Physics Letters B 749 (2015) 514–518
Contents lists available at ScienceDirect
Physics Letters B
www.elsevier.com/locate/physletb
A note on Boltzmann brains
Yasunori Nomura
∗
Berkeley Center for Theoretical Physics, Department of Physics, University of California, Berkeley, CA 94720, USA
Theoretical
Physics Group, Lawrence Berkeley National Laboratory, CA 94720, USA
Kavli
Institute for the Physics and Mathematics of the Universe (WPI), Todai Institutes for Advanced Study, University of Tokyo, Kashiwa 277-8583, Japan
a r t i c l e i n f o a b s t r a c t
Article history:
Received
11 August 2015
Accepted
12 August 2015
Available
online 14 August 2015
Editor:
M. Cveti
ˇ
c
Understanding the observed arrow of time is equivalent, under general assumptions, to explaining why
Boltzmann brains do not overwhelm ordinary observers. It is usually thought that this provides a
condition on the decay rate of every cosmologically accessible de Sitter vacuum, and that this condition
is determined by the production rate of Boltzmann brains calculated using semiclassical theory built on
each such vacuum. We argue, based on a recently developed picture of microscopic quantum gravitational
degrees of freedom, that this thinking needs to be modified. In particular, depending on the structure of
the fundamental theory, the decay rate of a de Sitter vacuum may not have to satisfy any condition
except for the one imposed by the Poincaré recurrence. The framework discussed here also addresses the
question of whether a Minkowski vacuum may produce Boltzmann brains.
© 2015 The Author. Published by Elsevier B.V. This is an open access article under the CC BY license
(http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP
3
.
1. Introduction
At first sight, the fact that we observe that time flows only
in one direction may seem mysterious, given that the fundamen-
tal
laws of physics are invariant under reversing the orientation
of time.
1
Upon careful consideration, however, one notices that
the problem is not the unidirectional nature per se. As discussed
in Refs. [1,2], given any final state | f whose coarse-grained en-
tropy
is lower than the initial state |i, the evolution history is
overwhelmingly dominated by the CPT conjugate of the standard
(entropy increasing) process |
¯
f →|¯ı. This implies that a physi-
cal
observer, who is necessarily a part of the whole system, sees
virtually always, i.e. with an overwhelmingly high probability, that
time flows from the “past” (in which correlations of the observer
with the rest of the system are smaller) to the “future” (in which
the correlations are larger).
The
problem of the arrow of time, therefore, is not to under-
stand
its unidirectional nature, but to explain why physical predic-
tions
are (probabilistically) dominated by what we observe in our
*
Correspondence to: Berkeley Center for Theoretical Physics, Department of
Physics, University of California, Berkeley, CA 94720, USA.
E-mail
address: ynomura@berkeley.edu.
1
The operation discussed here is not what is called the time reversal T in quan-
tum
field theory, which we know is broken in nature. It corresponds to CPT in the
standard language of quantum field theory.
universe, i.e. a flow from a very low coarse-grained entropy state
to a slightly higher entropy state. In particular, it requires the un-
derstanding
of the following facts:
• At least one set of states representing our observations, which
are mutually related by time evolution spanning the obser-
vation
time, are realized in the quantum state representing
the whole universe/multiverse. (Here and below we adopt the
Schrödinger picture.) This is the case despite the fact that
these states have very low coarse-grained entropies.
2
• The answer to a physical question, which may always be asked
in the form of a conditional probability [6], must be deter-
mined
by the class of low coarse-grained entropy states de-
scribed
above. In particular, the probability should not (always)
be dominated by the states in which the unconditioned part of
the system has the highest coarse-grained entropies.
2
Because of the Hamiltonian constraint, the full universe/multiverse state is ex-
pected
to be static, i.e. not to depend on any time parameter [3,4]. We may, how-
ever,
talk about effective time evolution if we focus on branches of the whole
universe/multiverse state, since they are not (necessarily) invariant under the ac-
tion
of the time evolution operator e
−iHτ
. This is the picture we adopt in this
paper. Note that this time evolution still does not have to be the same as “phys-
ical
time evolution” defined through correlations among physical subsystems, e.g.,
as in Ref. [5]. In the static-state picture, the statement here is phrased such that the
state of the universe/multiverse contains components representing our observations
despite the fact that they are not generic in the relevant Hilbert space.
http://dx.doi.org/10.1016/j.physletb.2015.08.029
0370-2693/
© 2015 The Author. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by
SCOAP
3
.