Vol.3, No.5, 397-400 (2011) Natural Science
http://dx.doi.org/10.4236/ns.2011.35053
Why a universe as a whole must be a quantum object
Pedro F. González-Díaz
Colina de los Chopos, Instituto de Física Fundamental, CSIC, Madrid, Spain;
Received 3 March 2011; revised 21 March 2011; accepted 26 March 2011.
ABSTRACT
Technical and physical reasons are given in fa-
vor of the idea that single universes, accelerat-
ing or not, essentially are quantum-mechanical
entities without any classical analogs, even
when they are forming part of a given multi-
verse.
Keywords: Decoherence; Baby Universes;
Bell's Inequalities
1. INTRODUCTION
Why can’t you be in two places at the same time? The
simple, obvious answer is: because of your interaction
with your environment, the superposition of states that
you are actually quantum-mechanically collapses into a
single classical state, what makes your personal and
unique yourself a phenomenon called quantum decoher-
ence. The ultimate reason for that phenomenon being
operative for macroscopic objects and not with atoms
and small molecules is still a mystery. Some have even
thought that it is due to interaction with the gravitational
waves that are pervading the whole universe. Whatever
it could be the reason for decoherence in macroscopic
object, what is very clear is that any universe as a whole
has no environment at all and therefore no quantum de-
coherence may collapse its quantum state into a single
classical one. Thus, the universe as a whole should be a
real quantum object which is a superposition of states
and cannot have any classical analog. It might still be
argued that quantum entanglement between distinct uni-
verses or tunnelling strips like wormholes, ring holes or
Klein-bottle holes connecting these universes to each
other could well make the job of quantum decoherence
rendering every individual single universe finally a clas-
sical object. However, the non locality properties of
quantum entanglement among different universes are far
from being shared by the required quantum decoherence
which rather plays the quite more conventional classical
role of the wave function collapse which can even be
induced by gravitational interaction (actually in this case,
besides the e.g. Zurek formulas [1], one should necessar-
ily make recourse to that gravitational interaction which
comes about due to correlated baby universe pairs [2] to
make it compatible with the whole scenario we were
dealing with) that might be a purely classical interaction
at the end of the day, and the kind of tunnelling we have
just mentioned are defined as being classical communi-
cation channels, at least when regarded as solutions to
Einstein equations.
Thus, the main aim of the present report is at discuss-
ing several compelling arguments in favour of the idea
that the single universe considered as a whole is purely a
quantum object devoid of any classical analog. These
arguments are based on the physics of baby universes
which are branched off from a large parent universe in
self entangled pairs using the method of quantum optical
gravity [2], both under the Zurek perspective (Section 2)
or employing field theory tools like the T-symmetry
(Section 3). The problem of the placement of observers
in quantum cosmology is briefly commented in Section
4, and we conclude and add some extra comments in
Section 5.
2. THE MASTER EQUATION
In this and the next sections we shall use the quan-
tum-optical formalism for quantum gravity [2] as ap-
plied to the density matrix of baby universes and scalar
fields. We will restrict ourselves to the simplest case of
the interaction between a massless, conformally invari-
ant scalar matter field,


,
x
t, and single doubly con-
nected Euclidean wormholes [3], using the quan-
tum-optical formalism of the density matrix in the inter-
action representation and ordinary time-dependent per-
turbation theory in first-order approximation. We con-
sider the interaction Hamiltonian


II
ii
i
H
HA
,
with i
A
the baby universe operators, and assume a full
density matrix
1,
b
j
ij

 ρρρ ρ, where

ρ
and b
ρ
are density matrices for the scalar matter field
and the baby universes, respectively. Now, from the
Heisenberg equation of motion for the full density ma-

P. F. González-Díaz / Natural Science 3 (2011) 397-400
398
trix, which we iterate for small increments of time, we
obtain with the same approximation as used in ordinary
time-dependent perturbation theory

,
,,
II
biijj
ij
ktTrHA HA 








ρ
 (1)
in which b
Tr means tracing over the baby universe
sector operators. Assuming then [2] convenient ortho-
normalization relation and commutation relations for
hermitian operators, so as the usual Fock expansion for
the quantum field operators in the continuity limit
4
0
,d ij
x

, after integrating over the insertion points
of the baby universes on the large universal spacetime
and the momentum that appears in the delta function of
the orthonormalization relations using the customary
quantum-optical measure [2], we obtain the master equa-
tion for the reduced density matrix for matrix elements
in the Fock space of the matter field number states in the
diagonal representation



2
0
11
,8sinh2 ,
22
nn
PktnNk Pkt
 
 
 
 
, (2)
where 0, 2, 4,N denotes the initial number of baby
universes, 2k is the proper distance on the wormhole
inner 3-manifold between the two correlated points at
which two baby universes are simultaneously created or
annihilated, and

2
00
2kkRk, and we have taken
the limit 0k, substracting it from the previously
derived expression, in order to eliminate changes in the
reduced density matrix which do not originate from
quantum non-locality. The crucial point for the baby
universe pairs now is that the density matrix in scalar
particle number representation actually corresponds to a
quantum state in position representation whose evolution
satisfies a generalized master equation given by [4]
 
2
1
,, ,,
2
n
P xxtPnPxxt


 


, (3)
with

2
2
4
1
8sinh
2o
x
x
PN r





 , (4)
where 0
r is the radius of the Euclidean wormhole
throat and the

,
x
x’s describe the insertion points of
the correlated pairs in the otherwise independent uni-
verses.
Now, depending on the physical situation we are
dealing with, we can have the following two essentially
distinct cases. For large objects which are placed as parts
(not the whole) of a given universe, a coherent superpo-
sition of two Gaussians separated by a space-like distance
x
xx


 should be considered (such as Zurek first
did [1]). Then, at macroscopic distances,
x
xx



will be much larger than the Gaussian width, and the
density matrix will show essentially four distinct peaks,
two corresponding to the diagonal elements basically
surviving intact the wave packet collapse, and two asso-
ciated with the off-diagonal elements amounting to the
quantum correlations that nearly fully disappear during
measurement, giving thus rise to position as an exactly
preferred basis. That is a typical example of what is
known as the decoherence process leading to classical
behaviour of the macroscopic objects that do not entail
the whole universe.
In case that you consider a set of universes related to
each other by means of e.g. Euclidean and Lorentzian
wormholes, all entities pertaining to the very nature of
the space-time separated structures, it will be needed that
in order for keeping the space-times of the single uni-
verses fully independent from each other, one should
integrate off the generalized above master equation over
the space-like separation
x
xx


 in such a way that
the final form of that generalized master equation does
not explicitly contain any dependence on
x
xx

 ,
being this replaced for a necessarily nonzero footprint
factor resulting from the integration process. This is the
key point which clearly avoids having in the case of a
single universe in the multiverse the position as an ex-
actly preferred basis, and hence an available classical
result is no longer allowed. Actually, because by the very
definition of cosmic space-time, well-defined mutual
position between single universes in the multiverse can
by no means be established, before any other alternative
interpretation might be made, one should be aware that
the off-diagonal matrix elements describing quantum
correlations between insertion points responsible for the
quantum nature of every single universe can by no
means be damped, always leaving a definitively nonzero
(quantum) footprint factor coming from the double inte-
gration over
x
xx


 which should be performed
both over P and P in the generalized master equa-
tion, which can no longer be erased off. These memories
from the off-diagonal matrix components can no longer
be eliminated during any measurement processes (such
as it could be made with the two peaks associated with
the Zurek off-diagonal elements amounting to the quan-
tum correlations that nearly fully disappear during
measurement, giving rise to position as an exactly pre-
ferred basis) and, therefore, the decoherence scenario
can by no means be driven to its classical completion, so
leaving an unavoidably quantum single universe evolv-
ing in the sea of all other single universes.

P. F. González-Díaz / Natural Science 3 (2011) 397-400 399
3. BABY UNIVERSES AND THE
CURRENT ACCELERATING
UNIVERSE
Moreover, there still is another technical reason am-
ounting to enhance even further the conclusion drawn in
the previous section in the case of an accelerating uni-
verse. In fact, it has been recently shown [5] that the
action integral for all kinds of baby universes can be
seen to be the same as that for their T-duality symmetric
space-times which turn out to be those of accelerating
universes. It follows that the accelerating universe sector
and the baby universe sector are equivalent physically to
each other. Now, the violation of Bell’s inequalities
which points to the essential quantum nature of the sys-
tem inducing it is attained when the following quan-
tum-optical inequality holds [6]


220.707
aaaa
C
aaaaa a

 


(5)
where the a’s are Fock annihilation and creation quan-
tum operators for the given field.
Then, from inequality (5) and the definition of the
second-order coherent function,

2
2
2
1
1
n
nn
gn
n


, (6)
where use has been made of the general condition
21,nn we get
 
22
2
2
11
1
1n
n
C
g
ng
n



(7)
We again compute then the master equation for the
second-order correlation function from the matrix ele-
ments in the baby universe Fock space of the matter field
number states [2], in the diagonal representation, fol-
lowing the same procedure as for obtaining Eq.2, but
without expliciting in this case the quantity k in terms
of the insertion spatial points, that is



2
0
11
,8sinh2 ,
22
nn
PktnNk Pkt
 
 
 
 
, (8)
in which again 0,2,4,N denotes the initial num-
ber of baby universes whenever these are branched off in
correlated pairs, 2k is the corresponding proper dis-
tance on the Euclidean wormhole inner 3-manifold be-
tween the two correlated points at which two baby uni-
verses are simultaneously created or annihilated in this
case, and

2
00
2kkRk, with 0 R the smallest value
of the scale factor in the connected manifold. Following
then the procedure described in Reference [2] we can
then derive the evolution rate of the second-order co-
herence function, to obtain [2]


 

 

2
0
2
22324 3
,
11
87 6
44
n
nnnnn
gPNk
ngn ggnngg



 





,
(9)
where

3
n
g
and

4
n
g
are the third- and fourth-order
coherence functions, respectively, and
 
00
1
,8sinh 2
2
PNk Nk



 . For the vacuum case,
Eq.9 admits the exact solution

 
2
00 0
7
0, exp,
2
g
kPNkt




, so that

0
70,
2
1
1e
P
kt
C 

. (10)
Thus, for the vacuum case there will always be a large
enough time for which Bell’s inequalities are violated.
Such a time is smaller than or as most equal to




0
2ln2.37 70,.
v
tPkThis conclusion is still valid
for small, nonzero values of n and even in the limit
of large n where



2
0
11exp2 ,
2
n
g
PNk t

 .
It finally follows that, though in his limit the right
hand side of expression (10) is in this case defined to be
smaller than 0.707 even for 0t, the inequality relat-
ing it with C can leave still a residual room for the
violation of Bell’s inequalities in the situation where we
usually expect the classical limit to hold, so allowing any
multiverse descriptions to admit a joint quantum treat-
ment. The conclusion can then be drawn that single ac-
celerating universes unavoidably entail the phenomena
of quantum entanglement.
4. OBSERVERS ARE ALL INSIDE THE
UNIVERSE
Besides the above rather technical reasons, one still
may have fundamental theoretical and almost philoso-
phical problems which concern the feature that quantum
theory generally splits the world into two parts: the sys-
tem under study and the rest of the world, which inexo-
rably must contain the observer. Now, cosmology suffers
from the paradoxical requirement that no observer can
be placed outside the universe. It is in this sense that the
universe is therefore doomed to spend eternity like
nothing more than a vague possibility, so far from actual

P. F. González-Díaz / Natural Science 3 (2011) 397-400
400
reality like the Schrödinger’s cat. And then quantum
cosmological models dictate that therefore we cannot
talk about the universe as a whole, but only what a given
observer inside it might measure.
Nevertheless, if we keep ourselves within the context
of what has been said above, then a quantum-cosmo-
logical observer must by itself be split into two un-
avoidably independent parts: the bone and flesh struc-
tures supporting the set of tools made of detectors, food
and breathing endorsements and displacement proce-
dures, so as the thermodynamic, psychological and cos-
mic arrow of times, etc., which all are classical in their
very nature and may be really separated from the very
concept of quantum observer to join the rest of the world,
so leaving the other, now quantum-mechanically rele-
vant part of the quantum observer: its mind. This is the
actual and unique designer of every observation or
measurement actions or decision making, and clearly
should form part of the entangled quantum universe, just
playing the role of that completing missing part required
by that universe to achieve quantum completion.
5. CONCLUSIONS AND FURTHER
COMMENTS
As one conclusion we shall notice that the above ar-
guments lend support to the idea that we are daring to
suggest in this report that every single universe, in the
multiverse or not, is by itself an essentially quan-
tum-mechanical system endowed with all tools of quan-
tum information, which violated Bell’s inequalities [7],
and could by no means have any classical analog. At
first sight it might also be reconsidered that to deal with
a macroscopic mass using quantum mechanics one must
consequently correct the derivation of the equations de-
scribing the evolution of the universe and the behavior
of that mass itself. However, besides the feature that the
mass density is what matter here and this mass density is
extremely small for our currently accelerating universe,
the development that we have considered here has noting
to do with such an issue but with the nuclea-
tion/annihilation balance of those baby universes being
branched off and in throughout the large spacetime of
the current universe. In fact, as important outcomes from
such a balance we have the fixing of all particle masses
and physical constants, according an improved Coleman
mechanism [8,9] and the existence of quantum-optical
master equations as those given by Eqs.3 and 8, accord-
ing to the mechanisms described in References [2] and
[4] for baby universes created in self-correlated pairs.
Now, since there will always exist a nonzero contribu-
tion for nucleation of pairs of baby universes it follows
that the Coleman mechanism for the big fix [8] becomes
consistent [9,10]. We finally point out that the quan-
tum-mechanical entanglement energy for a single uni-
verse should be interpreted in terms of the existence of a
future event horizon, which is granted for any model of
the current accelerating universe, where entanglement is
established between the two independent spacetime re-
gions created by that horizon [11].
No boubt, this paper is too brief to provide definitive
description, analysis or discussion on the problem of
why the universe as a whole ought to be regarded as a
quantum object devoid of any classical analog. Even
though one therefore cannot provide with a fully consis-
tent answer to the question posed in the title, the paper
still contains the main basic ingredients needed to prop-
erly cook such an answer which should in any event
given in terms of the entangled baby universe pairs.
6. ACKNOWLEDGEMENTS
The author thanks Carmen Sigüenza and Salvador Robles-Pérez for
enlightening discussions and decisive technical help, and the Estación
Ecológica de Biocosmogía de Medellín, Spain, where part of this work
was carried out. This paper was supported by MICINN under Research
Project No. FIS2008-06332.
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