The measurement paradox is not the only philosophically troublesome aspects of quantum

physics. Bell’s Theorem (1987), with its implication of instantaneous communication between

distant events, is equally unsettling. The simplest example of this is the Einstein-Podolsky-Rosen

(EPR) thought experiment. Two electrons, initially coupled, are shot off in different directions. It

is assumed that each one flies for millions of miles without hitting anything. Each one, according

to quantum physics, has a fifty-fifty chance of spinning to the right or to the left — there is no

way to make a more accurate prediction. However, the rules of quantum physics do imply that

the two are spinning in opposite directions: if one is spinning to the right, then the other one is

spinning to the left; and vice versa.

Now suppose someone measures one of the electrons, and that it all of a sudden assumes a

definite value. Then the other electron will immediately also assume a definite value — because

it is known that the two are spinning in opposite directions. If one is measured to be spinning to

the right, then the other is instantaneously known to be spinning to the left. When Einstein

conceived this example, he thought he had disproved quantum mechanics — because nothing so

absurd could possibly be true. After all, he asked how doesthe one electron tell the other one

which way to spin? Special relativity forbids information to travel faster than the speed of light;

so it would seem that if the particles were sufficiently distant, the value of the spin of one

particle could take eons to reach the other particle.

But, absurd as this may be, it is an experimentally proven fact (Aspect and Grangier, 1985).

Scenarios very similar to the original EPR thought experiment have been tested in the lab. It

turns out that, mathematically speaking, this peculiar "nonlocality" does not contradict special

relativity, because no information is being transmitted, only a correlation. But this is very little

consolation: it is a violation against the spirit, if not the letter, of special relativity.

Reality does not consist of pairs of electrons, coupled and then shot out into space a million

miles in opposite directions. Consider the following thought experiment. Split apart two coupled

physical systems, say A and B. Suppose that, from the state of A, one could infer the state of B,

and vice versa. Leave A alone but let B interact with C for a while, and then separate B from C.

Finally, measure A. A is collapsed into some definite state. If B had not interacted with C, one

could say that the state of B would also, immediately, collapse into some definite state. But the

state of B now depends also upon the state of C, which according to quantum physics has no

definite value but is rather an array of possibilities. So the measurement of A does not collapse B

to a definite state. But it does, however, decrease the uncertainty involved in the state of B. It

increases the "closeness" of B to a definite state.

Technically speaking, assume that p=(p1,p2,…,pn) denotes the probabilities of the various

possible states in which B might be. Then one may show that, in the situation described above,

the measurement of A necessarily changes p into a new set of probabilities p%=(p1%,…,pn%) so

that H(p1,…,pn) < H(p1%,…,pn%), where H is the entropy function

H(p1,…,pn) = -[p1logp1 + … + pnlogpn]

A similar statement may be made when the possible states of B form a continuum rather than a

discrete set. Recall that the entropy of a probability distribution is a measure of its uncertainty, or

its distance from the most certain distribution.

This thought experiment may be generalized. What if the state of B cannot be completely

determined from the state of A? If the state of A yields any information at all about the state of

B, then it is plain that the same result holds. If A and B were ever coupled, no matter how

loosely, no matter what they have done since, measurement of A reduces the uncertainty of the

probability distribution characterizing the states of B. Bell’s Theorem implies that this sort of

propagation of certainty is a necessary aspect of any physical theory that is mathematically

similar to quantum theory.

In terms of the quantum theory of consciousness, what does this mean? A little consciousness

can go a long way! If two sets of possibilities have been coupled in the past, and are then

separated, then whenever consciousness makes one of them definite, the other one becomes

definite automatically,instantaneously, without any physical causation involved.

QUANTUM CONSCIOUSNESS, BIOLOGICAL CON SCIOUSNESS

By introducing consciousness, one obtains a philosophically elegant resolution of the paradox

of quantum measurement. But in a way we are abusing the word "consciousness". What qualities

does this abstract entropy-decreasing consciousness share with the common-sense understanding

of consciousness? We have reconciled the physics of measurement with the phenomenology of

measurement only by separating the physics of consciousness from the phenomenology of

consciousness.

Mandler has proposed that

… [C]onscious constructions represent the most general interpretation that is appropriate to

the current scene in keeping with both the intentions of the individual and the demands of the

environment. …Thus, we are aware of looking at a landscape when viewing the land from a

mountaintop, but we become aware of a particular road when asked how we might get down or

of an approaching storm when some dark clouds "demand" inclusion in the current construction.

In a problem-solving task, we are conscious of those current mental products that are closest to

the task at hand, i.e. the likely solution to the problem. (1985, p.81)

Whether or not this particular formulation is exactly correct, it seems plain that some similar

characterization must hold true. Consciousness seems to have a role in planning and decision-

making, but it is rarely involved in the minute details of everyday life: walking, turning the pages

of a book, choosing words in conversation, doing arithmetic with small numbers, etc. In the

language of the previous chapters, this means that — as already stated — consciousness has

contact with only a certain restricted range of the perceptual hierarchy.

The decision-making aspect of consciousness is intuitively harmonious with quantum theory:

in making a decision, one is reducing an array of possibilities to one definite state. There is a

sense in which making a decision corresponds to selecting one of many possible universes. But

the quantum theory of consciousness gives us no indication of why certain decisions are

submitted to consciousness, but others are not.

One of the main problems here is that it is not clear what function the quantum theory of

consciousness is supposed to serve. In Wigner (1962) or Goswami (1990), consciousness is

essentially defined as the reduction to a definite state, or more generally as the decrease of the

entropy of an array of possible states. This interpretation gives a transcendentalist resolution of

the mind-body problem, made explicit by Goswami when he suggests that, as a heuristic tool, we

consider the mind to be a coupling of two computers, a classical computer and a quantum

computer. The quantum computer behaves in a way which transcends ordinary biophysics, and it

is this transcendencewhich is responsible for consciousness.

But there is another, more radical, way of interpreting the quantum theory of consciousness.

One may begin with the assertion that consciousness is a process which is part of the dynamics

of certain physical systems, e.g. human brains. This means that consciousness has some direct

physical effect: that, for instance, when a pattern of neural firings enters consciousness,

consciousness changes it in a certain characteristic way. The biochemical nature of this process

is of course largely unknown. However, Edelman (1989) has made some very interesting

hypotheses. In his notation, consciousness may be described as the continual interaction between

C(W) and C[C(W). C(I)], where

C(I) is the neural basis for categorization of I, the interoceptive input —

autonomic, hypothalamic, endocrine. It is evolutionarily earlier, driven by inner events,

mediated by limbic and brain-stem circuits coupled to biochemical circuits, and it shows

slow phasic activity. C[W] is the neural basis for perceptual categorization of W, the

exteroceptive input — peripheral, voluntary motor, proprioceptive

and polymodal sensory signals — and is mediated by the thalmus and

cortical areas. It is driven largely by outer events, is fast, and handles many more

signals in parallel. C(W).C(I) represents the neural basis of interaction and comparison of

two categorical systems that occurs, for example, at the hippocampus, septum, and

cingulate gyri. C[C(W).C(I)] is the neural basis of conceptual recategorization

of this comparison, which takes place in the cingulate gyri, temporal

lobes, and parietal and frontal cortex. (The boldface C indicates conceptual

categorization.)

Less technically, what Edelman proposes is that consciousness is the interaction between two

processes: 1) the recognition of patterns in perceptions, and 2) the interaction between the

recognition of patterns of perception and the recognition of patterns in internal, emotional,

chemical stimuli.

Given this biological characterization of consciousness, one may then hypothesize that the

entropy reduction of arrays of possible states is correlated with those changes the states of

conscious systems which correspond to conscious acts. This point of view — which I will call the

strong interaction postulate — places less responsibility on quantum theory than the

interpretation of Wigner and Goswami: it does not require quantum theory to explain

psychological facts. Rather, it portrays consciousness as the point of connection between psycho-

biological dynamics and physical dynamics; the bridge between the mind and the world.

The quantum theory of consciousness, as presented by Wigner or Goswami, implies a

transcendentalist resolution of the mind-body problem. But though it is useful for intuitively

understanding quantum theory, it is not at all adequate for understanding consciousness. The

strong interaction postulate is not merely a reinterpretation of quantum theory: it states that

consciousness, in some sense,plays an active role in forming the physical world.

In terms of the many-worlds interpretation, strong interaction implies that the brain-states of

conscious entities put a special bias on the possible universes of the future. Everything in the

universe figures into the array of probabilities of possible future universes — but conscious

systems are involved in an additional feedback process with this array.

The idea of strong interaction may be worked out in much more detail, but that would lead us

too far astray. It may be that future developments in physics will render this entire discussion

nonsensical. However, as Penrose (1989) has pointed out, it is also possible that the relation

between mind and body will be essential to the next revolution in physics.

SELF-AWARENESS

Finally, I would like to point out that the quantum view of consciousness yields an interesting

interpretation of that intangible feeling of self-awareness that accompanies consciousness of

external objects or definite ideas. Consider the following scenario. P and Q are closely coupled

algorithms, each one continually modifying the other. Simultaneously, consciousness greatly

reduces the uncertainty of both the distribution of possible states of P and the distribution of

possible states of Q. The reduction of the uncertainty P then reduces the uncertainty of Q yet

further; and vice versa. The result is that the combined entity P%Q has, in effect, looked at itself

and reduced its own entropy.

It is not justifiable to say that P%Q did not really look at itself, that what really happened was

that P and Q looked at each other. Because according to quantum physics, if we observed P % Q

to see what was really happening, this would change the probability distributions. P and Q are

quantum coupled, and this means they are effectively one entity. Clearly, this situation is not

rare: feedback between different prominent structures is probably not the exception but the rule.

According to this analysis, the feeling of self-awareness is not logically inherent to

consciousness; it is rather an extremely common by-product of consciousness. This accounts for

the fact that we are not continually absorbed with the sensation of self-awareness: it flits in and

out of consciousness. Self-awareness is not quite the same as consciousness, but the two are

inextricably interlinked.

INTELLIGENCE AND CONSCIOUSNESS

Clearly, the quantum theory of consciousness is in a very early stage of development.

However, none of the details are really essential here. The primary point of our excursion

through quantum theory was to arrive at one simple hypothesis: that whereas Turing machines

cannot possess consciousness,quantum computers can.

This hypothesis has profound implications for the relation between consciousness and

intelligence. To see this, we must consider a certain crucial but vastly under appreciated

shortcoming of the theory of Turing machines. Mathematically, it is easy to deal with Turing

machines of arbitrarily large processing capacity. But in physical reality, it is impossible to build

an arbitrarily powerful Turing machine.

If the parts of a machine are very small or very closely packed, then they are susceptible to

quantum effects, and the machine is a quantum computer, not strictly a Turing machine: its

behavior depends crucially on the peculiar properties of indeterminacy and nonlocality. But if the

parts of a machine are not very small, and not very closely packed, then they must spread over a

large expanse of space. However, according to the theory of special relativity, information

cannot travel any faster than the speed of light. Therefore, there is a limit to the speed of a

machine made of large and/or sparse parts.

From these considerations it follows that, for any given time period T, there is a certain limit

to the amount of computation that a physical Turing machine can do in time T. Even without

estimating the specific numbers, it is clear that this limit is considerably smaller than the total

amount of computation which a quantum computer can do in time T. Deutsch has shown that an

abstract quantum computer cannot compute any functions which an abstract Turing machine

cannot also compute. However, within any specified period of time, there is some physical

quantum computer which can compute functions that no physical Turing machine can.

Now, intelligence depends not only on absolute computing power but also on speed. Therefore

it follows from our assumptions that there is a certain degree of intelligence which quantum

computers can attain but Turing machines cannot. Coupling this with the hypothesis that

quantum computers but not Turing machines possess consciousness, one obtains the following

intriguing conclusion: there may be a certain level of intelligence which can be attained only

by conscious entities.

Kaynak: A New Mathematical Model of Mind

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