Why a universe as a whole must be a quantum object

doi:10.4236/ns.2011.35053

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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; [email protected]

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,





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





HA

,

with i

the baby universe operators, and assume a full

density matrix





ρρρ ρ, where



and b

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



biijj

ktTrHA HA



















 (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



, 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



,8sinh2 ,

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



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]

 

,, ,,

P xxtPnPxxt





 





, (3)

with



8sinh

PN r











 , (4)

where 0

r is the radius of the Euclidean wormhole

throat and the



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





 should be considered (such as Zurek first

did [1]). Then, at macroscopic distances,







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





 in such a way that

the final form of that generalized master equation does

not explicitly contain any dependence on



 ,

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





 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

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,







, (6)

where use has been made of the general condition

21,nn we get

 





(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



,8sinh2 ,

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



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]



 



 



22324 3

87 6

nnnnn

gPNk

ngn ggnngg







 











(9)

where



and



are the third- and fourth-order

coherence functions, respectively, and

 

,8sinh 2

PNk Nk







 . For the vacuum case,

Eq.9 admits the exact solution



 

00 0

0, exp,

kPNkt









, so that



70,

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









2ln2.37 70,.

tPkThis conclusion is still valid

for small, nonzero values of n and even in the limit

of large n where



11exp2 ,

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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