. Wigner claimed that a quantum measurement
observer, without which nothing ever happens in the universe.
The physicist friend inside the lab either sees a photon flash or not. (In a footnote Wigner notes that the human eye can perceive as few as three quanta.) But Wigner is outside the lab and does not know the outcome. Wigner says that without human consciousness, this leaves the world in a superposition of states."
Wigner says that any inanimate material measuring device will leave both himself and his friend in a superposition of states. The only thing he sees that could change this is human consciousness, He resolves the paradox by saying that his friend's consciousness collapses the wave function inside the laboratory.
Given any object, all the possible knowledge concerning that object
can be given as its wave function. This is a mathematical concept the
exact nature of which need not concern us here—it is composed of a
(countable) infinity of numbers. If one knows these numbers, one can
foresee the behavior of the object as far as it can be foreseen. More precisely,
the wave function permits one to foretell with what probabilities
the object will make one or another impression on us if we let it interact
with us either directly, or indirectly. The object may be a radiation field,
and its wave function will tell us with what probability we shall see a
flash if we put our eyes at certain points, with what probability it will
leave a dark spot on a photographic plate if this is placed at certain
positions. In many cases the probability for one definite sensation will be
so high that it amounts to a certainty—this is always so if classical mechanics
provides a close enough approximation to the quantum laws.
The information given by the wave function is communicable. If
someone else somehow determines the wave function of a system, he
can tell me about it and, according to the theory, the probabilities for
the possible different impressions (or "sensations") will be equally large,
no matter whether he or I interact with the system in a given fashion.
In this sense, the wave function "exists."
It has been mentioned before that even the complete knowledge of
the wave function does not permit one always to foresee with certainty
the sensations one may receive by interacting with a system. In some
cases, one event (seeing a flash) is just as likely as another (not seeing
a flash). However, in most cases the impression (e.g., the knowledge of
having or not having seen a flash) obtained in this way permits one to
foresee later impressions with an increased certainty. Thus, one may be
sure that, if one does not see a flash if one looks in one direction, one
surely does see a flash if one subsequently looks in another direction.
The property of observations to increase our ability for foreseeing the
future follows from the fact that all knowledge of wave functions is
based, in the last analysis, on the "impressions" we receive. In fact, the
wave function is only a suitable language for describing the body of
knowledge—gained by observations—which is relevant for predicting
the future behaviour of the system. For this reason, the interactions
which may create one or another sensation in us are also called observations,
or measurements. One realises that all the information which the
laws of physics provide consists of probability connections between subsequent
impressions that a system makes on one if one interacts with
it repeatedly, i.e., if one makes repeated measurements on it. The wave
function is a convenient summary of that part of the past impressions
which remains relevant for the probabilities of receiving the different
possible impressions when interacting with the system at later times.
An Example
It may be worthwhile to illustrate the point of the preceding section
on a schematic example. Suppose that all our interactions with the system
consist in looking at a certain point in a certain direction at times
t_{0}, t_{0} + 1, t_{0} + 2, ... , and our possible sensations are seeing or not seeing
a flash. The relevant law of nature could then be of the form: "If you
see a flash at time t, you will see a flash at time t + 1 with a probability
1/4, no flash with a probability 3/4; if you see no flash, then the next
observation will give a flash with the probability 3/4, no flash with a
probability 1/4; there are no further probability connections." Clearly,
this law can be verified or refuted with arbitrary accuracy by a sufficiently
long series of observations. The wave function in such a case depends
only on the last observation and may be Ψ_{1} if a flash has been seen
at the last interaction, Ψ_{2} if no flash was noted. In the former case, that
is for Ψ_{1}, a calculation of the probabilities of flash and no flash after
unit time interval gives the values 1/4 and 3/4; for Ψ_{2} these probabilities
must turn out to be 3/4 and1/4. This agreement of the predictions of the
law in quotation marks with the law obtained through the use of the
wave function is not surprising. One can either say that the wave function
was invented to yield the proper probabilities, or that the law given
in quotation marks has been obtained by having carried out a calculation
with the wave functions, the use of which we have learned from
Schrödinger.
The communicability of the information means, in the present example,
that if someone else looks at time t, and tells us whether he saw a
flash, we can look at timet + 1 and observe a flash with the same probabilities
as if we had seen or not seen the flash at time t ourselves. In
other words, he can tell us what the wave function is: Ψ_{1} if he did, Ψ_{2} if
he did not see a flash.
The preceding example is a very simple one. In general, there are
many types of interactions into which one can enter with the system,
leading to different types of observations or measurements. Also, the
probabilities of the various possible impressions gained at the next
interaction may depend not only on the last, but on the results of many
prior observations. The important point is that the impression which
one gains at an interaction may, and in general does, modify the probabilities
with which one gains the various possible impressions at later
interactions. In other words, the impression which one gains at an interaction,
called also the result of an observation, modifies the wave function
of the system. The modified wave function is, furthermore, in general
unpredictable before the impression gained at the interaction has
entered our consciousness: it is the entering of an impression into our
consciousness which alters the wave function because it modifies our
appraisal of the probabilities for different impressions which we expect
to receive in the future. It is at this point that the consciousness enters
the theory unavoidably and unalterably. If one speaks in terms of the
wave function, its changes are coupled with the entering of impressions
into our consciousness. If one formulates the laws of quantum mechanics
in terms of probabilities of impressions, these are ipso facto the primary
concepts with which one deals.
It is natural to inquire about the situation if one does not make the
observation oneself but lets someone else carry it out. What is the wave
function if my friend looked at the place where the flash might show
at time t? The answer is that the information available about the object
cannot be described by a wave function. One could attribute a wave
function to the joint system: friend plus object, and this joint system
would have a wave function also after the interaction, that is, after my
friend has looked. I can then enter into interaction with this joint system
by asking my friend whether he saw a flash. If his answer gives me
the impression that he did, the joint wave function of friend + object
will change into one in which they even have separate wave functions
(the total wave function is a product) and the wave function of the
object is Ψ_{1}. If he says no, the wave function of the object is Ψ_{2}, i.e., the
object behaves from then on as if I had observed it and had seen no
flash. However, even in this case, in which the observation was carried
out by someone else, the typical change in the wave function occurred
only when some information (the yes or no of my friend) entered my
consciousness. It follows that the quantum description of objects is
influenced by impressions entering my consciousness.
Solipsism may
be logically consistent with present quantum mechanics, monism in
the sense of materialism is not. The case against solipsism was given at
the end of the first section.
The Reasons for Materialism
The principal argument against materialism is not that illustrated in
the last two sections: that it is incompatible with quantum theory. The
principal argument is that thought processes and consciousness are the
primary concepts, that our knowledge of the external world is the content
of our consciousness and that the consciousness, therefore, cannot
be denied. On the contrary, logically, the external world could be
denied—though it is not very practical to do so. In the words of Niels
Bohr,
"The word consciousness, applied to ourselves as well as to others,
is indispensable when dealing with the human situation."
In view of
all this, one may well wonder how materialism, the doctrine
that "life
could be explained by sophisticated combinations of physical and chemical
laws," could so long be accepted by the majority of scientists.
The reason is probably that it is an emotional necessity to exalt the
problem to which one wants to devote a lifetime. If one admitted anything
like the statement that the laws we study in physics and chemistry
are limiting laws, similar to the laws of mechanics which exclude the
consideration of electric phenomena, or the laws of macroscopic physics
which exclude the consideration of "atoms," we could not devote ourselves
to our study as wholeheartedly as we have to in order to recognise
any new regularity in nature. The regularity which we are trying to
track down must appear as the all-important regularity—if we are to pursue
it with sufficient devotion to be successful. Atoms were also considered
to be an unnecessary figment before macroscopic physics was
essentially complete—and one can well imagine a master, even a great
master, of mechanics to say: "Light may exist but I do not need it in
order to explain the phenomena in which I am interested." The present
biologist uses the same words about mind and consciousness; he uses
them as an expression of his disbelief in these concepts. Philosophers
do not need these illusions and show much more clarity on the subject.
The same is true of most truly great natural scientists, at least in their
years of maturity. It is now true of almost all physicists—possibly, but
not surely, because of the lesson we learned from quantum mechanics.
It is also possible that we learned that the principal problem is no longer
the fight with the adversities of nature but the difficulty of understanding
ourselves if we want to survive.
Simplest Answer to the Mind-Body Question
Let us first specify the question which is outside the province of
physics and chemistry but is an obviously meaningful (because operationally
defined) question: Given the most complete description of my
body (admitting that the concepts used in this description change as
physics develops), what are my sensations? Or, perhaps, with what
probability will I have one of the several possible sensations? This is
clearly a valid and important question which refers to a concept—sensations—which
does not exist in present-day physics or chemistry. Whether
the question will eventually become a problem of physics or psychology,
or another science, will depend on the development of these
disciplines.
Naturally, I have direct knowledge only of my own sensations and
there is no strict logical reason to believe that others have similar experiences.
However, everybody believes that the phenomenon of sensations
is widely shared by organisms which we consider to be living. It is
very likely that, if certain physico-chemical conditions are satisfied, a
consciousness, that is, the property of having sensations, arises. This
statement will be referred to as our first thesis. The sensations will be
simple and undifferentiated if the physico-chemical substrate is simple;
it will have the miraculous variety and colour which the poets try to
describe if the substrate is as complex and well organized as a human
body.
The physico-chemical conditions and properties of the substrate not
only create the consciousness, they also influence its sensations most
profoundly. Does, conversely, the consciousness influence the physicochemical
conditions? In other words, does the human body deviate from
the laws of physics, as gleaned from the study of inanimate nature? The
traditional answer to this question is, "No": the body influences the
mind but the mind does not influence the body.
Yet at least two reasons
can be given to support the opposite thesis, which will be referred to
as the second thesis.
The first and, to this writer, less cogent reason is founded on the
quantum theory of measurements, described earlier in sections 2 and 3.
In order to present this argument, it is necessary to follow my description
of the observation of a "friend" in somewhat more detail than was
done in the example discussed before. Let us assume again that the object
has only two states, Ψ_{1} and Ψ_{2}. If the state is, originally, Ψ_{1}, the state
of object plus observer will be, after the interaction, Ψ_{1} x Χ_{1}; if the state
of the object is Ψ_{2}, the state of object plus observer will be Ψ_{2} x Χ_{2} after
the interaction. The wave functions Χ_{1} and Χ_{2} glve the
state of the observer;
in the first case he is in a state which responds to the question
"Have you seen a flash?" with "Yes"; in the second state, with "No."
There is nothing absurd in this so far.
Let us consider now an initial state of the object which is a linear
combination
α Ψ_{1} + β Ψ_{2} of the two states Ψ_{1} and Ψ_{2}. It then follows from
the linear nature of the quantum mechanical equations of motion that
the state of object plus observer is, after the interaction, α (Ψ_{1} x Χ_{1} ) + β (Ψ_{2} x Χ_{2}). If I now ask the observer whether he saw a flash, he will with
a probability |α|^{2}
say that he did, and in this case the object will also
give to me the responses as if it were in the state Ψ_{1}. If the observer
answers "No"—the probability for this is |β|^{2} —the object's responses from
then on will correspond to a wave function Ψ_{2}. The probability is zero
that the observer will say "Yes," but the object gives the response which
Ψ_{2} would give because the wave function α Ψ_{1} + β Ψ_{2} of the
joint system has no
(Ψ_{2} x Χ_{1}) component. Similarly, if the observer denies
having seen a flash, the behavior of the object cannot correspond to Χ_{1}
because the joint wave function has no (Ψ_{1} x Χ_{2}) component. All this is
quite satisfactory: the theory of measurement, direct or indirect, is
logically consistent so long as I maintain my privileged position as ultimate
observer.
However, if after having completed the whole experiment I ask my
friend, "What did you feel about the flash before I asked you?" he will
answer, "I told you already, I did [did not] see a flash," as the case may
be. In other words, the question whether he did or did not see the
flash was already decided in his mind, before I asked him.
If we
accept this, we are driven to the conclusion that the proper wave function immediately after the interaction of friend and object was already
either Ψ_{1} x Χ_{1}
or Ψ_{1} x Χ_{2}
and not the linear combination α (Ψ_{1} x Χ_{1} ) + β (Ψ_{2} x Χ_{2}). This is a contradiction, because the state described by the wave
function α (Ψ_{1} x Χ_{1} ) + β (Ψ_{2} x Χ_{2}) describes a state that has properties
which neither Ψ_{1} x Χ_{1} nor Ψ_{2} x Χ_{2} has. If we substitute for "friend" some
simple physical apparatus, such as an atom which may or may not be
excited by the light-flash, this difference has observable effects and
there is no doubt that
α (Ψ_{1} x Χ_{1} ) + β (Ψ_{2} x Χ_{2}) describes the properties
of the joint system correctly, the assumption that the wave function is
either Ψ_{1} x Χ_{1} or Ψ_{2} x Χ_{2} does not. If the atom is replaced by a conscious
being, the wave function
α (Ψ_{1} x Χ_{1} ) + β (Ψ_{2} x Χ_{2}) (which also follows
from the linearity of the equations) appears absurd because it implies
that my friend was in a state of suspended animation before he answered
my question.
It follows that the being with a consciousness must have a different
role in quantum mechanics than the inanimate measuring device: the
atom considered above. In particular, the quantum mechanical equations
of motion cannot be linear if the preceding argument is accepted.
This argument implies that "my friend" has the same types of impressions
and sensations as I—in particular, that, after interacting with the
object, he is not in that state of suspended animation which corresponds
to the wave function α (Ψ_{1} x Χ_{1} ) + β (Ψ_{2} x Χ_{2}). It is not necessary to see
a contradiction here from the point of view of orthodox quantum mechanics,
and there is none if we believe that the alternative is meaningless,
whether my friend's consciousness contains either the impression
of having seen a flash or of not having seen a flash. However, to deny
the existence of the consciousness of a friend to this extent is surely an
unnatural attitude, approaching solipsism, and few people, in their
hearts, will go along with it.
The preceding argument for the difference in the roles of inanimate
observation tools and observers with a consciousness—hence for a violation of physical laws where consciousness plays a role—is entirely cogent
as long as one accepts the tenets of orthodox quantum mechanics in all
their consequences.
("Remarks on the Mind-Body Question," pp.173-181)