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[Phys-l] Top Down Cosmology




Top Down Cosmology


Cosmological theories on the origin of the Universe fall into two broad
categories. The top down verses the bottom up models. Most cosmological
models fall into the bottom up category while the Hawking-Hertog-Hartle no
boundary model is a version of a top down model. Even if the no boundary model
is incorrect in detail the broader question stands on what choice we
should make, top down or bottom up.


In Bottom up models we postulate some initial state, a boundary
condition, and then evolve the Hamiltonian forward in time. This is of course is
quite problematic in cosmology, we have only one Universe to observe, we can't
experiment with different boundary conditions.

However, as Hawking argues this approach makes no sense from very some
basic considerations We have good reason to believe that nature has a
fundamental Quantum nature. The origin of the Universe is a Quantum event, which
means it can be described by the Feynman Sum Over Histories. The Universe
doesn't have just a single history, but every possible history. As Hawking
points out, some people makes a great mystery of the multiverse and the many
worlds interpretation of Quantum theory, but these are the same, just
different expressions of the Feynman path integral.

In the no boundary model this path integral is expressed by the sum over
paths over every possible Euclidean four space.


Y[ g_4,phi] = int Dg_4 Dphi exp -S_e[g_4,phi]


Where the Euclidean action is

S_e= -(1/2)*int d^4xsqrt[g_4]*{R+L(g_4,phi0} - int {S} d^3X sqrt[g_3]*K



In M Theory however, low energy particle physics is determined by the
topology of the internal space, generally though to be characterized as Calabi
Yau manifold. Based on the assumptions that all histories are possible we
might argue that the path integral should not be limited to four space
topologies. We might rewrite the path integral to reflect this.

Y[ g_N,phi] = int Dg_N Dphi exp -S_e[g_4,phi]





S_e= -(1/2)*int d^Nxsqrt[g_4]*{R+L(g_N,phi0} - int {S} d^N-1 X
sqrt[g_n-1]*K

Here N is the number of Euclidean space dimensions

This suggest a Universe of enormous possibilities. Based on the work of
Dowker and Kent we might assert that these possibilities reflect a huge number
of quasi classical realms, one of which is our own classical Universe. We
exist in the realm we do because the coarse grained histories of our realms
has a structure that allows being like us to exist. Perhaps many other
realms also allow life and intelligent beings, we can only guess about this
possibility. Therefore we have the set of all quasi classical realms, which
in turn are themselves sets of all possible Decoherent histories. The set of
all quasi classical realms would be the notorious set of all sets.

The Universe we observe would then be "merely" one particular set of
Decoherent histories in one particular quasi classical realm, that is of one
vacua Eigenstate. If any of this true this raises the unsolved Eigenstate
selection problem by at least an order of magnitude.

How do these quasi classical realms emerge from the Quantum State of the
Universe? Normally classical physics results from the process of Decoherence
where the interference terms of the wave function are delocalized into the
environmental states. But in the case of the Universe there is no external
system to serve as environmental states.



However, if we think carefully what Decoherence means we can answer this
question. What is happening in the Decoherence process is that information
is being lost into the environment. It's the practical impossibility of
observing the fine grained history of the entangled environmental states that
coarse grains the Quantum history to give us probabilities of ignorance.
Decoherence is all about the loss of the ability to observe, or actually never
having had, as a IGUS, the ability to observe a fine grained history.
Therefore the reason we observe classical behavior at all is because we can only
see part of the Universe. This is the same way black holes and
accelerating systems Decohere the vacuum Quantum State.


If this makes sense it paints an almost surrealistic picture of reality.
Common sense is far removed from this picture of the nature of reality. In
addition, if this true, it means we may always have vast gaps in our
understanding of the entire realm of reality, or should I say entire realms.

Bob Zannelli