of
catching Hawking radiation and looking
for signs of the experimental Cubit
though if we're being honest he's also
looking for signs of
Alice the black hole radiates it would
lose Mass this way if it weren't for the
fact that it eats more Cosmic microwave
background than it spews up but after
about 100 billion years or so the
universe has expanded enough to dim the
CMB below the temperature of the black
hole and finally Sagittarius AAR starts
to shrink assuming it doesn't eat
anything else Bob is aware that the
black hole will eventually completely
evaporate through this radiation he's
also aware of the law of conservation of
quantum information and the black hole
information Paradox from watching
ancient PBS SpaceTime episodes he knows
that quantum mechanics and perhaps his
own heart won't allow the Eraser of
Alice's information nor the experimental
Cubit from the universe but there's a
risk of that happening if the black hole
evaporates to nothing and so just like
many long dead 21st century physicists
Bob concludes that the information must
be hidden in the Hawking radiation many
lifetimes of the universe pass and the
Hawking radiation appears completely
random Bob has had to build several
starssized computers metrios brains to
store and analyze the data no big deal
really because Bob has nothing but time
on his
hands after the black hole has lost half
of its mass 10 to the power of 87 years
later when incidentally all the stars
have gone out and their Cellar remnants
have scattered to the void it's now just
Bob and the black hole then Bob analyzes
the next in the endless stream of
information Baron Hawking radiation but
this time he detects the first sign of a
faint
pattern the subtlest of correlations
starts to emerge between all past
radiation hinting at some profoundly
scrambled order in the randomness of the
bits stuck on the black hole Event
Horizon newly excited by his sophan task
Bob continues to collect eventually he
manages to recover the object of the
experiment the quantum bit proving
incontrovertibly that black holes do not
swallow Quantum information and just
before the black hole evaporates
entirely Bob also recovers all of the
bits that were once Alice revealing the
true source of his long patience he
brings to Bear the full might of the
enormous black hle powered matrioska
brains and reverse Engineers all of
Alice's cubits and reconstructs her
Consciousness in digital form and the
two live happily ever after digital
ghosts in a dead Universe how
sweet this might seem like a happy
ending and it is for Bob and for the
version of Alice encoded in the event
Horizon but not necessarily so for the
version of Alice that fell in nor for
physics let's get back to our experiment
what really happened to the Cubit Bob
saw it freeze on the horizon and then
eventually caught it when it emerged as
Hawking radiation but Ellis saw it fall
through the Horizon and then merge with
the singularity just before she did the
same in physics we often make progress
by identifying contradictions in a
theory this is perhaps the primary value
of the G Duncan experiment
so it seems we've identified a
contradiction two different observers
end up with irreconcilably different
answers for the question where is the
Cubit there's a reason we used a cubit
instead of just asking for example where
is Alice that's because the Cubit allows
us to break very specific rules in
quantum mechanics and so it sharpens our
contradiction I already talked about the
prohibition against deleting Quantum
information which is why Bob concluded
that the Cubit must be preserved in the
Hawking
radiation but there's another related
rule the no cloning theorem states that
Quantum bits can't be
duplicated if the bit Escapes in the
Hawking radiation then how can it also
be inside the black hole the problem
with deleting or duplicating Quantum
information is that it breaks what may
be the most fundamental tenant of
quantum mechanics as foundational as the
equivalence principle is to general
relativity and that's
unitarity the quantum wave function
describes probabilities probabilities
have to add up to one add up all the
probabilities of say an object's
possible position and they can't add up
to more than 100% because what would
that even mean deleting or duplicating a
cupid breaks unitarity and so is a no no
but it seems we have to either Break
unitarity by duplicating the cubit in
the Hawking radiation or by deleting it
as the black hole evaporates or we have
to break the equivalence principle by
saying that Alice and her it never got
past the Event Horizon to find out which
is the case you're going to have to wait
another week remember Bob waited 10 to
the^ of 87 years so a week isn't so bad
then we'll start to see some of the
possible solutions to this Paradox from
black hole complimentarity to the idea
of the firewall at the Event Horizon and
we will continue to sharpen the tools we
need to knit entangled cubits into the
very fabric of SpaceTime hey everyone
before we go I wanted to let you know
that we have two new limited edition
merch items up at the merch store first
up is our first ever black hole enamel
pin this is a 1 and 1/2 in enamel pin on
Hol foil backing card designed by the
SpaceTime gfx team these pins are
limited edition pre-sale with the pins
shipping during the second week of June
once we're out of stock from the
pre-sale that's it next up is our Star
Wars inspired SpaceTime t-shirt and and