Quantum Cosmology and the Hard Problem of the Conscious Brain
University of Auckland
v 1.4 © 6-8-4
The conscious brain poses the most serious unsolved problem for science at the beginning of the third millennium. Not only is the
whole basis of subjective conscious experience lacking adequate physical explanation, but the relationship between causality and
intentionally willed action remains equally obscure. We explore a model resolving major features of the so-called ‘hard problem in
consciousness research’ through cosmic subject-object complementarity. The model combines transactional quantum theory, with
chaotic and fractal dynamics as a basis for a direct relationship between phase coherence in global brain states and anticipatory
boundary conditions in quantum systems, complementing these with key features of conscious perception, and intentional will. The
aim is to discover unusual physical properties of excitable cells which may form a basis for the evolutionary selection of subjective
consciousness, because the physics involved in its emergence permits anticipatory choices which strongly favour survival.
1: Subject-Object Complementarity and the Hard Problem
In “The Puzzle of Conscious Experience” David Chalmers (1995) summarizes some of the main points of his deÞnition of the now
renowned ‘hard problem in consciousness research’. He contrasts with the hard problem what he calls the ‘easy’ problems such as:
‘How can a human subject discriminate sensory stimuli and react to them appropriately?’ ‘How does the brain integrate information
from many different sources and use this information to control behaviour?’ ‘How is it that subjects can verbalize their internal
states?’ Each of these deal broadly with problems of consciousness, but in ways which could in principle be resolved by straightfor-
ward functional explanations.
The ‘hard problem’, by contrast, is the question of how physical processes in the brain give rise to subjective experience. This puz-
zle involves the inner aspects of thought and perception and the way things feel for the subject - all of them subjective experiences
known only to the participant. This is much harder to resolve because trying to compare brain states, which are in principle objec-
tive and replicable, with subjective experiences, which, however rich for the experiencer, are unavailable to an external observer,
pose a severe problem of qualitative difference, which seems almost unbridgeable.
Chalmers rejects any simple resort to neuroscience explanations about brain states in solving the hard problem. He notes for exam-
ple that the 40 Hz oscillations made famous by Crick and Koch (1992) and others, which might provide an explanation for the
coherent binding together of different brain regions, for example visual and auditory into one attended perception, may explain how
the brain integrates different processing tasks (an easy problem) but don’t explain how any of these modes evoke the subjective con-
scious experiences of vision and sound. Likewise he rejects philosophical explanations such as Daniel Dennett’s (1991) ‘multiple
drafts’ theory of consciousness as an explanation of ‘how we produce verbal reports on our internal states’ (an easy problem) which
tells us very little about why there should be a subjective experience behind these reports.
Even when we proceed to theories which attempt to use new types of physics to bridge this chasm, Chalmers remains sceptical:
“Some have suggested that to solve the hard problem, we need to bring in new tools of physical explanation: nonlinear dynamics, say, or new
discoveries in neuroscience, or quantum mechanics. But these ideas suffer from exactly the same difÞculty. Consider a proposal from Stuart
R. Hameroff of the University of Arizona and Roger Penrose of the University of Oxford. They hold that consciousness arises from quan-
tum-physical processes taking place in microtubules, which are protein structures inside neurons. It is possible (if not likely) that such a
hypothesis will lead to an explanation of how the brain makes decisions or even how it proves mathematical theorems, as Hameroff and Pen-
rose suggest. But even if it does, the theory is silent about how these processes might give rise to conscious experience. Indeed, the same
problem arises with any theory of consciousness based only on physical processing.”
Following on to examine the trend in cosmology and uniÞed Þeld theories, Chalmers speculates that conscious experience may be a
fundamental feature cosmologically:
“If the existence of consciousness cannot be derived from physical laws, a theory of physics is not a true theory of everything. So a Þnal the-
ory must contain an additional fundamental component. Toward this end, I propose that conscious experience be considered a fundamental
feature, irreducible to anything more basic.”
This perception of the central nature of consciousness to the cosmological description is more acute than an academic or philosoph-
ical matter. Although the scientiÞc description is based exclusively on the objective physical universe, our contact with reality is
entirely sine que non through our subjective conscious experience. From birth to death, we experience only a stream of conscious-
ness through which all our experience of the physical world is gained. All scientiÞc experiments performed on the physical world
ultimately become validated by the subjective conscious experience of the experimenters, and the subsequent witnesses to the phe-
nomena and conclusions.
Because its subjective nature makes it unavailable to objective investigation, reductionist descriptions identify subjective conscious-
ness with functional attributes of the brain, inferring computational machines might also possess consciousness. At best in such
views, the subjectively conscious mind remains an enigma considered to be merely a passive ‘epiphenomenon’. However it is the
physical world which is secondary to our personal experience, a consensus of stable subjective representations we assemble into our
real world view. It thus remains unclear whether a physical universe without conscious observers could exist in any more than a
purely conceptual or theoretical sense. Subjective consciousness may be necessary for the actualization of physical reality, and thus
fundamental to physical existence in a cosmological sense, as expressed in the ‘anthropic cosmological principle’ that ‘observers’
are signiÞcant and possibly necessary boundary conditions for the existence of the universe (Barrow and Tipler 1988).
Of course this somewhat ‘idealistic’ view of subjectivity as a cosmic complement to the physical universe has a variety of critiques.
Our conscious experience, while it remains mysterious, appears to be an inner manifestation of a functioning brain. Knock us out
and consciousness is interrupted. The brain is a notoriously sensitive and easily damaged organ. Moreover it is a recent development
in a universe where brains are by no means a forgone conclusion, the product of an idiosyncratic process of biological evolution,
which at the surface appears to have little to do with the vast energies and forces shaping the cosmology of the universe as a whole.
Nevertheless an argument based on non-linear interactions arising from cosmic symmetry-breaking and evolutionary universality
can make the claim that the brain is accessing universal properties of a quantum nature, which may be the basis of its capacity for
The conscious mind can also be described functionally as an internal model of reality. While such an explanation does not address
the basis of subjectivity, it does help explain some of the more bizarre states of consciousness and is supported by many actively
constructive aspects of sensory processing and the modular architecture of the cerebral cortex. Such an internal model can be
described functionally in terms of dynamical brain processes which undergo unstable transitions to and from chaos (Skarda and
Freeman 1987). Dynamical resonance and phase coherence also provide direct means to solve the ‘binding problem’, how the uni-
tary nature of mind emerges from distributed parallel processing of many brain states.
A second critical property of subjective consciousness comes into play as we move from perception into volition. To quote Sir John
Eccles : “It is a psychological fact that we believe we have the ability to control and modify our actions by the exercise of ‘will’, and
in practical life all sane men will assume they have this ability” (Hooper and Teresi 1986). However this premise, which is basic to
all human action, contradicts physical determinism, because any action of mind on brain contradicts the brain functioning as a
deterministic computational machine, in its own right, in the physical world.
A conßuence between quantum physics and the science of mind may resolve this apparent paradox. Firstly physics has difÞculty
determining when collapse of the wave function from a set of probabilities into an actual choice takes place, leading to some inter-
pretations in which the conscious observer collapses the wave function. Secondly quantum uncertainty and non-locality provide
exactly the types of explanation which could enable the subjective experience of free-will to be consistent with a non-deterministic
model of brain function. The unpredictability of chaos (Stewart, Schuster) due to its ampliÞcation of arbitrarily small ßuctuations in
what is known as ‘sensitive dependence on initial conditions, could provide a means to link quantum indeterminacy to global brain
2: Wave-Particle Complementarity, Uncertainty and Quantum Prediction
Associated with the nature of quanta themselves are unreconciled problems, which share an intriguing logical homology with prob-
lem of conscious intent. To explore these we will Þrst summarize some of the core ideas of quantum reality.
If we have to Þnd the frequency of a wave using the beats we can produce by comparing it with another similar wave, without being
able to measure the exact amplitude of the wave at a given time (the actual situation in root quantum interactions), we then have let
a considerable time elapse, to gain enough beats for an accurate measurement so we don't know exactly when the frequency was at
this value. The relationship between the frequencies and the beats is: ∆υ∆t ≥ 1 , a smeared-out 2-D ‘interval’ of time and frequency
Fig 1: Measuring a wave frequency with beats has intrinsic
uncertainty as to the time
Einstein's law is a fundamental equation of quantum mechanics which connects to every ener-
getic particle a frequency E = hυ Measuring one is necessarily measuring the other. If we
apply the above together, we immediately get the Heisenberg uncertainty relation:
∆E∆t = h∆υ∆t ≥ h
Each quantum can be conceived as a particle or as a wave, but not both at the same time.
Depending on how we are interacting with it or describing it, it may appear as either. We can
visualize the interchange between particle and wave natures by generating photons and allowing them to ßow through a pair of
closely spaced slits. When many photons pass through, their waves interfere as shown and the photographic plate gets dark and light
interference bands where the waves from the two slits cancel or reinforce, because the photons are more likely to end up where their
superimposed wave amplitude is large. The experiment conÞrms the wave nature of light, since the size of the bands is determined
by the distance between the slits in relation to the wavelength where c is the velocity of light: λ
Fig 2: Two-slit interference experiment (Sci. Am. Jul 92)
We know each photon passes through both slits, because we can slow
the experiment down so much that only one photon is released at a time
and we still eventually get the interference pattern. Each photon
released from the light bulb is emitted as a particle from a single hot
atom, whose excited electron is jumping down from a higher energy
orbit to a lower one. It is thus released locally and as a single ‘particle’
created by a single transition between two stable electron orbitals, but it
spreads and passes through both slits as a wave. After this the two sets
of waves interfere as shown in Þg 2 to make bands on the photographic
The evolution of the wave is described by an equation involving rates of change of a wave function ϕ with respect to space and time.
For example for a massive particle in one dimension we have a differential equation:
+ m ⎟ ϕ = 0
For the bands to appear, each single photon has to travel through both slits as a wave. If you try to put any form of transparent detec-
tor in the slits to tell if it went through one or both, you will always Þnd only one particle, but now the interference pattern will be
destroyed. This happens even if you use the gentlest forms of detection possible, such as an empty resonant maser chamber (a maser
is a microwave laser). Any measurement sensitive enough to detect a particle alters its momentum enough to smear the interference
pattern into the same picture you would get if the particle just went through one slit. Knowing one aspect destroys the other.
At the other end of the process, the photon has to be absorbed again as a particle by an atom on the photographic plate, or some-
where else if it doesn’t career forever through empty space, something we shall deal with shortly. Where exactly does it go? The
rules of quantum mechanics are only statistical. They tell us only that the particle is more likely to end up where the amplitude of
the wave is large, not where it will actually go on any one occasion. The probability is precisely the complex square of the wave's
amplitude at any point:
P = ϕ∗ϕ
Hence the probability is spread throughout the extent of the wave function, potentially extending throughout the entire universe at
very low probabilities. Quantum theory thus describes all future (and past) states as probabilities. Unlike classical probabilities, we
cannot Þnd out more about the situation and reduce the probability to a certainty by deeper investigation, because of the limits
imposed by quantum uncertainty. The photon could end up anywhere the wave is non-zero. Nobody can tell exactly where, for a sin-
gle photon. However, each individual photon really does seem to end up getting absorbed as a particle somewhere, because we get a
scattered pattern of individual dark crystals on the Þlm at very low light intensities, which slowly build up to make the bands again.
This is the mysterious phenomenon known as reduction of the wave packet. Effectively the photon was in a superposition of states
represented by all the possible locations within the wave, but suddenly became one of those possible states, now absorbed into a sin-
gle localized atom, where we can see its evidence as a silver crystal on the Þlm. Only when there are many photons does the behav-
iour average out to the wave distribution. Thus each photon seems to make its own mind up about where it is going to end up, with
the proviso that on average many do this according to the wave amplitude’s probability distribution. So is this quantum ‘free-will’?
This situation is the subject of a famous thought experiment by Schrödinger, who invented the wave equation, called the ‘cat para-
dox’. In the cat paradox, we use an interference experiment with about one photon a second and we detect whether the photon hits
one of the bright bands to the left. If it does then a cat is killed by smashing a cyanide ßask. Now when the experimenter opens the
box, they Þnd the cat is either alive or dead, but quantum theory simply tells us that the cat is both alive and dead, each with differ-
ing probabilities - superimposed alive and dead states. This is very counterintuitive, but fundamental to quantum reality.
In the cat paradox experiment, Þg 3, the wave function remains uncollapsed, at least until the experimenter I opens the box. Heisen-
berg suggested representing the collapse as occurring when the system enters the domain of thermodynamic irreversibility, i.e. at C.
Schrödinger suggested the formation of a permanent record e.g. classical physical events D, E, or computer data G. However even
these classical outcomes could be superpositions, at least until a conscious observer experiences them, as the many-worlds theory
below suggests. Wigner's friend is a version of the cat paradox in which an assistant G reports on the result, establishing that unless
the Þrst conscious observer collapses the wave function, there will be a conscious observer in a multiplicity of alternative states,
which is an omnipresent drawback of the many worlds view. In a macabre version the conscious assistant is of course the cat.
According to the Copenhagen interpretation, it its not the system which collapses, but only our knowledge of its behavior. The
superimposed state within the wave function is then not regarded as a real physical entity at all, but only a means of describing our
knowledge of the quantum system, and calculating probabilities.
Fig 3: Varieties of forms of the ‘Cat Paradox’ experiment
This clash between subjective experience and quantum theory has lead
to much soul-searching. The Copenhagen interpretation says quantum
theory just describes our state of knowledge of the system and is essen-
tially incomplete. This effectively passes the problem back from physics
to the observer. Some physicists think the wave function never ‘col-
lapses’ - all the possibilities happen and there is a probability universe
for each case. This is the many-worlds interpretation of Hugh Everett III.
The universe then becomes a superabundant superimposed set of all pos-
sible probability futures, and indeed all pasts as well, in a smeared out
‘holographic’ multi-verse in which everything happens. It suffers from a
key difÞculty. All the experience we have suggests just one possibility is
chosen in each situation - the one we actually experience. Some scien-
tists thus think collapse depends on a conscious observer. Many worlds defenders claim an observer wouldn’t see the probability
branching because they too would be split but this leaves us either with inÞnite split consciousness, or all we lose all forms of deci-
sion-making process, all forms of historicity in which there is a distinct line of history, in which watershed events do actually occur,
and the role of memory in representing it.
Zurek (1991) describes decoherence as an inevitable result of interactions with other particles, however his theory forces the effect
as an artiÞcial parameter. Penrose in OOR, or ‘orchestrated objective reduction’, (Hameroff and Penrose 2003) singles out gravity
as the key unifying force because of its relationship with space-time, and suggests that interaction with gravitons splits the wave
function (Penrose 1989, 1994), causing reduction. Others try to discover hidden laws which might provide the sub-quantum pro-
cess, for example a particle piloted within a wave as suggested by David Bohm (1952). This has difÞculties deÞning positions when
new particles, with new quantum degrees of freedom, are created. Another approach we will explore, is the transactional interpreta-
tion, which has features of all these ideas and seeks to explain this process in terms of a hand-shaking relationship between the past
and the future, in which space-time itself becomes sexual in a quantum match-making. Key here is the fact that reduction is not like
any other physical process. One cannot tell when or where it happens, again suggesting it is part of the ‘spooky’ interface between
quantum and consciousness.
In many situations, people try to pass the intrinsic problems of uncertainty away on the basis that in the large real processes we wit-
ness, individual quantum uncertainties cancel in the law of averages of large numbers of particles. They will suggest for example
that neurons are huge in terms of quantum phenomena and that the ‘law of mass action’ engulfs quantum effects. However brain
processes are, by necessity, notoriously sensitive. Moreover history itself is a unique process out of many such ‘unstable’ possibili-
ties at each stage of the process. Critical decisions we make become watersheds. History and evolution are both processes littered
with unique idiosyncratic acts in a counterpoint to the major forces shaping the environment and landscape. Chaotic processes are
potentially able to inßate arbitrarily small ßuctuations, so molecular chaos may ‘inßate’ the ßuctuations associated with quantum
3: The Two-timing Nature of Special Relativity
We also live in a paradoxical relationship with space and time. While space is to all purposes symmetric and multidimensional, and
not polarized in any particular direction, time is singular in the present and polarized between past and future. We talk about the
arrow of time as a mystery related to the increasing disorder or entropy of the universe. We imagine space-time as a four dimen-
sional manifold, but we live out a strange sequential reality, in which the present is evanescent. In the words of the song “time keeps
slipping, slipping, slipping ... into the future”. There is also a polarized gulf between a past we can remember, the living present, and
a shadowy future of nascent potentialities and foreboding uncertainty. In a sense, space and time are complementary dimensionali-
ties, which behave rather like real and imaginary complex variables, as we shall see below.
A second fundamentally important discovery in twentieth century physics, complementing quantum theory, which transformed our
notions of time and space, was the special theory of relativity. In Maxwell’s classical equations for transmission for light, light
always has the same velocity, c regardless of the movement of the observer, or the source. Einstein realized that Maxwell's equa-
tions and the properties of physics could be preserved under all intertial systems - the principle of special relativity - only if the
properties of space and time changed according to the Lorenz transformations as a particle approaches the velocity of light c :
– ( Ú
= --------------, y′ = y, z′ = z,
t′ = --------------
1 – v2 Ú c
1 – v2 Ú c
Space becomes shortened along the line of movement and time becomes dilated. Effectively space and time are each being rotated
towards one-another like a pair of closing scissors. Consequently the mass and energy of any particle with non-zero rest mass tend
to inÞnity at the velocity of light: m = --------------
1 – v Ú c
By integrating this equation, Einstein was able to deduce that the rest mass must also correspond to a huge energy E
could be released for example in a nuclear explosion, as the mass of the radioactive products is less than the mass of the uranium
that produces them, thus becoming the doom equation of the atom bomb. General relativity goes beyond this to associate gravity
with the curvature of space-time caused by mass-energy.
In special relativity, space and time become related entities, which form a composite four dimensional space-time, in which points
are related by light-cones - signals travelling at the speed of light from a given origin. In space-time, time behaves differently to
space. When time is squared it has a negative sign just like the imaginary complex number i =
Hence the negative sign in the formula for space-time distance ∆S = x + y + z – c t and the scissor-like reversed rotations of
time and space into one another expressed in the Lorenz transformations. Stephen Hawking has noted that if we treat time as an
imaginary variable, the space-time universe could become a closed ‘manifold’ rather like a 4-D sphere, in which the cosmic origin
is rather like the north pole of Earth, because imaginary time will reverse the above negative sign and give us the usual Pythagorean
distance formula in four dimensions.
Space-time light cone permits linkage of ‘time-like’ points connected by slower-then-light communication. In the
‘space-like’ region, temporal order of events and causality depends on the observer.
A signiÞcant feature of special relativity is the fact that the relativistic energy-momentum equation
E2=p2+ m2 has dual energy solutions: E = ±( p + m )
The negative energy solution has reversed temporal direction. Effectively a negative energy anti-particle
travelling backwards in time is exactly the same as a positive energy particle travelling forwards in time
in the usual manner. The solution which travels in the normal direction (subsequent points are reached
later) is called the retarded solution. The one which travels backwards in time is called the advanced solution. A photon is its own
anti-particle so in this case we just have an advanced or retarded photon.
Fig 4: Quantum electrodynamics: (a,b) Two Feynman diagrams in the repulsion of two electrons. In
the Þrst a single virtual photon is exchanged between two electrons, in the second the photon
becomes a virtual electron-positron pair during its transit. All such diagrams are integrated together
to calculate the strength of the electromagnetic force. (c) A similar diagram shows how neutron
decay occurs via the W- particle of the weak nuclear force, which itself is a heavy charged photon.
(d) A time reversed electron scattering is the same as positron creation and annihilation.
4: Reality and Virtuality: Quantum Þelds and Seething Uncertainty
The theories describing force Þelds such as electromagnetism through the interaction of
wave-particles are the most succinct theories ever invented by the human mind. Richard
Feynman and others discovered the Þeld is generated by uncertainty itself through parti-
cles propagated by a rule based on wave spreading. These particles are called virtual
because they have no net positive energy and appear and disappear entirely within the win-
dow of quantum uncertainty, so we never see them except as expressed in the force itself. This seething tumult of virtual particles
exactly produces the familiar effects of the electromagnetic Þeld and other Þelds as well. We can Þnd the force between two elec-
trons by integrating the effects of every virtual photon which could be exchanged within the limits of uncertainty and of every other
possible virtual particle system, including pairs of electrons and positrons coming into a ßeeting existence. However, we can’t elim-
inate the wave description because the amplitudes with which the particles are propagated from point to point are wave amplitudes.
Uncertainty not only can create indeÞniteness but it can actively create every conceivable particle out of the vacuum, and does so.
Each more complex interaction involving one more particle vertex is smaller by a factor e
--- ∼ ---- where e is the electron charge
and h and c are as above, called the ‘Þne structure constant’. This allows the contribution of all the diagrams to sum to a Þnite inter-
action unlike many uniÞed theories, which are plagued by inÞnities. The electromagnetic force is generated by virtual photons
exchanged between charged particles existing only for a time and energy permitted by the uncertainty relation. The closer the two
electrons, the larger the energy ßuctuation possible over the shorter time taken to travel between them and hence the greater the
force upon them. Even in the vacuum, where we think there is nothing at all, there is actually a sea of all possible particles being
created and destroyed by the rules of uncertainty.
The virtual particles of a force Þeld and the real particles we experience as radiation such as light are one and the same. If we pump
energy into the Þeld, for example by oscillating it in a radio transmitter, the virtual photons composing the electromagnetic Þeld
become the real positive energy photons in radio waves entering the receiver as a coherent stream of real photons, encoding the
music we hear.
Relativistic quantum Þeld theories always have both advanced and retarded solutions, one with positive and the other with negative
energy, because of the two square roots of special relativity. They are often described by Feynman space-time diagrams. When the
Feynman diagram for electron scattering becomes time-reversed, it then becomes precisely the diagram for creation and annihila-
tion of the electron’s anti-particle, the positron, as shown above. This hints at a fundamental role for the exotic time-reversed
The weak and strong nuclear forces can be explained by similar Þeld theories related to electromagnetism through symmetry-break-
ing, but gravity holds out further serious catch-22s. Gravity is associated with the curvature of space-time, but this introduces funda-
mental contradictions with quantum Þeld theory. To date there remains no fully consistent way to reconcile quantum Þeld theory
and gravitation although higher-dimensional string and membrane theories show promise (Hawking 2001).
Fig 5: Wheeler delayed choice experiment: A very distant quasar is gravitation-
ally lensed by an intervening galaxy. We can sample photons either by an inter-
ference pattern, verifying they went around both sides of the galaxy, or place
separate directional detectors which will detect they went one way around only
as particles (which will destroy the interference pattern. Moreover, we can
decide which to perform after the photon has passed the galaxy, at the end of
its path. Thus the conÞguration of the latter parts of the wave appear to be able
to alter the earlier history.
5: The Spooky Nature of Quantum Entanglement
We have already seen how the photon wave passing through two slits
ends up being absorbed by a single atom. But how does the wave avoid
two particles accidentally being absorbed in far ßung parts of its wave
function out of direct communication? Just how large such waves can
become can be appreciated if we glance out at a distant galaxy, whose
light has had to traverse the universe to reach us. The ultimate size of
the wave of such a photon is almost as big as the universe. Only one
photon is ever absorbed for each such wave, so once we detect it, the
probability of Þnding the photon anywhere else, and hence the ampli-
tude of the wave, must immediately become zero everywhere. How can this happen, if information cannot travel faster than the
speed of light? The same thing happens when I shine my torch against the window. The amplitude of each photon is both reßected,
so I can see it, and transmitted, so that it could also escape into the night sky. Although the wave may spread far and wide, if the par-
ticle is absorbed anywhere, the probability across vast tracks of space has to suddenly become zero.
Moreover collapse may involve the situation at the end of the path inßuencing the earlier history, as in the Wheeler delayed choice
experiment illustrated in Þg 5. In this experiment we can determine whether a photon went both ways round a lensing galaxy, focus-
ing the light from a very distant quasar long after the light has passed across the universe, by either measuring the interference
between the paths as in the double slit experiment or by detecting light from one direction or another.
Because we can’t sample two different points of a single-particle wave, it is impossible to devise an experiment which can test how
a wave might collapse. One way to learn more about this situation is to try to Þnd situations in which two or more correlated parti-
cles will be released coherently in a single wave. This happens with many particles in a laser and in the holograms made by coherent
laser light and in Bose-Einstein condensates. It also happens in other situations where two particles of opposite spin or complemen-
tary polarization become created together. Many years ago Einstein, Rosen and Podolsky suggested we might be able to break
through the veil of quantum uncertainty this way, indirectly Þnding out more about a single particle than it is usually prepared to let
Fig 6: (a) Pair-splitting experiment for photons. (b) Time-varying analyzers are
added driven by an optical switch to fast for light to cross the apparatus. (c) The
results are consistent with quantum mechanics but inconsistent with Bell's ine-
qualities for a locally causal system. (d) The calcium transition (Aspect 1982).
For example a calcium atom’s electron excited into a higher orbital
sometimes cannot fall back to its original orbital in one step because a
photon always turns out to have spin 1 and the spins don’t match. For
example you can’t go between two orbits of equal spin and radiate a
spin-1 photon or the spins don’t tally. The atom however can radiate two
photons thereby cancelling one another’s spins, to transit to its ground
state, via an intermediate spin-1 orbit. This releases a blue and a yellow
photon, each of which travel off in opposite directions, with complemen-
When we perform the experiment, it turns out that the polarization of neither photon is deÞned until we measure one of them. When
we measure the polarization of one photon, the other immediately - instantaneously - has complementary polarization. The nature of
the angular correlations between the detectors is inconsistent with any locally-causal theory - that is no theory based on information
exchanged between the detectors by particles at the speed of light can do the trick, as proved in a famous result by John Bell (1966)
and subsequent experiments (Clauser and Shimony 1978). The correlation persists even if the detectors’ conÞgurations are changed
so fast that there is no time for information to be exchanged between them at the speed of light as demonstrated by Alain Aspect
(1982). This phenomenon has been called quantum non-locality and in its various forms quantum ‘entanglement’, a name itself very
suggestive of the throes of a sexual ‘affair’.
The situation is subtly different from any kind of classical causality we can imagine. The information at either detector looks ran-
dom until we compare the two. When we do, we Þnd the two seemingly random lists are precisely correlated in a way which implies
instantaneous correlatedness, but there is no way we can use the situation to send classically precise information faster than the
speed of light by this means. We can see however in the correlations just how the ordinary one-particle wave function can be instan-
taneously auto-correlated and hence not slip up in its accounting during collapse.
Since this result in the 1980s there have been a veritable conjurer's collection of experiments, including quantum teleportation, era-
sure computing and encryption, all of which verify the predictions of quantum mechanics in every case and conÞrm all the general
principles of the pair-splitting experiment. Even if we clone photons to form quartets of correlated particles, any attempt to gain
information about one of such a multiple collection collapses the correlations between the related twins.
Some of the more challenging aspects of quantum entanglement arise when we consider quantum computation. Classical computa-
tion has a problem which is the potentially unlimited time it takes to check out every one of a collection of possibilities. E.g. to
crack a code we need to check all the combinations, whose numbers can increase more than exponentially with the size of the code
numbers and possibly taking as long as the history of the universe to compute. For example factorizing a large number composed of
two primes is known to be computationally intractable enough to provide the basis for public key encryption by which banks
records and passwords are kept safe. Although the brain ingeniously uses massively parallel computation, there is as yet no system-
atic way to boot strap an arbitrary number of parallel computations together in a coherent manner. Quantum reality is a superposi-
tion of all the possible states in a single wave function, so if we can arrange a wave function to represent all the possibilities in such
a computation, superposition might give us the answer by a form of parallel quantum computation. A large number could in princi-
ple be factorized in a few superimposed steps, which would otherwise require vast time-consuming classical computer power to
check all the possible factors one by one.
6: Quantum Match-making: Transactional Supercausality and Reality
For reasons which immediately become apparent, the collapse in the pair-splitting experiment has to not only be immediate, but also
to reconcile information looking backwards in time. The two photons we are trying to detect are linked through the common cal-
cium atom. Their absorptions are thus actually connected via a path travelling back in space-time from one detector to the calcium
atom and forward again to the other detector. Trying to connect the detectors directly, for example by hypothetical faster-than-light
tachyons, leads to contradictions. Tachyons transform by the rules of special relativity, so a tachyon which appears to be travelling
at an inÞnite speed according to one observer, is travelling only at a little more than the speed of light according to another. One
travelling in one direction to one observer may be travelling in the opposite direction to another. They also cause weird causality
violations. There is thus no consistent way of knitting together all parts of a wave using tachyons. Even in a single-particle wave,
regions the wave has already traversed also have to collapse retrospectively so that no inconsistencies can occur in which a particle
is created in two locations in space-time from the same wave function, as the Wheeler delayed choice experiment makes clear.
Fig 7: (a) In the transactional interpretation, a single photon exchanged between emitter and absorber is formed by constructive interference
between a retarded offer wave (solid) and an advanced conÞrmation wave (dotted). (b) The transactional interpretation of pair-splitting. ConÞrma-
tion waves intersect at the emission point. (c) Contingent absorbers of an emitter in a single passage of a photon. (d) Collapse of contingent emit-
ters and absorbers in a transactional match-making (King). (e) Experiment by Shahri Afshar (see Chown 2004).
In the transactional interpretation (Cramer 1986), such an advanced ‘backward travelling’ wave in time gives a neat explanation,
not only for the above effect, but also for the probability aspect of the quantum in every quantum experiment. Instead of one photon
travelling between the emitter and absorber, there are two shadow waves, which superimposed make up the complete photon. The
emitter transmits an offer wave both forwards and backwards in time, declaring its capacity to emit a photon. The potential absorb-
ers of this photon transmit a corresponding conÞrmation wave. These, travelling backwards in time, send a hand-shaking signal
back to the emitter, Þg 7(a). The offer and conÞrmation waves superimpose constructively to form a real photon only on the space-
time path connecting the emitter to the absorber. The transactional approach offers the only viable explanation for the apparently
faster-than-light connections between detectors in pair-splitting EPR experiments in which a pair of correlated photons are emitted
by a single atom as in Þg 6. In Þg 7(b), rather than a super-luminal connection between detectors A1 and A2, the photons’ own
advanced waves meet at the source in a way which enables the retarded waves to be instantaneously correlated at the detectors.
A possible conÞrmation of the transactional approach comes from an intriguing experiment by Shahri Afshar (see Chown 2004), Þg
7e. A grid is placed at the interference minima of the wave fronts coming from two slits, just below a lens designed to focus the light
from each slit into a separate detector. Measurements by detectors (top) test whether a photon (particle) passed through the left or
right slit (bottom). There is no reduction in intensity when the grid is placed below the lens at the interference minima of the offer
waves from the two slits. The grid does however cause a loss of detector intensity when the dashed left-hand slit is covered and the
negative wave interference between the offer waves at the grid is removed, so that the non-interfered wave from the right slit now
hits the grid, causing scattering. This suggests both that we can measure wave and particle aspects simultaneously, and that the
transactional interpretation is valid in a way which neither many worlds (which predicts a splitting into histories where a photon
from the source goes through one slit or other) or the Copenhagen interpretation of complementarity (where detecting a particle for-
bids the photon manifesting as a wave).
In the extension of the transactional approach to supercausality (King 1989, 2003), a non-linearity reduces the set of contingent pos-
sibilities to one offer and conÞrmation wave, Þg 7 (c,d). Thus at the beginning, we have two set of contingent emitters and absorbers
as in Þg 7(c) and at the end each emitter is now exchanging with a speciÞc absorber. Before collapse of the wave function, we have
many potential emitters interacting with many potential absorbers. After all the collapses have taken place, each emitter is paired
with an absorber in a kind of marriage dance. One emitter cannot connect with two absorbers without violating the quantum rules,
so there is a frustration between the possibilities which can only be fully resolved if emitters and absorbers can be linked in pairs.
The number of contingent emitters and absorbers are not necessarily equal, but the number of matched pairs is equal to the number
of real particles exchanged, Þg 7(d).
The transition is not difÞcult to model as a sequence of non-linear bifurcations, in which one emitter-absorber pair becomes com-
mitted, but notice that the time parameter we are dealing with lies outside space-time, as it is transforming one space-time diagram
into another, yet it is happening experientially in real time. This is because collapse of the wave function is a space-time process.
Causality with its symmetry-broken sequential time and supercausality with its time-symmetric handshaking form complementary
domains, which is why the model is also called dual-time supercausality (King 1981). Directed and symmetric time thus coexist in
the model. Notice also that the past contains causal records as well as superpositions, but the future is purely extrapolation plus
superpositions. It is at this point that the inßuence of the conscious observer and the hard problem become pivotal. This transac-
tional time symmetry is paralleled in the time reversibility of a quantum computation so long as it remains in the original superposi-
tion of states contrasted with the time directed nature of classical computation, and with it the deÞnitive results of any quantum
computation arising from collapse.
The transactional process connects an emitter at an earlier time to an absorber at later time because a real positive energy photon is
a retarded particle which travels in the usual direction in time. If you wish, you can think of a negative energy photon travelling
backwards in time as the anti-particle of the positive one and it will have just the same effect. The two are thus identiÞable in the
transaction, just as in quantum electrodynamics above, where time-reversed electron scattering is the same as positron creation and
annihilation. One can also explain the arrow of time if the cosmic origin is a reßecting boundary that causes all the positive energy
real particles in our universe to move in the retarded direction we all experience in the arrow of time. This in turn gives the sign for
increasing disorder or entropy as it is called and the direction for the second law of thermodynamics to work in terms of positive
energy. In the pair-splitting experiment, Þg 7(b), one can also see that the calcium atom emits in response to the advanced conÞrma-
tion waves reaching it from both the detectors simultaneously right at the time it is emitting the photon pair. Thus the faster than
light linkage is neatly explained by the combined retarded and advanced aspects of the photon having a net forwards and backwards
connection which is instantaneous at the detectors.
The equivalence of real and virtual particles raises the possibility that all particles have an emitter and absorber and arose, like vir-
tual particles, through mutual interaction when the universe Þrst emerged. However even if dark-energy, ‘quintessence’ causes an
increasing expansion, or fractal inßation leads to an open universe model in which some photons may never Þnd an absorber, the
excitations of brain oscillations, because they are both emitted and absorbed by past and future brain states could still be universally
subject to transactional supercausal coupling.
The hand-shaking space-time relation implied by the transactional interpretation makes it possible that the apparent randomness of
quantum events masks a vast interconnectivity at the sub-quantum level, reßecting Bohm’s (1980) implicate order. Although one
can readily envisage a non-linear interaction where a sequence of bifurcations of the mutual frustration between the emitters and
absorbers, because this connects past and future in a time-symmetric way, it cannot be reduced to predictive determinism, because
the initial conditions are insufÞcient to describe the transaction, which also includes quantum ‘information’ coming from the future.
However this future is also unformed in real terms at the early point in time emission takes place. My eye didn’t even exist, when
the quasar emitted its photon, except as a profoundly unlikely branch of the combined probability ‘waves’ of all the events through-
out the history of the universe between the ancient time the quasar released its photon, my eye developing, and me being in the right
place at the right time to see it. Transactional supercausality thus involves a huge catch 22 about space, time and prediction, uncer-
tainty and destiny. It doesn’t suggest the future is determined, but that the contingent futures do superimpose to create a space-time
paradox in collapsing the wave function.
The transactional interpretation may combine with quantum computation to produce a space-time anticipating quantum entangled
system which may be pivotal in how the conscious brain does its computation (see section 12). The brain is not a marvelous com-
puter in any classical sense. We can barely repeat seven digits. But it is a phenomenally sensitive anticipator of environmental and
behavioral change. Subjective consciousness has its survival value in enabling us to jump out of the way when the tiger is about to
strike, not so much in computing which path the tiger might be on, because this is an intractable problem and the tiger can also take
it into account in avoiding the places we would expect it to most likely be, but by intuitive conscious anticipation.
.Fig 8: Human brain showing key underlying structures (Sci. Am. Sep 92) indicate a
massively parallel organization with feedback loops linking major cortical and lim-
bic areas and interfacing them with midbrain centres in the thalamus, and basal brain.
The limbic structures of the hippocampus and amygdala are indicated. There are
only about ten serial connections between sensory input and motor output.
7: Exploring the ‘Three Pound Universe’
The human brain has been described as the ‘three-pound universe’ (Hooper
and Teresi) because, along with some other mammalian brains, it is the sin-
gle most complex system so far discovered in the entire cosmological realm.
It is also the most mysterious. Although we have developed super-comput-
ers, their architecture remains that of a simplistic deterministic automaton
by comparison with the brain. Despite the vast increases of speed and mem-
ory capacity of modern computers, they remain trivial by comparison. Few
have more than a few processing units and the communication protocols for
parallel processing, outside simple matrix calculations, remain simple pro-
cedural farming out. The notion that a computer may some day also become
subjectively conscious is at this point a science Þction fantasy.
Theoretical models of neural nets likewise remain trivial by comparison
with brain structures. Neurons are frequently modeled as simple additive modules summing their inputs and making synaptic
adjustments to their connections in response to stimulus. Continuous nets such as the HopÞeld net have only transient dynamics
seeking a simple energy minimum as an equilibrium condition, perhaps with some thermodynamic annealing to avoid getting stuck
in the ‘rut’ of a sub-optimal local minimum. Biological neurons by contrast are dynamically active, adaptive single-celled ‘organ-
isms’, having up to 10,000 synaptic connections each and possessing a variety of excitatory and inhibitory neurotransmitters, as
well as both dynamical and pulse-coded means of activation. They display both chaos and self-organized criticality and threshold
The brain is par excellence a distributed parallel processing system in which there are only perhaps four to ten serial links between
sensory input and motor output, modulated by connections involving up to 1011 cells and 1015 synapses. Its protocols are thus ‘lat-
eral’ rather than ‘serial’. The mammalian brain is dominated by the cerebral cortex. We are now beginning to gain some idea of how
it processes sensory information through a combination of electrical probing and various types of scans.
Fig 9: Despite the development of sophisticated techniques for visu-
alizing brain activity such as those for speech (left), and ingenious
work tracing connectivity of activity between neurons in the cortex
such as that establishing distinct parallel processing regions for
colour and movement in vision (right, Zeki 1992), no objective
brain state is equivalent to a subjective conscious experience. The
difÞculty of bridging this abyss is called the hard problem in con-
sciousness research (Chalmers)
The cortex has a dynamic modular organization, in which
aspects of sensory ‘information’ are processed in parallel in
distinct areas, including the regions specialized for primary
vision and hearing and for somatosensory perception and
motor functions. Many of these modular regions can be
divided further, for example into speciÞc areas to do with
language, such as Wernicke’s and Broca’s areas for semantic meaning and linguistic articulation. Using active scanning by multi-
channel electroencephalograms, positron emission tomography, or functional magnetic resonance imaging, it is possible to follow
conscious activity and compare it with modular activation of the cortex, Þg 8. Visual processing can be divided into a signiÞcant
number of distinct modular areas Þg 9, complementing the primary visual area, with distinct processing for colour, movement and
moving form. These areas can be investigated, both in scans and through people who display sometimes bizarre perceptual anoma-
lies caused by local damage to these areas, such as colourless visual perception, or fragmented motion.
The cerebral cortex is divided between front and rear into broadly motor and broadly perception by the Sylvian Þssure, dividing
frontal regions and the motor cortex from the somatosensory (touch) and other sensory areas, including vision and hearing. The
broadly sensory ‘input’ and associated areas of the parietal and temporal cortices are complemented by frontal and pre-frontal areas
which deal with ‘output’ in the form of action rather than perception and with forming anticipatory models of our strategic and liv-
ing futures. These active roles of decision-making and ‘working memory’ (Goldman-Rakic 1992), which interact from pre-frontal
cortical areas complement the largely sensory-processing of the temporal, parietal and occipital lobes with a space-time representa-
tion of our ‘sense of future’ and of our will or intent.
Fig 10: Left: Ascending serotonin and norepinephrine pathways are
evidence for a parallel distributed cortex based on dynamical activa-
tion of conscious modes. Serotonin receptors are notably involved in
psychedelic effects. Right: Neural plasticity of local cortical function,
in changes in regions of optical dominance in the visual cortex after
the dominant eye is shade support dynamical rather than hard-wired
cortical organization. Such plasticity extends across the senses,
enabling the assignment of new functions under the demands of new
experiential situations such as learning a new language
However these areas are not rigidly hard-wired genetically.
Neurogenesis and neurophysiology are dynamic. The alloca-
tion of a given region is a dynamical consequence of a series of
interactive processes. These begin in embryogenesis, where
neurons migrate up the glial cellular scaffold to make speciÞc
types of global connection. Neurogenesis is accompanied by
growth and migration and also sacriÞce in programmed cell death, and removal as well as establishment of synapses. The overall
organization is not static, but derived from the dynamics itself. In visual development, the retina and then the geniculate and Þnally
the cortex become organized, each deriving organizing stimulus from the chaotic excitations established at the previous level. This
cortical dynamic plasticity is preserved into later life, where injury, compensation, or a major new learned skill can result in devel-
opment of new functional areas or signiÞcant rearrangement of existing areas. A person studied on live PET before and after becom-
ing a real time translator at the UN, for example, showed the development of a whole new language area.
The cortex itself is relatively inert in electrodynamical terms and may actually form a complex boundary constraint on the activity
of more active underlying areas such as the thalamus, which contains a number of centers with ordered projections to and from cor-
responding areas of the cortex. This suggests in turn that the thalamic centres are the driving force of cortical activity.
Fig 11: Typical cortical structures (centre) are a combina-
tion of Þve-layers of neurons each composed into columnar
modules on a scale of about 1mm on the cortical surface.
Such modules are sensitive to particular stimuli such as a
line of a given orientation. Blob centres in layer II are also
shown (see Þg 9). Although speciÞc sensory area have
functional and anatomical specializations neural plasticity
can enable changes of functional assignment indicating
common principles throughout the cortex. Left: anatomical
view of the Þve layers. Right: Ocular dominance columns
illustrate functional columnar architecture.
Finally we have the so-called limbic system, Þg 8,
around the edges of the cortex, involving the hippoc-
ampus, amygdala, hypothalamus and areas of the cin-
gulate cortex in a large feedback loop which has
becomes associated with emotional mood, ßight and
Þght, cross-sensory integration and the Þxation of
long-term sequential memory. These structures fall
very centrally into our concept of the psyche because they mediate the central emotional orientations which govern our survival and
our social interaction with others, including the capacity for love, hate, jealousy, compassion and non-genetic altruism.
The varying modes of alert consciousness, dreaming and deep sleep are generated from deeper brain stem centers which have
ascending neural pathways which fan out widely across the cortex into speciÞc cortical layers, thus providing long-term modulation
of mood and conscious attention Þg 10. Two pathways lead from the Raphe Nuclei and the Locus Coeruleus to diverse cortical areas
and involve the modulating neurotransmitters, serotonin and nor-epinephrine. The onset of dreaming sleep is heralded by activity of
cells in the Pons and silencing of cells in the Raphe Nuclei and Locus Coeruleus. Similar dopamine paths spread out from the Sub-
stantia Nigra selectively into the frontal lobes and motor centers. The ascending pathways have been implicated in mental illness,
addiction and motor syndromes such as Parkinson's disease. Dopamine is sometimes associated with pleasure and nor-adrenaline
with anxiety. The hallucinogens psilocin and mescalin are serotonin and catecholamine analogues, although both appear to interact
primarily with serotonin receptors. These pathways clearly have much to do with modulating conscious states of the cortex as a
whole and and understanding of their exact mechanism of action would give a very productive insight into the brain mechanisms
Dreaming or REM (rapid eye movement) sleep in which cortical activation alternates with phases of deep sleep is both one of the
most singular phases of conscious activity in which experiential feedback appears to be accentuated at the expense of external input,
generating episodic subjective realities or ‘worlds within’. The nature and function of dreaming consciousness and its wealth of
detail remain obscure although the experiences themselves are intense, sometimes in full sumptuous colour vision as evidenced in
lucid dreaming (La Berge 1990). There is some indication that these two phases are complementary and involve reciprocal commu-
nication between the hippocampus and the cortex in consolidating long-term sequential memories (Winson 1992, Stickgold 1998,
New Scientist 28 Jun 2003 29), but the subjective consequences, and the need for them to occur subjectively as well, as functionally
remain enigmatic. Accounts of precognitive dreaming (Dunne c1935) challenge our very notions of causality.
8: Chaos and Fractal Dynamics as a Source of Sensitivity, Unpredictability and Uncertainty
Walter Freeman's model of chaos in sensory perception, Þg 12(b,c), (Skarda and Freeman 1987, Freeman 1991) gives a good feel-
ing for how transitions in and out of chaos - a so-called ‘edge-of-chaos’ complexity phenomenon (Ruthen 1993), could play a key
role in sensory recognition. The olfactory cortex undergoes high energy chaotic excitation in time to form a spatially correlated
wave across the cortex, as a rabbit sniffs, causing the cortical dynamics to travel through its phase space of possibilities without
becoming stuck in any mode. As the sniff ends, the energy parameter reduces, carrying the dynamic down towards basins in the
potential energy landscape. If the smell is recognized, the dynamic ends in an existing basin, but if it is new, a bifurcation occurs to
form a new basin (a new symbol is created) constituting the learning process, as illustrated below. The same logic can be applied to
cognitive problem solving in which the unresolved aspects of the problem undergo chaotic evolution until a bifurcation from chaos
to order arrives at the ‘eureka’ of the solution.
A fundamental reason for any dynamical nervous system to enter chaos is that chaotic systems are arbitrarily sensitive on their ini-
tial or external conditions, so a system entering chaos is capable of being acutely responsive to its environment over time, while any
stable process heads inexorably towards its equilibrium states or periodicities, entrapped by its very stability. While artiÞcial neural