Quantum Mechanics and the Psyche

18 Pages·2008·0.37 MB·English

ISSN 1063-7796, Physics of Particles and Nuclei, 2008, Vol. 39, No. 4, pp. 560–577. © Pleiades Publishing, Ltd., 2008.
Quantum Mechanics and the Psyche¶
G. Galli Carminatia and F. Martinb
a Mental Development Psychiatry Unit—Adult Psychiatry Service, Department of Psychiatry,
University Hospitals of Geneva, Switzerland
b Laboratoire de Physique Théorique et Hautes Energies,
Universités Paris 6 et 7, Place Jussieu, 75252 Paris Cedex 05, France
e-mail: [email protected]; [email protected]
Abstract—In this paper we apply the last developments of the theory of measurement in quantum mechanics to
the phenomenon of consciousness and especially to the awareness of unconscious components. Various models of
measurement in quantum mechanics can be distinguished by the fact that there is, or there is not, a collapse of the
wave function. The passive aspect of consciousness seems to agree better with models in which there is no collapse
of the wave function, whereas in the active aspect of consciousness—i.e., that which goes together with an act or
a choice—there seems to be a collapse of the wave function. As an example of the second possibility we study in
detail the photon delayed-choice experiment and its consequences for subjective or psychological time. We apply
this as an attempt to explain synchronicity phenomena. As a model of application of the awareness of unconscious
components we study the mourning process. We apply also the quantum paradigm to the phenomenon of correla-
tion at a distance between minds, as well as to group correlations that appear during group therapies or group train-
ing. Quantum entanglement leads to the formation of group unconscious or collective unconscious. Finally we
propose to test the existence of such correlations during sessions of group training.
PACS numbers: 03.65.Tq
DOI: 10.1134/S1063779608040047
1. INTRODUCTION tem from the observing system (roughly dividing the
quantum system from the classical one) gives exactly
The problem of measurement in quantum physics is
the same experimental results as if we set this border
still a topical subject. In 1932, von Neumann [1] pro-
between the system composed of the observed object
posed to split the evolution of the wave function, as a
and the detector on one side and human consciousness
function of time, during a measurement into two pro-
on the other side.
cesses. The first process is the unitary and deterministic
evolution of this wave function. The second process is Following von Neumann and Wigner in this way,
the collapse of this wave function into one of the eigen- Stapp [6] set the interface between the observed system
states of the measured observable. If the first process is and the observing system in the observer’s brain. This
continuous and deterministic, the second one is discon- allowed him to explain some behaviors of conscious-
tinuous and non-deterministic (probabilistic). ness within quantum theory.
The theory of quantum decoherence [2] allows to In 1967 Ricciardi and Umezawa [7] suggested the
explain how, due to interaction with the environment, a use of the formalism of quantum field theory for the
quantum system composed of the observed object and states of the brain, especially for memory states.
the detector goes from a coherent superposition of In 2003 Baaquie and Martin [8] also proposed a
quantum states to a statistical mixture of states referred quantum field theory of consciousness. But this theory
to a given basis (reduced density operator). applies firstly to mental states before it applies to brain
Some theories (e.g., the “Relative State” theory of states. This theory considers dual aspects of mind and
H. Everett [3] and the quantum information theory of matter. Such theories considered within the scope of
N. Cerf and C. Adami [4]) try to escape the collapse of quantum theory go back to Jung and Pauli [9–11]1.
the wave function.
It is in the framework of this dualistic aspect of mind
How does consciousness play a part in the quantum
and matter that our work takes place. The observation
measurement process? Does there exist a quantum the-
of correlations at a distance between several minds, just
ory of consciousness? Works on the role of conscious-
as the observation of synchronicity phenomena, lead us
ness in the quantum measurement process go back to
to postulate a non-localization of unconscious mental
von Neumann [1] and Wigner [5]. Particularly, for von
Neumann, to set the border dividing the observed sys- 1Concerning this subject we shall read with interest the review of
H. Atmanspacher, Quantum Approaches to Consciousness, in the
Stanford Encyclopedia of Philosophy [12]. This paper reviews
¶ The text was submitted by the authors in English. the situation on present quantum theories of consciousness.
560
QUANTUM MECHANICS AND THE PSYCHE 561
states. These states are not exclusively localized in the d
t
human brain. Mental states are correlated (probably via
Mirror
quantum entanglement) to physical states of the brain,
but they are not reducible to those physical states. d
r
With regard to synchronicity phenomena, i.e., sig-
Semi-transparent
nificant coincidences that appear between a mental mirror (optional)
state (subjective) and an event occurring in the external
world (objective), they confirm that the border between
2–1/2|r〉
the observed object and the human consciousness does
not really exist. In this respect we are going further than
Stapp [6]. Mirror
In this paper we shall try to build up a quantum |φ〉 2–1/2|t〉
Source
model of the correlations at a distance that show them-
selves between several minds, for example, between Semi-transparent mirror
two people (e.g., Alice and Bob), or in a group of peo- (mirror 1)
ple (group correlations). We shall also try to model the
The photon delayed-choice experiment.
awareness of unconscious components from the present
theories of quantum measurement. We shall see that the
model of Cerf and Adami [4], in which there is no col-
path has been followed. At the crossing point of the two
lapse of the wave function, seems to fit to the phenom-
beams we can put a second semi-transparent mirror that
enon of awareness better, because it does not so greatly
brings in a new phase difference between the different
alter the state of the unconscious.
partial waves. The phase differences are such that all
Finally, let us mention some works on quantum the-
photons go into one of the detectors (d) and none into
ories of consciousness related to physical states of the r
the other (d). We can choose to put, or not to put, the
brain. In addition to those already quoted (by Ricciardi t
second semi-transparent mirror at the crossing point of
and Umezawa [7]), there are Beck and Eccles’ work
the beams. Thus we can make a choice on the photon:
[13], those of Penrose [14], and those in which Penrose
either it follows one of the two paths when the second
collaborated with Hameroff [15].
semi-transparent mirror is not set up, or “it follows the
In our work we restrict our considerations to human two paths simultaneously,” in such a way that there is
consciousness, which not only has the property “to be an interference phenomenon, when the second semi-
aware of itself,” but also to be aware of the surrounding transparent mirror is set up at the crossing point. We can
environment. Other works have explored the concept of make this choice at the last moment, just before the
universal consciousness [8, 14] and therefore, to char- photon reaches the crossing point, after it has left the
acterize the object of this work, we have chosen the source, reached the first semi-transparent mirror and
term psyche instead of the more general one of con- been deviated by the reflectors. We conclude that we
sciousness, which could be interpreted as universal have an effect on the past of the photon. We are able to
consciousness. choose the past of the photon after this past has gone by.
This experiment, conceived by John Archibald
2. CHOICE OF THE PAST Wheeler [19], has been performed in laboratories [20].
It could be interesting to consider some psychologi- According to Wheeler this experiment could be
cal phenomena (correlations between minds at a dis- achieved with photons that have traveled through a gal-
tance, synchronicity effects) in light of some phenom- axy and thus have been deviated in several different
ena observed in quantum mechanics which pose prob- ways by the galaxy. Photons would have been emitted
lems with “classical” causality, such as the Einstein– by their source millions, or even billions, of years
Podolsky–Rosen “paradox” (EPR paradox) [16], Bell’s before they reach the detectors. In such a case, the
inequalities [17] and Alain Aspect’s experiments [18], delayed-choice experiment (“the choice on the past of
or the photon delayed-choice experiment. the photon”) would be performed on millions, or bil-
lions, years and not simply on millionths of a second as
Let us consider this last experiment (figure). An
they are performed in laboratories.
electromagnetic wave (photon beam) is divided into
two equal parts by a semi-transparent mirror (mirror 1, The quantum interpretation of the delayed-choice
half-silvered mirror). Then, two reflectors deviate each experiment is that we can say nothing about the photon
of the two beams in such a way that they intersect again as a particle between the moment it has been emitted by
at some point. Next, two detectors are set on each path the source and the moment it has been detected,
of the two beams, just after the crossing point. Half of because at the last moment we can make the choice we
the photons are recorded in one detector (dt), while the like. As said by Niels Bohr, “No elementary quantum
other half are recorded in the other detector (d). There- phenomenon is a phenomenon until it is a registered
r
fore, for each detected photon we can determine which phenomenon—that is, indelibly recorded or brought to
PHYSICS OF PARTICLES AND NUCLEI Vol. 39 No. 4 2008
562 GALLI CARMINATI, MARTIN
a close by an irreversible act of amplification.” What The choice to put or not to put the second semi-
happens between the time the photon is emitted by the transparent mirror has no influence on the past of the
source and the time it is detected has no localization in photon as a quantum system before the photon reaches
space–time as we conceive it usually. The delayed- this mirror or the crossing point. This past has gone by
choice experiment leads us to rethink the notion of past. and as a quantum system the photon has evolved in a
There is indeterminacy in the past of the photon. This deterministic way. On the other hand, due to the choice
indeterminacy comes from the wave–particle duality2. that we make about the second semi-transparent mirror,
we have an influence on the past of the photon consid-
The past of the photon is not fully determined either as
ered as a classical system before it reaches this mirror
a wave or as a particle. The delayed-choice experiment
or the crossing point. We have an influence on the “clas-
allows us to remove this indeterminacy, even if we act
sical” vision of the photon. This is what John Wheeler
on “things” that have already happened. John Archibald
calls observer-participancy. When the second semi-
Wheeler stresses upon the fact that “the past has no
transparent mirror is not set up, as a detected particle,
existence except as it is contained in the records, near
the photon will have followed one of the two paths.
and far, of the present.”
When this mirror is set up we are led to say that the
A superposition of quantum states persists in the
detected photon has behaved like a wave and therefore
past. Unless a measure has been performed or a choice
has followed the two paths simultaneously. It is on the
has been made, this coherent superposition of states
classical reconstruction of the past of the photon that
still exists as indeterminacy of the past.
we have an influence. The “quantum past” of the pho-
Quantum mechanics teaches us that there exist two
ton is itself fully determined and therefore cannot be
levels of reality. First there is the quantum level of real-
modified. On the other hand, we can make choices on
ity in which there exist superpositions of quantum
the classical reconstruction of the past of the photon. As
states that evolve in time in a deterministic way. For
we said before, what happens between the moment the
example, in the experiment described above the wave
photon is emitted by the source and the moment it
function of the photon (or the quantum electromagnetic
makes a click in one of the two detectors so far has no
field) evolves in a deterministic way, this evolution
localization in space–time as we usually conceive it.
being given by a unitary operator.
The result is that any “classical” reconstruction of what
The second level of reality is what we call the level happened is ambiguous.
of classical reality. It is the level of the single reality
In our consciousness the past appears as a succes-
that we observe with our consciousness. It is also the
sion of events that already happened and therefore can-
level that in physics is given by the (single) result of a
not be modified. However, this is a restriction of our
measure. The crossing of the bridge between the quan-
consciousness that is confined in the linear flow of time
tum and the classical reality is accomplished through an
(the stream of consciousness). A particular event that
operation that we call “the reduction of the wave
reaches our consciousness (that is registered by our
packet” (or “the collapse of the wave function”). This
consciousness) is like a photon that is registered by a
crossing is done in an irreversible and non-determinis-
detector. In the photon delayed-choice experiment, if
tic (probabilistic) way. In the delayed choice experi-
we don’t put the second semi-transparent mirror at the
ment the wave function of the photon evolves in a deter-
crossing point of the two paths, the probability of the
ministic way in space and time, up to the two detectors
photon reaching one of the two detectors is 50 percent
set up on each path of the photon. The collapse of the
for one and 50 percent for the other one. It is a probabi-
wave function happens in the two detectors. It is prob-
listic prediction of quantum mechanics. On the other
abilistic and, hence, non-deterministic.
hand, if we set up the second semi-transparent mirror,
When, at the crossing point of the two beams, we the probability becomes 100 per cent for one of the
decide to put or not to put the second semi-transparent detectors (d) and zero for the other one (d). The act of
r t
mirror, the past of the photon as a quantum state is fully
putting the second semi-transparent mirror modifies the
determined. On the other hand, as a classical system,
probabilities. In this case it transforms a probability
and especially as a particle, the state of the photon is not
into a certainty.
fully determined. The act of putting or not putting the
We can make an analogy between physical states
second semi-transparent mirror will not modify its
and mental states, and try to apply quantum mechanics
quantum aspect before the photon reaches this mirror or
to mental states as we do for physical states. In order to
the crossing point. However, it will modify the “classi-
do that we will consider mental states as quantum
cal” vision that we have of this photon. When the mirror
states, i.e., as vectors of a Hilbert space, obeying, for
will is not set up the photon will have followed one of
example, the superposition principle, … (see [8]).
the two paths when it is registered by one of the two
Among the mental states we will distinguish the states
detectors. When the mirror is set up the photon will
of consciousness that correspond to the thoughts and
have followed the two paths when it is registered.
ideas we are aware of. The states of consciousness will
constitute a part of the whole Hilbert space of mental
2The photon is, in itself, neither a wave nor a particle; it is the
states. On the other hand there will be states of uncon-
smallest possible excitation, in terms of energy, of the electro-
magnetic field. sciousness and pre-consciousness (insight) that will be
PHYSICS OF PARTICLES AND NUCLEI Vol. 39 No. 4 2008
QUANTUM MECHANICS AND THE PSYCHE 563
the states of our mind we are not aware of. As psycho- coherent superposition of states of our unconscious still
analysts such as Freud and Jung did, we will suppose exists as indeterminacy of the past. In the photon
the existence of an unconscious for every human being. delayed-choice experiment we can make a choice on
As for the states of consciousness, we will suppose that the “classical” past of this photon, and therefore have
the states of this unconscious are also quantum states, an influence on this past, by choosing to put, or not to
i.e., are vectors of a Hilbert space. The states of con- put, the second semi-transparent mirror. By analogy, to
sciousness together with the states of unconsciousness what extent can we have an influence on our own past
and pre-consciousness will form the whole set of men- and eventually modify it? At the quantum level, i.e., at
tal states. the level of our unconscious, this “past” is determined.
On the other hand, at the classical level, at the level of
If we now make the analogy between quantum
our consciousness, it is not necessarily fully deter-
mechanics and the phenomena of meaningful coinci-
mined. The “classical” reconstruction of our past has
dences (synchronicity effects), we can say that these
always to be done. In the photon delayed-choice exper-
coincidences are “ready for use” before they happen.
iment the influence on the “classical” past lies in the
They already belong to the Potentia but are not yet actu-
choice between the two possibilities of the second
alized. They exist in the past only as potentialities, such
semi-transparent mirror. It would be the same for our
as quantum states, or such as unconscious states. They
psyche. According to the “mirror” that we “set up” in
can be called phenomena only when “they are indelibly
the present our “classical” past appears in one way or in
recorded by an irreversible act of amplification,” i.e., by
another. The phenomena recorded by our unconscious
consciousness. The delayed choices that trigger off (or
persist as coherent superposition of quantum states.
don’t trigger off) a phenomenon of meaningful coinci-
The way our consciousness sheds light on these super-
dence are our acts of our everyday life. The analogue of
position makes a choice among the different quantum
setting up or not setting up the second semi-transparent
states and therefore gives it its “classical” aspect.
mirror at the crossing point of the two paths lies in our
acts. Every act is a choice. The analogy with “the cross- Let us examine in detail the experimental device of
ing point of the two paths” is really meaningful because the photon delayed-choice experiment (figure). Let us
we can imagine that for a significant coincidence to consider the case in which there is only one semi-trans-
happen there should be a constructive interference parent mirror (mirror 1). At the crossing of mirror 1 the
between two paths: one path is in our mind, a subjective wave function of the photon splits into two parts:
path, unconscious path, and the other path is in the
–1/2 –1/2
|φ〉 = 2 |r〉+2 |t〉, (1)
external world, an “objective” path. These two paths
cross at some point in space–time, they interfere and a reflected part 2–1/2|r〉 and a transmitted part 2–1/2|t〉.
are actualized by a choice and an act of consciousness. |r〉 will interact with detector d and |t〉 with detector d.
r t
However, one difference with the photon delayed- The wave function of the system composed by the pho-
choice experiment is that in this experiment the delayed ton and the two detectors is thus:
choice is made by the physicist who knows exactly the
–1/2 –1/2
|ψ〉 = 2 |r〉|d 〉+2 |t〉|d〉. (2)
phenomenon that will happen. In the case of meaning- r t
ful coincidences the delayed choices are unconscious: The density operator of the system is the one of a
unconscious of the phenomenon of coincidence that pure state:
will happen and will be brought to our consciousness.
ρ = |ψ〉〈ψ|. (3)
The quantum-entangled systems, non-separable
systems, are not locally but globally defined in space– However, the two detectors d and d interact with
r t
time. As said by Antoine Suarez [21], “In those systems the environment. Let us suppose that environment is
there is a dependence between events, but this depen- also a quantum system. The wave function of the over-
dence does not correspond to a temporal order. The all system is
quantum world cannot be anymore defined in terms of
–1/2 –1/2
‘before’ and ‘after.’ Things happen, but time, itself, |Ψ〉 = 2 |r〉|dr〉|Er〉+2 |t〉|dt〉|Et〉. (4)
does not go by.”
The information transmitted to the environment
If in a quantum mechanics experiment the “classi- being lost for the observer, the system is therefore
cal” past of the photon remains indeterminate, what described by a reduced density operator:
about the indeterminacies of our own past? As far as our
ρ = Tr |Ψ〉〈Ψ| = 1/2|r〉〈r||d 〉〈d |
mind is concerned, the analogue of a classical system is r E r r
(5)
our consciousness, which acts as a detector. As for the +1/2|t〉〈t||d〉〈d|.
t t
analogue of a quantum system, it is our whole psyche,
This density operator does not correspond anymore
in which there is especially our unconscious. As we
to a pure state but to a statistical mixture.
said above, we can imagine that as time flows our
unconscious exists as a superposition of quantum How is the choice made between the two detectors
states. Unless a “classical” measure has been done by d and d, and consequently between the two states |r〉
r t
our consciousness, unless a choice has been done, this and |t〉?
PHYSICS OF PARTICLES AND NUCLEI Vol. 39 No. 4 2008
564 GALLI CARMINATI, MARTIN
Let us notice that there is a symmetry between d We can imagine that something similar happens for
r
and d in the reduced density operator (5). psychological processes. When our consciousness reg-
t
isters an event (like a detector registers the click made
We can imagine that it is a spontaneous breakdown
by a photon) there is also a collapse of the wave func-
of this symmetry which causes the choice between d
r tion corresponding to the potentiality of this event. This
and dt (the photon is detected either in dr or in dt)3. Let collapse occurs in all space but also in an interval of
us notice that as long as we consider the photon as a time that can go back far in the past. When the present
wave the symmetry is preserved. It is only when the event recorded by our consciousness is in significant
photon is registered as a particle that the symmetry is coincidence with an event belonging to the past the col-
broken. lapse of the wave function occurs on all the temporal
The choice between d and d could be a spontaneous duration between this past event and the present.
r t
broken symmetry similar to the one of the bowls of When we perform an act for which, thanks to our
salad set on both sides of each guest having dinner on a free will, we have the choice to accomplish or not to
round table (left–right symmetry)4. In this example it is accomplish and when immediately after we observe in
the world that surrounds us symbolic events that are in
the choice of one of the guests that causes the sponta-
significant coincidence with the act we have just
neous breakdown of symmetry. It could be also a spon-
accomplished, this means that the completion of our act
taneous broken symmetry similar to the one that occurs
causes the collapse of a wave function which affects the
in a ferromagnet below a critical temperature. In such a
past. This collapse can even affect a remote past. This
material the choice of a direction of alignment for all
collapse is not a local one but a global one. This is the
the magnetic moments happens globally.
reason why synchronicity phenomena (significant coin-
Let us come back to “our” photon. If we make the
cidences) appear as non-causal (or acausal).
classical reconstruction of the route of the photon
between the moment it has been emitted by the source
and the moment it has been recorded, for example in 3. QUANTUM ENTANGLEMENT
detector d, there is a collapse of the wave function of
t The paper of Ray Streater, “Locality in the EPR
the photon between the moment the photon has crossed
experiment” [22], allows to make the following conclu-
mirror 1 and the moment it has been registered by d. In
t sions.
fact there is a collapse of the wave function on all the
Suppose that Alice and Bob each own a part of a
temporal duration bounded by the moment the photon
quantum-entangled system, for example, two photons
has been emitted by the source and the moment it has
or two electrons whose spins are correlated. If Alice
been detected. But the photon delayed choice experi-
does a measurement on the quantum object she pos-
ment shows that this collapse happens at the right
sesses and reads the result of the measurement, in case
moment the photon is recorded. We conclude that there
Bob has not yet done the measurement on his own
is a repercussion of the collapse of the wave function in
quantum object (or if he has done the measurement cor-
the past. Let us emphasize again that this effect appears
responding to the one done by Alice), Alice knows the
only when we consider the flow of time, the reconstruc-
quantum state of the object in Bob’s possession.
tion of the “classical” past, the construction of “one”
history. At the quantum level there is not only one clas- However she does not know the “classical” state of
sical history; there are many histories that are there as this object, i.e., the state resulting from a measurement
potentialities. done by Bob. There is one exception to this assertion. It
is when Bob does, has done, or will do the (classical)
The reduction of the wave packet, or the collapse of
measurement corresponding to the (classical) measure-
the wave function, thus occurs in space but also in time
ment that Alice has done herself on her own object. In
(in the past). Then this reduction of the wave packet
this case, and only in this case, does Alice know the
appears, on a classical level, as a process that is global
“classical” state of the object in Bob’s possession.
and not local in space–time (the reduction of the wave
packet of the photon registered by d does not occur If we assume that minds can be entangled like quan-
t
only at the level of detector d but in all the space, tum particle states, in the case of two quantum-entan-
t
including the source and the two detectors, and in all gled minds (e.g., Alice and Bob’s), if (at a distance)
time, between the moment the photon has been emitted Alice becomes aware of information which concerns
and the moment it has been recorded). Bob, Alice knows the quantum state of some part of
Bob’s psyche (the one that is quantum-entangled with
Let us notice that the setting of the experimental
her own psyche).
device is due to the human consciousness. Afterwards
it is the recording of the photon by one of the two detec- However, she does not know the “classical” state of
tors that collapses the wave function in space and time Bob’s psyche, i.e., what Bob becomes aware of. It
(especially by going back in the past). could be that what Bob becomes aware of is related to
that part of his psyche that is quantum-entangled with
3Alain Connes’ private communication. the one of Alice. In this situation there would be corre-
4Example given by Alain Connes. lation between the two consciousnesses (the one of
PHYSICS OF PARTICLES AND NUCLEI Vol. 39 No. 4 2008
QUANTUM MECHANICS AND THE PSYCHE 565
Alice and the one of Bob). But it could be also be that projected” [22]. When the statistical mixture is the
what Bob becomes aware of does not concern at all that result of the interaction of the measuring device—con-
part of his psyche that is quantum-entangled with sidered also as a quantum system—with the environ-
Alice’s. In this situation the appearance of quantum ment we use the term “pointer-state.”
entanglement (the correlation) of which Alice becomes According to Ray Streater the details of the measur-
aware remains unconscious for Bob. ing device do not affect the reading of the measurement
When two twins buy simultaneously (at a distance) result by the observer: “Thus, a complete description of
two identical ties without having consulted each other the measuring device is given by the label n, element of
beforehand, the entanglement (the correlation) appears J.” We can describe the “pointer-states” of the measur-
in the “classical” world only when a human conscious- ing device with the help of a family of operators χ
n
ness (one of the two twins or a third party) becomes which act on the Hilbert space L2(J):
aware of the fact.
χ (m) = δ (Kronecker’s symbol) = 1
When C.G. feels bad she makes a phone call to her n nm
twin sister. This one, who is a psychotherapist, tells her if m = n and = 0 if m is different from n.
that she is presently treating a difficult case. C.G. has The result of the first stage of the measurement is
the insight that her feeling of sickness is the result of described by the reduced density operator
her quantum entanglement with her twin sister. How-
ever, she needs to telephone her sister, that is to say, she
needs the transmission of information by a “classical” ρ = ∑ p χ ⊗|ψ 〉〈ψ | (7)
red n n n n
channel, in order to confirm that her feeling of sickness
n∈J
is really the demonstration of her correlation with her
acting on the tensor product of L2(J) and H. Let us sup-
twin sister. While she is treating the case of a difficult
pose now that the quantum object has left the neighbor-
patient, her twin sister is probably not aware of the fact
hood of the measuring instrument, that Alice reads the
that it causes a feeling of sickness for her sister. How-
result of the measurement, and that this result corre-
ever by experiencing this fact several times she can
sponds to the label m, element of J. After the measure-
become aware of it. Nevertheless, she will never be
ment the quantum system is thus in the pure state |ψ 〉.
sure, because her sister does not necessarily have a feel- m
The density operator of the quantum system is therefore
ing of sickness every time she is treating a difficult case.
one of a pure state:
There is still a difference between what is quantum-
entangled at the unconscious level and what reaches ρ = |ψ 〉〈ψ |. (8)
m m
insight and consciousness and appears in the “classi-
cal” world. The von Neumann entropy (S = –Tr(ρlnρ)) of the
quantum system is therefore equal to zero. Let us sup-
pose now that Alice has done an incomplete reading of
4. MEASUREMENT AND ENTROPY the measuring instrument, so that she only knows that
the label n lies in some subset K of J. The density oper-
In a slightly different way from von Neumann’s
ator of the quantum system as it observed by Alice is
splitting of the measurement process into two pro-
(von Neumann)
cesses, we can consider that the first stage of a measure-
ment process in quantum physics is the interaction of
∑ p |ψ 〉〈ψ |
the quantum object (the observed object) with the mea- n n n
suring device (which can be considered as a classical ρ = n---∈----K------- ---------------------. (9)
K
object after interaction with the environment). The sec- ∑ p
n
ond stage is the reading of the result of the measure-
n∈K
ment by the observer (e.g., Alice). Let us suppose that
the measurement concerns an observable X whose The von Neumann entropy of this system is
eigenstates are |ψ 〉 (with no multiplicity), n running
n ⎛ ⎞
over a set of labels J. Let us suppose in addition that the ⎜ ⎟
p
initial state of the quantum system is a pure state |φ〉 ∑ p ln⎜ ----- -----n-----⎟--
belonging to a Hilbert space H. n ⎜ ∑ p⎟
n∈K ⎝ m⎠
At the end of the first stage the state of the quantum
m∈K
system is a statistical mixture of all the eigenstates of X SK = –------------------- -------------------------
with weights given by the quantum transition probabil- ∑ pn (10)
ities:
n∈K

p = 〈ψ |φ〉 2. (6) ⎛ ∑ p lnp ⎞
n n ⎜ n n ⎟
⎛ ⎞
“A good measuring device is a classical system in = –⎜⎜ n---∈----K--- ----------------– ln⎝ ∑ p⎠n⎟⎟ .
which the “pointer” of the device is 100% correlated ⎝ ∑ pn n∈K ⎠
with the eigenstate into which the quantum system is
n∈K
PHYSICS OF PARTICLES AND NUCLEI Vol. 39 No. 4 2008
566 GALLI CARMINATI, MARTIN
When the measurement done by Alice is complete balanced by an increase of a quantity at least equal to
(measure of an eigenstate |ψ 〉 of the observable X) we the entropy of the environment (for example, the heat
m
find again an entropy equal to zero, and when the mea- emitted by Alice’s body).
surement done by Alice is totally incomplete, e.g.,
Let us suppose that we have a system O (which may
when she has not yet read the result of the measure-
be a quantum one) on which we want to obtain some
ment, we find again the usual entropy of a statistical
information (e.g., on an observable quantity X of this
mixture result of the interaction of the quantum system
system). The missing information, that is to say, the
with the measuring device followed by the interaction
Shannon entropy (or the von Neumann entropy if this is
of this device with the environment:
a quantum system that interacts with the environment),
is given by formula 11.
S = –∑ p ln(p ). (11)
J n n If we split the information that we can obtain on sys-
n∈J tem O into two subsets, corresponding to two subsets of
We see in these examples that the entropy (of von indexes J and J of J (such that J ∪ J = J and J ∩ J =
1 2 1 2 1 2
Neumann) of the quantum system after the measure- 0), and if p and p indicate respectively the proba-
J J
ment is directly linked up to the knowledge, i.e., the 1 2
bilities that the missing information is indexed in J or
information, that Alice has of the quantum system that 1
in J , we can rewrite equation 11 as
has gone through the process of measurement. 2
If Alice has done a complete measurement of the S = p S + p S –(p ln(p )+ p ln(p )), (15)
J J J J J J J J J
observable X, her information has increased by the 1 1 2 2 1 1 2 2
amount SJ given by equation 11, which corresponds to in which SJ and SJ are the relative entropies given by
an increase of the entropy of the environment (includ- 1 2
expressions similar to 13:
ing Alice’s body) by a quantity at least equal to S . The
J
fact that the information acquired by Alice on the quan- p ⎛ p⎞
tum object has increased by the quantity SJ tells us that SJ1 = – ∑ -p----n--ln⎝ -p----n⎠-- , (16)
the von Neumann entropy of the system quantum – n∈J J1 J1
1
object + Alice’s consciousness has decreased by this

vtoe rtyh es ainmcer eqausaen otift yth bea elanntrcoepdy b oyf a t hqeu aenntvitiyro antm leeanstt. equal SJ2 = – ∑ -p-p---n--ln⎝⎛ -p-p---n⎠⎞-- . (17)
J J
n∈J 2 2
Let us come back now to the case where Alice has 2
done an incomplete reading of the measurement of the If Alice performs a measurement and she finds that
observable X, and that she only knows that the eigen- the information she is looking for is in the subset
value of the observable X lies in the subset of eigenval- indexed by J , her Shannon entropy (her missing infor-
1
ues labeled by the subset K of J. If we write mation) will be decreased by
pK = ∑ pn, (12) pJ2SJ2–(pJ1ln(pJ1)+ pJ2ln(pJ2)), (18)
n∈K which is a positive quantity, or increased by
which is nothing other than the probability of measur-
ing the eigenvalue of X in the subset labeled by K, –pJ SJ +(pJ ln(pJ )+ pJ ln(pJ )), (19)
2 2 1 1 2 2
equation 10 can be rewritten:
which is a negative quantity.

p ⎛ p⎞
SK = –n∑∈K-p---K-n-ln⎝ -p---K-⎠n- . (13) thenT heex pirnefsosremda btiyo nS Jw1.hich is still missing for Alice is
The quantity S measures the missing information At each level of information acquired by Alice, the
K
of Alice regarding the observable X linked to the quan- entropy of the environment increases by a quantity at
tum object. We are faced with an entropy relative to the least equal to the quantity of information obtained.
subset of labels K. We note that everything that has been said in this
If the measuring device is macroscopic and if it has section, as well as what will be exposed in the follow-
registered a specific eigenvalue of the observable X, the ing one, corresponds to classical information,
entropy of the environment has increased by the quan- expressed by the classical Shannon–Boltzmann–Gibbs
tity S given by formula 11. If it is the reading made by entropy, given that, after interaction with the environ-
J
Alice of the measuring device that is incomplete, then ment, the von Neumann entropy becomes such a classi-
the von Neumann entropy of the system quantum – cal entropy. Indeed, information on the phases between
object + Alice’s consciousness will have decreased by the various quantum states, phases that are characteris-
the quantity tic of the coherent superposition of quantum states, is
not accessible any longer for the kind of measurement
SJ– pKSK, (14) under consideration.
PHYSICS OF PARTICLES AND NUCLEI Vol. 39 No. 4 2008
QUANTUM MECHANICS AND THE PSYCHE 567
5. LAYERED INFORMATION Let us suppose that the state which came to Alice’s
consciousness was |C11〉, showing that Bob’s uncon-
The first step of the construction of the psyche of a
scious is in the state |C21〉. Let us further suppose that
given individual is the creation of the fundamental state
Alice wanted to refine her information on Bob’s uncon-
of the human species |G(t)〉 (see formulas 13–16 in [8])
scious and that, starting from this state |C21〉 of Bob’s
from the vacuum state |Ω〉. The second step is the con-
unconscious, she wanted to get access to deeper layers
struction, starting from the state |G(t)〉, which describes
of his unconscious.
the collective unconscious, of a family unconscious
To this end, she tries to gain access to the eigenval-
described by the state |G (t)〉 (formula 19 in [8]), and
Effective ues and eigenstates of a new observable X of Bob’s
then the creation of an individual unconscious, described 2
unconscious. Let us suppose, as in the preceding para-
by the state |G (t)〉 (formula 19 in [8]). The state of
Individual graph, that the eigenstates of X , |C21n 〉, are labeled in
the psyche of this individual is therefore described, at a 2 1
a set J (n ∈ J ). After the interaction with the environ-
given moment t, by the action of the creation operator spe- 1 1 1
ment, the corresponding pointer-states of Alice’s
†
cific to this individual a (t, x (t)) on the state
Individual Individual psyche will be the states |C11n 〉 (each state |C11n 〉 of
1 1
|GIndividual(t)〉 (his individual unconscious at time t): Alice’s psyche being correlated to the state |C21n1〉 of
Bob’s unconscious). Let p be the probability that
|P(t, x(x))〉 = a† (t, x (t))|G (t)〉. (20) n1
Individual Individual Individual Bob’s psyche is in the state |C21n 〉. The relative prob-
1
We therefore have a kind of layered model for the ability after the first measurement performed by Alice
human psyche that we can compare to the layered p
n
model of matter: molecules, atoms, nuclei, protons, (observable X ) is -------1, and Alice’s missing information
1 p
neutrons, and finally, at our present level of knowledge, 1
quarks and gluons. We note that the latter are confined (Shannon or von Neumann entropy) is given by a for-
inside nucleons (protons and neutrons). We could then mula similar to 16:
compare this confinement of quarks and gluons to the
dreeperpeessste dla pyaerrtss .of our unconscious, in particular, its S1 = – ∑ -p-p--n---1ln⎝⎛ -p-p--n-⎠⎞--1 . (23)
1 1
n ∈J
Let us suppose that Alice (described by mental state 1 1
|C1〉) wants to obtain some information about Bob’s Before Alice becomes aware of what concerns the
unconscious (mental state |C2〉). At first, when Alice observable X2, the entropy of the system Bob’s uncon-
and Bob meet, their unconscious states interact, and scious + Alice’s consciousness is S1. When Alice
this generates a state of quantum entanglement of their obtains the information, that is, when she comes to
unconscious states. Let us further suppose that at first know the pointer-state |C11n 〉, the entropy of this sys-
1
Alice wants to obtain information on an observable X tem decreases by S , compensated by an increase of the
1 1
with two eigenvalues and eigenstates (binary situation). environment entropy of at least the same magnitude.
The mental (unconscious) interaction of Alice with the We can of course follow the same argument for new
environment (represented here by the collective uncon- and deeper layers of Bob’s unconscious.
scious |G(t)〉) generates two “pointer states” |C11〉 and
|C12〉 in Alice’s psyche, which are respectively corre-
lated with the states |C21〉 and |C22〉 of Bob’s psyche 6. IS THERE A COLLAPSE
(eigenstates of the X observable about which Alice OF THE WAVE FUNCTION?
wants to obtain some information).
Nicolas J. Cerf and Chris Adami [4] have analyzed
If p and p are the respective probabilities that the the measurement process in quantum mechanics from
1 2
pointer states |C11〉 and |C12〉 come to Alice’s con- the point of view of information theory applied to quan-
sciousness, the information that she is still missing tum entanglement. In their interpretation, the measure-
(Shannon or von Neumann entropy) is given by the for- ment process is described by entropy-conserving uni-
mula tary interactions. In this framework, during the mea-
surement process, there is neither collapse of the wave
–(p ln(p )+ p ln(p )). (21) function nor quantum jump. Cerf and Adami take into
1 1 2 2
consideration a quantum object Q and a measurement
When Alice acquires the information |C11〉 or |C12〉,
device A, itself a quantum system. The measurement
that is, when this information comes to her conscious-
process begins with quantum entanglement between Q
ness, the entropy of the system Bob’s unconscious +
and A (the first step of von Neumann’s measurement
Alice’s consciousness is decreased by the quantity
process), which corresponds to the creation of an EPR
state “QA,” that creates “super-correlations” between
–(p ln(p )+ p ln(p )), (22)
1 1 2 2 Q and A, rather than correlations.
while the entropy of the environment increases by the “The system QA thus created is inherently quantum,
same quantity. and cannot reveal any classical information. To obtain
PHYSICS OF PARTICLES AND NUCLEI Vol. 39 No. 4 2008
568 GALLI CARMINATI, MARTIN
the latter, we need to create classical correlations Such a superposition of two elementary states has
between part of the EPR-pair QA and another ancilla been studied by Yuri Orlov [23] for doubt mental states.
A'; i.e., we need to observe the quantum observer.” An Let us further suppose that, in the framework of this
EPR triplet QAA' is then created via unitary process, binary information, Alice’s unconscious (C1) connects
and it is a pure state |QAA'〉 described by the density to Bob’s one to form an EPR state:
matrix
iφ
|C1,C2〉 = sinθ|C10〉|C20〉+ cosθe |C11〉|C21〉.(27)
ρ = |QAA'〉〈QAA'|. (24)
QAA'
We can consider that, due to the interaction of
Alice’s psyche with the environment (a phenomenon
“Experimentally, we are only interested in the corre-
akin to quantum decoherence for physical systems),
lations between A and A' and not in the correlations
Alice’s consciousness cannot access the pure state |C1,
between A and Q (which are unobservable anyway)….
C2〉 but rather a reduced density matrix similar to equa-
It is immediately obvious that when ignoring the quan-
tion (25):
tum state Q itself, as paradoxically as it may appear at
first sight, A and A' find themselves classically corre-
ρ = Tr (ρ ), (28)
lated and in a mixed state”: C1C2 C3 C1C2C3
the trace being taken on an unknown degree of freedom
ρ = Tr (ρ ). (25) that forms an EPR triplet with Alice’s and Bob’s uncon-
AA' Q QAA'
scious (this can be the unconscious of a third person C3,
or even the collective unconscious |G(t)〉). We then
The entropy of the AA' system is positive, but it is
obtain
compensated by a conditional entropy of Q (the entropy
of Q when the AA' system is known) that is negative, the
2
ρ = sin θ|C10〉〈C10||C20〉〈C20|
total entropy of the QAA' system remaining null and C1C2
(29)
QAA' staying as a pure state. 2
+ cos θ|C11〉〈C11||C21〉〈C21|
It is difficult to justify how the EPR triplet QAA' can
remain a pure state described by |QAA'〉 after the mea- related to an increase in entropy
surement. Indeed, in all known models of quantum
2 2 2 2
measurement, if the measurement of the classical cor- S = –(sin θln(sin θ)+ cos θln(cos θ)). (30)
relation between A and A' reveals a given eigenvalue of
the observable X, the quantum object Q is left in the We will suppose that this realization (awareness) by
corresponding eigenstate. A choice, namely, the choice Alice, linked to an entropy production, does not destroy
of the measured eigenstate, has happened. We have had the EPR state |C1, C2〉 (27); this realization can, never-
a quantum jump and a collapse of the wave function. theless, introduce an unitary transformation of the |C1,
This does not happen in the model of Cerf and Adami. C2〉 EPR state (27), specifically changing the θ and φ
angles as functions of time.
We would need to find an experimental test that
We note that our development does not correspond
could discriminate between the theories of quantum
to Cerf and Adami’s one. In contrast to them, we did not
measurement that does not imply either the collapse of
take the trace on the quantum state of the measured
the wave function or a quantum jump (Everett’s “Rela-
object (Bob’s unconscious), but on a third quantum
tive State” theory [3], negative entropy theory of Cerf
state |C3〉 with which Bob and Alice are quantum-cor-
and Adami [4]) and the more “ordinary” theories that
related. This method is closer to the one used in quan-
suppose (or imply) a collapse of the wave function and
tum decoherence, which implies the dispersion in the
quantum jumps (Copenhagen school theory, von Neu-
environment of some degrees of freedom.
mann’s theory [1], quantum decoherence [2], etc.).
Nevertheless, starting from the next paragraph, we
Nevertheless, the fact that there is no quantum jump will treat the measurement of the unconscious in a way
and that an EPR system remains practically in the pure very similar to the one elaborated by Cerf and Adami.
state in which it was before the measurement is very
Let us come back for a moment to Cerf and Adami’s
interesting as far as the unconscious is concerned.
theory of negative entropy. In their article “What Infor-
Let us suppose that, with respect to a given piece of mation Theory Can Tell Us About Quantum Reality”
information (for example, mourning or not-mourning5, [24], they claim to solve the “Schrödinger’s Cat” para-
dox summing on all quantum states of the radioactive
Bob’s unconscious (C2) is described by a superposition
substance causing (or not causing) the death of the cat.
two states (representation similar to Bloch’s sphere):
However, as they do not define at any moment pointer-
states (which are usually defined by the interaction with
iφ
|C2〉 = sinθ|C20〉+ cosθe |C21〉. (26) the environment), it is always possible to make a
change of basis before summing the states of the radio-
5See Section 7. active atom, and therefore we will obtain real states that
PHYSICS OF PARTICLES AND NUCLEI Vol. 39 No. 4 2008
QUANTUM MECHANICS AND THE PSYCHE 569
are superpositions of the state “live cat” and the state of being conscious: either minimize/maximize
“dead cat” (we note that the same problem exists in entanglement entropy in order to achieve knowl-
Everett’s theory of “Relative State” [3]). edge about world/power to change it.
Moreover, they write, “Fundamentally, the reason This comforts us in the idea that consciousness
why the observer does not register a cat mired in a states are related to quantum jumps that are not associ-
quantum superposition of the living and non-living ated with a collapse of the wave function of the uncon-
states is because the observer, having interacted with scious. In particular, they do not destroy the states of
the cat, is entangled with, and thus part of, the same quantum entanglement of the unconscious. This is very
wave function. As the wave function is indivisible, an similar to Cerf and Adami’s point of view. However, in
observer (or measurement device) would have to mon- our opinion, pointer-states, which are those states that
itor itself in order to learn about the wave function. This come to be known to consciousness, are defined by the
is logically impossible.” interaction of the psyche with the environment. This
interaction with the environment brings to conscious-
This is opposed by D.G. Chakalov [25]: “I think
ness states that are in harmony with the environment
self-monitoring is an essential introspective feature of
and thus with the classical reality that surrounds us.
human consciousness: we do know the quale of our
This is why a state of superposition of a “dead cat” with
brain’s wave function—the human self?—being entan-
a “live cat” does not become manifest to our conscious-
gled with our brain, and thus part of the same wave
ness. There can, however, be situations where con-
function. Psychologically, this is manifested in our
sciousness acquires knowledge of mystical states that
ability to think ABOUT that which we think (our
are not in harmony with the classical reality around us.
brain), BY that with which we think (our brain). Hence
In these rare occurrences, the conscious realization of a
the statement by C. Adami and N.J. Cerf is NOT valid
fundamentally quantum state is “protected” from the
for human consciousness.”
interaction with the environment.
In a similar way, Matti Pitkanen [26] writes
Quantum jump/state function collapse can
explain the active aspect of conscious (bodily 7. QUANTUM MODEL OF MOURNING
actions, etc.). But can it explain the passive aspect
We will study how Bob faces mourning, for exam-
of consciousness involving no conscious choice
ple, the loss of his father6. We will consider the part of
(sensory experience)?
Bob’s unconscious related to this mourning. We will
That standard quantum jump between eigen-
designate it by |CD2〉, a vector of a Hilbert space.
states of observables is not enough to understand
consciousness is suggested by several argu- As a consequence of interaction with the environ-
ments, besides this self-monitoring aspect ment, we will suppose that there exist two pointer-
emphasized by Dimitri Chakalov. states, i.e., two stable states as far as the mourning is
concerned, of which Bob can become aware. Thus there
(a) Sensory experience does not involve expe-
would be, first, the state |CD21〉 that would correspond
rience of free will.
to a totally not carried through mourning (Bob would
(b) If contents of contents are defined by the
not have accepted at all his father’s death). Then there
initial and final states of quantum jumps which
would be the state |CD20〉 for which the mourning
are different, then it would be impossible to have
would be achieved (Bob would have accepted com-
objective information about quantum states but
pletely his father’s death). It seems to us that these two
only quantum state pairs.
states can represent realistic pointer-states insofar as
(c) It would be difficult to understand the each of them is associated to some reality. The first state
apparent continuity of conscious experience, is associated to the reality in which the father is still
since same subsystem could not participate in alive, while the second state is associated to the reality
subsequence quantum jumps.
in which the father is deceased. Those two pointer-
If one assumes also that quantum jumps states also correspond each to the answers that Bob can
changing only the phase associated with sub- make to the question “Is your father dead?”, the reply
systems state function so that physical state being “No” in the first case and “Yes” in the second
remains as such, are possible then one can solve one. We will suppose that each of those two states is of
these problems. In Topological Geometrody- minimal entropy as far as the interaction with the envi-
namics context the strong form of Negentropy ronment is concerned. We are thus dealing with a
Maximization Principle allows systems with binary situation.
minimal quantum entanglement to perform these
Therefore, the state of Bob’s unconscious related to
quantum jumps. These passive quantum jumps
this mourning is a superposition of the two pointer-
could also correspond to the self-monitoring
states |CD21〉 and |CD20〉, a superposition that we
aspect of consciousness. They are also very close
to classical measurements since they do not 6One of the two authors of this paper (GGC) has published a study
change the physical state, but of course, respect
of the mechanism of mourning within the framework of chaos
uncertainty principle. This leads to two strategies theory [27].
PHYSICS OF PARTICLES AND NUCLEI Vol. 39 No. 4 2008