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I
am very pleased that Lenny Susskind has taken the time
to respond to my paper on the Anthropic Principle (AP) ["Scientific
alternatives to the anthropic principle"] and
to discuss cosmological natural selection (CNS). Susskind
is for me the most inspiring figure of his generation of
elementary particle physicists. Indeed, the initial ideas
that became loop quantum gravity came from applying to
quantum gravity some of what I had learned from his work
on gauge theories. And when in the late 1990's I began
to work again on string theory, it was because of papers
of his describing how special relativity was compatible
with string theory.
I
was thus extremely pleased when Susskind began arguing
for a view of string theory I came to some time ago — that
there is not one theory, but a "landscape" of many theories.
But I was equally disturbed when he and other string theorists
embraced versions of the Anthropic Principle that I had,
after a lot of thought, concluded could not be the basis
for a successful scientific theory. To see if we could
do better, I formulated conditions that would allow a theory
based on a landscape to be a real scientific theory. As
an example I had invented the CNS idea. This was all described
in my book, The Life of the Cosmos.
Susskind's papers on these issues led me to revisit them,
to see if anything that had happened since might change
my mind. So I undertook a carefully argued paper on the
AP and alternatives to it [a]. The
dialogue with Lenny began when I sent a note to him, asking
whether he might have any response to the arguments in
that paper. At first there were some misunderstandings,
because Susskind responded only to a summary, and not
the full paper. Nevertheless, some important points were
raised, although nothing that requires modification of
my original paper. This letter is my response to a paper
Susskind put out in the course of our dialogue, making
certain criticisms of cosmological natural selection (CNS)
[b], and is mostly devoted to answering
them.
We
agree on several important things, among them that fundamental
physics likely gives us a landscape of possible theories,
while cosmology may give a multiverse containing a vast
number of regions like our own universe. We disagree here
mainly on one thing: the mechanism of reproduction we believe
has been most important in populating the multiverse.
My
main point is that string theory will have much more
explanatory power if the dominant mode of reproduction
is through black holes, as is the case in the original
version of CNS. This is the key point I would hope
to convince Susskind and his colleagues about, because
I am sure that the case they want to make is very much
weakened if they rely on the Anthropic Principle (AP) and
eternal inflation.
Susskind
believes instead that eternal inflation is the mode of
reproduction. But suppose that everything Susskind wants
to be true about both eternal inflation and the string
theory landscape turns out to be true. What is the best
thing that could reasonably be expected to happen?
Weinberg,
Vilenkin, Linde and others proposed that in this case we
might be able to explain the value of the vacuum energy,
both during and after inflation. This is because it is
the vacuum energy that determines how many universes are
made in eternal inflation, and how large each one is.
However,
a careful examination exposes two problems. The first is
that the methods so far proposed to make predictions in
this scenario are either logically flawed or ambiguous,
so that the assumptions can be manipulated to get different
predictions. This is explained in detail in section 5.1
of my paper. A second piece of bad news is that, even if
this can somehow be made to work, you can't expect to explain
much more than the vacuum energy. The reason, as I explain
in some detail in section 5.1.4, is that a statistical
selection mechanism can only act to tune those parameters
that strongly influence how many universes get created.
As the selection mechanism in eternal inflation involves
inflation, which happens at the grand unified scale, the
low energy parameters such as the masses of the light quarks
and leptons are not going to have much of an effect on
how many universes get created.
In
order to tune the low energy parameters, there must be
a selection mechanism that is differentially sensitive
to the parameters of low energy physics. So we can ask,
what possible mechanisms are there for production of universes
within a multiverse, such that the number of universes
made is sensitive to the values of light quark and lepton
masses? I asked myself this question when I realized there
would be a landscape of string theories.
The only answer I could come up with is reproduction through
black holes. It works because a lot of low energy physics and
chemistry goes into the astrophysics that determines how many
black holes get made.
Susskind
complains that this is complicated, but it has to be complicated.
The reason is that we are trying to understand a very curious
fact, which is that, as noted by the people who invented
the anthropic principle, the low energy parameters seem
tuned to produce carbon chemistry and long lived stars.
This is explained if CNS is true, because the formation
of stars massive enough to become black holes depend on
there being both carbon and a large hierarchy of stellar
lifetimes.
Thus,
if you like eternal inflation because it has a chance of
explaining the tuning the vacuum energy, you should like
cosmological natural selection much more — because
it has potentially much more explanatory power. It offers
the only chance so far proposed to actually explain from
string theory the parameters that govern low energy physics.
Also, as I argued in detail in my paper, the selection
mechanism in CNS is falsifiable, whereas those proposed
for eternal inflation so far are too ambiguous to lead
to clean predictions.
Moreover,
because the selection mechanism is dominated by known low
energy physics and chemistry, we really do know much more
about it than about eternal inflation. We know the dynamics,
we know the parameters, and we can use relatively well
tested astrophysical models to ask what the effect on the
number of universes is of small changes in the parameters.
None of this is true for inflation, where unfortunately
there are a large variety of models which all are in agreement
with observation, but which give different predictions
concerning eternal inflation.
Of
course it is possible that both mechanisms play a role.
It might be useful to study this, so far no one has. It
is premature to conclude, as Susskind does, that the production
of universes by eternal inflation will dominate. Our universe
has "only" 1018 black holes, but the total number of universes
in CNS is vastly bigger than this, as there must have been
a very large number of previous generations for the mechanism
to work.
Susskind
made a few direct criticisms of CNS, which are easy to
answer, as they have been considered earlier.
He raises the question of how many new universes are created
per astrophysical black hole. In the initial formulation
of CNS I presumed one, but some approximate calculations
have suggested that the number could be variable. I discussed
this in detail on page 320 of Life of the Cosmos.
The reader can see the details there, what I concluded
is that if theory predicts that the number of new universes
created increases with the mass, by at least the first
power of the mass, the theory can easily be disproved.
This hasn't happened, but it could, and it is one of the
ways CNS could be falsified. This is of course good not
bad, for the more vulnerable a theory is to falsification,
the better science it is, and the more likely we are to
take it seriously if it nonetheless survives.
One
of the assumptions of CNS is that the average change in
the low energy parameters when a new universe is created
is small. Susskind says he doubts this is true in string
theory. If Susskind is right then CNS and string theory
could not both be true. But I don't share his intuitions
about this. I would have to invoke technicalities to explain
why, but all that need be said here is that so far there
are no calculations detailed enough to decide the issue.
But there could be soon, as I mentioned before, using methods
developed recently in loop quantum gravity. These methods
may help us study what happens to singularities in string
theory and may also provide a better framework to understand
eternal inflation.
The
rest of this note concerns Susskind's comments about black
holes. He says, "...we have learned some things about black
holes over the last decade that even Stephen Hawking agrees
with [13]. Black holes do not lose information." From this
he draws the conclusion that "the quantum state of the
offspring is completely unique and can have no memory of
the initial state. That would preclude the kind of slow
mutation rate envisioned by Smolin."
This
is the central point, as Susskind is asserting that black
holes cannot play the role postulated in CNS, without contradicting
the principles of quantum theory and results from string
theory. I am sure he is wrong about this. I would like
to carefully explain why. This question turns out to rest
on key issues in the quantum theory of gravity, which many
string theorists, coming from a particle physics background,
have insufficiently appreciated.
The
discussion about black holes "losing information" concerns
processes in which a black hole forms and then evaporates.
Hawking had conjectured in 1974 that information about
the initial state of the universe is lost when this happens.
Susskind and others have long argued that this cannot be
true, otherwise the basic laws of quantum physics would
break down.
As
Hawking initially formulated the problem, the black hole
would evaporate completely, leaving a universe identical
to the initial one, but with less information. This could
indeed be a problem, but this is not the situation now
under discussion. The present discussion is about cases
in which a black hole singularity has bounced, leading
to the creation of a new region of spacetime to the future
of where the black hole singularity would have been. In
the future there are two big regions of space, the initial
one and the new one. If this occurs then some of the information
that went into the black hole could end up in the new region
of space. It would be "lost" from the point of view of
an observer in the original universe, but not "destroyed",
for it resides in the new universe or in correlations between
measurements in the two universes.
The first point to make is that if this happens it does
not contradict the laws of quantum mechanics. Nothing
we know about quantum theory forbids a situation in which
individual observers do not have access to complete information
about the quantum state. Much of quantum information theory
and quantum cryptography is about such situations. Generalizations
of quantum theory that apply to such situations have been
developed and basic properties such as conservation of
energy and probability are maintained. Using methods related
to those developed in quantum information theory, Markopoulou
and collaborators have shown how to formulate quantum
cosmology so that it is sensible even if the causal structure
is non-trivial so that no observer can have access to
all the information necessary to reconstruct the quantum
state [c]. Information is never
lost — but it is not always accessible to every
observer.
So there is nothing to worry about: nothing important
from quantum physics [d] is lost
if baby universes are created in black holes and some
information about the initial state of the universe ends
up there.
A second point is that there is good reason to believe
that in quantum gravity information accessible to local
observers decoheres in any case, because of the lack of
an ideal clock. In particle physics time is treated in
an ideal manner and the clock is assumed to be outside
of the quantum system studied. But when we apply quantum
physics to the universe as a whole we cannot assume this:
the clock must be part of the system studied. As pointed
out independently by Milburn [e]
and by Gambini, Porto and Pullin [f],
this has consequences for the issue of loss of information.
The reason is that quantum mechanical uncertainties come
into the reading of the clock — so we cannot know
exactly how much physical time is associated with the
motion of the clock's hands. So if we ask what the quantum
state is when the clock reads a certain time, there will
be additional statistical uncertainties which grow with
time. (In spite of this, energy and probability are both
conserved.) But, as shown by Gambini, Porto and Pullin,
even using the best possible clock, these uncertainties
will dominate over any loss of information trapped in
a black hole. This means that even if information is lost
in black hole evaporation, no one could do an experiment
with a real physical clock that could show it.
I
believe this answers the worries about quantum theory,
but I haven't yet addressed Susskind's assertion that "we
have learned some things about black holes over the last
decadeÅ .Black holes do not lose information."
I've found that to think clearly and objectively about
issues in string theory it is necessary to first carefully
distinguish conjectures from the actual results. Thus,
over the last few years I've taken the time to carefully
read the literature and keep track of what has actually
been shown about the key conjectures of string theory.
The results are described in two papers [g].
In
this case, I am afraid it is simply not true that the
actual results in string theory — as opposed to
so far unproven conjectures — support Susskind's
assertions [h].
There
are two classes of results relevant for quantum black holes
in string theory. One concerns the entropy of very special
black holes, which have close to the maximal possible charge
or angular momenta for black holes. For this limited class
of back holes the results are impressive, but it has not,
almost ten years later, been possible to extend them to
typical black holes. The black holes that were successfully
described by string theory have a property that typical
astrophysical black holes do not have — they have
positive specific heat. This means that when you put in
energy the temperature goes up. But most gravitationally
bound systems, and most black holes have the opposite property — you
put in energy and they get colder. It appears that the
methods used so far in string theory only apply to systems
with positive specific heat, therefore no conclusions can
be drawn for typical astrophysical black holes.
A
second set of results concerns a conjecture by Maldacena.
According to it, string theory in a spacetime with negative
cosmological constant is conjectured to be equivalent to
a certain ordinary quantum system, with no gravity. (That
ordinary system is a certain version of what is called
a gauge theory, which is a kind of generalization of electromagnetism).
Even
if Maldacena's conjecture is true, that is no reason to
assume there could not be baby universes where information
was kept apart from an observer in the initial universe
for a very long, but not infinite, time. This can be accomplished
so long as all the different regions eventually come into
causal contact so that, if one waits an infinite time,
it becomes possible to receive the information that has
gone into the baby universes.
But
in any case, Maldacena's conjecture has so far not been
proven. There is quite a lot of evidence showing there
is some relation between the two theories, but all of the
results so far are consistent with a far weaker relationship
holding between the two theories than the full equivalence
Maldacena conjectured. This weaker relationship was originally
formulated in a paper by Witten, shortly after the one
of Maldacena. Except for a few special cases, which can
be explained by special symmetry arguments, all the evidence
is consistent with Witten's weaker conjecture. We should
here recall a basic principle of logic that when a collection
of evidence is explained by two hypotheses, one stronger
and one weaker, only the weaker one can be taken to be
supported by the evidence.
But
Witten's conjecture requires only that there be a partial
and approximate correspondence between the two theories.
It does not forbid either baby universes or the loss of
information by black holes. For example, Witten shows how
some black holes can be studied using results in the other
theory, but again it turns out that these are atypical
black holes with positive specific heat.
This discussion is related to a conjecture called the
Holographic Principle (HP), an idea proposed by 't Hooft
(and a bit earlier Crane) that Susskind brought into string
theory. Susskind proposes a strong form of the HP, which
holds that a complete description of a system resides
in the degrees of freedom on its boundary. He takes Maldacena's
conjecture as a demonstration of it. I believe here also
the evidence better supports a weaker form (proposed with
Markopoulou) according to which there is a relation between
area and information, but no necessity that the boundary
has a complete description of its interior [i].
I would urge a similar caution with respect to Susskind's
claim, "As repeatedly emphasized by 't HooftÅ black
holes are the natural extension of the elementary particle
spectrum. This is especially clear in string theory where
black holes are simply highly excited string states. Does
that mean that we should count every particle as a black
hole?"
As
I mentioned, the only results in string theory that describe
black holes in any detail describe only very atypical black
holes. In those cases, they are related — at least
by an indirect argument — to states described by
string theory, but they are not in fact excitations of
strings. They involve instead objects called D-branes.
So Susskind must mean by "a highly excited string state" any
state of string theory. But in this case the argument has
no force as stars, planets and people must also be "highly
excited string states". In any case, until there are detailed
descriptions of typical black holes in string theory, it
is premature to judge whether Susskind and 't Hooft have
conjectured correctly.
Susskind
attempts to invoke Hawking's authority here, and it is
true that Hawking has announced that he has changed his
view on this subject. But he has not yet put out a paper,
and the transcript of the talk he gave recently doesn't
provide enough details to judge how seriously we should
take his change of opinion.
Next
Susskind refers to a paper by Horowitz and Maldacena, of
which he says that "The implication [14] is that if there
is any kind of universe creation in the interior of the
black hole, the quantum state of the offspring is completely
unique and can have no memory of the initial state. That
would preclude the kind of slow mutation rate envisioned
by Smolin."
I read that paper and had some correspondence with its
authors about it; unfortunately Susskind misstates its
implications. In fact, that paper does not show that there
is no loss of information, it merely assume it and proposes
a mechanism — which the authors acknowledge is speculative
and not derived from theory — that might explain
how it is that information is not lost. They do not show
that information going into baby universes is precluded,
in fact Maldacena wrote to me that "If black hole singularities
really bounce into a second large region, I also think
our proposal is false [j]."
Finally, Susskind suggests that loop quantum gravity will
be inconsistent unless it agrees with his conjectures
about black holes. I should then mention that there are
by now sufficient rigorous results (reviewed in [k])
to establish the consistency of the description of quantum
geometry given by loop quantum gravity . Whether it applies
to nature is an open question, as is what it has to say
about black hole singularities, but progress in both directions
is steady.
Let
me close with something Susskind and I agree about — which
I learned from him back in graduate school: an idea called
string/gauge duality according to which gauge fields, like
those in electromagnetism and QCD, have an equivalent description
in terms of extended objects. For Susskind, those extended
objects are strings. I believe that may be true at some
level of approximation, but the problem is we only know
how to make sense of string theory in a context in which
the geometry of spacetime is kept classical — giving
a background in which the strings move.
But general relativity teaches us that spacetime cannot
be fixed, it is as dynamical as any other field. So a
quantum theory of gravity must be background independent.
We should then ask if there is a version of this duality
in which there is no fixed, classical background, so that
the geometry of spacetime can be treated completely quantum
mechanically? Indeed there is, it is loop quantum gravity.
Moreover, a recent uniqueness theorem [l]
shows essentially that any consistent background independent
version of this duality will be equivalent to loop quantum
gravity. For this reason, I believe it is likely that,
if string theory is not altogether wrong, sooner or later
it will find a more fundamental formulation in the language
of loop quantum gravity.
Indeed,
what separates us on all these issues is the question of
whether the quantum theory of gravity is to be background
independent or not. Most string theorists have yet to fully
take on board the lesson from Einstein's general theory
of relativity; their intuitions about physics are still
expressed in terms of things moving in fixed background
spacetimes. For example, the view of time evolution that
Susskind wants to preserve is tied to the existence of
a fixed background. This leads him to propose a version
of the holographic principle which can only be formulated
in terms of a fixed background. The strong form of Maldacena's
conjecture posits that quantum gravity is equivalent to
physics on a fixed background. The approaches string theory
takes to black holes only succeed partially, because they
describe black holes in terms of objects in a fixed background.
Eternal inflation is also a background dependent theory,
indeed, some of its proponents have seen it as a return
to an eternal, static universe.
On the other hand, those who have concentrated on quantum
gravity have learned, from loop quantum gravity and other
approaches, how to do quantum spacetime physics in a background
independent way. After the many successful calculations
which have been done, we have gained a new and different
intuition about physics, and it leads to different expectations
for each of the issues we have been discussing. There
is still more to do, but it is clear there need be —
and can be — no going back to a pre-Einsteinian
view of space and time. Anyone who still wants to approach
the problems of physics by discussing how things move
in classical background spacetimes — whether those
things are strings, branes or whatever — are addressing
the past rather than the future of our science.
________________________
[a]
Lee smolin, Scientific Alternatives to the Anthropic
Principle, hep-th/0407213.
[b] Leonard Susskind, Cosmic natural selection,
hep-th/0407266
[c] E. Hawkins, F. Markopoulou, H. Sahlmann, Evolution
in Quantum Causal Histories,
hep-th/0302111.
[d] In particular, global unitarity is automatically present
whenever there is a global time coordinate, but need not
be if that condition is not met. Quantum information accessible
to local observables is propagated in terms of density
matrices following rules that conserve energy and probability,
because a weaker property, described in terms of completely
positive maps, is maintained.
[e] G.J. Milburn, Phys. Rev A44, 5401 (1991).
[f] Rodolfo Gambini, Rafael Porto, Jorge Pullin, Realistic
clocks, universal decoherence and the black hole information
paradox hep-th/0406260, gr-qc/0402118 and references
cited there.
[g] L. Smolin, How far are we from the quantum theory
of gravity? , hep-th/0303185; M. Arnsdorf and L.
Smolin, The Maldacena conjecture and Rehren duality,
hep-th/0106073.
[h] This is one of several key cases in which conjectures,
widely believed by string theorists, have not so far been
proven by the actual results on the table. Another key
unproven conjecture concerns the finiteness of the theory.
[i] F. Markopoulou and L. Smolin, Holography in a quantum
spacetime, hepth/9910146; L. Smolin, The strong and the
weak holographic principles, hep-th/0003056.
[j] Juan Maldacena, email to me, 1 November 2003, used
with permission.
[k] L. Smolin, An invitation to Loop Quantum Gravity,
hep-th/0408048.
[l] By Lewandowski, Okolow, Sahlmann and Thiemann, see
p. 20 of the previous endnote.
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