Stephen Hawking has always been a very independent and out of the mainstream
cosmologist. But in my opinion all too often it isn't clear just how
different Hawking's views are to other cosmologists like Linde, Steinhartdt and
others.
Most Cosmologists build their models from the bottom up. They start at the
origin and apply the laws of physics and hope the resulting evolution
produces something that looks like our Universe. But as we all know the lack of
constrain in our best theories has made this approach not all that useful.
In a recent paper by Hertog and Hawking they suggest an alternate model
building technique which takes seriously the lack of constrain but more
importantly takes seriously the quantum nature of reality. Classical physics
predicts a singularity at the origin of the Universe. But it makes no sense
trying to describe physics at the Planck scale classically. At this scale even
gravity must be described by a quantum theory. While it is true we have no
quantum theory of gravity , it seems reasonable to expect that any future QG
theory to eliminate this singularity.
Based on this , Hawking, Hartle, Turok and Hertog in various papers
suggest that above a certain energy scale we need to perform a wick rotation and
describe the physics in terms of Euclidian path integrals. This is a highly
contentious proposal as the mathematical formalism is not well settled according
to critics.
The idea here is that just as a particles path through space time is a
supposition of all possible paths , the resulting geometry of space time , the
foliation of space and time , is the result of the decoherence of the
supposition of all possible geometries and matter fields. This is expressed
mathematically as
Psi ( g^3,theta) = approx Integral ( all C) [Dg] Dtheta] exp[ i*s[g,theta]
Where Psi the probability amplitude of a three dimension geometry ,
Dg is the summation over all geometries , Dtheta is the summation over all
matter fields and S is the action term as a function of these
same geometry and matter fields.
The relationship of this model to the multiverse model isn't completely
clear. But Hawking and Hertog are very critical of the multiverse theory They
point out that the multiverse model is based on a classical description of
the history of the Universe which in a closed system is questionable based on
the fundamental quantum nature of reality. In the multiverse model you have a
unique classical history of many Universes whereas in the top down model ,
the one single Universe is described by a quantum sum over histories. Susskind
seems to be suggesting that these are really two complementary descriptions
, because he equates the MWI with the multiverse.
In any case the top down model eliminates the need for a boundary
condition at the origin thereby eliminating the problem of explaining the
beginning of the Universe , making the pre bubble inflating Universe an unnecessary
theoretical consideration. Pure quantum states in a closed systems are
static, hence the Euclidian formalism.
This is however is troubling to some cosmologists because it seems to
throw out the window a unique observer independent cosmology. But Hawking and
Hertog point that this is only true if we could stand outside the Universe ( the
bird's eye view) where we could see the present affecting the past. But
limited as we are to the Frog's eye view , we see the final state as one entire ,
causally consistent history or another ,
so from within any given history, cause and effect proceed in the usual
way.
Finally the top down model predicts a slightly different structure for the
CMB from the classical versions of inflationary theory. This is due to
difference in contributions of geometries which are significantly different from
our geometry as compared with geometries which are closer to the geometry we
see in our history. Just as in the summation of particle paths , the wildly
divergent amplitudes cancel giving us amplitudes peaked around the classical
paths. This feature of the no boundary theory predicts a different CMB
structure though only detectable at a very fine scale. The no boundary model also
predicts an easier to differentiate spectrum of gravitational waves. Hopefully
progress in the technology of measuring gravity waves will improve to the
point where this part of the top down model can be tested.
Bob Zannelli
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