- September 4th 2015, by Alma Ionescu
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10- The Black Hole Wars
Matter
falls in a black hole and matter never comes out. At least this is what was
widely believed until the end of the 90’s because black holes provide a
straightforward mechanism to destroy information forever. 'The Black Hole War', written by Leonard Susskind, Felix Bloch professor of Theoretical
physics at Stanford University, is a historical account of this raging war
fought over the fate of matter lost inside black holes. At the beginning
of the 80’s, Susskind met Stephen Hawking and the dispute began. Hawking, a
general relativist, thought that since the black hole singularity
was shown to annihilate whatever fell in, then so be it. This was what the
theory told us and there was no point denying it. Moreover, particles couldn't avert
this dire fate because of the Penrose Singularity Theorems, which say that all
the paths of the infalling matter must and will encounter the central
singularity in a finite time. From life and black holes no one comes out alive.
Susskind, supporting the quantum mechanical point of view, claimed that
information must be preserved one way or another. Things don’t just vanish
from the universe. In 2008 when the book was published, it was considered that
the war was over as of 2004, when Hawking conceded the bet he took on the fate of information and had to pay up by means of the famous baseball encyclopedia,
“from which information can be retrieved at will.”
9- No cloning
You
can clone sheep (unsuccessfully), but you can’t clone physical information. The no-cloning theorem is a no-go theorem in quantum mechanics showing that you cannot copy quantum information. If information falls inside a black hole, you can't hope to store it somewhere and recover it later on. Period.
Quantum information is unique. This theorem is a mathematical account of how,
if you presume that you can in fact copy any quantum state, you will reach a contradiction. To put it simply, cloning information requires applying a mathematical
transformation to it (called a unitary operator) and assuming that the result should be equal to the initial state plus an identical state. Going through the calculation produces an inequality placed on both sides of an
equal sign, and therefore a contradiction. In fact, there are some states that
respect this strange equality, but they have to obey very restrictive criteria,
and this means that cloning is not a reliable, useful way to copy just any type of information.
8- Event
horizons
According to the theory of general relativity, the universal point of no return and scene of
many scenarios involving the famous couple Alice and Bob is supposed to be
invisible for the observer passing through it. The event horizon is actually a singularity, much like the central
singularity. One of the dimensions of the spacetime vanishes at this point. However, researchers discovered that this singularity, unlike the central one, can
be fixed - mathematically speaking - and therefore crossed. This means that you can
still find a geodesic way through it and get to the other side. For many years,
it was thought that event horizons are points of no return because nothing can
come out as a consequence of classical physics. Yet the evaporation of black holes through Hawking radiation changed this notion. Today, horizons are seen more like surfaces that can shrink or grow with the influx of matter, often called trapping surfaces. It was Jacob Bekenstein, who sadly died of a heart attack in August 2015,
who advanced the idea that there must be a relation between the surface of the event horizon and the entropy of a black hole. Later on,
Hawking rigorously underpinned the idea and found the equation for black hole
entropy. This equation, simplified, tells us that the quantity of information
inside is equal to the area of the event horizon in Planck units divided by four.
7- Evaporation
In the 1970s, after exiting the shower and while going to bed, the young
Stephen Hawking independently realized that black holes resemble entropy. Later on, he figured that there must be an area law linking the surface of the horizon with the entropy inside. No, we don't know how to get such an idea or what soap he used. This idea still
stands today as a hugely successful step towards the reconciliation of general
relativity with quantum mechanics. Evaporation is a mechanism through which black
holes shed weight and shrink, thus returning to the universe the
matter/energy they hogged. As a consequence of quantum field theory, the whole universe - even the void - is filled with virtual particles, which are
nothing else than the potential to have particles in that region. These virtual
particles appear in pairs everywhere, including near or at black hole horizons.
Half of the pair, the part carrying negative energy, falls into the hole,
whereas the positive energy solution falls out and escapes to infinity. The
total energy of the black hole plus the negative energy particle equals a lower
total energy, thus causing the black hole to slowly lose mass. This process is
thermodynamic - heat circulates to cold regions - and therefore can only start once the
temperature of the black hole, however small, is larger than the surrounding
temperature, which is the thermal radiation left over from the Big
Bang, known as the cosmic microwave background (CMB). The still open question is whether this process can recover all the information
associated to the matter or energy that initially collapsed to form the black
hole. Again, quantum information.
6- Complementarity
The
solution Susskind proposed to save quantum information from being
destroyed is the complementarity principle. Complementarity
basically tells us that if we can’t see something, it doesn’t exist. It is
a case of selective blindness of the universe. Since he had to go around the no-cloning theorem which prevented information from being copied, Susskind proposed that information gets captured at horizon and falls into the black hole, at the same time. This shouldn’t violate
the no-cloning theorem because an observer never sees both copies simultaneously.
For whoever is outside, the information is trapped at the horizon. For whoever
falls in, only the information inside the black hole is available, and that observer won’t be able to get out. Further, no one outside cares that the copy
inside gets destroyed because the universe is left with a copy. Complementarity
does not violate the Einstein equivalence principle either, because information remains on the horizon only for the exterior observer. If we were
to go through the horizon and continue the path inside the black hole, we would
not have any means to observe anything different while crossing the boundary, therefore equivalence is saved. Still, this solution never explained how exactly is the information stored on the horizon.
5- Firewalls
Firewalls are a very hot topic in theoretical physics, but they also are a whole theory themselves, connecting information preservation, Hawking
radiation, event horizons, and complementarity. But when putting together black hole
radiation and complementarity, we quickly run into a paradox. Complementarity
saves the information at the horizon, and the information is radiated back later on without even falling in - only a copy is lost. However, the same property helping complementarity solve the information paradox requires Hawking radiation
to be entangled with every other particle that was radiated before it. This is a
problem because quantum entanglement only acts between pairs of two particles.
To break the entanglement, a group of four physicists - the AMPS String Quartet - proposed a mathematical solution showing how the matter near the horizon heats up and acts to break the
connection, like a firewall barrier. Yet firewalls
fix a problem and create another one, proving that trying to reconcile a
handful of principle in fundamental physics is a little like trying to eat olives with a fork out of a round soup bowl - slippery. You catch one but lose another, and generally there's more chasing than eating. Firewalls can be shown
to be hot even locally, so they break the equivalence principle because observers know when they cross the horizon.
There is no definitive agreement on this one, so the jury is still out.
4- Chaotic
horizons
We
certainly remember 2014’s hype about Hawking’s declaration that there
are no black holes. What he actually said was this "The absence of event
horizons mean that there are no black holes - in the sense of regimes from
which light can’t escape to infinity." His exact statement can be found in his
paper on 'Information Preservation and Weather Forecasting for Black Holes'.
What he meant was very simple - general relativity treats event horizons as perfect spheres, completely smooth and undisturbed. On the other hand, quantum theory shows huge numbers of virtual particle pairs swarming at the horizon. When seen up close, all this turmoil makes the horizon look as irregular and wrinkly as the surface of the human brain and as
unpredictable as the weather (ergo the name of the paper). There is a lot of
chaos taking place there, small pockets where the gravitational curvature
varies immensely. This means that light can easily escape from some of these
pockets and, as easily, get trapped inside others. Because of the swarming,
it’s very difficult to keep track of what is actually happening. All you can say for
sure is that light can escape from unexpected places. This is another hot topic
right now, but it’s outweighed by more fundamental subjects.
3- Quantum
gravity
In
1915, Einstein announced that gravity is actually the
curvature of space. It is not a force, but geometry. Later on, with the
developments of field theories treating quantized matter, it became obvious
that if we are to have a unified description of relativity and quantum
mechanics, we need a solution showing how to quantize the gravitational field
itself. The quanta of this field would be the gravitons. However, the problem is
that no matter how you try to quantize gravity you obtain a field interacting with itself infinitely many times. The theory is diverging and the
solutions to its equations are infinities. A fix to that is to stop the
interaction once it reaches the Planck scale, but this solution bumps into a
whole new set of problems. We don’t know, to date, whether gravity is quantum
and, moreover, we don’t know how the theory should look like. We don’t even know
if this theory exists in the mathematical sense, if it can make sense on
paper as a whole.
2- Quantum
information
So
what is this quantum information we're talking about? Orthodox quantum
mechanics (read 'Bohr') treats particles as points (whereas quantum field
theory says they’re excitations in a field, but let’s not get into
technicalities), and points have a size of zero because they are
zero-dimensional. It’s not that they’re really very small, it’s that they don’t
occupy dimensions larger than zero. It’s a dimension problem, not a size
problem. We can’t even look at a point because it doesn’t really exist. Its
total extent occupies a volume and an area of zero units. So these quantum
mechanical particles are invisible, semi-existent dots that have nothing except for their lists of properties, which they carry around. These properties are electric charge, spin, color charge (the strong interaction), weak
isospin (the weak interaction), and various other quantum numbers. They tell us
how particles interact with all the fields in the universe. And the billion
dollar question is how can that information be physically stored in a point?
Answer that and you’ll get a call from Sweden saying that you received the
Nobel Prize. And you become the most famous person in the known universe.
Just to be clear, even if particles would not really be points (although
all experiments to date tell us that they are indistinguishable from being
dot-like) we would still not have any kind of explanation as to how does matter
carry information telling it how to interact with the rest of the universe. Lee
Smolin, researcher for the Perimeter Institute and author of 'Time Reborn',
expressed this in a very simple way: how does an electron know that it is an
electron? We can add that an electron also needs to know how to be an
electron. Quantum information is the greatest mystery of them all.
1- Supertranslations
After
last year's hype, Hawking takes the stage again this year, at a conference in Sweden where he announced that he found the solution to the black hole paradox.
The community still needs to evaluate the proposal but his speech makes it
clear that information stays on or near the event horizon. This sounds a lot
like complementarity, we might say! However, the mechanism seems to be
different, which is all we can say without a paper being yet published. His
proposal relies on the shape of the gravitational field itself, so it works in
a semi-classical regime. We know that general relativity describes the
spacetime in an approximate way. If you look at space from up close, it
seems flat no matter how curved it really is on a larger scale. This
approximation holds very well for almost all purposes, but when it comes to
approximating the small imprints left by particles - which are
very tiny - it might not still hold. Should he be right, the difference between a point on a particle's trajectory and the next
would be given by (equal to) a supertranslation. It’s easy, the minuscule difference
between two points in space and in time. This should be visible in the geometry
of the space and would work like something that we can call gravitational memory. When it comes to scales that small, we need to be precise and
approximations may not hold. This is the absolute winner of our list, because
it set the whole physics community abuzz.
Update: A first preliminary article by Hawking is out as of September 3rd.
Update: A first preliminary article by Hawking is out as of September 3rd.
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