Re: Black holes and decoherence

Date: Fri, 13 Sep 1996 00:27:48 -0700 (PDT)
From: Andrew Matacz <andrewm@maths.su.oz.au>
To: quantum-d@teleport.com
Subject: Re: Black holes and decoherence


Lawrence Crowell:
"To conclude it should be more reasonable to treat the issue of wave function
collapse as a process where a measurement apparatus or environment couples
into a quantum system with a finite number of states.  The result is that the
recurrence of the finite system is prevented and the system is reduced to
a single state.  This is true if we are talking about coupling a system to a
vacuum with an infinite number of unoccupied modes.  The result is spontaneous
emission.  The other environmental impact is that of thermal noise.  This
more "accessible physics" approach is far more likely to succeed than positing
quantum black holes and spacetime foam as the source of collapse."

Andrew Matacz:
Lawrence Crowell has suggested that a successful theory of quantum biology
is much more likely to emerge if we focus on thermal environmental decoherence
mechanisms rather the gravitional mechanism of Penrose. This argument appears
to use the two  mechanisms of decoherence interchangebly which is dangerous.
A common misconception regarding environmental decoherence is that the
environment objectively destroys quantum coherence. This misconception comes
from taking a density operator, which provides the statistical information
required to calculate ensemble avergages, and using it to make statements
about actual "happenings" of individual members of an ensemble. Environmental
decoherence explains the quantum-to-classical transition of an ensemble but
this does not allow us to say that an individual member of the ensemble
has objectively undergone a quantum-to-classical transition. In fact it
does not allow us to say anything about an individual system unless we also
specify how the environment is to be monitored. This leads into the concept
of quantum trajectories used in quantum optics.

This point is explained in detail in an excellent article by H.J  Carmichael
in "Quantum Optics VI" ed. J.D. Harvey and D.F. Walls.

He illustrates the point quite dramatically by showing how a decohered
classical ensemble can be constructed out of individual systems that show
macroscopic quantum coherence. This is in stark contrast to the gravitational
induced reduction mechanism of Penrose which applies to an individual system
and does objectively describe the quantum-to-classical transition of an
individual system.

I think its useful to distinguish between a field of quantum biology
and an explanation of consciousness. Penrose and hameroff wish to explain
consciousness and this is the reason, quite reasonably I beleive, that
they introduce new physics. However if a field of quantum biology is to
emerge we only have to show that important quantum effects do exist in
biological systems. It is then perfectly clear that for this limited aim
we do not need to worry about any new physics. The value of Penrose and
Hameroff's work then becomes in identifying a possible site for quantum
effects.

The critical issue then becomes how do biological systems avoid
environmental quantum decoherence? It will be impossible for quantum
biology to be a serious subject unless this is addressed theoretically
or observed experimentally.

I have worked on environmental decoherence considerably as a PHD student
and now as a research fellow and thus I have been an interested observer
of these new ideas in biology. The vast majority of the work done to date
on environmental decoherence is based on the Quantum Brownian Motion
paradigm of non-equilibrium statistical physics. This paradigm successfully
describes quantum dissipation in a very large range of problems. Most work
is based on the simplest models in which the environment is described as
having an ohmic spectral density (which generates white noise at high
temperatures). These models shows clearly that decoherence occurs very
quickly at room temperatures. A very small amount of work has studied the
more complex type of environments characterized as having what are known
as "supra-ohmic" (colored noise) environments. Interestingly this class of
environment induces very little decoherence. I recently attended a workshop
on quantum dissipation. Present were some quantum chemists and biophysicist
who study the dissipation on biological molecules induced by the biological
environment. As is normal the damping induced by the cellular environent is
modelled within the quantum brownian motion paradigm. They use complex
molecular simulations to derive an effect spectral density of the medium.
>From what I learned there was nothing to suggest that the cellular environ-
ments were "supra-ohmic". They were very skeptical of any possibility of
mesoscale quantum effects.

Penrose and Hameroff have suggested some novel mechanisms that may shield
microtubules from the noisy environment. This may be partially true but I
doubt if its possible to completely shield the microtubules from noise and
we know that decoherence requires very little noise to occur. If mesoscopic
quantum coherence is to occur in biology I think it will be necessary for
the system (eg microtubules) to operate in a highly non-linear regime where
quantum coherence is continously generated, hopefully at a rate strong
enough to not be entirely lost to quantum decoherence effects. This may
well require some form of strong pumping. In these regimes it would be
necessary to consider system-environment couplings, used in the quantum
brownian motion models, that are non-linear in the system variable. It is
interesting to note that as far as I know there have been no detailed
studies of quantum decoherence outside of the linear coupling models.
Relaxing this assumption may give some unexpected and interesting results.

To conclude a serious study of quantum coherence in biophysics will require
a very careful application of the principles of non-equilibrium quantum
statistical physics. This is never a simple matter when done properly.
One must bear in mind that we want to be able to demonstate that mesoscopic
quantum decoherence can be robust against environmental fluctuations. As
discussed above decoherence can be very sensitive to the nature of the
environmental spectral density used. This in turn determines the spectrum
of the environmental fluctuations. It is dangerous and usually wrong to
simply impose white noise fluctuations and local damping. Some people may
be tempted to dismiss Penrose and Hameroffs ideas very quickly because of
environmental decoherence. However our understanding of this area of physics
is limited to the simplest of models and therefore too incomplete to be
able to do this.

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Andrew Matacz 	               ARC Research Fellow
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School of Mathematics          Phone(office):+61 2 9351 5788
and Statistics,	               Fax: +61 2 9351 4534
University of Sydney,          Phone(home):+61 2 9950 9821
NSW 2006, Australia            Email: andrewm@maths.su.oz.au
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