Since the
beginning of the 20th century, black holes have aroused the interest of
physicists. While some of their physical
characteristics have a solid theoretical description, others are still nebulous. This is particularly the
case for the horizon of events and the
question of what happens once the information gets into it.
In 1976, the
physicist Stephen Hawking highlights the contradiction between general
relativity and quantum mechanics concerning information within black holes. In
fact, on the one hand, general relativity postulates that all information
passing the horizon of a black hole is definitely trapped there. However, under
the effect of Hawking radiation, the black hole eventually evaporates, the
information is then permanently lost.
On the other
hand, quantum mechanics postulates the reversibility and unity of the quantum
states, necessarily implying the conservation of information. Since then,
physicists have constantly sought solutions to the paradox of information.
A solution
to the paradox of information: the complementarity of black holes
In 1993,
physicists Leonard Susskind and Larus Thorlacius develop a hypothesis (see
image below) potentially solving the paradox of information: the
complementarity of black holes. Susskind describes this hypothesis as follows:
" The information that comes into contact with the horizon of the events
of the black hole is both reflected by the horizon and at the same time trapped
by the horizon; however, no observer can confirm these two issues
simultaneously . " The term "complementarity" was used for the
first time concerning the waveparticle duality of a particle; the authors have
reused this term to apply this analogy to black holes.
This
solution includes two hypotheses, depending on whether an observer is viewed
from outside the horizon or from the point of view of an observer crossing the
horizon. For an outside observer, the information coming into contact with the
horizon is absorbed by a membrane surrounding the horizon on the Planck scale
and then reemitted via the Hawking radiation. On the other hand, an observer
crossing the horizon would not notice anything particular, it would simply fall
with the information towards the singularity.
Although correctly solving the information paradox, Susskind and Thorlacius's theory is not devoid of problems. Indeed, it contradicts a key principle of quantum mechanics: the monogamy of entanglement.
Complementarity
of black holes and monogamy of entanglement
Let's first
briefly recall what Hawking's radiation is. According to Heisenberg's principle
of indeterminacy on energy and time, the quantum vacuum fluctuates continuously.
From these quantum fluctuations arise virtual particleantiparticle pairs that
annihilate almost immediately after their appearance. However, near a black
hole the gravitational field is so intense that it separates the
particleantiparticle pairs before annihilation. One particle is absorbed by
the black hole, while the other is emitted by escaping from its attraction.
According to
quantum field theory (the theory describing the behavior of fundamental
interactions), Hawking radiation produces an entangled system between the
absorbed particle and the emitted particle. But that's not all. Indeed, in
1993, the physicist Don Page, in collaboration with Susskind, published works
demonstrating that the emitted particle, in addition to being entangled with
the absorbed particle, is also entangled with all the information previously
emitted by Hawking radiation. . Thus, in the case of the black hole
complementarity theory, Hawking's reradiated information is entangled both
with the definitively absorbed information and with all the information
previously radiated before it.
However,
there is a fundamental principle in quantum mechanics called "monogamy of
entanglement". This principle asserts that it is impossible for a quantum
system (for example a particle) to be entangled simultaneously with two systems
independent of each other. In other words, applied to the Hawking radiation, it
is forbidden for the emitted particle to be simultaneously entangled with the
absorbed particle and with the information previously emitted.
Diagram illustrating the principle of monogamy of entanglement: it is forbidden for a particle to be fully entangled with two other other independent particles. Credits: Universereview.ca

A "wall of fire" as a solution to the problem of monogamy of entanglement
In order to
solve this contradiction, the physicists D. Marolf, J. Polchinski, A. Almheiri
and J. Sully publish in July 2012 a theory entitled "black hole
firewall", literally "wall of fire of the black hole".
In this
theory, physicists propose the idea that during the separation of the absorbed
particle and the emitted particle, the quantum entanglement connecting the two
particles breaks down immediately. During this break, a phenomenal amount of
energy would be released around the horizon. In this regard, Polchinski
explains that " it is an extremely violent process, like breaking the
bonds between molecules, it releases a large amount of energy ". He goes
on to say that " the horizon of events would then literally be a ring of
fire that would burn anyone who would pass through ".
Thus, the continual breaking of the entanglement of all particleemitted particleabsorbed systems would result in the permanent formation, at Planck's scale, of a chaotic maelstrom of ultraenergetic particles constituting a real "firewall" all around of the event horizon. To cross this wall of fire would result in an immediate and violent incineration. It should be noted, however, that from the point of view of an outside observer, the wall of fire is perfectly invisible.
If such a
wall of fire exists, then it should leave gravitational traces during important
cosmological phenomena such as the fusion of two black holes. In this case, an
impression of the two walls of fire would be present in the gravitational waves
emitted during the fusion. Such traces were sought in the first data collected
by LIGO in 2016; however, the amount of data was insufficient to confirm or
rigorously deny their existence. In the coming years, with the accumulation of
new data, physicists should be able to provide a definitive answer to this
hypothesis.
This theory
thus makes it possible to complete the theory of the complementarity of black
holes by preserving the monogamy of entanglement. However, to be viable, this
hypothesis must sacrifice a fundamental postulate of general relativity: the
principle of equivalence. By virtue of this principle, an observer crossing the
horizon of a black hole should not feel anything. This is why the authors, at
the end of their publication, leave a choice to the scientific community: to
accept the hypothesis of the "firewall" and to abandon the principle
of equivalence and thus to a part of the general relativity, or to reject this
hypothesis and adhere to the loss of information and thus give up some of the
quantum mechanics.
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