For sixty years physicists have struggled with the paradox of quantum measurement.
However, despite a number of theoretical advances, rather little progress has been made toward
resolution of the basic dilemma. The problem is one of physics versus phenomenology.
According to quantum physics, no physical entity is ever in a definite state; the most one can
ever say about a given entity is that it has certain probabilities of being in certain states. And yet,
both in daily life and in the laboratory, things do sometimes appear to have definite states.
For instance, the equations of quantum physics predict that, in many situations, an electron has
a 50% "chance" of having a positive spin, and a 50% "chance" of having a negative spin. Yet
when the physicist probes the electron in his laboratory, it appears to have either a positive spin
or a negative spin. According to the equations of quantum physics — the Heisenberg equation
and the Schrodinger equation — such a reduction to a definite state is impossible. Of course,
one may have various degrees of probabilistic knowledge. In certain situations, one might know
an electron to have a 90% "chance" of having positive spin, and a 10% "chance" of having
negative spin. But there can never be 100% definite knowledge. Heisenberg’s indeterminacy
principle says that one can never have complete knowledge of the state of any particle: the
greater the accuracy with which one knows its position, the less the accuracy with which one can
know its momentum; and vice versa. In order to predict what the particle will do in the future,
one needs to know both the position and the momentum; but according to quantum physics, this
is possible only probabilistically.
This sort of indeterminacy is a proven scientific fact, inasmuch as quantum theory is the only
known theory that correctly explains the behavior of microscopic particles, and it predicts only
probabilities. Classical mechanics and electromagnetism gave definite answers about the
behavior of microscopic particles, but these answers were experimentally wrong. Furthermore, it
seems likely that, if quantum theory is someday superseded, the theory which followsit will build
on the probabilistic nature of quantum theory, rather than regressing to classical ideas. In fact, it
has been proved mathematically (Bell, 1964, 1987) that any physical theory satisfying certain
simple requirements must necessarily have properties similar to those of quantum theory: it must
deal only in probabilities.
BEYOND THE PROJECTION POSTULATE
In his classic treatise on quantum theory, John von Neumann (1936) introduced the
"projection postulate", an addition to the basic principles of quantum physics which states that,
when an entity is measured, it reduces to a definite state. This approach appears to be adequate
for most practical problems of quantum mechanics; and, although, many physicists find it
unacceptable, there is no equally elegant alternative. The only trouble is that no one has ever
given a satisfactory definition of "measurement".
Originally it was thought that a microscopic event could be considered to be measured when it
"registered" an effect on some macroscopic entity. The justification for this was the belief that, as
entities become larger and larger, the probabilistic nature of quantum physics becomes less and
less relevant to their behavior. For instance, according to quantum physics a baseball dropped
from a window has an infinity of possible paths, but one of them, or one small class of them, is
overwhelmingly more likely than the others.
But this naive identification of measurement with macroscopic effect cannot stand up to
criticism. Spiller and Clark (1986) have constructed a Superconducting Quantum Interference
Device (SQUID) which is about the size of a thumbnail and yet displays the same sort of
uncertainty as an electron. One can never know both the intensity and the flux of its magnetic
field with perfect accuracy; there is a finite limit beyond which further accuracy is impossible. Its
state is fundamentally a probabilistic superposition.
And it appears that the brain may display a similar form of quantum indeterminacy
(Changeaux, 1985; Penrose, 1990). Recall that a neuron fires when its charge exceeds a certain
threshold amount. It follows that, on occasion, highly unpredictable quantum phenomena may
push the charge of a neuron over the threshold. And this neuron may then set other neurons off,
and so on — in this manner a tiny quantum indeterminacy may give rise to a huge
neurophysiological uncertainty. If the extra charge has a fifty-fifty chance of being there, then
the entire pattern of neuronal firing that ensues from its presence probably has about a fifty-fifty
chance of being there. A pattern of neuronal firing might, for instance, represent a state of mind.
And when you consider the fact that there are over a hundred billion neurons in the brain, the
possibilities for interlocking quantum uncertainties are astounding. The exact numbers are
difficult to estimate, but it appears that this may be a significant phenomenon.
One intriguing alternative to the projection postulate is Everett’s (1957)"many-worlds
hypothesis", which assigns to each uncertain situation an array of universes, one corresponding
to each possible outcome. For instance, according to the many-worlds hypothesis, every time a
physicist observes an electron to have positive spin, there is an alternate universe which is
exactly identical to this one, except that in the alternate universe the physicist observes the
electron to have negative spin. This is an interesting possibility, but it is empirically
indistinguishable from the projection postulate, since these alternate universes can never be
THE QUANTUM THEORY OF CONSC IOUSNESS
Another alternative, first proposed by Wigner (1962), is that "measurement" may be defined as
"registration into consciousness." To see the motivation for this radical idea, let us turn to the
infamous paradox of Schrodinger’s cat (1948). Here the peculiarity of quantum theory is elevated
to the level of absurdity. Put a cat in a soundproofed cage with a radioactive atom, a Geiger
counter and a vial of poison gas. Suppose that the atom has a half-life of one hour. Then it has a
fifty-fifty chance of decaying within the hour. According to the dynamical equations of quantum
physics, this is all one can know about the atom: that it has a fifty-fifty chance of decaying.
There is no possible way of gaining more definite information.
Assume that, if the atom decays, the Geiger counter will tick; and if the Geiger counter ticks,
the poison vial will be broken. This set-up is bizarre but not implausible; a clever engineer could
arrange it or something similar. What is the state of the cat after the hour is up? According to
quantum theory without the projection postulate, it is neither definitely alive nor definitely dead –
– but half and half. Because the atom never either definitely decays or definitely doesn’t decay:
quantum physics deals only in probabilities. And if the atom never either definitely decays or
definitely doesn’t decay, then the cat never definitely dies or definitely doesn’t die.
One might argue that the cat is not in a state of superposition between life and death, but rather
has a fifty percent chance of being alive and a fifty percent chance of being dead. But according
to quantum theory without the projection postulate, the cat will never collapse into a definite
state of being either alive or dead. What sense does it make to suggest that the cat has a fifty
percent chance of entering into a state which it will never enter into? The function of the
projection postulate is to change the statement that the cat is half dead and half alive into a
statement about the probabilities of certain definite outcomes.
Of course, the fact is that if we look in the box after the hour is up, we either see a dead cat or
a living cat. Phenomenologically, by the time the observation is made, one of the two
possibilities is selected — definitely selected. But when, exactly, does this selection occur? Since
measurement cannot be defined as macroscopic registration, this is a very serious problem.
And the problem is resolved very neatly by the hypothesis that probabilisticoccurrences are
replaced by definite occurrences whe n they enter consciousness.
For instance, this implies that Schrodinger’s cat is not half dead and half alive, but rather has a
fifty percent chance of being dead and a fifty percent chance of being alive. The cat becomes
definitely dead or definitely alive when a conscious being sees it. As Goswami put it,
it is our consciousness whose observations of the cat resolves its dead-or-alive dichotomy.
Coherent superpositions, the multifaceted quantum waves, exist in the transcendent order until
consciousness brings them to the world of appearance with the act of observation. And, in the
process, consciousness chooses one facet out of two, or many, that are permitted by the
mathematics of quantum mechanics, the Schrodinger equation; it is a limited choice, to be sure,
subject to the overall probability constraint of quantum mathematics (i.e. consciousness is
lawful)…. [C]onsciousness… is not about doing something to objects via observing, but
consists of choosing among the alternative possibilities that the wave function presents and
recognizing the result of choice. (1990, p. 142)
That is, the mind does not create the world in the sense of reaching out and physically modifying
events. But it creates the world by selecting from among the wide yet limited variety of options
presented to it by the probabilistic equations of physics.
Kaynak: A New Mathematical Model of Mind
For sixty years physicists have struggled with the paradox of quantum measurement.