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[Phys-l] Induced Gravity, Decoherence and Causal Horizons





Induced Gravity, Decoherence and Causal Horizons


Jacobson writes;


"When one thinks of entropy as missing information , it seems rather
natural for an event horizon to have associated entropy, since a horizon
certainly hides information. But what is the nature of this missing
information, and why does classical General Relativity know about it? In this essay I
will recap what is known about this puzzle, including some very recent
developments, I will argue that all indications point to the following answer :
the missing information is that contained in correlations between quantum
field fluctuations inside and outside the horizon, and the reason that
classical General Relativity knows about this is that gravitational dynamics is
governed by an action that is "induced" by those same quantum
fluctuations, as suggested originally by Sakharov."

End quote



The merging of the Holographic principle and gravity as an effect induced
by the collective action of the zero point fluctuation of quantum fields,
may represent a promising approach to the problem of how do we reconcile
gravity with the quantum. Vlatko Vedral writes in his article " Living in a
quantum World"


An even more interesting possibility is that Gravity is not a force in its
own right but the residual noise emerging from the quantum fuzziness of the
other forces of the Universe. This idea on induced gravity goes back to
the nuclear physicist and Soviet dissident Andrei Sakharov in the 1960's. If
true, it would not only demote gravity from the status of a fundamental
force but also suggest that efforts to "quantize" Gravity are misguided.
Gravity may not even exist on the Quantum level."

End Quote

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Black Hole Entropy and Induced Gravity
Authors: _Ted Jacobson_
(http://arxiv.org/find/gr-qc/1/au:+Jacobson_T/0/1/0/all/0/1)
(Submitted on 19 Apr 1994)

Abstract: In this short essay we review the arguments showing that black
hole entropy is, at least in part, ``entanglement entropy", i.e., missing
information contained in correlations between quantum field fluctuations
inside and outside the event horizon. Although the entanglement entropy depends
upon the matter field content of the theory, it turns out that so does the
Bekenstein-Hawking entropy $A/4\hbar G_{ren}$, in precisely the same way,
because the effective gravitational constant $G_{ren}$ is renormalized by
the very same quantum fluctuations. It appears most satisfactory if the
entire gravitational action is ``induced", in the manner suggested by Sakharov,
since then the black hole entropy is purebred entanglement entropy, rather
than being hybrid with bare gravitational entropy (whatever that might
be.)


_http://arxiv.org/PS_cache/gr-qc/pdf/9404/9404039v1.pdf_
(http://arxiv.org/PS_cache/gr-qc/pdf/9404/9404039v1.pdf)


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Even more interesting perhaps, is that we may be able to generalize this
connection between horizons and total entropy for all possible metrics as
suggested by the paper below. If we could somehow formulate a density
matrix for our entire causal patch of space time we might be able to write:

-k*{[ rho_U*ln[rho_U]} = pi*c^5/(hbar*G*H^2) =S_unv

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Horizon Entropy
Authors: _Ted Jacobson_
(http://arxiv.org/find/gr-qc/1/au:+Jacobson_T/0/1/0/all/0/1) , _Renaud Parentani_
(http://arxiv.org/find/gr-qc/1/au:+Parentani_R/0/1/0/all/0/1)
(Submitted on 25 Feb 2003)

Abstract: Although the laws of thermodynamics are well established for
black hole horizons, much less has been said in the literature to support the
extension of these laws to more general settings such as an asymptotic de
Sitter horizon or a Rindler horizon (the event horizon of an asymptotic
uniformly accelerated observer). In the present paper we review the results
that have been previously established and argue that the laws of black hole
thermodynamics, as well as their underlying statistical mechanical content,
extend quite generally to what we call here "causal horizons". The root of
this generalization is the local notion of horizon entropy density.
Comments: 21 pages, one figure, to appear in a special issue of
Foundations of Physics in honor of Jacob Bekenstein Subjects: General
Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th)
Journal reference: Found.Phys. 33 (2003) 323-348 Cite as:
_arXiv:gr-qc/0302099v1_ (http://arxiv.org/abs/gr-qc/0302099v1)





_http://arxiv.org/PS_cache/gr-qc/pdf/0302/0302099v1.pdf_
(http://arxiv.org/PS_cache/gr-qc/pdf/0302/0302099v1.pdf)

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This highlights the interesting possibility that in our Universe our
observation of apparently non local correlation between the evolution of the
Hubble parameter ( Referenced by the common co moving frame established by
the Big Bang) and local energy processes throughout the causal patch of space
time we live in, may relate to causal horizon ability to serve as the
coarse graining process that gives us our classical Universe.

Susskind and Bousso argue in;


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The Multiverse Interpretation of Quantum Mechanics
Authors: _Raphael Bousso_
(http://arxiv.org/find/hep-th/1/au:+Bousso_R/0/1/0/all/0/1) , _Leonard Susskind_
(http://arxiv.org/find/hep-th/1/au:+Susskind_L/0/1/0/all/0/1)
(Submitted on 19 May 2011 (_v1_ (http://arxiv.org/abs/1105.3796v1) ), last
revised 22 Jul 2011 (this version, v3))

Abstract: We argue that the many-worlds of quantum mechanics and the many
worlds of the multiverse are the same thing, and that the multiverse is
necessary to give exact operational meaning to probabilistic predictions from
quantum mechanics.
Decoherence - the modern version of wave-function collapse - is subjective
in that it depends on the choice of a set of unmonitored degrees of
freedom, the "environment". In fact decoherence is absent in the complete
description of any region larger than the future light-cone of a measurement
event. However, if one restricts to the causal diamond - the largest region that
can be causally probed - then the boundary of the diamond acts as a
one-way membrane and thus provides a preferred choice of environment. We argue
that the global multiverse is a representation of the many-worlds (all
possible decoherent causal diamond histories) in a single geometry.
We propose that it must be possible in principle to verify
quantum-mechanical predictions exactly. This requires not only the existence of exact
observables but two additional postulates: a single observer within the
universe can access infinitely many identical experiments; and the outcome of
each experiment must be completely definite. In causal diamonds with finite
surface area, holographic entropy bounds imply that no exact observables
exist, and both postulates fail: experiments cannot be repeated infinitely many
times; and decoherence is not completely irreversible, so outcomes are not
definite. We argue that our postulates can be satisfied in "hats"
(supersymmetric multiverse regions with vanishing cosmological constant). We
propose a complementarity principle that relates the approximate observables
associated with finite causal diamonds to exact observables in the hat.

_http://arxiv.org/PS_cache/arxiv/pdf/1105/1105.3796v3.pdf_
(http://arxiv.org/PS_cache/arxiv/pdf/1105/1105.3796v3.pdf)



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Susskind and Bousso write:

Decoherence has two important limitations: it is subjective, and it is
in principle reversible. This is a problem if we rely on Decoherence for
precise tests of Quantum mechanical predictions. We argue in section 2 that
causal diamonds provide a natural definition of environment in the
multiverse , leading to an observer independent notion of decoherent histories.

End Quote



Bob Zannelli