On Wednesday, June 13, 2018 at 6:30:27 PM UTC-5, Jason wrote:
>
>
> Physical Theories, Eternal Inflation, and Quantum Universe
> <https://arxiv.org/abs/1104.2324>, Yasunori Nomura
>
> We conclude that the eternally inflating multiverse and many worlds in
> quantum mechanics are the same. Other important implications include:
> global spacetime
> can be viewed as a derived concept; the multiverse is a transient
> phenomenon during the
> world relaxing into a supersymmetric Minkowski state. We also present a
> theory of “initial
> conditions” for the multiverse. By extrapolating our framework to the
> extreme, we arrive at a
> picture that the entire multiverse is a fluctuation in the stationary,
> fractal “mega-multiverse,”
> in which an infinite sequence of multiverse productions occurs.
>
> "Therefore, we conclude that the multiverse is the same as (or a specific
> manifestation
> of ) many worlds in quantum mechanics."
>
> "In eternal inflation, however, one first picks a causal patch; then one
> looks for observers in it.” Our framework does not follow this approach. We
> instead pick an observer first, and then construct the relevant spacetime
> regions associated with it.
>
> Instead of admitting the existence of the “beginning,” we may require that
> the quantum observer principle is respected for the whole history of
> spacetime. In this case, the beginning of our multiverse is a fluctuation
> of a larger structure, whose beginning is also a fluctuation of an even
> larger structure, and this series goes on forever. This leads to the
> picture that our multiverse arises as a fluctuation in a huge, stationary
> “megamultiverse,” which has a fractal structure."
>
>
> The Multiverse Interpretation of Quantum Mechanics
> <https://arxiv.org/abs/1105.3796>, Raphael Bousso and Leonard Susskind
>
> In both the many-worlds interpretation of quantum mechanics and the
> multiverse
> of eternal inflation the world is viewed as an unbounded collection of
> parallel universes.
> A view that has been expressed in the past by both of us is that there is
> no need to
> add an additional layer of parallelism to the multiverse in order to
> interpret quantum
> mechanics. To put it succinctly, the many-worlds and the multiverse are
> the same
> thing [1].
>
>
> Jason
>
My tendency is to say no. The type II multiverse, Vilenkin bubbles etc, I
tend not to think is somehow equivalent to the MWI. I dislike the prospect
that cosmology is somehow equivalent to a particular quantum
interpretation. Quantum interpretations are not empirically verifiable and
tend in some ways to be more metaphysics meant to make quantum nonlocal
strangeness somehow sensible within our intuitive grasp on reality. This
might however have something to do with type I multiverse. I will discuss
the type II multiverse first.
The Speaker of the House of Representatives in the 1980s Tip O'Neil said
that all politics is local. In physics we may have a similar situation; all
physics is local. Maybe it is better to put this as all causal principles
are local. There are reasons to suspect this might be the case. General
relativity itself has a funny relationship with energy; it is not
localizable in general.
The Hamiltonian constraint in general relativity H = 0 leads to a
Schrödinger-like equation HΨ[g] = 0 for quantum gravity where the term
i∂Ψ[g] /∂t is absent or zero. We may write this as K_tΨ[g] = 0 for K_t a
Killing vector. This says the Killing vector along timelike directions is
in general zero or does not exist. This means there is no Noetherian
principle for a conservation law of energy. In general relativity
conservation laws are due to the imposition of symmetries on the structure
of spacetime that are in addition to the local Lorentz symmetry.
This may also be seen with a Gauss' law argument. If you have a spacetime
with an even distribution of mass-energy or galaxies it is not possible to
establish a Gaussian surface to evaluate the mass-energy content of the
manifold. For solutions such as type D solutions for black holes the
solution has an asymptotically flat region where such an evaluation may be
made.
This carries over to a multiverse situation. The eternal inflation of
Vilenkin et al posits a manifold with a large vacuum energy density on any
local frame, where the vacuum collapses into low energy configuration and
there is a bubble in this inflationary region. It is possible to think of
this bubble percolating into its own spacetime manifold, but from the
perspective of any observer in this bubble it does not matter if this
bubble is Swiss cheese bubble in the inflationary manifold or if it is a
closed spacetime region that pops off the inflationary manifold. This may
happen if the physical vacuum in the bubble is sufficiently small that
there can't be any causal interaction across it. In this setting the
boundary of the Swiss cheese bubble propagates no information to the
interior. This means there is then no casual information and thus no
Killing vector K_t that propagates anything from the boundary or beyond to
the interior.
If you have a Swiss-cheese multiverse with low vacuum energy bubbles that
form that if the boundary of that bubble is receding away fast enough it
will not propagate information into the interior. This means there is no
geometric or topological information on the boundary that is relevant to
the physics in the interior. Such a bubble is then equivalent to a
spacetime with no topological boundary defined according to time. In other
words this recovers the Hartle-Hawking no-boundary condition. Physically
this means there is an inflationary spacetime with a very large vacuum
energy that frame drags points away with an acceleration g ~ c^2/ℓ_p =
c^3sqrt{c/Għ}, which means the boundary is being accelerated away at this
Planck acceleration. For there to be a bubble with a boundary that
accelerates at this rate it means the accelerated expansion in that bubble
must be small enough so that no quantum information from the boundary
reaches the interior. The accelerated expansion with the scale factor a =
a_0 exp(t sqrt{3/Λ}) is such that the accelerated expansion of the bubble
region is
ä = (3/Λ)a = (3/8πGρ)a
is such that any Planck unit of information on the cosmological horizon
(not this boundary) reaches the interior stretched to a wavelength
comparable to the radius of the region in the cosmological horizon. In this
way the no-boundary condition of Hartle and Hawking can occur in a bubble
with a boundary. The Swiss-cheese bubble and the boundary-less spacetime of
Hartle and Hawking are equivalent.
This can serve as a selection mechanism. Physical cosmologies are those
with a sufficiently small physical internal vacuum energy the HH
no-boundary condition holds for a bubble. This would then mean the other
cosmologies are virtual off-shell fluctuations that are not strictly
observable. Whether this reduces the system to the one spacetime cosmology
we observe or to some limited number, say defined in decoherent sets etc,
is uncertain. However, just as with the e-e^+ system there is this quantum
region that connects things, which is the inflationary physics. This then
does mean the type II multiverse connects with quantum strangeness, but I
hesitate this is the same as the MWI.
The type I multiverse is a bit different, and in some ways more prosaic.
This is just a case of where the spatial surface of cosmology is large
enough (infinite?) that it contains duplicate copies of the local world we
observe. We might think of the flat spatial surface as form of the 3-torus,
where if one can extend out far enough you reach back into the region you
left. This would be potentially a form of the Poincare dodecahedral space
for the universe. This region is big enough and expanding at a rate such
that no causal information can ever propagate from one cell to the next.
Under those conditions it could be the cells of this torus, or g = 2 double
torus for the Poincare dodecahedral space, are quantum superpositions of
each other. I make no theory along these lines (as yet), but a quantum MWI
sort of interpretation might work in this setting.
LC
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