Black holes as tools for quantum computing by advanced extraterrestrial civilizations
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Astronomy & Astrophysics manuscript no. BHSETI_arxiv ©ESO 2023
November 30, 2023
Black holes as tools for quantum computing by advanced
extraterrestrial civilizations
Gia Dvali1, 2 and Zaza N. Osmanov3, 4
1
Arnold Sommerfeld Center, Ludwig Maximilians University, Theresienstraße 37, 80333 Munich, Germany e-mail:
gdvali@mpp.mpg.de
arXiv:2301.09575v3 [physics.pop-ph] 28 Nov 2023
2
Max Planck Institute for Physics, Föhringer Ring 6, 80805 Munich, Germany
3
School of Physics, Free University of Tbilisi, 0183, Tbilisi, Georgia e-mail: z.osmanov@freeuni.edu.ge
4
E. Kharadze Georgian National Astrophysical Observatory, Abastumani, 0301, Georgia
Received ; accepted
ABSTRACT
Context.
Aims. We explain that black holes are the most efficient capacitors of quantum information. It is thereby expected that all sufficiently
advanced civilizations ultimately employ black holes in their quantum computers.
Methods. We use the methods developed for the study of black hole physics and by applying the Drake formula we estimate the
observational characteristics.
Results. The accompanying Hawking radiation is democratic in particle species. Due to this, the alien quantum computers will radiate
in ordinary particles such as neutrinos and photons within the range of potential sensitivity of our detectors.
Conclusions. This offers a new avenue for SETI, including the civilizations entirely composed of hidden particles species interacting
with our world exclusively through gravity.
Key words. astrobiolog - SETI - technosignatures
1. Introduction noting that, on average, the solar-type stars in the Milky Way are
much older than the Sun. Therefore, potentially detected tech-
The search for extraterrestrial intelligence (SETI) is one of the nosignatures will belong to advanced alien societies.
longstanding problems of humanity. It is clear that any techno- It is natural to assume that the technological advancement of
logical civilization most probably should have certain technosig- any civilization is directly correlated with the level of its com-
natures that might be potentially detectable by our facilities. The putational performance. This is fully confirmed by our own his-
first SETI experiments started in the last century in the frame- tory. Here, we wish to point out that there exist certain universal
work of radio listening to stars (Tarter 2001). Nowadays, the markers of computational advancement which can be used as
most advanced technology is the five hundred meter aperture new signatures in SETI.
spherical radio telescope FAST, which is dedicated to observ- In particular, in the present paper we wish to argue that any
ing the sky, and one of the missions is to search for radio mes- highly advanced civilization is expected to employ black holes
sages from extraterrestrial civilizations (Lu et al. 2020). In 1960 for the maximal efficiency of their quantum computations. The
Freeman Dyson proposed a revolutionary idea of searching for optimization between the information storage capacity and the
megastructures visible in the infrared spectrum (Dyson 1960). time scale of its processing suggests that a substantial fraction of
He has proposed that if an advanced alien civilization is capable the exploited black holes must be the source of highly energetic
of constructing a spherical shell around their host star to utilise Hawking radiation.
its total emitted energy, the megastructure, having a radius of the This gives new ways for the SETI. It also provides us with
order of 1AU, will be visible in the infrared spectral band. This new criteria for constraining the parameters of highly advanced
idea has been revived thanks to the discovery of the Tabby’s star civilizations.
(Boyajian et al. 2016) (characterized by flux dips of the order of The logic flow of the paper is as follows. We first intro-
20%, automatically excluding the possibility of a planet shading duce the current framework of fundamental physics and justify
the star). This stimulated further research and a series of papers why the most basic laws of quantum theory and gravity must be
have been published considering the Fermi’s paradox (Osmanov shared by all ETI. This applies to civilizations that may entirely
2021a) the planetary megastructures (Osmanov 2021b), the sta- be composed by yet undiscovered elementary particle species
bility of Dyson spheres (DS) (Wright 2020); extension to hot and experiencing some unknown interactions.
DSs (Osmanov & Berezhiani 2018, 2019); megastructures con- We then argue that for all civilizations, regardless their com-
structed around black holes (Hsiao et al. 2022); white dwarfs position, black holes are the most efficient storers of quantum
(Zuckerman 2022) and pulsars (Osmanov 2016, 2018). information. This does not exclude the parallel use of other hy-
Since the search for technosignatures is very complex and pothetical objects which within their particle sector maximize
therefore sophisticated, the best strategy for SETI should be to the information storage capacity, the so-called “saturons" (Dvali
test all possible channels. In the light of this paradigm, it is worth 2021). Following the previous paper, we explain that among all
Article number, page 1 of 13A&A proofs: manuscript no. BHSETI_arxiv
such objects the black holes are the most efficient and universal the shortest distances directly probed at the human made accel-
capacitors of quantum information. erators. In particular, the scale ∼ 10−17 cm has been reached at
Our conclusions are based on recent advancements in devel- the Large Hadron Collider (LHC) at CERN. This extraordinary
opment of a microscopic theory of a black hole (Dvali & Gomez resolution is achieved in particle collisions at around ∼TeV en-
2011; Dvali & Gomez 2012; Dvali et al. 2013) as well as on ergies.
understanding the universal mechanisms of enhanced infor- In addition, the predictions obtained by the theoretical ex-
mation capacity (Dvali 2017a,b,c; Dvali, Michel, Zell 2018; trapolations of the quantum framework to much higher energies,
Dvali & Panchenko 2016; Dvali 2018; Dvali et al. 2020) and are fully consistent with all the existing data. A classic exam-
using them for “black hole inspired" quantum computing in pro- ple is provided by Quantum Chromo-Dynamics (QCD), which is
totype systems (Dvali & Panchenko 2016). the theory of the nuclear forces. QCD is an asymptotically-free
Especially important is the knowledge that among objects quantum field theory, self-consistently valid at arbitrarily short
saturating the universal quantum field theoretic bound on mi- distances/high energies.
crostate entropy, black holes posses the maximal capacity (Dvali This success by no means implies that our knowledge of fun-
2021). damental forces is complete. Certainly, new interactions can (and
Distilling the above knowledge, we argue that black hole hopefully will) be discovered by the experiments with higher
based computer technologies represent an universal attractor energies and/or higher precisions. Many such interactions have
points in the advancement path of any sufficiently long-lived civ- been hypothesized and studied. These are motivated by various
ilization. open questions, such as the origin of dark matter, early cosmol-
Relying solely on the laws of physics that must be shared ogy, unification of forces and so on. For none of these exten-
by all ETI, we draw some very general conclusions about their sions, there exists even a slight evidence for non applicability of
usage of black hole computing. The optimization of informa- the basic laws of quantum physics. Even the string theory, which
tion storage capacity and the time of its retrieval suggests that theoretically culminates the idea of unification of all known in-
it is likely that ETI invest their energy in manufacturing a high teractions, fully relies on the laws of quantum physics.
multiplicity of microscopic black holes, as opposed to few large Of course, the particular realizations of the quantum frame-
ones. Correspondingly, their computers are likely to produce a work may encounter some computational difficulties in cer-
Hawking radiation of high temperature and intensity. tain regimes. This happens, for instance, when the interactions
Another source of radiation of comparable frequency is ex- among the elementary particles become strong. In such a case,
pected to come from the manufacturing process of black holes. the perturbation theory in a given coupling constant may break
As we explain, this process likely requires the high energy parti- down and one needs to resort to non-perturbative techniques
cle collisions. such as, for example, the lattice simulations. None of these com-
We give some estimates of what the above implies for SETI. putational obstacles bare any indication of the invalidity of the
In particular, considering the IceCube instruments (the most ef- basic concepts of the quantum theory. Rather, they only signal
ficient neutrino observatory), based on their sensitivity and the the need for improvement of computational tools without going
observed VHE neutrino flux in the energy domain 40 TeV, we outside of the quantum framework.
conclude that the mentioned observatory can detect emission In the light of all the above, in our analysis we shall assume
from the black holes of advanced civilizations if their numbers the validity of the laws of quantum physics for ETI.
are in the following intervals: 2.5 × 103 ≤ NIIν ≤ 4.2 × 104 ,
2 × 106 ≤ NIIIν
≤ 1.4 × 108 .
2.2. Gravity
Finally, we discuss the possibility that nature houses a large
number of hidden particle species interacting with us via grav- The second powerful factor is gravity. At the classical level, the
ity. We point out that because of the known universal relation gravitational interaction is described by Einstein’s General Rela-
between the number of species and the mass of the lightest black tivity (GR). Again, this is a remarkably successful theory, tested
holes (Dvali 2007; Dvali & Redi 2008), the existence of many by direct observations within an impressive range of distances,
species makes black hole manufacturing more accessible for 10−1 − 1028 cm. In addition, various successes of the early cos-
ETI. mology suggest that the validity domain of GR extends to much
This applies equally to our civilization. In this light, a possi- shorter distances.
ble creation of microscopic black holes at our particle accelera- At the quantum level, the excitations of the gravitational field
tors, shall reveal a powerful information about the computational are gravitons, the massless particles of spin = 2. All the classi-
capacities of ETI. cal interactions of macroscopic sources can be derived from the
The paper is organized as follows: in sections 2 - 10, we quantum theory in form the exchanges of virtual gravitons, in the
examine basic concepts of quantum computing by using black expansion in series of Newton’s constant G.
holes, in section 11 we discuss the observational features of such The unique property of graviton is that it is sourced by the
black holes, in sec.12 we discuss the hidden sector of particles energy momentum tensor. This feature is universal and accounts
and in sec.13, we summarise our findings. for all contributions including the energy-momentum of the
graviton itself. Due to this property, the gravitons self-gravitate.
In other words, any graviton acts as a source for others.
2. The framework The quantum states of the isolated gravitons have never been
2.1. Quantum physics and elementary particles tested directly in lab experiments. This is explained by an ex-
traordinary weakness of their coupling at laboratory scales. For
Our current framework for describing nature at a fundamental example, an interaction strength of a graviton of ∼cm wave-
level is based on quantum physics. This framework passes all length is suppressed by ∼ 10−66 (Dvali & Gomez 2011). The
the tests, both theoretical and experimental, available to our civ- strength of the classical gravitational field produced by the
ilization. The experiments prove that the quantum laws work to macroscopic sources is a collective effect of a large number of
Article number, page 2 of 13Gia Dvali and Zaza N. Osmanov: Black holes as tools for quantum computing by advanced extraterrestrial civilizations
gravitons. This is why, it is much easier to detect the classical 3. Optimization of information storage
effects of gravity as opposed to its quantum manifestations.
The two essential ingredients of any type of computation are
The story however is scale-dependent. In the quantized ver- hardware and software. We shall not attempt to make any as-
sion of Einstein gravity, the interactions among the individual sumptions about the software used by the advanced ETI. The
gravitons are weak at distances larger than the Planck length,
power of programming and the sophistication of their algorithms
p are most likely way beyond our imagination.
LP ≡ ~G/c3 , (1) However, since the laws of quantum physics and gravity are
common, we can make certain conclusions about the limiting
where ~ is the Planck’s constant and c is the speed of light. The capacities of their hardware. We shall parameterize these limits
Planck length is approximately 10−33 cm. At such separation, the according to certain well-defined characteristics. The main fea-
characteristic momentum-transfer among the individual gravi- tures we will be interested in are the efficiencies of the quantum
tons is of order the Planck momenta, ∼ MP c, where information storage and of its retrieval. These parameters are not
payed much attention at the present stage of development of the
quantum computing by our civilization, due to more urgent tech-
~
MP ≡ , (2) nological issues. However, they must become crucial for any civ-
cLP ilization that is able to approach the limiting capacities.
In order to understand what this limits imply, we go in two
is the Planck mass. The quantum gravitational effects become steps. First, in the current section we define what it means for
strong at this scale. Due to this, LP is commonly considered to a generic device to have an enhanced capacity of information
be an ultimate cutoff of the Einstein theory of gravity, viewed as (memory) storage and what is the underlying mechanism behind
effective quantum field theory. it. That is, we shall reduce the feature of the enhanced capacity
However, in any extension of the pure Einstein gravity, of information storage to its bare essentials borrowing the results
the actual length-scale, L∗ , at which quantum gravity becomes of the series of papers (Dvali 2017a,b,c; Dvali, Michel, Zell
strong, is longer than LP . In general, if a theory includes 2018; Dvali 2018; Dvali et al. 2020). The reader can find a self-
Nsp distinct elementary particle species, we have (Dvali 2007; contained summary and discussion in (Dvali et al. 2020).
Dvali & Redi 2008), Next, we shall explain that among all possible hypothetical
devices that saturate the information storage capacity, the black
L∗ =
p
Nsp LP . (3) holes are the most efficient ones (Dvali 2021).
In general, the quantum information is stored in a quantum
state of the system. These states are usually labeled by the exci-
The corresponding scale of the momentum-transfer, M∗ c, is re- tation levels of a set of N elementary degrees of freedom. Their
spectively lowered to choice is a matter of convenience depending on the system pa-
rameters, available technology and the computational task. The
MP c choice may range from atomic spin states, for less advanced ETI,
M∗ c = p . (4)
Nsp all the way to graviton excitations that can be used by highly
advanced civilizations. Regardless of their particular nature, it is
customary to describe them as quantum oscillators in the number
This scale is usually referred to as the “species scale". representation. Following the terminology of (Dvali 2017a,b,c;
The scale L∗ imposes an absolute lower bound on compact- Dvali, Michel, Zell 2018; Dvali 2018; Dvali et al. 2020), we
ness. In particular, the localization radius of a quantum informa- shall refer to these as the “memory modes".
tion bit is bounded by L∗ (Dvali & Gomez 2011). The simplest mode is a qubit, a quantum degree of freedom
The currently known elementary particle species include that can exist in two basic states. These states can be labelled
the degrees of freedom of the Standard Model (quarks, lep- as the occupation number eigenstates |0 > and |1 > of the cor-
tons, Higgs and gauge bosons) and the graviton. Counting all responding quantum oscillator with a number operator n̂ j , and
physical polarizations, this amounts to Nsp ∼ 100. Correspond- j = 1, 2, ..., N the mode label.
ingly, the theory-independent bound on the compactness cutoff Correspondingly, the set of N qubits produces n st = 2N ba-
is L∗ & 10LP ∼ 10−32 cm. sic states. These represent the tensor products of individual ba-
sis states of N distinct memory modes, |n1 , n2 , ..., nN >≡ |n1 >
⊗|n1 > ⊗, ..., ⊗|nN >, where n j = 0 or 1, for each j. In short, they
2.3. Universal criteria obeyed by ETI
count all possible sequences of 0-s and 1-s, such as, |0, 0, ..., 0 >
Putting all the knowledge together, we cannot assume that an , |1, 0, ..., 0 >, ..., |1, 1, ..., 1 >. We shall refer to these states as
advanced ETI necessarily shares the elementary particle com- the “basic memory patterns". They form a Hilbert (sub)space,
position with us. In particular, some ETIs may originate from which we shall call the “memory space".
entirely different particle species, interacting with us only gravi- The system can exist in an arbitrarily entangled state of
tationally. the memory modes. A typical entangled state would represent
In the light of the above, we shall make the following a linear superposition of order-one fraction of n st basis states.
(maximally-conservative) assumption: However, there can exist the maximally entangled states of spe-
cial types, such as the generalized EPR state, √12 (|0, 0, ..., 0 >
We share with ETI the laws of quantum physics and gravity. +|1, 1, ..., 1 >).
As a measure of the information storage capacity of the sys-
One of the consequences of this is that the physics of black tem, it is convenient to use the microstate entropy. As usual, we
holes is common, irrespectively by which ETIs they are manu- define it as the log from the dimensionality of the memory space,
factured. This shall play the crucial role in our idea of SETI. S = kB ln(nts ) . (5)
Article number, page 3 of 13A&A proofs: manuscript no. BHSETI_arxiv
We shall focus on two important characteristics of the efficiency compactness and the energy efficiency of its computations must
of a quantum memory device: The energy-efficiency and the find the way of optimizing the information storage capacity of
compactness. the system. That is, it has to manufacture devices that maximizes
The first one is determined by the energy gap of qubits, ǫ. the microstate entropy per given size of the system. Basically, the
This also determines the total energy gap occupied by all n st goal is to maximize S for given R.
memory states, which we denote by ∆E. Let us now explain that, for achieving the above goal, the
For example, if for each degree of freedom the states |0 > sufficiently advanced ETIs are expected to use black holes.
and |1 > are gapped by ǫ, the gap spanned by the memory space
will be ∆E = Nǫ.
Another important parameter is the radius of localization, R, 4. Why Black Holes?
of the quantum information storing device. Ordinarily, the com- Black holes exhibit an extraordinary capacity of the information
pactness of the system increases the gap. For example, consider storage and processing. For various comparisons, it is illuminat-
a qubit realized by a relativistic particle, say a photon, localized ing to take the human brain as a reference point (Dvali 2017c).
within a box of size R. The two basis states can for example be For example, a black hole of a mass of a human brain (∼kg) has
chosen as the states with one and zero photons. If the interac- a million times larger memory capacity while being in size only
tions of the photon inside the box are weak, the minimal energy ∼ 10−25 cm and having the operational time of memory read-out
gap due to quantum uncertainty is ǫ ∼ c R~ . Consequently, the lo- tq ∼ 10−19 sec. This is impressive, but are they the optimal tools?
calization of N such qubits within the same box, will result in a In order to classify black holes as the ultimate device used
basic energy cost ∆E ∼ N ~c R. in quantum computing by advanced ETIs, the following set of
The first necessary requirement fulfilled by the device of the questions must be answered:
enhanced memory capacity is to minimize the gap of the mem-
ory qubits below the “naive" quantum uncertainty, – How unique are black holes in their ability of information
~c storage?
ǫ≪ , (6) – What are the general mechanisms behind this ability?
R
– Can these mechanisms be implemented in other devices for
while maximizing their number N (equivalently, S ). achieving a comparable, or even a higher, efficiency of infor-
The crucial point is that the two are not independent: for a mation storage and processing?
system of given compactness R there exists an absolute upper
bound on S imposed by unitarity (Dvali 2021). We shall discuss Fortunately, these questions have already been largely ad-
this bound later. dressed in a research program consisting of three parallel strate-
At the same time, the energy gap of a quibt ǫ, sets the lower gies:
bound on the time-scale required for processing the information
stored in that qubit, – Formulate a microscopic theory of a black hole
~ (Dvali & Gomez 2011). Demonstrate that the analo-
tq = . (7) gous mechanisms of information storage and process-
ǫ ing can be implemented in other quantum systems
In particular, this is the minimal time required for extracting the (Dvali & Gomez 2012; Dvali et al. 2013; Dvali et al. 2015;
information from the qubit. For example, (7) is the minimal time Dvali & Panchenko 2016).
required for detecting a photon of energy ǫ. – Use the well stablished features of a black hole in order to de-
Notice that ǫ stands for an effective energy gap in which duce the properties of its memory modes, such as, the energy
the contributions due to interactions with the environment, with gaps of qubits, their diversity and the evolution time scales.
other qubits and other parts of the device, are already taken into Next, identify the mechanisms in generic quantum systems
account. leading to the similar features. Implement such systems
The expression (7) shows that there is a tradeoff. The cheap for quantum information processing (Dvali & Panchenko
storage of information requires a longer time for its retrieval. 2016; Dvali 2017b,c,a, 2018; Dvali, Michel, Zell 2018;
This shall play an important role in estimating the computational Dvali et al. 2020)
parameters of ETI. – Identify objects in generic quantum field theories that are
At the earliest stages of the development of quantum com- equally (or more) efficient in information storage and pro-
puters, as it is currently the case with our civilization, the press- cessing as black holes. Extract the universal underlying
ing issues related to the hardware are the problems of decoher- physical reasons behind these features (Dvali 2021).
ence. The questions of the energy efficiency of qubits, posed
above, are secondary and not payed much attention. This makes Remarkably, all three strategies have converged on one and
sense, since even for highly optimistic numbers of the memory the same picture of the properties of the black hole memory
qubits, the energy costs due to the minimal quantum uncertainty modes (qubits) and the mechanism behind their gaplessness and
are insignificant. abundance.
For example, for N ∼ 1010 , the energy gap of the mem- In particular, it turns out that these features are generic for
ory space for a modern-technology information-storing device the objects saturating a certain universal upper bounds on the
of size R ∼cm, is only ∆E ∼ 105 eV. This is less than the rest microstate degeneracy imposed by unitarity (Dvali 2021). The
energy of a single electron. Obviously, this is negligible as com- objets are called “saturons". Since, the bound is universal, it is
pared to the rest energy of a typical supporting device that consist shared by all sectors of the universe, regardless their particle
of the macroscopic number of atoms. composition. In particular, it is applicable even for yet unde-
However, the amount of quantum information processed by tected hypothetical particle species from the hidden sectors.
an advanced civilization must require uncomparably larger val- A long list of such objects has been identified in
ues of N. Therefore, an advanced civilization that cares about the various consistent quantum field theories (Dvali 2019a,b;
Article number, page 4 of 13Gia Dvali and Zaza N. Osmanov: Black holes as tools for quantum computing by advanced extraterrestrial civilizations
Dvali & Sakhelashvili 2021; Dvali, Kaikov & Bermúdez 2021; This leads to the following Stephen-Boltzmann law
Dvali, Kühnel & Zantedeschi 2021). Interestingly, they evi-
dently exist in already discovered interactions, such as QCD, in dM
c2 = −Nsp 4πσR2H T 4 . (9)
form of color glass condensate of gluons (Dvali & Venugopalan dt
2021).
Here Nsp counts all particle species (all polarizations) lighter
The universal mechanism of enhanced information storage than T . That is, all species are produced with an universal ther-
capacity can be potentially implemented in laboratory settings, mal rate. The particles heavier that T are Boltzmann suppressed
such as cold atoms. This is a realistic prospect even for our civi- and can be ignored. The democratic production of all particle
lization in not far future. species is one of the important properties of the Hawking ra-
The bottomline of this discussion is that an advanced civi- diation. This feature originates from the universal nature of the
lization can certainly use non gravitational saturons for the effi- gravitational interaction.
cient information storage. Of course, in Hawking’s computation the black hole has in-
Depending on the perspective, this may be regarded as good finite mass and therefore it evaporates eternally.
news or bad news. On one hand, it is exciting to be able to ex- For a finite mass black hole, the story is different. In order
ploit the black hole mechanism of information storage without to estimate the decay time, one needs to make some additional
the need of manufacturing the actual black holes, which for our assumptions. The most common is to assume that the black hole
civilization can be a long prospect. Instead, we can implement evaporation is self-similar. That is, the relation between the mass
the same mechanism in ordinary systems such as cold atoms or and the temperature (8) holds throughout the evaporation pro-
the nuclear matter. cess. Under this assumption, the system can be easily integrated
On the other hand, one may worry that this option makes the and one gets the following expression for the half-decay time,
signatures for SETI less universal and more technology depen-
dent. −1 4480πG2 M 3
However, we can claim with certainty (Dvali 2021) that τ1/2 = Nsp sec (10)
~c4
among all possible saturons, the black holes stand out as the
most efficient information storers. This gives us a confidence that For getting a better feeling about time scales, it is useful to
a highly advanced ETI must be using them as the information rewrite this as an approximate expression,
storing device. !3
This provides us with a prospect of search for advanced civi- 100 M
τ1/2 ≃ 0.7 × × sec . (11)
lizations even if they are composed out of entirely unknown par- Nsp 109 g
ticle species. For example, ETI may consist of particles from a
hidden sector not sharing any constituents with the species that The factor ∼ 100 in the numerator stands for a normalization
are known to us. relative to the number of known particle species, while Nsp refers
Nevertheless, the black hole quantum computing device of to a total number of species available at initial temperature of a
such a hidden civilization will provide signatures detectable by black hole.
our observers. This is because Einstein gravity is universal for all However, it is important to keep in mind that for the finite
the particle species. A direct consequence of this fact is the uni- mass black holes, the thermality is only an approximation, since
versality of the Hawking radiation. Correspondingly, the quan- the back reaction is finite. By the time the black hole looses half
tum computers of dark ETI will radiate democratically into the of its mass, both expressions are expected to receive the sub-
particles of all the species, including the particles of the Standard stantial corrections due to quantum back reaction. This is ev-
Model which we can potentially detect. ident from various sources: the general consistency arguments
(Dvali 2015), the detailed analysis of prototype quantum sys-
tems (Dvali et al. 2020), as well as, from the explicit microscopic
5. Closer Look at Black Holes theory of a black hole (Dvali & Gomez 2011). It is indepen-
dently evident that due to the back reaction from the carried
5.1. Generalities quantum information, the black hole evaporation cannot stay self
similar throughout the process, and certainly not beyond its half-
Black holes are the most compact objects of nature. Their ef- decay (Dvali et al. 2020).
fective size is given by the gravitational radius R. For a non- This knowledge is no obstacle for our analysis. For the con-
rotating and electrically-neutral black hole, this is set by the servative estimates, the above expressions can be used as good
Schwarzschild radius, R = 2GM/c2 . approximation till the black hole half-decay time. This self-
In the classical description, black holes are stable and eter- consistently shows that the expression (11) gives a correct order
nal. In quantum picture the story changes. Due to quantum ef- of magnitude approximation for this time scale. This is fully suf-
fects, the black holes evaporate by emitting Hawking radiation. ficient for our purposes. Our discussions will be limited by this
Hawking’s original calculation (Hawking 1974) was performed time-scale.
in exact semi-classical limit. This implies taking the black hole Let us now discuss the information storage capacity of black
mass to infinity and Newton’s constant to zero, while keeping holes. It is well known that a black hole of radius R has a mi-
the black hole radius fixed, G = 0, M = ∞, R =finite. In this crostate entropy equal to its surface area measured in units of G
limit, the back reaction from the emitted quanta vanishes and the (Bekenstein 1973),
emission rate can be evaluated exactly. The resulting spectrum
of radiation is thermal, with an effective temperature given by πc3 R2 πR2
(Hawking 1974), S = kB = kB 2 , (12)
~G LP
~c3 where in the last part of equation we have expressed it through
T= . (8) the Planck length.
8πkB MG
Article number, page 5 of 13A&A proofs: manuscript no. BHSETI_arxiv
Another important feature of a black hole is the information attractive interaction with the condensate. These excitations can
retrieval time. The huge entropy of a black hole shows that it be described in several equivalent languages. For example, they
can carry a large amount of information. During the evaporation, can be viewed as Goldstone modes of the symmetries that are
the black hole looses its mass. However, initially a very little spontaneously broken by a black hole. Their emergence can also
information comes out. This is because at initial stages of decay, be understood in terms of the mechanism of “assisted gapless-
the spectrum of Hawking radiation is thermal within a very good ness" Dvali (2017a). The essence of this phenomenon is that
approximation. The quantum information about the black hole the negative energy of the attractive interaction compensates the
state is encoded in deviations from thermality, which are of order positive kinetic energy of the would-be free mode.
1/S per one emission time (Dvali & Gomez 2011; Dvali 2015). The independent derivation of the relations (8), (12), (13),
Initially, the effects of these corrections are small and it takes a (14), (16) from the microscopic theory provides an important
very long time to resolve them. cross-check for the validity of these equations.
Page argued (Page 1993) that the start of the information re-
trieval from a black hole is given by its half decay time (11).
As we shall discuss below, this feature has a physically trans- 6. Competing Devices: Saturons
parent explanation in terms of gaps of the black hole qubits Let us now ask: How do we know that there exist no information-
(Dvali & Gomez 2011). It also was shown that the same feature storing devices competing with black holes? For a long time, it
is shared by all objects of maximal microstate entropy (Dvali was implicitly assumed that the area form of the entropy (12)
2021). was exclusively the property of black holes. However, this under-
Taking (12) as a fact, one can deduce an useful knowl- standing has changed recently (Dvali 2021). It has been shown
edge about the information-storing qubits without making any that the area-law expression is common for all field theoretic ob-
assumptions about their nature (Dvali 2017a,c,b; Dvali et al. jects that have maximal entropy permitted by unitarity. Namely,
2020; Dvali et al. 2015). In particular, it is clear that the number for a localized object of radius R, there exists the following uni-
of qubits is N ∼ S /kB . From here it follows that the energy gap versal upper bound on the microstate entropy (Dvali 2021),
of black hole qubits is around,
πc3 R2
kB ~c ~2 G S = kB , (17)
ǫ= = 2 3. (13) ~G̃
S R πc R
Notice that for Nsp ∼ 1, the corresponding information storage where G̃ is the coupling of the Nambu-Goldstone mode of spon-
time-scale (7), taneously broken Poincare symmetry. This mode is universally
present for an arbitrary localized object, since any such object
~ S R πc2 R3 breaks the Poincare symmetry spontaneously. Due to this, G̃ rep-
tq = = = , (14)
ǫ kB c ~G resents a well-defined parameter for an arbitrary macroscopic
object. The objects saturating the above bound are referred to as
is of the same order as the half-decay time (11). Thus, we have, “saturons" (Dvali 2021).
tq ∼ τ1/2 . (15) Various explicit examples of such objects have been con-
structed in non-gravitational quantum field theories, includ-
This nicely reproduces the Page’s estimate. It also shows that this ing some candidates of cold atomic systems(Dvali 2019a,b;
estimate is a straightforward consequence of the energy gaps of Dvali & Sakhelashvili 2021; Dvali, Kaikov & Bermúdez 2021;
the black hole qubits. Dvali, Kühnel & Zantedeschi 2021).
Of course, for Nsp ≫ 1, the decay time is shortened and so is An important finding of these studies is that all saturons ex-
the time-scale of information processing, hibit the same information processing properties as black holes,
with the role of G taken up by G̃. Namely, all saturons decay by
1 S R 1 πc2 R3 emission of Hawking-like radiation with temperature given by
tq = = , (16)
Nsp kB c Nsp ~G (8),
~c
5.2. Cross-check from a microscopic theory T= . (18)
4πkB R
The expressions (8), (12), (13), (14), (16) have been indepen-
dently derived within a microscopic theory of a black hole, the The energy gap of saturon quibts is,
so-called “quantum N-portrait" (Dvali & Gomez 2011). This
kB ~c ~2G̃
theory tells us that at the fundamental level a black hole is de- ǫ= = 2 3, (19)
scribed as a bound-state of N ∼ S gravitons of wavelengths ∼ R. S R πc R
This collection of gravitons can be regarded as a coherent state and the corresponding information recovery time is,
or a condensate.
The black hole qubits originate from the collective ~ S R πc2 R3
Bogoliubov-type excitations of the graviton condensate. As tq = = = . (20)
ǫ kB c ~G̃
shown in (Dvali & Gomez 2012), and further studied in series of
papers (Dvali et al. 2013; Dvali et al. 2015; Dvali & Panchenko Of course, unlike black holes, the generic saturons radiate only
2016; Dvali 2017b,a,c, 2018; Dvali, Michel, Zell 2018; in particle species to which their constituents interact.
Dvali et al. 2020), a similar emergence of gapless qubits is char- It is certainly conceivable that some civilizations use non-
acteristic to systems of attractive Bose-Einstein condensates at gravitational saturon devices, as opposed to black holes, for their
quantum critical points. quantum computations. In fact, even our civilization may not be
For a black hole, the qubits represent the excitations of gravi- too far from implementing the saturated systems for such a pur-
ton with high angular momentum, which become gapless due to pose.
Article number, page 6 of 13Gia Dvali and Zaza N. Osmanov: Black holes as tools for quantum computing by advanced extraterrestrial civilizations
2
R
First, soon after the formulation of black hole N-portrait, This requires making G̃ = πc3 ~N as small as G. But this
the existence of similar gaplessness mechanisms were estab- implies that the gravitational coupling αgr must become equal
lished in the prototype N-boson models (Dvali & Gomez 2012; to the one of non-gravitational binding force α ∼ 1/N. Thus, we
Dvali et al. 2013; Dvali et al. 2015) . are pushed to equality αgr = α. Remembering that the rest energy
Further, it has been proposed (Dvali & Panchenko 2016; of the object is ∼ Nc~/R, it is easy to evaluate its gravitational
Dvali 2017b,c; Dvali, Michel, Zell 2018) that critical Bose- radius, which comes out equal to ∼ R.
Einstein condensates, can be used for implementing this black It is clear that at this point the object is within its gravitational
hole mechanism for controlled information processing. radius and thus is a black hole. That is, any attempt of pushing
More recently, it has been argued (Dvali & Venugopalan the entropy of the saturon of size R beyond the entropy of the
2021) that saturated states have already been created in labora- same size black hole, collapses the saturon into a black hole.
tory experiments in form of the color glass condensate of gluons Correspondingly, if the civilization is sufficiently advanced,
(Gelis et al, 2010). It is not necessarily too far-fetched to expect for information processing, it will ultimately resort to black
the use of such states for quantum information processing on a holes rather than to other saturons.
reasonable time-scale of the advancement of our civilization. This gives an exciting prospect of searches for advanced civ-
ilizations based on a detection of Hawking radiation from their
quantum computers. This applies equally to the civilizations be-
7. Can ETI use other saturons instead of black longing to hidden particle species, interacting with us exclu-
holes? sively via gravity. Regardless, due to its universal nature, the
Hawking radiation from their quantum computers will inevitably
In the above light, one may wonder whether the existence of
contain our particle species.
saturons as of alternative information storing devices may impair
our idea of SETI. The reason is that the radiation signature from
such quantum computers will not be universal and will rather
8. Some remarks on black hole manufacturing
depend on a particle composition of ETI. Fortunately, this is not
the case. technology
The point is that among all saturated objects of any given size An universal prescription for a creation of a black hole of mass
R, the black holes are unbeatable in their information storage ca- M is that the energy E = Mc2 must be localized within the
pacity (Dvali 2021). This is due to the fact that the spontaneous sphere of the corresponding Schwarzschild radius R = 2MG/c2 .
breaking of Poincare symmetry is maximized by a black hole. Of course, we cannot make a precise prediction of the meth-
Correspondingly, the coupling of the Poincare Goldstone in case ods used by an advanced civilization for achieving this goal.
of a black hole is the weakest. That is, for any other object of the However, it is possible to outline some expectations depending
same size, we have G̃ > G. In other words, the non-black-hole on the masses of black holes manufactured by ETI.
saturons, irrespective of their composition, must have G̃ > G. In particular, we wish to separate the two regimes of black
Any decrease of G̃ below G, will collapse the saturon into a black hole formation, to which we shall refer as “soft" and “hard" re-
hole. spectively.
The details of the proof can be found in the original article If the mass of a black hole is sufficiently high, it can be man-
(Dvali 2021). However, due to an interdisciplinary nature of the ufactured softly, by putting together a low density of many non-
present paper, for the sake of the reader’s comfort, we shall make relativistic particles and letting them to collapse. This is essen-
the presentation maximally self-contained. For this purpose, we tially how an ordinary stellar collapse works.
provide the following physical explanation. However, for creation of microscopic black holes this
Imagine we would like to produce a saturated device of size method may not be used. Instead, one needs to accelerate par-
∼ R in form of a self-sustained bound state of N quanta of the ticles to high energies and collide them with small impact pa-
wavelengths ∼ R. Let us assume that the dominant interaction rameters. Such collisions are usually referred as “hard" in the
responsible for binding the system has an interaction strength set sense that the momentum-transfer per colliding particle exceeds
by a dimensionless coupling α. That is, the attractive potential their rest masses.
energy among the pair of particles is V = −α~c/R. Let us explain the difference on a concrete example. In order
Of course, at the same time these particles interact gravi- to produce a solar mass black hole (R ∼km), it is sufficient to
L2
tationally, with the strength αgr = c~G 3 R2 = cRP2 . The physical place of order 1057 non-relativistic neutrons within the proximity
meaning of this parameter is easy to understand if we recall that of few km. Such a system will collapse into a black hole without
the energies of quanta are ∼ ~c/R (see, e.g., (Dvali & Gomez the need of any hard collision among the neutrons.
2011)). However, we have assumed that gravity is subdominant At the same time, if we wish to produce a black hole of the
with respect to the binding force of coupling α. size of a neutron R ∼ 10−14 cm, this method will not work. The
It is clear that in order to form a bound state, the kinetic mass of such a black hole is approximately 1038 GeV, which is
energy of each quantum c~ R must be balanced by the potential 1038 times the rest mass of a neutron. We thus need to localize
energy of attraction from the rest, V = αNc~/R. This gives an about 1038 neutrons within a Compton wavelength of a single
equilibrium condition αN ∼ 1. neutron. This cannot be done softly due to the resistance from
Now, the bound state breaks Poincare symmetry sponta- the nuclear forces. For example, a chunk of a nuclear matter con-
neously. It breaks both the translations and the Lorentz boosts. sisting of 1038 neutrons will not collapse easily into a black hole,
The order parameter for breaking of Poincare symmetry is due to Fermi pressure and other factors.
R2
~N/πc3 R2 , and the Goldstone coupling is G̃ = πc3 ~N . Then, Instead, in order to achieve the goal, the neutrons have to be
according to the unitarity bound (17), the maximal possible en- accelerated to ultra-relativistic energies and collided with a very
tropy of such a bound state is S = kB N. Let us assume that this high momentum transfer.
entropy is attained. Can it exceed the entropy of the same size For example, in an extreme case we can accelerate two neu-
black hole (12)? trons to a center of mass energy of ∼ 1038 GeV and collide them
Article number, page 7 of 13A&A proofs: manuscript no. BHSETI_arxiv
with an impact parameter ∼ 10−14 cm. Of course, one can in- This allows us to draw some general conclusions about
stead collide more neutrons each with less energy. However, for a likely arrangement of information storing devices by ETI.
each choice the collision must be hard since the neutrons must Namely, for a given tq , the only way of increasing the amount of
be relativistic and exchange momenta exceeding (or comparable stored information, is by multiplying the number of black holes.
to) their rest masses. Increasing the entropies of individual black holes is not possible,
This example shows the general tendency: manufacturing the as this will increase tq .
microscopic black holes, requires hard collisions among high en- As it is clear from (16), for a system of n black holes, each
ergy particles. of mass M, the information retrieval time tq ∝ M 3 /MP2 is inde-
Of course, one can imagine an exotic situation when an ad- pendent of n. One can thus arbitrarily increase the entropy of
vance civilization has at its disposal a new type of a heavy ele- the system by increasing n without altering tq . The total entropy
mentary particle, interacting purely via gravity. For example, we grows as n while tq stays the same.
can imagine a stable scalar particle of mass ∼ MP . Notice, such In contrast, taking a single black hole of the mass M ′ = nM,
a particle is essentially a quantum black hole, since its Comp- increases the entropy of the system by extra power of n relative
ton wavelength as well as its gravitational radius are both of to the total entropy of n separated black holes. However, simulta-
order LP (Dvali & Gomez 2011). Using this elementary build- neously the information retrieval time grows as the cubic power
ing block, the black holes of arbitrary masses can be produced of n,
softly. Indeed, an arbitrary number of non-relativistic particles
with proper initial velocities can collapse into a black hole. Of tq → tq′ = n3 tq . (21)
course, upon crossing the Schwarzschild radius, the system al-
ways becomes relativistic. But the process is soft in the sense Obviously, this compromises the information processing effi-
that such particles need not exchange momenta exceeding their ciency of the system. Thus, the optimal way of increasing the
rest masses. information capacity of the system for a fixed tq is to increase
Putting such highly exotic possibilities aside, it is reasonable the number of black holes instead of investing the same total en-
to expect that for manufacturing small black holes, the advanced ergy into a creation of bigger ones.
ETI use the method of colliding highly energetic elementary par- We thus arrive to a very general conclusion:
ticles.
Such collisions are expected to be accompanied by the radi- The quantum computing devices of advanced ETI are more
ation of quanta of the typical energy given by the inverse impact likely to consist of multiple small black holes rather than a fewer
parameter. Since the latter is of order the black hole radius, the big ones.
expected energy of the radiated quanta is ∼ ~c/R. This is compa-
rable to the temperature of the Hawking radiation from a black This implies that from black hole “farms" of ETI, we are
hole that is the outcome of the collision. The difference of course more likely to expect the Hawking radiation of higher tempera-
is that the collision radiation is neither thermal nor democratic in ture and intensity.
particle species.
Due to this, its detectability, unlike the Hawking radiation, 10. Time scales and messengers
will depend on the composition of particle species used in colli-
sions for manufacturing black holes. The relation (16) between the information processing time tq and
In conclusion, the following general message emerges. The the black hole radius/temperature allows us to give some esti-
ETI can also be searched through the primary radiation emitted mates about the energies and the nature of the emitted Hawk-
during the process of their manufacturing of black holes. The ing radiation. We must however note that such estimates change
characteristic energy is set by the inverse impact parameter and if we move beyond Einstein gravity. This departure is scale-
is comparable to the energy of the Hawking quanta emitted by a dependent. As already discussed, in any theory with number
black hole manufactured in the process. of particle species Nsp , the gravitational cutoff is lowered to
the species scale L∗ given by the equation (3) (Dvali 2007;
9. Remarks on optimisation of information Dvali & Redi 2008).
This length gives an absolute lower bound on the size of
processing a black hole tractable within Einstein gravity. By taking into
Another remark we would like to make concerns the optimisa- account the number of all currently known elementary particle
tion of information processing by ETI. Of course, we are not species (Nsp ∼ 100), the minimal size of a black hole is still very
going to speculate about the details. Our point will be limited short, L∗ ∼ 10−32 cm.
by aspects that are imposed by laws of physics which all ETI The corresponding half-life of an Einsteinian black hole is
have to respect. These are the laws of quantum field theory and only slightly longer than the Planck time, tq ∼ 10−43 sec. This
gravity. These laws imply the relation (16) between the informa- time sets an absolute lower bound on the information processing
tion extraction time from a black hole and its radius/temperature speed offered by any ETI.
and entropy. The analogous relation holds for all saturons (20) Here, for definiteness, we shall assume that L∗ ∼ 10−32 cm
(Dvali 2021). marks the validity domain of Einsteinian gravity. A discussion
This universal relation shows that for a single black hole the of the cases with much larger number Nsp will be postponed to-
information extraction time tq is fixed in terms of its radius R wards the end of the paper. However, here we wish to note that
(or temperature, T ∼ 1/R) and Nsp . Of course, from the same increasing Nsp only helps in more efficient manufacturing of “ar-
relation, the entropy of a black hole is also uniquely fixed in tificial" black holes. This is due to the fact that the threshold
terns of tq and Nsp . Notice that the total number of species Nsp at energy of black hole formation in particle collisions is lowered
a given scale is the constant of nature, which ETI cannot change. according to (4) (Dvali & Redi 2008). The size of the smallest
The optimization problem must thereby be solved for the fixed black hole (4) is correspondingly much larger than in Einstein
Nsp . gravity with a small number of species.
Article number, page 8 of 13Gia Dvali and Zaza N. Osmanov: Black holes as tools for quantum computing by advanced extraterrestrial civilizations
Correspondingly, existence of large number of species makes erg s−1 , classifying our civilization as level 0.7 (Sagan 1973).
the black hole quantum computing more likely accessible for Type-II civilization utilizes the whole stellar power, PII ≃ L⊙ ,
less advanced civilizations. In particular, for the limiting case of and Type-III is an alien society, that consumes the total power of
Nsp ∼ 1032 , manufacturing of smallest black holes will become a host galaxy, PIII ≃ 1011 × L⊙ . Here, L⊙ ≃ 3.8 × 1033 erg s−1 is
(or perhaps already is) possible by our civilization. the Solar luminosity, RAU ≃ 1.5 × 1013 cm is the distance from
Assuming for the time being that we are within the validity the Earth to the Sun (astronomical unit - AU) and RE ≃ 6.4 × 108
of Einstein gravity for the scales of interest, we can estimate the cm denotes the radius of the Earth. From these estimates it is
parameters of the expected Hawking radiation for certain rea- obvious that even Type-I civilization can build a black hole with
sonable time-scales. the aforementioned mass: it only needs to accumulate the energy
For example, demanding that tq is not much longer than a incident on the planet during ∼ 7 days.
few seconds, we arrive to the conclusion that the energy of the In the search for extraterrestrial intelligence, the major task
Hawking quanta is above ∼TeV energy. With such a high tem- is to find specific fingerprints of their activity. Using black holes
perature all the known particle species will be radiated by ETI will inevitably lead to such observational features which, on
black hole computers. the one hand, might be detected and, on the other hand, distin-
Of course, how efficiently the radiation can reach us depends guished from typical astrophysical events. In particular, we use
on number of factors. These factors include the presence of a the knowledge that black holes emit particles with energy in the
medium that can absorb or shield the radiation. range (E, E + dE) with the rate (Hawking 1974)
In general, since the neutrinos have the deepest penetration
length, they appear to be the most robust messengers. In ad- d2 N 1 Γ s (E, M)
R(E, M) ≡ = × 8πGME , (22)
dition, the mediation by high energy gamma quanta and other dtdE 2π~ e ~c3 − (−1)2s
species is certainly a possibility.
Of course, the high energy radiation coming from the dis- where Γ s (E, M) = E 2 σ s (E, M)/(π~2c2 ), s denotes the spin of a
tant ETI, will be subjected to the same universal cutoffs as the particle, σ s = α sG2 M 2 /c4 , α1/2 = 56.7, α1 = 20.4 and α2 = 2.33
high energy cosmic rays produced by the natural sources. The (MacGibbon & Webber 1990). As discussed, the flux of parti-
example is given by the Greisen-Zatsepin-Kuzmin (GZK) cut- cles might be screened out but, we assume that neutrinos escape.
off (Greisen 1966; Zatsepin, Kuzmin 1966) due to scattering of Therefore, the major observational feature might be the energetic
high energy protons at the cosmic microwave background. flare of neutrinos. Using Eq. (22), one can easily demonstrate
On top of the known natural factors, there can be unknown that the spectral power, ER, of neutrinos, (s = 1/2), has a peak
artificial shielding effects. For instance, ETI may compose ab- at energies
sorbing shields around their black hole computers. The motiva- !1/3
ν 3.13~c3 100 1 sec
tion may vary from a simple defence against the life-threatening Em ≃ ≃ 48 × × T eV, (23)
high energy radiation, as it is the case for humans, all the way to 8πGM N sp τ1/2
sophisticated energy-recycling purposes. These are the factors which can be detected by the IceCube detector (Ahrens et al.
about which it is hard to speculate. However, in their light the 2004). For the neutrino emission luminosity at Em we obtain
case for neutrino, as of a most promising known messenger, is
strengthened. Lνm ≃ 3 × (Emν )2 R(Emν , M) ≃
!2/3
11. Some general estimates 120 1 sec
≃ 1.2 × 1028 × × erg/s. (24)
N sp τ1/2
All the parameters required for our estimates - such as the time
scale of processing, the temperature of accompanying radiation, where the multiplier, 3, comes from the three flavors of neutri-
the black hole mass and the entropy - can be expressed through nos. As it is evident, even a single event is characterized by the
one another. The only extra quantity is Nsp , which shortens the very high luminosity of the neutrino flare. In general, it is obvi-
processing time. At the moment we assume that this quantity is ous that a civilization might perform many calculations per sec-
not much different from the number of known species. Then, we ond. On the other hand, any civilization is limited by the level of
are left with a single input parameter which we shall take to be technology it possesses. The maximum number of quantum pro-
the information processing time tq (14). As we already discussed cessings per second, n x (where x = (I, II, III) denotes the level
(15), this time is approximately equal to a half decay time of a of technology), is severely constrained by a civilization’s maxi-
black hole τ1/2 , which shall be used below. mum power, n x ≃ P x /hLi, where hLi ≃ Mc2 /2τ1/2 is the average
We assume that the typical timescale which is required for luminosity of black hole’s emission:
computation is of the order of 1 sec. Then, from Eq. 11 one can !1/3
show that the black hole mass will be of the order of 1.2 × 109 g. 100 τ1/2 2/3
nI = 3.5 × 10−6 × × sec−1 , (25)
In this context, an important issue a civilization has to address is N sp 1 sec
energy, which is required for constructing an extremely compact !1/3
object, Mc2 ≃ 1030 erg. 3 100 τ1/2 2/3
nII = 7.7 × 10 × × sec−1 , (26)
In order to understand the capabilities of extraterrestrial civ- N sp 1 sec
ilizations, one should examine them in the light of the classifi- !1/3
cation introduced by Kardashev (1964). According to this ap- 100 τ1/2 2/3
proach, alien societies should be distinguished by their techno- nIII = 7.7 × 1014 × × sec−1 . (27)
N sp 1 sec
logical level. Type-I civilizations, in particular, use the entire
power attained on a planet. In the case of the Earth, the corre- Since the value of nI is very small, the best way is to capture
2 a single event of duration τ1/2 . For Type-I alien societies the lu-
sponding value is of the order of PI ≃ L4⊙ × RRAUE ≃ 1.7×1024 erg minosity will be defined by Eq. (24), but for Type-II,III civiliza-
s−1 , whereas the current power consumption is about 1.5 × 1020 tions the luminosity might be much higher, reaching the solar
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