The Brain, the Nernst Equation, Quantum DNA Computing and Objective Reduction
Italo Vecchi
email: vecchi@weirdtech.com
In this paper a model for brain processes is proposed and some possibly relevant phenomena are
pointed out.
Brain Processes and Quantum DNA computing
The most influential model for brain processes is probably the tubulin-based Hameroff-Penrose model
[13], where the brain is construed as an algorithmic quantum devices. An alternative possiblity is that
the brain be rather a diffused biological quantum device, not unlike a DNA computers. In DNA
computing the strand carrying the solution emerges from the random interaction of a multitude of
DNA strands and is endowed with physical properties enabling the observer to sieve it out and
access the information it carries.The crucial aspect of DNA computing is its irreversiblity. Unlike
classical computers, which implement fundamentally reversible processes, DNA devices harness the
entropy increase due to the random motion and binding of the DNA strands. It is worth pointing out
that entropy increase characterises quantum computers too, where the amplification process depends
on reduction of the state vector induced by a measurement, as in Shor‟s algorithm, where the
desirable perodicity on the first register is induced by an entropy increasing measurement on the
second register. Irreversiblity appears to play a crucial role both in quantum and DNA computers.
Sketching a model of the brain one can just replace DNA strands with molecular superpositions,
where the chemical configuration encoding the solution of a problem results from one of a multitude
of molecular quantum evolution paths and is then picked out by the observer. It is worth pointing out
that that neither this tentative model nor the already functioning DNA computers comply with the
„predictabilty sieve“ of decoherence theory [14]. The system is an inscrutable black box, a boiling pot
from which the solution is sieved out just at the end, beyond any local observer‟s capability to track
its evolution.
The main problem in this setting is that of identifying the solution, i.e. that of detecting the presence of
a small amplitude. In DNA computing the strands carrying the solution can be sieved out because they
are longer than the others, but in quantum processes picking out the interesting amplitudes is the
hard part. In this regard one may consider some chemical phenomena in chemistry that can be
interpreted in terms of macroscopic superpositions. As pointed out in [1], solubility products and
complexation constants are routinely and effectively used at dilutions far below the single-ion
threshold. In particular the Nernst formula for ion-selective electrodes fits measured data at calculated
sub-single-ion concentrations. One may construe the brain as a DNA quantum device where neurons
act as selective electrodes sieving out information-carrying molecular amplitudes
Electrochemical high dilutions
The analogy between the persistence of Nerstian response in high dilution electrochemistry and the
results by Jacques Benveniste and his team on basophils‟ degranulation ([6]) was pointed out by
Henry Bauer in [3]. In [3] the "unreasonable accuracy " of standard formulations of the solubility
product and of complexation constants even at levels where no ions or molecules can be present is
documented across different analytical techniques. Indeed concentration below the Avogadro
threshold appear routinely in chemical calculations (see e.g. 7.4 in [11]). An remarkable instance of
this phenomenon is the validity of the Nerst equation relating the electrodes potential to the the
reactants´ concentration even at dilutions where the calculated probability of any reactant´s ion being
localised in the sample is far below one, as reported by Dick Durst in [1], based on previous work ([7},
see also [5] and the references therein).
In the setting of of ion-selective membrane electrodes the Nernst equation relates the equilibrium
electrode potential E to the concentration A of the free ions in the sample solution
E= E°+ 59.16/n ln A
where E° is the standard potential and n is the ion´s charge. The Nerst formula applies continuously to
potential differences for which one of the two species is present in the samples in amounts far below a
single atom. The results in [1] refer to ion-selective silver sulfide membrane electrodes where the silver
electrode is immersed in a reference solution separated from the sample solution by a silver sulfide
membrane, which is permeable only to silver ions. At equilibrium the potential across the membrane
will prevent movement of silver ions , so that the measured potential corresponds to a specific amount
of silver ions in the sample solution.
The experimental evidence for Nerstian response at concentrations below the Avogadro threshold
appears to be well-established, while the theoretical issues behind it appear to be controversial (see
[5],[2],[3]).
Measured Potential vs. Calculated pAg
800
600
400
Potential, mV
200
0
-200 0 5 10 15 20 25 30
-400
-600
-800
-1000
pAg
In Figure 9 in [7] , reproduced in [1] and sketched above , the response of a silver sulfide solid-state
membrane electrode is plotted. The electrode‟s response turns out to be Nernstian down to molar
concentrations of 10E-25 of silver ion on a sample volume of 5 microliters. The activity of silver ions
are calculated from the solution's molar composition, which in the case associated with the lowest free
silver concentration consists of 0.1 Na_S + 1 Na_OH. The silver ion concentrations in the table are
obtained using the silver sulphide solubility product relating the concentration A of Ag+ (released by
the membrane) and the known concentration B = 5.5*10E-2 of S-- (released by Na2_S) in the solution.
The equation
K = 1.48*10E-51= (2 * A)E2 * B
yields the value A = 10E-24.9. This implies a probability below 10E-6 of a free silver ion being
localised in the sample. An "ad hoc" explanation for the persistence of Nerstian response at this sub-
single-ion concentration is hinted at in [1], but no concrete indication is provided. An alternative
explanatory model is proposed in [5]. In [2] the issue is discussed and contributions to the solution of
the problem are again solicited.
The model and the experimental evidence
The model proposed in [8] to explain the results by Jacques Benveniste and his team can be applied
to Nerstian response at very low concentrations, as well as to the whole issue of the efffectiveness of
standard analytical formulations at very low concentrations. which may well be interpreted in terms of
stable superpositions of states where ions are present in the solutions and states where there are no
ions. The usual objections based on ion's concentration being so low that in all likelihood no ions are
present in the sample do not apply, since no "demolition" measurement (à la Braginsky) determining
the position of the diluted ions is performed. Diluted ions may well subsist in the sample's wave-packet
and induce physically observable effects also when their amplitude over the sample is less than one.
The probability of a ion being present in the sample is just the modulus of the amplitude of the
corresponding state in the sample's wave-packet. As long as no direct measurement of the
ion's position is made, its non-null amplitude will induce a corresponding Nernstian response. Indeed it
is unclear whether a position measurement of the free ions is possible in this setting, even in principle.
An intriguing further analogy between the biological and the electrochemical phenomena is provided
by the experimental results reported a. o. by Srinivasan et al. in [4] , where Nernstian response at low
concentrations is shown to be enhanced by stirring of the solution. According to the model expounded
here shaking the solution enhances the spread of the diluted ion‟s wave-packet and therefore
strengthens the induced response, as it appears to do both in Srinivasans‟s and in Benveniste‟s
experiments. It is not "a priori" clear how the explanatory model based on the theory of ´´coherent
domains´´ ( [9]) could be applied to the electrochemical setting.
Amplitude amplification
The Nernst equation corresponds to a theoretical model whose validity appears to persist at very low
concentrations. While in the case of basophil„s degranulation [8] little is known in detail about the
mechanisms triggering antibody detection, in this case we have a well-established model which
appears to maintain its validity at concentrations below the Avogadro threshold. In other
words the theoretical model underlying equation (1) provides us with a concrete instance of the
resonant device whose presence was conjectured in [8]. Indeed the logarithm in Nernst's formula
provides ion-selective electrodes with the the amplitude-detecting and amplitude-boosting property
that was conjectured in [8]. Ion-selective electrodes for the detection of specific antibodies have
already been developed and their sensitivity is being improved. They may yield some surprise.
Objective reduction
This paragraph is devoted to a tricky but obviously relevant issue. The criteria for quantum state
reduction are crucial problem for any model of the brain as a quantum device. Some of the models
appear to support „a la carte“ reduction, where the collapse of the wave function can be induced
either by an act of observation or by an objective physical process. In [14] Roger Penrose proposes a
gravity-based criterium for the spontaneous reduction of a superposition of two different mass
distributions A1 and A2. Simlilar criteria were proposed previously by Diosi [15].
The argument in [2] can be briefly summed up as follows. Let A be a lump of matter in a superposition
of two different localisations A1 and A2 . Penrose claims that objective reduction takes place after a
time T inversely proportional to the gravitational self-energy SE(A1, A2) of the difference between the
two lump localisations. However there appears to be an ambiguity on how the lump is to be identified.
Consider two distant objects A and B both in superpositions of different localizations A1, A2 and B1,
B2 respectively. We can consider a lump C consisting of A and B. C is then in a superposition of
C(i,j)=(Ai,Bj) with i,j=1,2. The „objective“ reduction time of C is approximately
h/(SE(A1,A2)+SE(B1,B2)). The reduction of C affects both A and B and its time depends on what is
in the lump The basic question that arises is how a lump knows that it is not part of a bigger lump with
a shorter reduction time.
A possible solution might be sought looking for a local formulation of the lump's gravitational self-
energy. However, as indeed pointed out in [14] (p. 597), there is no local expression for gravitational
energy.
The integral yielding the gravitational self-energy SE involves integration on the whole space, so that
SE is a global quantity properly defined only for the lump consisting of the whole universe, weighing
contributions from superpositions all over space. This implies that only a reduction time for the whole
universe can be determined. If it were so the implications would be perplexing, since the whole
universe would undergo state vector reduction from time to time.
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