Anna,

I strongly suggest that any interested party read the paper
http://arxiv.org/ftp/astro-ph/papers/0602/0602420.pdf as the copy below
leaves out a most interesting discussion of emergence and entanglement. And
besides the string landscape is not 10500 but rather the vastly larger
number 10^500. To wet your appetite here is a key paragraph:

"It is of interest to determine just how complex a physical system has to
be to encounter
the Lloyd limit. For most purposes in physical science the limit is too
weak to make a jot
of difference. But in cases where the parameters of the system are
combinatorically
explosive, the limit can be significant. For example, proteins are made of
strings of 20
different sorts of amino acids, and the combinatoric possibility space has
more
dimensions than the Lloyd limit of 10^120  when the number of amino acids
is greater than
about 60 (Davies, 2004). Curiously, 60 amino acids is about the size of the
smallest
functional protein, suggesting that the threshold for life might correspond
to the threshold
for strong emergence, supporting the contention that life is an emergent
phenomenon (in
the strong sense of emergence). Another example concerns quantum
entanglement. An
entangled state of about 400  particles also approaches  the Landauer-Lloyd
complexity
limit (Davies, 2005a). That means the Hilbert space of such a state has
more dimensions
than the informational capacity of the universe; the state simply cannot be
specified
within the real universe. (There are not enough degrees of freedom in the
entire cosmos
to accommodate all the coefficients!) A direct implication of this result
is the prediction
that a quantum computer with more than about 400 entangled components will
not
function as advertised (and 400 is well within the target design
specifications of the
quantum computer industry).  "

Richard

On Sun, Nov 4, 2012 at 1:20 AM, Anna <panth...@mail.com> wrote:

> **
>
>
>   **
> *The problem of what exists**
> **
> *P.C.W. Davies*
> *Australian Centre for Astrobiology, Macquarie University, New South
> Wales, Australia 2109*
> *Abstract*
> **
> **
> *Popular multiverse models such as the one based on the string theory
> landscape require an underlying set of unexplained laws containing many
> specific features and highly restrictive prerequisites. I explore the
> consequences of relaxing some of these prerequisites with a view to
> discovering whether any of them might be justified anthropically. Examples
> considered include integer space dimensionality, the immutable, Platonic
> nature of the laws of physics and the no-go theorem for strong emergence.
> The problem of why some physical laws exist, but others which are seemingly
> possible do not, takes on a new complexion following this analysis,
> although it remains an unsolved problem in the absence of an additional
> criterion.*
>
> 1. Background
> The puzzle of why the universe consists of the things it does is one of
> the oldest problems of philosophy. Given the seemingly limitless
> possibilities available, why is it the case that atoms, stars, clouds,
> crystals, etc. are “chosen” to exist in profusion in preference to, say,
> pulsating green jelly or pentagonal chain mail? A related question is why
> the entities that do exist conform to the particular physical laws that
> they do as opposed to any other set of laws one might care to imagine.
> Physicists have mostly ignored this problem, content to accept the observed
> physical systems and their specific laws as “given,” and preferring to
> concentrate on the job of elucidating them. *Notable exceptions were
> Einstein, who famously remarked that he wanted to know whether “God had any
> choice” in the nature of his creation, and Wheeler, whose rhetorical
> question “How come existence?” provided the basis for a series of
> speculative papers (Wheeler, 1979, 1983, 1988, 1989, 1993).*
>
> Recently, however, theoretical physicists and cosmologists have been
> giving increasing attention to the problem of “what exists”. In part this
> stems from the growing interest in unification, especially string/M theory,
> and the concomitant sharp disagreements about uniqueness (see, for example,
> Danielsson, 2001). *Meanwhile, the popularity of multiverse cosmological
> models has prompted a dramatic reappraisal of the very concept physical
> existence.*
> **
> The issues are clarified in Fig. 1. The picture shows three sets separated
> by two boundaries, A and B. The middle region is the set of all things that
> observers can in principle observe. *(At the moment, of course, humans
> have actually observed only a fraction of what is “out there”.)* The set
> delineated by A can be a subset of all that exists. Then there is a bigger
> set, containing the other two: the set of all that can exist. The principal
> question I shall address in this paper is how one might determine the
> location of the boundaries A and B.
>
> A common claim among string/M theorists is that A coincides with B; that
> is, the set of all that can be observed is the same as the set of all that
> exists (Danielsson, 2001). (By this, I refer to all fundamental entities
> and laws that can in principle be observed. I am excluding unique or
> unusual macroscopic objects that might be unobservable because they form
> beyond an event or particle horizon, for example.) This claim derives from
> the hope that the final unified theory will be in some sense unique, so
> that it describes a single possible world consistent with the known facts.
> A very different claim is made, however, by another group of theoretical
> physicists and cosmologists, who postulate a multiverse of different
> universes, and invoke an observer selection effect to define boundary A.
> For example, in the string theory landscape model of Susskind (2005), there
> are > 10500 possible vacuum states of the theory, each with distinct
> low-energy physics. When the landscape concept is combined with eternal
> inflation (see for example Linde, 1990), there is a mechanism to populate
> the landscape with actual universes. The vast majority of these universes
> would be inconsistent with the emergence of life and observers, and so
> would go unseen. In that case, “what is observed” is a minute subset of all
> that exists, and boundary A is defined by the criteria necessary for the
> emergence of life and observers (Barrow and Tipler, 1986). We don’t have a
> very clear idea of what those criteria are (the existence of carbon, water
> and stable stars are often cited); however, this is a purely scientific
> matter that could one day be settled.
>
> It is not my intention to review the arguments for and against the
> competing positions in regard to boundary A, since they have been
> thoroughly discussed elsewhere (see, for example, Susskind 2005). Rather I
> wish to focus the discussion on boundary B, and specifically on three
> attempts to explain it (or explain it away). Boundary B, remember,
> separates that which exists from that which is possible but in fact
> non-existent.
>
> 1. Unique universe
> The claim is sometimes made that boundary B does not exist, that is, the
> set of all that exists is the set of all that can exist. Expressed
> differently, this claim says that the universe must exist necessarily as it
> is or, to paraphrase Einstein, that “God had no choice” in its nature
> because there is only one possible world. The justification for this
> viewpoint rests on a belief that a truly unified theory of physics would
> have no free parameters, and its mathematical form would be so tightly
> constrained by logical self-consistently that it would be unique, and
> possess a unique “solution” representing the physical state of the
> universe. (There may of course be flexibility within this unique state on
> account of quantum indeterminism.)
>
> It is easy to demonstrate that the foregoing claim is false in the form
> stated. A traditional practice among theoretical physicists is to construct
> self-consistent mathematical models that are simpler than the real
> universe. For example, the Thirring model in quantum field theory,
> mini-superspace models of quantum gravity, Boltzmann gases. These models
> offer impoverished descriptions of reality, and are studied because they
> capture in some useful way a restricted feature of nature. Although they
> are not serious contenders for descriptions of the real world, nevertheless
> they describe possible worlds. And it is hard to see any limit on the
> number of different artificial mathematical models of this sort. So the
> universe quite clearly could have been otherwise in a seemingly limitless
> number of ways.
> It might be possible to establish a weaker claim: that there is a unique
> universe consistent with all current observations. The additional criterion
> seems to be implicit in discussions of uniqueness in final theories,
> although the restriction is often quietly dropped when applying it to the
> problem of boundary B. Other possible additional criteria come to mind. It
> could be that the observed universe is the uniquely simplest universe that
> is nevertheless rich enough to permit the existence of life. In that case
> boundaries A and B coincide, but it remains the case that the common
> boundary delineates only a small subset of all that can exist.
>
> 2. The best of all possible worlds
> Leibniz (1697) was among the first to recognize that the world could have
> been otherwise, that the arrangement of matter in time and space could have
> varied in an endless number of ways. He even considered the possibility of
> a multiverse containing other regions of space and time, although he
> subsumed them all under his definition of “World.” Famously, Leibniz
> claimed that ours is the best of all possible Worlds. So Leibniz recognized
> the existence of boundary B (as far as I know he made no attempt to discuss
> boundary A), and he defined it in terms of some form of optimization
> criterion. Leibniz did not mean that our universe possesses maximum
> happiness or maximum goodness among its inhabitants (as Voltaire portrayed
> in his cynical lampooning). Rather, he had in mind a mathematical criterion
> of “best”:
> “God has chosen the most perfect World, that is, the one which is at the
> same time the simplest in hypotheses and the richest in phenomena, as might
> be a line in geometry whose construction is easy and whose properties and
> effects are extremely remarkable and widespread.”
>
> Although Leibniz did not attempt to write down a mathematical quantity
> that might be optimized by the observed universe, it is not hard to think
> of candidates that could be tested. For example, one might appeal to
> algorithmic information theory to describe economy of hypotheses and to
> complexity theory to describe the richness of physical states. It remains
> an interesting challenge to mathematical physics whether the laws and 3
> initial conditions of the observed universe might in fact maximize a
> quantity of the form that Leibniz had in mind.
>
> 3. Multiverse
> On general grounds we expect our universe to be part of a multiverse, if
> one proceeds from the default assumption that the universe originated in a
> physical process. To be sure, this process remains mysterious.
> Nevertheless, if it is a law-like physical process then, by definition of
> law, it can happen more than once. Logically, that does not compel there to
> be more than one universe. For example, I believe that the origin of Paul
> Davies was a law-like physical process, but I also believe that, in a
> sufficiently bounded universe, Paul Davies would be unique. So a law-like
> process might happen only once, if there are bounds. As we know of no
> bounds in the realm of multiverse cosmology, it seems reasonable to
> contemplate a multiplicity of big bangs spawning a multiplicity of
> universes. Eternal inflation provides a concrete model for such a
> multiverse. By combining eternal inflation with string/M theory, or any
> system involving symmetry breaking via a random process, we are led
> naturally to an ensemble of alternative universes with differing low-energy
> physics.
>
> Multiverse models are arguably successful in determining boundary A, but
> the problem of boundary B remains. Although a multiverse contains a
> (possibly infinite) variety of universes, the multiverse model will
> generally not exhaust the set of all possible universes. This is easy to
> see. For example, in the case of the string theory landscape combined with
> eternal inflation, the following assumptions are made:
>
> A. The universes are described by quantum mechanics.
> B. Space has an integer number of dimensions. There is one dimension of
> time.
> C. Spacetime has a causal structure described by pseudo-Riemannian
> geometry.
> D. There exists a universe-generating mechanism subject to some form of
> transcendent physical law.
> E. Physics involves an optimization principle (e.g. an action principle)
> leading to well-defined laws, at least at relatively low energy.
> In addition to these prerequisites drawn from physics, there are certain
> more basic assumptions:
> F. The multiverse and its constituent universes are described by
> mathematics.
> G. The mathematical operations involve computable functions and standard
> logic.
> H. There are well-defined “states of the world” that have properties which
> may be specified mathematically.
> I. The basic physical laws, and the underlying principle/s from which they
> derive, are independent of the states.
> J. At least one universe contains observers, whose observations include
> sets of rational numbers that are related to the (more general)
> mathematical objects describing the universe by a specific and restricted
> projection rule, which is also mathematical.
>
> K. There is a meaningful distinction between “real” and “virtual,” or
> simulated, universes.
> Any or all of these restrictions might be relaxed, and we would still be
> dealing with possible universes. Therefore, the string theory landscape
> version of the multiverse represents only one among many possible
> multiverse models, and hence the members of the landscape multiverse – the
> 10500 or more distinct sorts of universes – legion though they may be, are
> nevertheless merely an infinitesimal restricted fraction of the totality of
> possible universes. So boundary B remains.
>
> A bold attempt to eliminate boundary B has been made by Tegmark (2003,
> 2005), who proposes that all possible universes that can exist, do exist.
> That includes universes with bizarre mathematical properties, such as
> fractal dimensions or non-Haussdorf spacetimes. Tegmark argues that the
> whole can be simpler than any of its parts, so that the set of all possible
> mathematical systems instantiated as universes might be preferable, on the
> grounds of Occam’s razor, to any of its subsets (other than perhaps the
> empty set, which we can rule out by observation). Tegmark also claims that
> the vast majority of universes in this mathematically extended set are
> inconsistent with life and observers. If so, the obvious question then
> arises of whether one may find constraints among the members of this larger
> multiverse by appeal to observer selection. That is, might some of the
> assumed properties of the universe listed above (A – K), which are taken
> almost completely for granted by most physicists, be given an anthropic
> explanation rather than simply be assumed a priori?
>
> Consider, for example, assumption A. The role of quantum mechanics is
> central to almost all multiverse models. But there is no fundamental reason
> why quantum mechanics has to apply to all possible universes. Standard
> quantum mechanics supplies a calculus for projecting from a Hilbert space
> defined over the complex field to the set of rational numbers representing
> real measurements. But there is no deeper-level law to say this is the way
> it has to happen. One could, for example, consider alternative projection
> rules. In addition, one can consider describing states in a space defined
> over different fields, such as the reals (Stueckelberg, 1960) or the
> quaternions (Adler, 1995) rather than the complex numbers. These
> alternative schemes possess distinctly different properties. For example,
> if entanglement is defined in terms of rebits rather than qubits, then
> states that are separable in the former case may not be separable in the
> latter (Caves, et. al., 2001). This raises the interesting question of
> whether there is something anthropically special about Hilbert spaces over
> the complex field, i.e. quantum mechanics as we know it. Quantum mechanics
> is normally considered peripheral to biology, but I suspect this is too
> hasty. I have suggested some lines of evidence that the emergence of life
> might depend critically on quantum mechanics (Davies, 2005), and that its
> efficient function may also exploit quantum effects (Davies 2004a). If that
> were right, quantum mechanics might not after all be isolated in the space
> of dynamical schemes, but might be anthropically selected.
>
> to continue:
>  http://arxiv.org/pdf/astro-ph/0602420v1.pdf
> * Based on a lecture delivered at the symposium “Multiverse and String
> Theory: Toward Ultimate
> Explanations in Cosmology” Stanford University, March 19-21, 2005
>
>
>
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