## 1. Introduction



The problem of how mind and matter are related to each other has many
facets, and it can be approached from many different starting points.
The historically leading disciplines in this respect are philosophy
and psychology, which were later joined by behavioral science,
cognitive science and neuroscience. In addition, the physics of
complex systems and quantum physics have played stimulating roles in
the discussion from their beginnings.



As regards the issue of complexity, this is evident: the brain is one
of the most complex systems we know. The study of neural networks,
their relation to the operation of single neurons and other important
topics do and will profit a lot from complex systems approaches. As
regards quantum physics, there can be no reasonable doubt that quantum
events occur and are efficacious in the brain as elsewhere in the
material world--including biological
 systems.[1]
 But it is controversial whether these events are efficacious and
relevant for those aspects of brain activity that are correlated with
mental activity.



The original motivation in the early 20th century for relating quantum
theory to consciousness was essentially philosophical. It is fairly
plausible that conscious free decisions ("free will") are
problematic in a perfectly deterministic
 world,[2]
 so quantum randomness might indeed open up novel possibilities for
free will. (On the other hand, randomness is problematic for
goal-directed volition!)



Quantum theory introduced an element of randomness standing out
against the previous deterministic worldview preceding it, in which
randomness expresses our ignorance of a more detailed description (as
in statistical mechanics). In sharp contrast to such epistemic
randomness, quantum randomness in processes such as the spontaneous
emission of light, radioactive decay, or other examples has been
considered a fundamental feature of nature, independent of our
ignorance or knowledge. To be precise, this feature refers to
*individual* quantum events, whereas the behavior of
*ensembles* of such events is *statistically*
determined. The indeterminism of individual quantum events is
constrained by statistical laws.



Other features of quantum theory, which became attractive in
discussing issues of consciousness, were the concepts of
complementarity and entanglement. Pioneers of quantum physics such as
Planck, Bohr, Schrodinger, Pauli (and others) emphasized the
various possible roles of quantum theory in reconsidering the old
conflict between physical determinism and conscious free will. For
informative overviews with different focal points see e.g., Squires
(1990), Kane (1996), Butterfield (1998), Suarez and Adams (2013). 


## 2. Philosophical Background Assumptions



Variants of the dichotomy between mind and matter range from their
fundamental distinction at a primordial level of description to the
emergence of mind (consciousness) from the brain as an extremely
sophisticated and highly developed material system. Informative
overviews can be found in Popper and Eccles (1977), Chalmers (1996),
and Pauen (2001).



One important aspect of all discussions about the relation between
mind and matter is the distinction between *descriptive* and
*explanatory* approaches. For instance, *correlation* is
a descriptive term with empirical relevance, while *causation*
is an explanatory term associated with theoretical attempts to
understand correlations. Causation implies correlations between cause
and effect, but this does not always apply the other way around:
correlations between two systems can result from a common cause in
their history rather than from a direct causal interaction.



In the fundamental sciences, one typically speaks of causal relations
in terms of interactions. In physics, for instance, there are four
fundamental kinds of interactions (electromagnetic, weak, strong,
gravitational) which serve to explain the correlations that are
observed in physical systems. As regards the mind-matter problem, the
situation is more difficult. Far from a theoretical understanding in
this field, the existing body of knowledge essentially consists of
empirical correlations between material and mental states. These
correlations are descriptive, not explanatory; they are not causally
conditioned. It is (for some purposes) interesting to know
*that* particular brain areas are activated during particular
mental activities; but this does, of course, not explain *why*
they are. Thus, it would be premature to talk about mind-matter
interactions in the sense of causal relations. For the sake of
terminological clarity, the neutral notion of relations between mind
and matter will be used in this article.



In many discussions of material [ma] brain states and mental [me]
states of consciousness, the relations between them are conceived in a
*direct* way
 (A):


 
\[
[\mathbf{ma}] \substack{\leftarrow \\ \rightarrow} [\mathbf{me}]
\]


This illustrates a minimal framework to study reduction,
supervenience, or emergence relations (Kim 1998; Stephan 1999) which
can yield both monistic and dualistic pictures. For instance, there is
the influential stance of *strong reduction*, stating that all
mental states and properties can be reduced to the material domain or
even to physics
 (physicalism).[3]
 This point of view claims that it is both necessary and sufficient to
explore and understand the material domain, e.g., the brain, in order
to understand the mental domain, e.g., consciousness. It leads to a
monistic picture, in which any need to discuss mental states is
eliminated right away or at least considered as epiphenomenal. While
mind-brain correlations are still legitimate though causally
irrelevant from an epiphenomenalist point of view, eliminative
materialism renders even correlations irrelevant.



Much discussed counterarguments against the validity of such strong
reductionist approaches are qualia arguments, which emphasize the
impossibility for physicalist accounts to properly incorporate the
quality of the subjective experience of a mental state, the
"what it is like to be" (Nagel 1974) in that state. This
leads to an explanatory gap between third-person and first-person
accounts for which Chalmers (1995) has coined the notion of the
"hard problem of consciousness". Another, less discussed
counterargument is that the physical domain itself is not causally
closed. Any solution of fundamental equations of motion (be it
experimentally, numerically, or analytically) requires to fix boundary
conditions and initial conditions which are not given by the
fundamental laws of nature (Primas 2002). This causal gap applies to
classical physics as well as quantum physics, where a basic
indeterminacy due to collapse makes it even more challenging. A third
class of counterarguments refer to the difficulties to include notions
of temporal present and nowness in a physical description (Franck
2004, 2008; Primas 2017).



However, relations between mental and material states can also be
conceived in a non-reductive fashion, e.g. in terms of emergence
relations (Stephan 1999). Mental states and/or properties can be
considered as emergent if the material brain is not necessary or not
sufficient to explore and understand
 them.[4]
 This leads to a dualistic picture (less radical and more plausible
than Cartesian dualism) in which residua remain if one attempts to
reduce the mental to the material. Within a dualistic scheme of
thinking, it becomes almost inevitable to discuss the question of
causal influence between mental and material states. In particular,
the causal efficacy of mental states upon brain states
("downward causation") has recently attracted growing
interest (Velmans, 2002; Ellis *et al.*
 2011).[5]
 The most popular approaches along those lines as far as quantum
behavior of the brain is concerned will be discussed in
 Section 3,
 "Quantum Brain". 



It has been an old idea by Bohr that central conceptual features of
quantum theory, such as complementarity, are also of pivotal
significance outside the domain of physics. In fact, Bohr became
familiar with complementarity through the psychologist Edgar Rubin
and, more indirectly, William James (Holton 1970) and immediately saw
its potential for quantum physics. Although Bohr was also convinced of
the extraphysical relevance of complementarity, he never elaborated
this idea in concrete detail, and for a long time after him no one
else did so either. This situation has changed: there are now a number
of research programs generalizing key notions of quantum theory in a
way that makes them applicable beyond physics.



Of particular interest for consciousness studies are approaches that
have been developed in order to pick up Bohr's proposal with
respect to psychology and cognitive science. The first steps in this
direction were made by the group of Aerts in the early 1990s (Aerts
*et al.* 1993), using non-distributive propositional lattices
to address quantum-like behavior in non-classical systems. Alternative
approaches have been initiated by Khrennikov (1999), focusing on
non-classical probabilities, and Atmanspacher *et al.* (2002),
outlining an algebraic framework with non-commuting operations. The
recent development of ideas within this framework of thinking is
addressed in
 Section 4,
 "Quantum Mind". Other lines of thinking are due to Primas
(2007, 2017), addressing complementarity with partial Boolean
algebras, and Filk and von Muller (2008), indicating links
between basic conceptual categories in quantum physics and
psychology.



As an alternative to (A), it is possible to conceive mind-matter
relations *indirectly*
**(B)**,
 via a third category:

 

\[\begin{gather}
[\mathbf{ma}] \quad [\mathbf{me}] \\
 \searrow\nwarrow \swarrow\nearrow \\
 [\mathbf{mame}]
\end{gather}\]


This third category, here denoted [mame], is often regarded as being
neutral with respect to the distinction between [ma] and [me], i.e.,
psychophysically neutral. In scenario (B), issues of reduction and
emergence concern the relation between the unseparated
"background reality" [mame] and the distinguished aspects
[ma] and [me].



Such "dual aspect" frameworks of thinking have received
increasing attention in contempory discussion, and they have a long
tradition reaching back as far as to Spinoza. In the early days of
psychophysics, Fechner (1861) and Wundt (1911) advocated related
views. Whitehead, the modern pioneer of process philosophy, referred
to mental and physical poles of "actual occasions", which
themselves transcend their bipolar appearances (Whitehead 1978). Many
approaches in the tradition of Feigl (1967) and Smart (1963), called
"identity theories", conceive mental and material states
as essentially identical "central states", yet considered
from different perspectives. Other variants of this idea have been
suggested by Jung and Pauli (1955) [see also Meier (2001)], involving
Jung's conception of a psychophysically neutral, archetypal
order, or by Bohm and Hiley (Bohm 1990; Bohm and Hiley 1993; Hiley
2001), referring to an implicate order which unfolds into the
different explicate domains of the mental and the material. They will
be discussed in more detail in
 Section 5,
 "Brain and Mind as Dual Aspects". 



Velmans (2002, 2009) has developed a similar approach, backed up with
empirical material from psychology, and Strawson (2003) has proposed a
"real materialism" which uses a closely related scheme.
Another proponent of dual-aspect thinking is Chalmers (1996), who
considers the possibility that the underlying, psychophysically
neutral level of description could be best characterized in terms of
information.



Before proceeding further, it should be emphasized that many
present-day approaches prefer to distinguish between first-person and
third-person perspectives rather than mental and material states. This
terminology serves to highlight the discrepancy between immediate
conscious experiences ("qualia") and their description, be
it behavioral, neural, or biophysical. The notion of the "hard
problem" of consciousness research refers to bridging the gap
between first-person experience and third-person accounts of it. In
the present contribution, mental conscious states are implicitly
assumed to be related to first-person experience. This does not mean,
however, that the problem of how to define consciousness precisely is
considered as resolved. Ultimately, it will be (at least) as difficult
to define a mental state in rigorous terms as it is to define a
material state.


## 3. Quantum Brain



In this section, some popular approaches for applying quantum theory
to brain states will be surveyed and compared, most of them
speculative, with varying degrees of elaboration and viability.
 Section 3.1
 addresses three different neurophysiological levels of description,
to which particular quantum approaches refer. Subsequently, the
individual approaches themselves will be discussed --
 Section 3.2:
 Stapp,
 Section 3.3:
 Vitiello and Freeman,
 Section 3.4:
 Beck and Eccles,
 Section 3.5:
 Penrose and Hameroff. 



In the following, (some of) the better known and partly worked out
approaches that use concepts of quantum theory for inquiries into the
nature of consciousness will be presented and discussed. For this
purpose, the philosophical distinctions A/B
 (Section 2)
 and the neurophysiological distinctions addressed in
 Section 3.1
 will serve as guidelines to classify the respective quantum
approaches in a systematic way. However, some preliminary
qualifications concerning different ways to use quantum theory are in
order.



There are quite a number of accounts discussing quantum theory in
relation to consciousness that adopt basic ideas of quantum theory in
a purely *metaphorical* manner. Quantum theoretical terms such
as entanglement, superposition, collapse, complementarity, and others
are used without specific reference to how they are defined precisely
and how they are applicable to specific situations. For instance,
conscious acts are just *postulated* to be interpretable
somehow analogously to physical acts of measurement, or correlations
in psychological systems are just *postulated* to be
interpretable somehow analogously to physical entanglement. Such
accounts may provide fascinating science fiction, and they may even be
important to inspire nuclei of ideas to be worked out in detail. But
unless such detailed work leads beyond vague metaphors and analogies,
they do not yet represent scientific progress. Approaches falling into
this category will not be discussed in this contribution.



A second category includes approaches that use the *status quo*
of present-day quantum theory to describe neurophysiological and/or
neuropsychological processes. Among these approaches, the one with the
longest history was initiated by von Neumann in the 1930s, later taken
up by Wigner, and currently championed by Stapp. It can be roughly
characterized as the proposal to consider intentional conscious acts
as intrinsically correlated with physical state reductions. Another
fairly early idea dating back to Ricciardi and Umezawa in the 1960s is
to treat mental states, particularly memory states, in terms of vacuum
states of quantum fields. A prominent proponent of this approach at
present is Vitiello. Finally, there is the idea suggested by Beck and
Eccles in the 1990s, according to which quantum mechanical processes,
relevant for the description of exocytosis at the synaptic cleft, can
be influenced by mental intentions.



The third category refers to *further developments or
generalizations* of present-day quantum theory. An obvious
candidate in this respect is the proposal by Penrose to relate
elementary conscious acts to gravitation-induced reductions of quantum
states. Ultimately, this requires the framework of a future theory of
quantum gravity which is far from having been developed. Together with
Penrose, Hameroff has argued that microtubuli might be the right place
to look for such state reductions. 


### 3.1 Neurophysiological Levels of Description



A mental system can be in many different conscious, intentional,
phenomenal mental states. In a hypothetical state space, a sequence of
such states forms a trajectory representing what is often called the
stream of consciousness. Since different subsets of the state space
are typically associated with different stability properties, a mental
state can be assumed to be more or less stable, depending on its
position in the state space. Stable states are distinguished by a
residence time at that position longer than that of metastable or
unstable states. If a mental state is stable with respect to
perturbations, it "activates" a mental representation
encoding a content that is consciously perceived.


#### Neural Assemblies



Moving from this purely psychological, or cognitive, description to
its neurophysiological counterpart leads us to the question: What is
the neural correlate of a mental representation? According to standard
accounts (cf. Noe and Thompson (2004) for discussion), mental
representations are correlated with the activity of neuronal
assemblies, i.e., ensembles of several thousands of coupled neurons.
The neural correlate of a mental representation can be characterized
by the fact that the connectivities, or couplings, among those neurons
form an assembly confined with respect to its environment, to which
connectivities are weaker than within the assembly. The neural
correlate of a mental representation is activated if the neurons
forming the assembly operate more actively, e.g., produce higher
firing rates, than in their default mode.



![figure 1](figure1.jpg)

Figure 1. Balance between inhibitory and
excitatory connections among neurons.




In order to achieve a stable operation of an activated neuronal
assembly, there must be a subtle balance between inhibitory and
excitatory connections among neurons (cf. Figure 1). If the transfer
function of individual neurons is strictly monotonic, i.e., increasing
input leads to increasing output, assemblies are difficult to
stabilize. For this reason, results establishing a non-monotonic
transfer function with a maximal output at intermediate input are of
high significance for the modeling of neuronal assemblies (Kuhn *et
al.* 2004). For instance, network models using lattices of coupled
maps with quadratic maximum (Kaneko and Tsuda 2000) are paradigmatic
examples of such behavior. These and other familiar models of neuronal
assemblies (for an overview see Anderson and Rosenfeld 1988) are
mostly formulated in a way *not* invoking well-defined elements
of quantum theory. An explicit exception is the approach by Umezawa,
Vitiello and others (see
 Section 3.3).


####  Single Neurons and Synapses



The fact that neuronal assemblies are mostly described in terms of
classical behavior does not rule out that classically undescribable
quantum effects may be significant if one focuses on individual
constituents of assemblies, i.e., single neurons or interfaces between
them. These interfaces, through which the signals between neurons
propagate, are called synapses. There are electrical and chemical
synapses, depending on whether they transmit a signal electrically or
chemically.



At electrical synapses, the current generated by the action potential
at the presynaptic neuron flows directly into the postsynaptic cell,
which is physically connected to the presynaptic terminal by a
so-called gap junction. At chemical synapses, there is a cleft between
pre- and postsynaptic cell. In order to propagate a signal, a chemical
transmitter (glutamate) is released at the presynaptic terminal. This
release process is called exocytosis. The transmitter diffuses across
the synaptic cleft and binds to receptors at the postsynaptic
membrane, thus opening an ion channel (Kandel *et al.* 2000,
part III; see Fig. 2). Chemical transmission is slower than electric
transmission.



![Figure 2](figure2.jpg)

Figure 2. Release of neurotransmitters
at the synaptic cleft (exocytosis).




A model developed by Beck and Eccles applies concrete quantum
mechanical features to describe details of the process of exocytosis.
Their model proposes that quantum processes are relevant for
exocytosis and, moreover, are tightly related to states of
consciousness. This will be discussed in more detail in
 Section 3.4.



At this point, another approach developed by Flohr (2000) should be
mentioned, for which chemical synapses with a specific type of
receptors, so-called NMDA
 receptors,[6]
 are of paramount significance. Briefly, Flohr observes that the
specific plasticity of NMDA receptors is a necessary condition for the
formation of extended stable neuronal assemblies correlated to
(higher-order) mental representations which he identifies with
conscious states. Moreover, he indicates a number of mechanisms caused
by anaesthetic agents, which block NMDA receptors and consequently
lead to a loss of consciousness. Flohr's approach is
physicalistic and reductive, and it is entirely independent of any
specific quantum ideas.


####  Microtubuli



The lowest neurophysiological level, at which quantum processes have
been proposed as a correlate to consciousness, is the level at which
the interior of single neurons is considered: their cytoskeleton. It
consists of protein networks essentially made up of two kinds of
structures, neurofilaments and microtubuli (Fig. 3, left), which are
essential for various transport processes within neurons (as well as
other cells). Microtubuli are long polymers usually constructed of 13
longitudinal a and b-tubulin dimers arranged in a tubular
array with an outside diameter of about 25 nm (Fig. 3, right). For
more details see Kandel *et al.* (2000), Chap. II.4.




![Figure 3a](figure3a.jpg)
  


![Figure 3b](figure3b.jpg)


Figure 3. (left) microtubuli and
neurofilaments, the width of the figure corresponds to approximately
700nm; (right) tubulin dimers, consisting of a- and
b-monomers, constituting a microtubule.




The tubulins in microtubuli are the substrate which, in
Hameroff's proposal, is used to embed Penrose's
theoretical framework neurophysiologically. As will be discussed in
more detail in
 Section 3.5,
 tubulin states are assumed to depend on quantum events, so that
quantum coherence among different tubulins is possible. Further, a
crucial thesis in the scenario of Penrose and Hameroff is that the
(gravitation-induced) collapse of such coherent tubulin states
corresponds to elementary acts of consciousness.


### 3.2 Stapp: Quantum State Reductions and Conscious Acts



The act of measurement is a crucial aspect in the framework of quantum
theory, that has been the subject of controversy for more than eight
decades now. In his monograph on the mathematical foundations of
quantum mechanics, von Neumann (1955, Chap. V.1) introduced, in an
*ad hoc* manner, the projection postulate as a mathematical
tool for describing measurement in terms of a discontinuous,
non-causal, instantaneous (irreversible) act given by (1) the
transition of a quantum state to an eigenstate *bj*
of the measured observable *B* (with a certain probability).
This transition is often called the *collapse* or
*reduction* of the wavefunction, as opposed to (2) the
continuous, unitary (reversible) evolution of a system according to
the Schrodinger equation.



In Chapter VI, von Neumann (1955) discussed the conceptual distinction
between observed and observing system. In this context, he applied (1)
and (2) to the general situation of a measured object system (I), a
measuring instrument (II), and (the brain of) a human observer (III).
His conclusion was that it makes no difference for the result of
measurements on (I) whether the boundary between observed and
observing system is posited between I and (II & III) or between (I
& II) and III. As a consequence, it is inessential whether a
detector or the human brain is ultimately referred to as the
 "observer".[7]



By contrast to von Neumann's fairly cautious stance, London and
Bauer (1939) went further and proposed that it is indeed human
*consciousness* which completes the quantum measurement process
(see Jammer (1974, Sec. 11.3 or Shimony (1963) for a detailed
account). In this way, they attributed a crucial role to consciousness
in understanding quantum measurement in terms of an update of the
observer's knowledge. In the 1960s, Wigner (1967) radicalized
this
 proposal,[8]
 by suggesting an impact of consciousness on the physical state of the
measured system, not only an impact on observer knowledge. In order to
describe measurement as a real dynamical process generating
irreversible facts, Wigner called for some nonlinear modification of
(2) to replace von Neumann's projection
 (1).[9]



Since the 1980s, Stapp has developed his own point of view on the
background of von Neumann and Wigner. In particular, he tries to
understand specific features of consciousness in relation to quantum
theory. Inspired by von Neumann, Stapp uses the freedom to place the
interface between observed and observing system and locates it in the
observer's brain. He does not suggest any formal modifications
to present-day quantum theory (in particular, he stays essentially
within the "orthodox" Hilbert space representation), but
adds major interpretational extensions, in particular with respect to
a detailed ontological framework.



In his earlier work, Stapp (1993) started with Heisenberg's
distinction between the potential and the actual (Heisenberg 1958),
thereby taking a decisive step beyond the operational Copenhagen
interpretation of quantum mechanics. While Heisenberg's notion
of the *actual* is related to a measured event in the sense of
the Copenhagen interpretation, his notion of the *potential*,
of a *tendency*, relates to the situation *before*
measurement, which expresses the idea of a reality independent of
 measurement.[10]



Immediately after its actualization, each event holds the tendency for
the impending actualization of another, subsequent actual event.
Therefore, events are by definition ambiguous. With respect to their
actualized aspect, Stapp's essential move is to "attach to
each Heisenberg actual event an experiential aspect. The latter is
called the *feel* of this event, and it can be considered to be
the aspect of the actual event that gives it its status as an
intrinsic actuality" (Stapp 1993, p. 149). 



With respect to their tendency aspect, it is tempting to understand
events in terms of
 scheme (B)
 of
 Section 2.
 This is related to Whitehead's ontology, in which mental and
physical poles of so-called "actual occasions" are
considered as psychological and physical aspects of reality. The
potential antecedents of actual occasions are psychophysically neutral
and refer to a mode of existence at which mind and matter are
unseparated. This is expressed, for instance, by Stapp's notion
of a "hybrid ontology" with "both idea-like and
matter-like qualities" (Stapp 1999, 159). Similarities with a
dual-aspect approach (B) (cf.
 Section 5)
 are evident.



In an interview of 2006, Stapp (2006) specifies some ontological
features of his approach with respect to Whitehead's process
thinking, where actual occasions rather than matter or mind are
fundamental elements of reality. They are conceived as based on a
processual rather than a substantial ontology (see the entry on
 process philosophy).
 Stapp relates the fundamentally processual nature of actual occasions
to both the physical act of state reduction and the correlated
psychological intentional act.



Another significant aspect of his approach is the possibility that
"conscious intentions of a human being can influence the
activities of his brain" (Stapp 1999, p. 153). Different from
the possibly misleading notion of a direct interaction, suggesting an
interpretation in terms of scheme (A) of
 Section 2,
 he describes this feature in a more subtle manner. The requirement
that the mental and material outcomes of an actual occasion must
match, i.e. be correlated, acts as a constraint on the way in which
these outcomes are formed within the actual occasion (cf. Stapp 2006).
The notion of interaction is thus replaced by the notion of a
constraint set by mind-matter correlations (see also Stapp 2007).



At a level at which conscious mental states and material brain states
are distinguished, each conscious experience, according to Stapp
(1999, p. 153), has as its physical counterpart a quantum state
reduction actualizing "the pattern of activity that is sometimes
called the neural correlate of that conscious experience". This
pattern of activity may encode an intention and, thus, represent a
"template for action". An intentional decision for an
action, preceding the action itself, is then the key for anything like
free will in this picture.



Stapp argues that the mental effort, i.e. attention devoted to such
intentional acts, can protract the lifetime of the neuronal assemblies
that represent the templates for action due to quantum Zeno-type
effects. Concerning the neurophysiological implementation of this
idea, intentional mental states are assumed to correspond to
reductions of superposition states of neuronal assemblies. Additional
commentary concerning the concepts of attention and intention in
relation to James' idea of a holistic stream of consciousness
(James 1950 [1890]) was given by Stapp (1999).



For further progress, it will be mandatory to develop a coherent
formal framework for this approach and elaborate on concrete details.
For instance, it is not yet worked out precisely how quantum
superpositions and their collapses are supposed to occur in neural
correlates of conscious events. Some indications are outlined by
Schwartz *et al.* (2005). With these desiderata for future
work, the overall conception is conservative insofar as the physical
formalism remains unchanged.



This is why Stapp insisted for years that his approach does not change
what he calls "orthodox" quantum mechanics, which is
essentially encoded in the statistical formulation by von Neumann
(1955). From the point of view of standard present-day quantum
physics, however, it is certainly unorthodox to include the mental
state of observers in the theory. Although it is true that quantum
measurement is not yet finally understood in terms of physical theory,
introducing mental states as the essential missing link is highly
speculative from a contemporary perspective.



This link is a radical conceptual move. In what Stapp now denotes as a
"semi-orthodox" approach (Stapp 2015), he proposes that
the blind-chance kind of randomness of individual quantum events
("nature's choices") be reconceived as "not
actually random but positively or negatively biased by the positive or
negative values in the minds of the observers that are actualized by
its (nature's) choices" (p. 187). This hypothesis leads
into mental influences on quantum physical processes which are widely
unknown territory at present. 


### 3.3 Vitiello and Freeman: Quantum Field Theory of Brain States



In the 1960s, Ricciardi and Umezawa (1967) suggested to utilize the
formalism of quantum field theory to describe brain states, with
particular emphasis on memory. The basic idea is to conceive of memory
states in terms of states of many-particle systems, as inequivalent
representations of vacuum states of quantum
 fields.[11]
 This proposal has gone through several refinements (e.g., Stuart
*et al.* 1978, 1979; Jibu and Yasue 1995). Major recent
progress has been achieved by including effects of dissipation, chaos,
fractals and quantum noise (Vitiello 1995; Pessa and Vitiello 2003;
Vitiello 2012). For readable nontechnical accounts of the approach in
its present form, embedded in quantum field theory as of today, see
Vitiello (2001, 2002).



Quantum field theory (see the entry on
 quantum field theory)
 deals with systems with infinitely many degrees of freedom. For such
systems, the algebra of observables that results from imposing
canonical commutation relations admits of multiple Hilbert-space
representations that are not unitarily equivalent to each other. This
differs from the case of standard quantum mechanics, which deals with
systems with finitely many degrees of freedom. For such systems, the
corresponding algebra of observables admits of unitarily equivalent
Hilbert-space representations.



The inequivalent representations of quantum field theory can be
generated by spontaneous symmetry breaking (see the entry on
 symmetry and symmetry breaking),
 occurring when the ground state (or the vacuum state) of a system is
not invariant under the full group of transformations providing the
conservation laws for the system. If symmetry breaks down, collective
modes are generated (so-called Nambu-Goldstone boson modes), which
propagate over the system and introduce long-range correlations in
it.



These correlations are responsible for the emergence of ordered
patterns. Unlike in standard thermal systems, a large number of bosons
can be condensed in an ordered state in a highly stable fashion.
Roughly speaking, this provides a quantum field theoretical derivation
of ordered states in many-body systems described in terms of
statistical physics. In the proposal by Umezawa these dynamically
ordered states represent coherent activity in neuronal assemblies.



The *activation* of a neuronal assembly is necessary to make
the encoded content consciously accessible. This activation is
considered to be initiated by external stimuli. Unless the assembly is
activated, its content remains unconscious, unaccessed memory.
According to Umezawa, coherent neuronal assemblies correlated to such
memory states are regarded as vacuum states; their activation leads to
excited states and enables a conscious recollection of the content
encoded in the vacuum (ground) state. The stability of such states and
the role of external stimuli have been investigated in detail by
Stuart *et al.* (1978, 1979).



A decisive further step in developing the approach has been achieved
by taking *dissipation* into account. Dissipation is possible
when the interaction of a system with its environment is considered.
Vitiello (1995) describes how the system-environment interaction
causes a doubling of the collective modes of the system in its
environment. This yields infinitely many differently coded vacuum
states, offering the possibility of many memory contents without
overprinting. Moreover, dissipation leads to finite lifetimes of the
vacuum states, thus representing temporally limited rather than
unlimited memory (Alfinito and Vitiello 2000; Alfinito *et al.*
2001). Finally, dissipation generates a genuine arrow of time for the
system, and its interaction with the environment induces entanglement.
Pessa and Vitiello (2003) have addressed additional effects of chaos
and quantum noise.



Umezawa's proposal addresses the brain as a many-particle system
as a whole, where the "particles" are more or less
neurons. In the language of
 Section 3.1,
 this refers to the level of neuronal assemblies, which correlate
*directly* with mental activity. Another merit of the quantum
field theory approach is that it avoids the restrictions of standard
quantum mechanics in a formally sound way. Conceptually speaking, many
of the pioneering presentations of the proposal nevertheless confused
mental and material states (and their properties). This has been
clarified by Freeman and Vitiello (2008): the model "describes
the brain, not mental states." 



For a corresponding description of brain states, Freeman and Vitiello
2006, 2008, 2010) studied neurobiologically relevant observables such
as electric and magnetic field amplitudes and neurotransmitter
concentration. They found evidence for non-equilibrium analogs of
phase transitions (Vitiello 2015) and power-law distributions of
spectral energy densities of electrocorticograms (Freeman and Vitiello
2010, Freeman and Quian Quiroga 2013). All these observables are
classical, so that neurons, glia cells, "and other physiological
units are *not* quantum objects in the many-body model of
brain" (Freeman and Vitiello 2008). However, Vitiello (2012)
also points out that the emergence of (self-similar, fractal)
power-law distributions in general is intimately related to
dissipative quantum coherent states (see also recent developments of
the Penrose-Hameroff scenario,
 Section 3.5).



The overall conclusion is that the application of quantum field theory
describes why and how classical behavior emerges at the level of brain
activity considered. The relevant brain states themselves are viewed
as classical states. Similar to a classical thermodynamical
description arising from quantum statistical mechanics, the idea is to
identify different regimes of stable behavior (phases, attractors) and
transitions between them. This way, quantum field theory provides
formal elements from which a standard classical description of brain
activity can be inferred, and this is its main role in large parts of
the model. Only in their last joint paper, Freeman and Vitiello (2016)
envision a way in which the mental can be explicitly included. For a
recent review including technical background see Sabbadini and
Vitiello (2019). 


### 3.4 Beck and Eccles: Quantum Mechanics at the Synaptic Cleft



Probably the most concrete suggestion of how quantum mechanics in its
present-day appearance can play a role in brain processes is due to
Beck and Eccles (1992), later refined by Beck (2001). It refers to
particular mechanisms of information transfer at the synaptic cleft.
However, ways in which these quantum processes might be relevant for
mental activity, and in which their interactions with mental states
are conceived, remain unclarified to the present
 day.[12]




As presented in
 Section 3.1,
 the information flow between neurons in chemical synapses is
initiated by the release of transmitters in the presynaptic terminal.
This process is called exocytosis, and it is triggered by an arriving
nerve impulse with some small probability. In order to describe the
trigger mechanism in a statistical way, thermodynamics or quantum
mechanics can be invoked. A look at the corresponding energy regimes
shows (Beck and Eccles 1992) that quantum processes are
distinguishable from thermal processes for energies higher than
10-2 eV (at room temperature). Assuming a typical length
scale for biological microsites of the order of several nanometers, an
effective mass below 10 electron masses is sufficient to ensure that
quantum processes prevail over thermal processes.



The upper limit of the time scale of such processes in the quantum
regime is of the order of 10-12 sec. This is significantly
shorter than the time scale of cellular processes, which is
10-9 sec and longer. The sensible difference between the
two time scales makes it possible to treat the corresponding processes
as decoupled from one another.



The detailed trigger mechanism proposed by Beck and Eccles (1992) is
based on the quantum concept of quasi-particles, reflecting the
particle aspect of a collective mode. Skipping the details of the
picture, the proposed trigger mechanism refers to tunneling processes
of two-state quasi-particles, resulting in state collapses. It yields
a probability of exocytosis in the range between 0 and 0.7, in
agreement with empirical observations. Using a theoretical framework
developed earlier (Marcus 1956; Jortner 1976), the quantum trigger can
be concretely understood in terms of electron transfer between
biomolecules. However, the question remains how the trigger may be
relevant for conscious mental states. There are two aspects to this
question.



The first one refers to Eccles' intention to utilize quantum
processes in the brain as an entry point for mental causation. The
idea, as indicated in
 Section 1,
 is that the fundamentally indeterministic nature of individual
quantum state collapses offers room for the influence of mental powers
on brain states. In the present picture, this is conceived in such a
way that "mental intention (volition) becomes neurally effective
by *momentarily increasing the probability of
exocytosis*" (Beck and Eccles 1992, 11360). Further
justification of this assumption is not given.



The second aspect refers to the problem that processes at
*single* synapses cannot be simply correlated to mental
activity, whose neural correlates are coherent assemblies of neurons.
Most plausibly, *prima facie* uncorrelated random processes at
individual synapses would result in a stochastic network of neurons
(Hepp 1999). Although Beck (2001) has indicated possibilities (such as
quantum stochastic resonance) for achieving ordered patterns at the
level of assemblies from fundamentally random synaptic processes, this
remains an unsolved problem.



With the exception of Eccles' idea of mental causation, the
approach by Beck and Eccles essentially focuses on brain states and
brain dynamics. In this respect, Beck (2001, 109f) states explicitly
that "science cannot, by its very nature, present any answer to
[...] questions related to the mind". Nevertheless, their
biophysical approach may open the door to controlled speculation about
mind-matter relations.



A more recent proposal targeting exocytosis processes at the synaptic
cleft is due Fisher (2015, 2017). Similar to the quasi-particles by
Beck and Eccles, Fisher refers to so-called Posner molecules, in
particular to calcium phosphate, Ca\(\_9\)(PO\(\_4\))\(\_6\). The nuclear
spins of phosphate ions serve as entangled qubits within the
molecules, which protect their coherent states against fast
decoherence (resulting in extreme decoherence times in the range of
hours or even days). If the Posner molecules are transported into
presynaptic glutamatergic neurons, they will stimulate further
glutamate release and amplify postsynaptic activity. Due to nonlocal
quantum correlations this activity may be enhanced over multiple
neurons (which would respond to Hepp's concern).



This is a sophisticated mechanism that calls for empirical tests. One
of them would be to modify the phosphorus spin dynamics within the
Posner molecules. For instance, replacing Ca by different Li isotopes
with different nuclear spins gives rise to different decoherence
times, affecting postsynaptic activity. Corresponding evidence has
been shown in animals (Sechzer et al. 1986, Krug et al. 2019). In
fact, lithium is known to be efficacious in tempering manic phases in
patients with bipolar disorder.


### 3.5 Penrose and Hameroff: Quantum Gravity and Microtubuli



In the scenario developed by Penrose and neurophysiologically
augmented by Hameroff, quantum theory is claimed to be effective for
consciousness, but the way this happens is quite sophisticated. It is
argued that elementary acts of consciousness are non-algorithmic,
i.e., non-computable, and they are neurophysiologically realized as
gravitation-induced reductions of coherent superposition states in
microtubuli.



Unlike the approaches discussed so far, which are essentially based on
(different features of) *status quo* quantum theory, the
physical part of the scenario, proposed by Penrose, refers to future
developments of quantum theory for a proper understanding of the
physical process underlying quantum state reduction. The grander
picture is that a full-blown theory of quantum gravity is required to
ultimately understand quantum measurement (see the entry on
 quantum gravity).



This is a far-reaching assumption. Penrose's rationale for
invoking state reduction is not that the corresponding randomness
offers room for mental causation to become efficacious (although this
is not excluded). His conceptual starting point, at length developed
in two books (Penrose 1989, 1994), is that elementary conscious acts
cannot be described algorithmically, hence cannot be computed. His
background in this respect has a lot to do with the nature of
creativity, mathematical insight, Godel's incompleteness
theorems, and the idea of a Platonic reality beyond mind and
matter.



Penrose argues that a valid formulation of quantum state reduction
replacing von Neumann's projection postulate must faithfully
describe an *objective physical process* that he calls
*objective reduction*. As such a physical process remains
empirically unconfirmed so far, Penrose proposes that effects not
currently covered by quantum theory could play a role in state
reduction. Ideal candidates for him are gravitational effects since
gravitation is the only fundamental interaction which is not
integrated into quantum theory so far. Rather than modifying elements
of the theory of gravitation (i.e., general relativity) to achieve
such an integration, Penrose discusses the reverse: that novel
features have to be incorporated in quantum theory for this purpose.
In this way, he arrives at the proposal of *gravitation-induced
objective state reduction*.



Why is such a version of state reduction non-computable? Initially one
might think of objective state reduction in terms of a stochastic
process, as most current proposals for such mechanisms indeed do (see
the entry on
 collapse theories).
 This would certainly be indeterministic, but probabilistic and
stochastic processes can be standardly implemented on a computer,
hence they are definitely computable. Penrose (1994, Secs 7.8 and
7.10) sketches some ideas concerning genuinely non-computable, not
only random, features of quantum gravity. In order for them to become
viable candidates for explaining the non-computability of
gravitation-induced state reduction, a long way still has to be
gone.



With respect to the neurophysiological implementation of
Penrose's proposal, his collaboration with Hameroff has been
instrumental. With his background as an anaesthesiologist, Hameroff
suggested to consider microtubules as an option for where reductions
of quantum states can take place in an effective way, see e.g.,
Hameroff and Penrose (1996). The respective quantum states are assumed
to be coherent superpositions of tubulin states, ultimately extending
over many neurons. Their simultaneous gravitation-induced collapse is
interpreted as an individual elementary act of consciousness. The
proposed mechanism by which such superpositions are established
includes a number of involved details that remain to be confirmed or
disproven.



The idea of focusing on microtubuli is partly motivated by the
argument that special locations are required to ensure that quantum
states can live long enough to become reduced by gravitational
influence rather than by interactions with the warm and wet
environment within the brain. Speculative remarks about how the
non-computable aspects of the expected new physics mentioned above
could be significant in this
 scenario[13]
 are given in Penrose (1994, Sec. 7.7).



Influential criticism of the possibility that quantum states can in
fact survive long enough in the thermal environment of the brain has
been raised by Tegmark (2000). He estimates the decoherence time of
tubulin superpositions due to interactions in the brain to be less
than 10-12 sec. Compared to typical time scales of
microtubular processes of the order of milliseconds and more, he
concludes that the lifetime of tubulin superpositions is much too
short to be significant for neurophysiological processes in the
microtubuli. In a response to this criticism, Hagan *et al.*
(2002) showed that a corrected version of Tegmark's model
provides decoherence times up to 10 to 100 msec, and it has been
argued that this can be extended up to the neurophysiologically
relevant range of 10 to 100 msec under particular assumptions of the
scenario by Penrose and Hameroff.



More recently, a novel idea has entered this debate. Theoretical
studies of interacting spins have shown that entangled states can be
maintained in noisy open quantum systems at high temperature and far
from thermal equilibrium. In these studies the effect of decoherence
is counterbalanced by a simple "recoherence" mechanism
(Hartmann *et al.* 2006, Li and Paraoanu 2009). This indicates
that, under particular circumstances, entanglement may persist even in
hot and noisy environments such as the brain.



However, decoherence is just one piece in the debate about the overall
picture suggested by Penrose and Hameroff. From another perspective,
their proposal of microtubules as quantum computing devices has
recently received support from work of Bandyopadhyay's lab at
Japan, showing evidence for vibrational resonances and conductivity
features in microtubules that should be expected if they are
macroscopic quantum systems (Sahu *et al.* 2013).
Bandyopadhyay's results initiated considerable attention and
commentary (see Hameroff and Penrose 2014). In a well-informed
in-depth analysis, Pitkanen (2014) raised concerns to the effect
that the reported results alone may not be sufficient to confirm the
approach proposed by Hameroff and Penrose with all its
ramifications.



In a different vein, Craddock *et al.* (2015, 2017) discussed
in detail how microtubular processes (rather than, or in addition to,
synaptic processes, see Flohr 2000) may be affected by anesthetics,
and may also be responsible for neurodegenerative memory disorders. As
the correlation between anesthetics and consciousness seems obvious at
the phenomenological level, it is interesting to know the intricate
mechanisms by which anesthetic drugs act on the cytoskeleton of
neuronal
 cells,[14]
 and what role quantum mechanics plays in these mechanisms. Craddock
*et al.* (2015, 2017) point out a number of possible quantum
effects (including the power-law behavior addressed by Vitiello, cf.
 Section 3.3)
 which can be investigated using presently available technologies.
Recent empirical results about quantum interactions of anesthetics are
due to Li *et al.* (2018) and Burdick *et al.* (2019).




From a philosophical perspective, the scenario of Penrose and Hameroff
has occasionally received outspoken rejection, see e.g., Grush and
Churchland (1995) and the reply by Penrose and Hameroff (1995).
Indeed, their approach collects several top level mysteries, among
them the relation between mind and matter itself, the ultimate
unification of all physical interactions, the origin of mathematical
truth, and the understanding of brain dynamics across hierarchical
levels. Combining such deep and fascinating issues certainly needs
further work to be substantiated, and should neither be too quickly
celebrated nor offhandedly dismissed. After more than two decades
since its inception one thing can be safely asserted: the approach has
fruitfully inspired important innovative research on quantum effects
on consciousness, both theoretical and empirical. 


## 4. Quantum Mind


### 4.1 Applying Quantum Concepts to Mental Systems



Today there is accumulating evidence in the study of consciousness
that quantum concepts like complementarity, entanglement, dispersive
states, and non-Boolean logic play significant roles in mental
processes. Corresponding quantum-inspired approaches address purely
mental (psychological) phenomena using formal features also employed
in quantum physics, but without involving the full-fledged framework
of quantum mechanics or quantum field theory. The term "quantum
cognition" has been coined to refer to this new area of
research. Perhaps a more appropriate characterization would be
non-commutative structures in cognition. 



On the surface, this seems to imply that the brain activity correlated
with those mental processes is in fact governed by quantum physics.
The quantum brain approaches discussed in
 Section 3
 represent attempts that have been proposed along these lines. But is
it necessarily true that quantum features in psychology imply quantum
physics in the brain? 



A formal move to incorporate quantum behavior in mental systems,
without referring to quantum brain activity, is based on a state space
description of mental systems. If mental states are defined on the
basis of cells of a neural state space partition, then this partition
needs to be well tailored to lead to robustly defined states. Ad hoc
chosen partitions will generally create incompatible descriptions
(Atmanspacher and beim Graben 2007) and states may become entangled
(beim Graben *et al.* 2013). 



This implies that quantum brain dynamics is not the only possible
explanation of quantum features in mental systems. Assuming that
mental states arise from partitions of neural states in such a way
that statistical neural states are co-extensive with individual mental
states, the nature of mental processes depends strongly on the kind of
partition chosen. If the partition is not properly constructed, it is
likely that mental states and observables show features that resemble
quantum behavior although the correlated brain activity may be
entirely classical: *quantum mind without quantum brain*.



Intuitively, it is not difficult to understand why non-commuting
operations or non-Boolean logic should be relevant, even inevitable,
for mental systems that have nothing to do with quantum physics.
Simply speaking, the non-commutativity of operations means nothing
else than that the sequence, in which operations are applied, matters
for the final result. And non-Boolean logic refers to propositions
that may have unsharp truth values beyond yes or no, shades of
plausibility or credibility as it were. Both versions obviously abound
in psychology and cognitive science (and in everyday life).
Pylkkanen (2015) has even suggested to use this intuitive
accessibility of mental quantum features for a better conceptual grasp
of quantum *physics*. 



The particular strength of the idea of generalizing quantum theory
beyond quantum physics is that it provides a formal framework which
both yields a transparent well-defined link to conventional quantum
physics and has been used to describe a number of concrete
psychological applications with surprisingly detailed theoretical and
empirical results. Corresponding approaches fall under the third
category mentioned in
 Section 3:
 further developments or generalizations of quantum theory.



One rationale for the focus on psychological phenomena is that their
detailed study is a necessary precondition for further questions as to
their neural correlates. Therefore, the investigation of mental
quantum features resists the temptation to reduce them (within
scenario A) all-too quickly to neural activity. There are several
kinds of psychological phenomena which have been addressed in the
spirit of mental quantum features so far: (i) decision processes, (ii)
order effects, (iii) bistable perception, (iv) learning, (v) semantic
networks, (vi) quantum agency,and (vii) super-quantum entanglement
correlations. These topics will be outlined in some more detail in the
following
 Section 4.2.


 It is a distinguishing aspect of these approaches that they have led
to well-defined and specific theoretical models with empirical
consequences and novel predictions. A second point worth mentioning is
that by now there are a number of research groups worldwide (rather
than solitary actors) studying quantum ideas in cognition, partly even
in collaborative efforts. For about a decade there have been regular
international conferences with proceedings for the exchange of new
results and ideas, and target articles, special issues, and monographs
have been devoted to basic frameworks and new developments (Khrennikov
1999, Atmanspacher *et al.* 2002, Busemeyer and Bruza 2012,
Haven and Khrennikov 2013, Wendt 2015).

### 4.2 Concrete Applications


####  Decision Processes



An early precursor of work on decision processes is due to Aerts and
Aerts (1994). However, the first detailed account appeared in a
comprehensive publication by Busemeyer *et al.* (2006). The key
idea is to define probabilities for decision outcomes and decision
times in terms of quantum probability amplitudes. Busemeyer *et
al.* found agreement of a suitable Hilbert space model (and
disagreement of a classical alternative) with empirical data.
Moreover, they were able to clarify the long-standing riddle of the
so-called conjunction and disjunction effects (Tversky and Shafir
1992) in decision making (Pothos and Busemeyer 2009). Another
application refers to the asymmetry of similarity judgments (Tversky
1977), which can be adequately understood by quantum approaches (see
Aerts *et al.* 2011, Pothos *et al.* 2013).


####  Order Effects



Order effects in polls, surveys, and questionnaires, recognized for a
long time (Schwarz and Sudman 1992), are still insufficiently
understood today. Their study as contextual quantum features (Aerts
and Aerts 1994, Busemeyer *et al.* 2011) offers the potential
to unveil a lot more about such effects than the well-known fact that
responses can drastically alter if questions are swapped. Atmanspacher
and Romer (2012) proposed a complete classification of possible
order effects (including uncertainty relations, and independent of
Hilbert space representations), and Wang *et al.* (2014)
discovered a fundamental covariance condition (called the QQ equation)
for a wide class of order effects.



An important issue for quantum mind approaches is the complexity or
parsimony of Hilbert space models as compared to classical (Bayesian,
Markov, etc.) models. Atmanspacher and Romer (2012) as well as
Busemeyer and Wang (2018) addressed this issue for order effects, with
the result that quantum approaches generally require less free
variables than competing classical models and are, thus, more
parsimonious and more stringent than those. Busemeyer and Wang (2017)
studied how measuring incompatible observables sequentially induces
uncertainties on the second measurement outcome. 


####  Bistable Perception



The perception of a stimulus is bistable if the stimulus is ambiguous,
such as the Necker cube. This bistable behavior has been modeled
analagous to the physical quantum Zeno effect. (Note that this differs
from the quantum Zeno effect as used in
 Section 3.2.)
 The resulting Necker-Zeno model predicts a quantitative relation
between basic psychophysical time scales in bistable perception that
has been confirmed experimentally (see Atmanspacher and Filk 2013 for
review).



Moreover, Atmanspacher and Filk (2010) showed that the Necker-Zeno
model violates temporal Bell inqualitities for particular
distinguished states in bistable
 perception.[15]
 This theoretical prediction is yet to be tested experimentally and
would be a litmus test for quantum behavior in mental systems. Such
states have been denoted as *temporally nonlocal* in the sense
that they are not sharply (pointwise) localized along the time axis
but appear to be stretched over an extended time interval (an extended
present). Within this interval, relations such as
"earlier" or "later" are illegitimate
designators and, accordingly, causal connections are ill-defined.


####  Learning Processes



Another quite obvious arena for non-commutative behavior is learning
behavior. In theoretical studies, Atmanspacher and Filk (2006) showed
that in simple supervised learning tasks small recurrent networks not
only learn the prescribed input-output relation but also the sequence
in which inputs have been presented. This entails that the recognition
of inputs is impaired if the sequence of presentation is changed. In
very few exceptional cases, with special characteristics that remain
to be explored, this impairment is avoided.


####  Semantic Networks



The difficult issue of meaning in natural languages is often explored
in terms of semantic networks. Gabora and Aerts (2002) described the
way in which concepts are evoked, used, and combined to generate
meaning depending on contexts. Their ideas about concept association
in evolution were further developed by Gabora and Aerts (2009). A
particularly thrilling application is due to Bruza *et al.*
(2015), who challenged a long-standing dogma in linguistics by
proposing that the meaning of concept combinations (such as
"apple chip") is not uniquely separable into the meanings
of the combined concepts ("apple" and "chip").
Bruza *et al.* (2015) refer to meaning relations in terms of
entanglement-style features in quantum representations of concepts and
reported first empirical results in this direction. 


#### Quantum Agency



A quantum approach for understanding issues related to agency,
intention, and other controversial topics in the philosophy of mind
has been proposed by Briegel and Muller (2015), see also
Muller and Briegel (2018). This proposal is based on work on
quantum algorithms for reinforcement learning in neural networks
("projective simulation", Paparo *et al.* 2012),
which can be regarded as a variant of quantum machine learning (Wittek
2014). The gist of the idea is how agents can develop agency as a kind
of independence from their environment and the deterministic laws
governing it (Briegel 2012). The behavior of the agent itself is
simulated as a non-deterministic quantum random walk in its memory
space.


####  Super-Quantum Correlations



Quantum entanglement implies correlations exceeding standard classical
correlations (by violating Bell-type inequalitites) but obeying the
so-called Tsirelson bound. However, this bound does not exhaust the
range by which Bell-type correlations can be violated in principle.
Popescu and Rohrlich (1994) found such correlations for particular
quantum measurements, and the study of such super-quantum correlations
has become a vivid field of contemporary research, as the review by
Popescu (2014) shows. 



One problem in assessing super-quantum correlations in mental systems
is to delineate genuine (non-causal) quantum-type correlations from
(causal) classical correlations that can be used for signaling.
Dzhafarov and Kujala (2013) derived a compact way to do so and
subtract classical context effects such as priming in mental systems
so that true quantum correlations remain. See Cervantes and Dzhafarov
(2018) for empirical applications, and Atmanspacher and Filk (2019)
for further subtleties. 


## 5. Mind and Matter as Dual Aspects


### 5.1 Compositional and Decompositional Approaches



Dual-aspect approaches consider mental and material domains of reality
as aspects, or manifestations, of one underlying reality in which mind
and matter are unseparated. In such a framework, the distinction
between mind and matter results from the application of a basic tool
for achieving epistemic access to, i.e., gather knowledge about, both
the separated domains and the underlying
 reality.[16]
 Consequently, the status of the underlying, psychophysically neutral
domain is considered as *ontic relative to* the mind-matter
distinction.



As mentioned in
 Section 2,
 dual-aspect approaches have a long history, essentially starting with
Spinoza as a most outspoken protagonist. Major directions in the 20th
century have been described and compared to some detail by
Atmanspacher (2014). An important distinction between two basic
classes of dual-aspect thinking is the way in which the
psychophysically neutral domain is related to the mental and the
physical. For Russell and the neo-Russellians the
*compositional* arrangements of psychophysically neutral
elements decide how they differ with respect to mental or physical
properties. As a consequence, the mental and the physical are
reducible to the neutral domain. Chalmers' (1996, Chap. 8) ideas
on "consciousness and information" fall into this class.
Tononi's theoretical framework of "integrated information
theory" (see Oizumi *et al.* 2014, Tononi and Koch 2015)
can be seen as a concrete implementation of a number of features of
Chalmers' proposal. No quantum structures are involved in this
work.



The other class of dual-aspect thinking is *decompositional*
rather than compositional. Here the basic metaphysics of the
psychophysically neutral domain is holistic, and the mental and the
physical (neither reducible to one another nor to the neutral) emerge
by breaking the holistic symmetry or, in other words, by making
distinctions. This framework is guided by the analogy to quantum
holism, and the predominant versions of this picture are quantum
theoretically inspired as, for instance, proposed by Pauli and Jung
(Jung and Pauli 1955; Meier 2001) and by Bohm and Hiley (Bohm 1990;
Bohm and Hiley 1993; Hiley 2001). They are based on speculations that
clearly exceed the scope of contemporary quantum theory. 



In Bohm's and Hiley's approach, the notions of implicate
and explicate order mirror the distinction between ontic and epistemic
domains. Mental and physical states emerge by explication, or
unfoldment, from an ultimately undivided and psychophysically neutral
implicate, enfolded order. This order is called *holomovement*
because it is not static but rather dynamic, as in Whitehead's
process philosophy. De Gosson and Hiley (2013) give a good
introduction of how the holomovement can be addressed from a formal
(algebraic) point of view. 



At the level of the implicate order, the term *active
information* expresses that this level is capable of
"informing" the epistemically distinguished, explicate
domains of mind and matter. It should be emphasized that the usual
notion of information is clearly an epistemic term. Nevertheless,
there are quite a number of dual-aspect approaches addressing
something like information at the ontic, psychophysically neutral
 level.[17]
 Using an information-like concept in a non-epistemic manner appears
inconsistent if the common (syntactic) significance of Shannon-type
information is intended, which requires distinctions in order to
construct partitions, providing alternatives in the set of given
events. Most information-based dual-aspect approaches do not
sufficiently clarify their notion of information, so that
misunderstandings easily arise.


### 5.2 Mind-Matter Correlations



While the proposal by Bohm and Hiley essentially sketches a conceptual
framework without further concrete details, particularly concerning
the mental domain, the Pauli-Jung conjecture (Atmanspacher and Fuchs
2014) concerning dual-aspect monism offers some more material to
discuss. An intuitively appealing way to represent their approach
considers the distinction between epistemic and ontic domains of
*material* reality due to quantum theory in parallel with the
distinction between epistemic and ontic *mental* domains.



On the physical side, the epistemic/ontic distinction refers to the
distinction between a "local realism" of empirical facts
obtained from classical measuring instruments and a "holistic
realism" of entangled systems (Atmanspacher and Primas 2003).
Essentially, these domains are connected by the process of
measurement, thus far conceived as independent of conscious observers.
The corresponding picture on the mental side refers to a distinction
between conscious and unconscious
 domains.[18]
 In Jung's depth psychological conceptions, these two domains
are connected by the emergence of conscious mental states from the
unconscious, analogous to physical measurement.



In Jung's depth psychology it is crucial that the unconscious
has a *collective* component, unseparated between individuals
and populated by so-called *archetypes*. They are regarded as
constituting the psychophysically neutral level comprising both the
collective unconscious and the holistic reality of quantum theory. At
the same time they operate as "ordering factors", being
responsible for the arrangement of their psychical and physical
manifestations in the epistemically distinguished domains of mind and
matter. More details of this picture can be found in Jung and Pauli
(1955), Meier (2001), Atmanspacher and Primas (2009), Atmanspacher and
Fach (2013), and Atmanspacher and Fuchs (2014).



This scheme is clearly related to
 scenario (B)
 of
 Sec. 2,
 combining an epistemically dualistic with an ontically monistic
approach. Correlations between the mental and the physical are
conceived as non-causal, thus respecting the causal closure of the
physical  *against the mental*. However, there is a causal
relationship (in the sense of formal rather than efficient causation)
between the psychophysically neutral, monistic level and the
epistemically distinguished mental and material domains. In
Pauli's and Jung's terms this kind of causation is
expressed by the ordering operation of archetypes in the collective
unconscious.



In other words, this scenario offers the possibility that the mental
and material manifestations may inherit mutual correlations due to the
fact that they are jointly caused by the psychophysically neutral
level. One might say that such correlations are remnants reflecting
the lost holism of the underlying reality. They are *not* the
result of any *direct* causal interaction between mental and
material domains. Thus, they are *not* suitable for an
explanation of *direct* efficient mental causation. Their
existence would require some psychophysically neutral activity
entailing correlation effects that would be misinterpreted as mental
causation of physical events. Independently of quantum theory, a
related move was suggested by Velmans (2002, 2009). But even without
mental causation,
 scenario (B)
 is relevant to ubiquitous correlations between conscious mental
states and physical brain states.


### 5.3 Further Developments



In the Pauli-Jung conjecture, these correlations are called
*synchronistic* and have been extended to psychosomatic
relations (Meier 1975). A comprehensive typology of mind-matter
correlations following from Pauli's and Jung's dual-aspect
monism was proposed by Atmanspacher and Fach (2013). They found that a
large body of empirical material concerning more than 2000 cases of
so-called "exceptional experiences" can be classified
according to their deviation from the conventional reality model of a
subject and from the conventional relations between its components
(see Atmanspacher and Fach 2019 for more details). Synchronistic
events in the sense of Pauli and Jung appear as a special case of such
relational deviations. 



An essential condition required for synchronistic correlations is that
they are *meaningful* for those who experience them. It is
tempting to interpret the use of meaning as an attempt to introduce
semantic information as an alternative to syntactic information as
addressed above. (Note the parallel to active information as in the
approach by Bohm and Hiley.) Although this entails difficult problems
concerning a clear-cut definition and operationalization, something
akin to meaning, both explicitly and implicitly, might be a relevant
informational currency for mind-matter relations within the framework
of decompositional dual-aspect thinking (Atmanspacher 2014).



Primas (2003, 2009, 2017) proposed a dual-aspect approach where the
distinction of mental and material domains originates from the
distinction between two different modes of time: tensed (mental) time,
including nowness, on the one hand and tenseless (physical) time,
viewed as an external parameter, on the other (see the entries on
 time
 and on
 being and becoming in modern physics).
 Regarding these two concepts of time as implied by a symmetry
breaking of a timeless level of reality that is psychophysically
neutral, Primas conceives the tensed time of the mental domain as
quantum-correlated with the parameter time of physics via
"time-entanglement". This scenario has been formulated in
a Hilbert space framework with appropriate time operators (Primas
2009, 2017), so it offers a formally elaborated dual-aspect quantum
framework for basic aspects of the mind-matter problem. It shows some
convergemce with the idea of temporally nonlocal mental states as
addresed in
 Section 4.2.



As indicated in
 Section 3.2,
 the approach by Stapp contains elements of dual-aspect thinking as
well, although this is not much emphasized by its author. The
dual-aspect quantum approaches discussed in the present section tend
to focus on the issue of a generalized mind-matter
"entanglement" more than on state reduction. The primary
purpose here is to understand correlations between mental and material
domains rather than direct causally efficacious interactions between
them.



A final issue of dual-aspect approaches in general refers to the
problem of panpsychism or panexperientialism, respectively (see the
review by Skrbina 2003, and the entry on
 panpsychism).
 In the limit of a *universal* symmetry breaking at the
psychophysically neutral level, *every* system has both a
mental and a material aspect. In such a situation it is important to
understand "mentality" much more generally than
"consciousness". Unconscious or proto-mental acts as
opposed to conscious mental acts are notions sometimes used to
underline this difference. The special case of human consciousness
within the mental domain might be regarded as special as its material
correlate, the brain, within the material domain.


## 6. Conclusions



The historical motivation for exploring quantum theory in trying to
understand consciousness derived from the realization that
collapse-type quantum events introduce an element of randomness, which
is primary (ontic) rather than due to ignorance or missing information
(epistemic). Approaches such as those of Stapp and of Beck and Eccles
emphasize this (in different ways), insofar as the ontic randomness of
quantum events is regarded to provide room for mental causation, i.e.,
the possibility that conscious mental acts can influence brain
behavior. The approach by Penrose and Hameroff also focuses on state
collapse, but with a significant move from mental causation to the
non-computability of (particular) conscious acts.



Any discussion of state collapse or state reduction (e.g. by
measurement) refers, at least implicitly, to superposition states
since those are the states that are reduced. Insofar as entangled
systems remain in a quantum superposition as long as no measurement
has occurred, entanglement is always co-addressed when state reduction
is discussed. By contrast, some of the dual-aspect quantum approaches
utilize the topic of entanglement differently, and independently of
state reduction in the first place. Inspired by and analogous to
entanglement-induced nonlocal correlations in quantum physics,
mind-matter entanglement is conceived as the hypothetical origin of
mind-matter correlations. This exhibits the highly speculative picture
of a fundamentally holistic, psychophysically neutral level of reality
from which correlated mental and material domains emerge.



Each of the examples discussed in this overview has both promising and
problematic aspects. The approach by Beck and Eccles is most detailed
and concrete with respect to the application of standard quantum
mechanics to the process of exocytosis. However, it does not solve the
problem of how the activity of single synapses enters the dynamics of
neural assemblies, and it leaves the mental causation of quantum
processes as a mere claim. Stapp's approach suggests a radically
expanded ontological basis for both the mental domain and status-quo
quantum theory as a theory of matter without essentially changing the
formalism of quantum theory. Although related to inspiring
philosophical and some psychological background, it still lacks
empirical confirmation. The proposal by Penrose and Hameroff exceeds
the domain of present-day quantum theory by far and is the most
speculative example among those discussed. It is not easy to see how
the picture as a whole can be formally worked out and put to empirical
test.



The approach initiated by Umezawa is embedded in the framework of
quantum field theory, more broadly applicable and formally more
sophisticated than standard quantum mechanics. It is used to describe
the emergence of classical activity in neuronal assemblies on the
basis of symmetry breakings in a quantum field theoretical framework.
A clear conceptual distinction between brain states and mental states
has often been missing. Their relation to mental states is has
recently been indicated in the framework of a dual-aspect
approach.



The dual-aspect approaches of Pauli and Jung and of Bohm and Hiley are
conceptually more transparent and more promising. Although there is
now a huge body of empirically documented mind-matter correlations
that supports the Pauli-Jung conjecture, it lacks a detailed formal
basis so far. Hiley's work offers an algebraic framework which
may lead to theoretical progress. A novel dual-aspect quantum proposal
by Primas, based on the distinction between tensed mental time and
tenseless physical time, marks a significant step forward,
particularly as concerns a consistent formal framework.



Maybe the best prognosis for future success among the examples
described in this overview, at least on foreseeable time scales, goes
to the investigation of mental quantum features without focusing on
associated brain activity to begin with. A number of corresponding
approaches have been developed which include concrete models for
concrete situations and have lead to successful empirical tests and
further predictions. On the other hand, a coherent theory behind
individual models and relating the different types of approaches is
still to be settled in detail. With respect to scientific practice, a
particularly promising aspect is the visible formation of a scientific
community with conferences, mutual collaborations, and some
perspicuous attraction for young scientists to join the field.