Black Holes, Decoherence and
Objective Reduction, I

Date: Sun, 6 Oct 1996 00:14:28 -0700 (PDT)
From: Lawrence B. Crowell <lcrowell@unm.edu>
 and Stuart Hameroff  <srh@ccit.arizona.edu>
To: quantum-d@teleport.com
Subject: Black Holes, Decoherence and Objective Reduction, part I

   "the two processes are in some way related..."
                              L. Crowell

Lawrence Crowell on 9/11:
A central issue for quantum biology is decoherence.  In order for a
wave function to play a real role in biological systems there must be a
mechanism that prevents the phase space volume of the quantum system
from being absorbed into the environment. At issue is the mechanism of
decoherence and the process that prevents decoherence, or "recoheres"
the system.

The Penrose-Hameroff approach invokes the role of quantum black holes
as the source of wave function collapse...

Stuart Hameroff, 9/12: It does? Where did we say that?

Lawrence Crowell:
The result dating back to Stephen Hawking is that a quantum field will
scatter off a black hole with a different value for the trace of the
square of the density matrix.  This is similar to what occurs to a wave
function with a measurement [cf. part II]...

Before passing judgement on which process is the most relevant to the
issue of quantum biology, I will first indicate that the two processes
are in some way related...

   ....So we have two models of decoherence.  One that involves black
holes and the thermodynamics of quantum fields in their environment, and
an approach that involves the breakdown of recurrence by coupling a
system to an external environment with an infinite dimensional Hilbert
space.

Stuart Hameroff:
Interaction with the environment is what Penrose denotes as R. Penrose's
objective reduction (OR) is something else again. In OR, environmental
decoherence is avoided but the system inevitably self-collapses when its
coherence (as measured by a product of its gravitational self-energy and
coherence time) reaches a certain value related to quantum gravity (E=h/T).

LC: The problem is that this value for E is given according to the Planck
mass. Now it appears to me that this approach involves self-collapse
through the interaction of a system with virtual black holes, or at
least virtual Planck scale masses. This involves the "processing" of
phase space information through the virtual black holes in the vacuum
so that the value of the trace of the density matrix squared is not
conserved. This appears to involve the role of quantum gravity super-
scattering operators. The statement by Hawking that "God not only plays
dice, but sometimes he throws them where they cannot be read" is being
invoked here.

SH: In OR, fundamental spacetime underlying the superposed, separated mass
itself separates - there is a bifurcation, or separation of spacetime
(as illustrated on page 338 of Shadows of the Mind). This separation is
an instability which "decays" to one or the other spacetime configuration.
It is not a black hole. Quantum gravity is relevant to spacetime itself.

LC: Hmmm! this appears to be some sort of quantum topology idea, where
this decay process is a sort of self collapse of the manifold to one of
the topological quantum states.

While these ideas may be quite applicable to structures on the Planck
scale I still have a difficult time seeing that this high frequency
domain is relevant to processes that half of the time involve hydrogen
bonds of a fraction of an ev. It would be as if a virtual glue ball
structure predicted by lattice QCD has something to do with the formation
of a hurricane!

SH: The spacetime separation in OR *is* in the Planck scale of 10^-33 cm
(no black holes up our sleeves)...

This is discussed in Hameroff and Penrose, 1996 (on the web):

     "It should be made clear that this measure of separation is only very
 schematically illustrated as  the "distance" between the two [separated
 spacetime] sheets in the lower diagram in Figure 1. As remarked above,
 there is no physically existing "ambient higher dimensional space" inside
 which the two sheets reside. The degree of separation between the space-
 time sheets is a more abstract mathematical thing; it would be more
 appropriately described in terms of a symplectic measure on the space
 of 4-dimensional metrics (cf. Penrose, 1993) - but the details (and
 difficulties) of this will not be important for us here. It may be noted,
 however, that this separation is a space-time separation, not just a
 spatial one. Thus the time of separation contributes as well as the
 spatial displacement. Roughly speaking, it is the product of the temporal
 separation T with the spatial separation S that measures the overall
 degree of separation, and OR takes place when this overall separation
 reaches the critical amount. [This critical amount would be of the order
 of unity, in absolute units, for which the Planck-Dirac constant h bar
 (=h/2pi), the gravitational constant G, and the velocity of light c all
 take the value unity (cf. Penrose, 1994 pp. 337-39).] Thus for small S,
 the lifetime T of the superposed state will be large; on the other hand,
 if S is large, then T will be small."

LC: To be honest I will have to look more closely at the logic here, but
it appears as if the phase space of a quantum system is being processed
through a virtual quantum gravity fluctuation.

SH and RP:

"To calculate S, we compute (in the Newtonian limit of weak gravitational
 fields) the gravitational self-energy E of the difference between the mass
 distributions of the two superposed states.

 (That is, one mass distribution counts positively and the other,
 negatively; see Penrose, 1994; 1995.)

 The quantity S is then given by:

 S= E h^-1

 Thus

 T=h E^-1"

LC: This is just the Heisenberg uncertainty principle centered around a
virtual Planck mass.



Go to part II.



References

Hawking, S., Comm. Math. Phys. 43 (1975), 199

Hameroff, S.R., and Penrose, R., (1996) Conscious events as orchestrated
spacetime selections, Journal of Consciousness Studies 3(1):36-53
http://www.u.arizona.edu/~hameroff/penrose2.html

Penrose, R. (1993) Gravity and quantum mechanics. In General Relativity
and Gravitation. Proceedings of the Thirteenth International Conference
on Genera Relativity and Gravitation held at Cordoba, Argentina 28 June-4
July 1992. Part 1: Plenary Lectures. (eds. R.J. Gleiser, C.N. Kozameh
and O.M. Moreschi) Institute of Physics Publications, Bristol.

Penrose, R. (1994) Shadows of the Mind. Oxford Press

Penrose, R. (1995) On gravity's role in quantum state reduction