COSMOLOGY OF CONSCIOUSNESS : Towards Quantum-Theoretic ...qncvc.dei.ac.in/abstracts/106_Prof_PS_Satsangi.pdf · Spirit-mind-brain consciousness interactions are at the microscopic

MHRD Quantum-Nano Centre Project

COSMOLOGY OF CONSCIOUSNESS : Towards Quantum-Theoretic Systems Modelling; Spirit-Mind-Brain Interactions

Prem Saran Satsangi Chairman

Advisory Committee on Education Dayalbagh Educational Institutions

Dayalbagh, Agra, INDIA

O-Theory (Omni-Quantum Theory) for Spiritual Consciousness System Modelling in Cosmology Consciousness is intrinsic to the grand cosmos, both at macroscopic as well as microscopic levels. Man, a creation on planet Earth happens to be a perfect microcosm of the macrocosm. Spirit-mind-brain consciousness interactions are at the microscopic levels analogous to consciousness interactions between Supreme Being (Universal Spirit)-Universal Mind-Physical Universe at the macrocosmic levels. Physical System Theory Generalized for Spiritual System Modelling The spiritual system theory framework presented in this section underlies the rudimentary systems modelling framework for spiritual domains of consciousness as shown in Figure A (with Post-Creational Evolution as summarized in Chart 1) and leads to the formulation of the corresponding abstract system linear graph model of Figure B. Notice that by identifying spiritual potential difference, an across variable, and spiritual force-current, a through variable, as the pair of fundamental complementary variables (Table 1) in conjunction with the system linear graph, the whole body of mathematical physical systems theory becomes available for developing models for spiritual domains. It must also be noticed that the system linear graph shown in Figure B is a simplified classical lumped parameter approximation while a graph-theoretic “Omni-quantum” field-model would be more appropriate for rigorous representation (Satsangi 2006). Notice further that the simplified version gives complete solution for 52 each of spiritual potential difference variables and spiritual force-current variables without requiring solutions of any equation of the system model as implied by the branch equation count of zero. This pre-supposes that the precise states representing grades of closure (whether completely closed, closed to a large extent, closed to a medium extent, closed to a small extent or completely open) of the “intuitive” resonance operated switches in Figure A are known in advance such that the associated current sources (Nos. 36-52) are characterized deterministically in terms of specified spiritual current flows.


Table 1 Examples of systems and complementary variables

System Electrical Mechanical Hydraulic/ Pneumatic

Trans-portation

Economic Ecosystem Infor-mation System

Quantum Infor-mation System

Spiritual

X-across variable (effort variable)

Voltage Linear velocity (Rotational velocity)

Pressure Propensity or level-of-service or traffic density

Unit price Unit energy or Monetary cost

Treatment Quantum across variable directional vectors (Orthonormal unit basis vectors) “ket 0” and “ket 1”

Spiritual Potential Difference

Y-through variable (flow variable)

Current Force (Torque)

Flow-rate Flow-rate Flow rate of goods and services

Material flow-rate

Data flow rate

Quantum through variable as quanta of information / computation flow-rates (given by von Neumann entropy) with associated probability parameters (amplitudes) along directional vectors “ket 0” and “ket 1”

Spiritual Force-current (Inward:- Sound Current, Outward:- Spirit-Current)


Figure A Schematic : A Rudimentary Modelling Framework for Spiritual Domains

(The entire creation is evolved out of the pre-creational Nether Pole)

The second sub-division sphere of a set of six sub-divisions of each grand-division of Macrocosm or Human-Microcosm is the one which is endowed with generative function :

e.g. e2 (Sat Lok), f2 (Sphere of Brahma); and g2’ (Man : Ganglion at the organ of reproduction)

Radhasoami Dham

Agam Lok

Alakh Lok

Anami Lok

Sat Lok

Bhanwar Gufa

Sunna

Trikuti

Sahas Dal Kamal

Sphere of Vishnu

Sphere of Brahma

Sphere of Shiva

Spirit or Moon Orb

Sun

Earth

Jupiter

Saturn

Neptune

a' e6' 6

e5' 5

e4' 4

e3' 3

e2' 2

e1' 1

f6' 6

f5' 5

f4' 4

f3' 3

f2' 2

f1' 1

g6' 6

g5' 5

g4' 4

g3' 3

g2' 2

g1' 1

Seat of the Spirit

Ganglion at the Throat

Ganglion at theSolar Plexus

Ganglion at the Navel

Ganglion at the organ of Reproduction

Ganglion at the Rectum

Apertures or Nerve

Centres or Ganglia for communion

IPurely Spiritual Region in which the (inward spiritualizing) Sound-Current and (outward) Spirit-Current are not distinguishable and both act together conjointly

IIBrahmanda

Region (Universal

Mind)

IIIPind Region (Material Plane)

Correspondence & Communion

of the Microcosm with the Macrocosm through apertures (nerve-centres) in the brain

MICROCOSM (HUMAN BODY)

MACROCOSM (UNIVERSE)

Sub-Divisions

SUPREME BEING (SUPER POSITIVE POLE)

Inward Spiritualizing

Sound-Current Sources (c’s)

Switch closure through

“Resonance”in “Surat-Shabda-Yoga”

(Meditation)

Negative Pole or Nether Pole

Outward (focus or centre-

forming) Spirit-

Currents (d’s)

f4

f3

f2

f1

g6

g5

g4

g3

g2

g1: Quantum Spiritual Force-Field

Grand Divisions(Apex) Top of the Head

Grand Divisions Sub-Divisions

III

b'b

IIGrey

Matter of the Brain

IWhite Matter of the Brain

Third ‘Til’ in the middle of the line

joining the pupils of the two eyes

a'

Spiritual Potential Sources (e’s)

Spiritual Potential Sources (f’s)

Spiritual Potential Sources (g’s)

56Ic

45Ic

34

Ic

23

Ic

56

IIc

45IIc

34IIc

23

IIc

12

IIc

56IIIc

45

IIIc

34

IIIc

23

IIIc

12

IIIc

12Ic

I

IIc

II

IIIc

65

Id

54

Id

43

Id

32

Id

21

Id

65

IId

54

IId

43IId

32

IId

21

IId

65

IIId

54

IIId

43

IIId

32

IIId

21

IIId

II

IIId

I

IId

1s−

2s−

3s−

4s−

5s−

1s

2s

3s

4s

5s

0

6/s s

+∞∞

6−s 0s

Normally closable switches

1s

2s

3s

4s

5s

Normallyopen switch

Normally closable switches

(Infinite Region of Full Spirituality)

Normally open

switches

Normally closed

switches

*s0 / *s6 and*s-6 / *s0 are particularly difficult to close switches

Pind Region is located in the pre-creational Region of Nether Pole

Phase III : Physical Big Bang in Chikakasaor Expanse at the Bottom of Brahmanda

(Subregions 5-1 in the Purely Spiritual Region are located in the vast Pre-creational Upper Region of the Neutral Zone)

Phase II : Big Bang : Universal Mind in Maha Sunna or Expanse at the bottom of Purely Spiritual Region

Phase I : Original Purely Spiritual Big Bang in the Expanse at the bottom of Super Positive Pole

Brahmanda is located in the Pre-creational Lower Region of the Neutral Zone adjoining the Region Proper of the Original Nether Pole

Region of Hell in the Nether Pole Properi.e. in the Expanse at the bottom of the lowest subregion of the Pind region

Normally open

switches

Normally open

switches

Normally closed

switches

Great Dissolution (Maha Pralaya)

Dissolution (Pralaya)

or Big Crunch “Chakra” of “Chaurasi”

(Cycle / circle of 84 subtle currents)

Sunna


Vertices v = 19Edges e = 52Spiritual Potential Sources = 18 nx (Nos. 1 - 18)Spiritual Conductance Channels = 17 (Nos. 19 - 35)Resonance operated switch-mediated current sources = 17 ny

(Nos. 36 - 52)Formulation Tree Edges v-1=18 (Nos. 1 – 18)Equation Count = v – 1 – nx = 0

System Linear Graph G3317

1615

1413

12

11

10

9

8

7

6

5

43

2

1

26

25

24

23

22

21

20

19

32

31

30

29

28

27

18 34

35

36

37

38

39

40

41

42

43

44

49

48

47

46

45

52

51

50

g0

g1

g2

g3

g4

g5

g6

f1

f2

f3

f4

f5

f6

e1

e2

e3

e4

e6

e5

Figure B System Linear Graph Model G :

A Rudimentary Modelling Framework for Spiritual Domains


Science of Consciousness Consciousness implies awareness : subjective experience of internal and external phenomenal worlds. Consciousness is central also to understanding, meaning and volitional choice with the experience of free will (Penrose and Hameroff 2011). While the science of consciousness in ancient India as given in Vedas and Upanishads dates back to second millennia B.C.; it is over the past 50 years or so there has been considerable interest in the modern science in the West, in terms of cognitive psychology and neuro-science (neuro-physiology or neuro-medicine) in studying the consciousness (Satsangi, 2010). The most radical departure from classical physics (based on Newtonian mechanics) instituted by the founders of quantum mechanics was the introduction of human consciousness into the dynamical and computational machinery (Henry Stapp, 2006). However, the quantum generalization of the classical mechanical laws proposed by Heisenberg and his colleagues (called the Copenhagen Interpretation of Quantum Theory as propounded by Niels Bohr et. al.) do not generate by themselves a dynamically complete deterministic physical theory free from any causal gap. Von Neumann / Stapp Formulation The von Neumann / Stapp formulation of quantum theory provides the foundations of a pragmatic neuro-psycho-dynamics that is built on contemporary physical theory (quantum theory) rather than an inadequate classical theory [The Cambridge Handbook of Consciousness, 2007]. John von Neumann converted Copenhagen quantum theory, in a series of steps, into a form in which the entire physical universe including the brain of each agent, is represented in one basic quantum state, which is called the state of the physical universe : The dynamics consists of three processes. Process 1 is the so-called Heisenberg choice on the part of the experimenter about how to act. At the pragmatic level, it is a “free choice” because it is controlled in practice by the conscious intentions (thought, actions and feelings) of the experimenter / participant (agent). Each intentional action involves an effort to produce a conceived experimental feedback, which, if it occuirs, will be an experiential confirmation of the success of that effort. Within the von Neumann framework our conscious choices fix the orientations of the basis vectors. These choices can strongly influence our actions. Process 2 is the quantum analog of the equations of motion of classical physics (obtained by certain quantization procedure); such that resulting equations of motion are local (i.e. interactions are between immediate neighbours) and also deterministic as in classical physics. Evolution via the quantum Process 2 normally has the effect of expanding the microscopic uncertainties beyond what is demanded by the Heisenberg Uncertainty Principle : the cloud of microscopic possibilities spreads out, if unchecked by any other process, into the macroscopic domain and causes disparity.


Process 3 called the Dirac choice (“choice on the part of Nature”) can be regarded as Nature’s answer to the question posed by Process 1 (such as : Will the detecting device be found to be in the state that signifies, “Yes, a detection has occurred”? Or, “Will the Geiger counter be observed to “fire” in accordance with the experimental conditions that define a ‘Yes’ response? Each Process 3 reply must be preceded by a Process 1 question. This is because Process 2 generates a continuous infinity of possible questions that cannot all be answered consistently within the mathematical framework provided by quantum theory. This tripartite quantum dynamics involving Choice, Causation and Chance (Processes 1, 2 & 3 respectively) and the implementation of Will (Volition) via the conscious control of the rapidity of Process 1 events provides the mathematical and logical foundation of a pragmatic quantum approach to neuropsychology. Support from Psychology Support from Psychology may be drawn for study of mind-consciousness in respect of Will and Attention – “Passively Attend” or “Actively Attend” i.e. Reappraise (“Reinterpret”) (Henry Stapp, 2006). William James (“Psychology : The Briefer Course”, 1992) writes “Volitional effort (will) is effort of attention” . . . Everywhere, then, the function of effort is the same : to keep affirming and adapting the thought which, if left to itself, would slip away.” James’ description of the effort of volition (will) on the mind-brain process is remarkably in line with what had been proposed independently, from purely theoretical considerations of the quantum physics of this process (Stapp, 2006). Harold Pashler (“The Psychology of Attention”, 1998) describes the key concepts of “attention”, a processing “capacity” and “effort” which is linked to incentive and to reports by subjects of “trying harder”. Pashler separates perceptual processing (for categorical identification of stimuli) from post-perceptual processing, covering the tasks of producing motor action and cognitive action. The “perceptual” aspect of brain process described by Pashler can be associated with the unconscious (quantum) mechanical brain process called Process 2 and with essentially passive Process 1 (determined by brain activity alone) implied by James’s assertion that “No object can catch our attention except by the neural machinery”, whereas the higher level post-perceptual processing that Pashler identifies can be associated with the active mode of Process 1. Such an active mode of Process 1 action could, within the quantum framework induce a rapid sequence of similar actions that would activate a quantum Zeno effect, which would tend to produce the intended action. All of these empirical actions, noted by Pashler, are in line with the general principle that effort increases the rate of conscious events, each of which inputs a mental intention, and that this resource can be divided between tasks. Applying the quantum approach to an experiment in neuropsychology of Kevin Ochsner et. al. (2002) in essence consists first of a training phase in which the subject is taught how to distinguish, and respond differently to two alternative instructions given while viewing emotionally disturbing visual images. One instruction, “Attend”, means “Passively be aware of, but not try to alter, any feelings elicited by the stimulus,” whereas “Reappraise” means “Actively


reinterpret the content so that it no longer elicits a negative response”. The subject then performs these mental actions during brain imaging of MRI. The visual stimuli when passitively attended to activate limbic (emotional) brain areas and when actively reappraised activate prefrontal cerebral regions. Penrose-Hameroff Formulation : Orchestrated Objective Reduction Perhaps the most ambitious attempt to create a quantum theory of consciousness is the one of Roger Penrose and Stuart Hameroff (2011). It has three parts : the Gödel Part, the Gravity Part, and the Microtubule Part. The Gödel Part is an effort to use the famous Gödel’s Incompleteness Theorem [Any finite set of rules that encompass the rules of arithmetic is either inconsistent or incomplete; it entails either statements that can be proved to be both true and false, or statements that cannot be proved to be either true or false] to prove that human beings have intellectual powers of “non-computable” thought and understanding that they could not have if they functioned in accordance with the principles of classical physical theory. Proving this would reaffirm a conclusion of the von Neumann formulation of quantum theory, namely, that a conscious human being can behave in ways that a classical mechanical model cannot. [However, the Gödel Part cannot now be regarded as having been established successfully]. The Gravity Part addresses a key question pertaining to quantum dynamics : Exactly when do the sudden quantum jumps occur? The Diösi-Penrose (DP) expectation is that Objective Reduction (OR) occurs when the overall separation (the product of the temporal separation T with the spatial separation S) reaches a critical amount given by the Planck-Dirac constant = Planck constant 2h π , such that the quantity S is given by : GS E≈ (the gravitational self-energy) of the difference between the mass distributions of the two superposed state and T Z= (the life-time)

GE= . Penrose-Hameroff (PH) theory proposes that this time interval is the duration of time for which Nature will endure this bifurcation of space-time structure into the two, incomputible parts, before jumping to one or the other of these two forms. This conjectured rule is based on two very general features of Nature : Planck’s universal constant of action h and Newton-Einstein universal law of gravitation. It invokes quantum gravity attempting to combine quantum theory with Einstein’s theory of gravity, namely General Relativity. Moreover, according to Orchestrated Objective Reduction (Orch OR), this is accompanied by an element of proto-consciousness. The best known temporal correlate for consciousness is gamma synchrony, EEG / MEG, 30-90 Hz, often referred to as coherent 40 Hz, representing a succession of 40 or so conscious moments per second (τ = 25 milliseconds). Global macroscopic states such as superconductivity ensue from quantum coherence (with attendant superposition) among only very small fractions (say 1%) of components (six tubulins per neuron). For τ = 25 msec, 20,000 such neurons would be required to elicit OR. In human brain, cognition and consciousness are, at any one time, thought to involve tens of thousands of neurons (10,000 to 1,00,000 neurons) which may be widely distributed throughout the brain. At 80 Hz or higher frequency, associated with Tibetan or other


meditators, expanded awareness states of consciousness might be expected with more neuronal brain involvement. Does this rule have any empirical support? An affirmative answer can be provided by the Microtubule Part of Penrose-Hameroff (PH) theory by linking DP objective reduction rule to Hameroff’s belief that consciousness is closely linked to the microtubular structure of the neuron. Topological Quantum Computation Topological quantum computing in ‘Orch OR’ is shown in Figure 1 (Penrose and Hameroff, 2011).

Figure 1 extending microtubule A-lattice hydrophobic channels results in helical winding patterns matching Fibonacci geometry (Fibonacci series : e.g. 1, 1, 2, 3, 5, 8 etc. in which each Fibonacci number is the sum of the preceding numbers). Bandyopadhyay (2011) has evidence for ballistic conductance and quantum interference along such helical pathways which may be involved in topological quantum computing. Quantum electronic states of London forces in hydrophobic channels result in slight superposition separation of atomic nuclei, sufficient EG for Orch OR. This image may be taken to represent superposition of four possible topological qubits

which, after time T = tau = GE

, will undergo OR, and reduce to specific pathway(s) which then

implement function. B-lattice microtubules have a vertical seam dislocation. In the quantum theory, the quantum state of the n indistinguishable particles (e.g. quasiparticle, anyons) belongs to a Hilbert space that transforms as a unitary representation of the non-abelian braid group nB of n strands (Sahni, Lakshminarayanan and Srivastava, 2011). The braid group nB can be presented as a set of generators that obey particular defining relations. To understand the defining relations, we may imagine that the n (say 3) particles occupy n (say 3) ordered positions (labeled 1, 2, 3, . . ., n) arranged on a line. Let 1σ denote a counterclockwise exchange of the particles that initially occupy positions 1 and 2, let 2σ denote


a counterclockwise exchange of the particles that initially occupy positions 2 and 3, and so on. Any braid can be constructed as a succession of exchanges of neighboring particles; hence

1 2 1, ,..., nσ σ σ − are the group generators. The second, slightly more subtle type of relation is

1 1 1j j j j j jσ σ σ σ σ σ+ + += , 1, 2,..., 2j n= − which is called the Yang-Baxter relation. We can verify the Yang-Baxter relation by drawing the two braids 1 2 1 2 1 2σ σ σ σ σ σ= on a piece of paper (Fig. 2), and observing that both describe a process in which the particles initially in positions 1 and 3 are exchanged counterclockwise about the particle labeled 2, which stays fixed — i.e., these are topologically equivalent braids.

Figure 2 A simple diagram showing the two braids 1 2 1 2 1 2σ σ σ σ σ σ= with 3n = strands each The most important issues facing topological quantum computation are twofold : (1) finding or identifying a suitable system with the appropriate topological properties, that is, non-abelian statistics, to enable quantum computation, and (2) figuring out a scheme to carry out the braiding operations necessary to achieve the required unitary transformations. The only topological system known to exist in nature is the quantum Hall regime. Thus, there is a strong need to find other systems satisfying the above two criteria for topological quantum computation. Topological quantum computation can then be carried out by moving quasi particles around one another in two space dimensions. The quasi particle world-lines form topologically nontrivial braids in three (= 2 + 1) dimensional space-time, and because these braids are topologically robust (i.e., they cannot be unbraided without cutting one of the strands) the resulting computation is protected against error. An Orch. OR qubit based on topological quantum computing specific to microtubule polymer geometry was suggested by Hameroff et. al. in 2002 (Penrose and Hameroff, 2011). Conductances along particular microtubule lattice geometry, e.g. Fibonacci helical pathways, were proposed to function as topological bits and qubits. Bandopadhyay (2011) has preliminary evidence for ballistic conductance along different, discrete helical pathways in single microtubules.

1 2 3 1 2 3

3 2 1 3 2 1

Initial time slice (t=0)

Intermediate time slices

Final time-slice (t=T)


Graph Theoretic Quantum System Modelling (GTQSM) Srivastava, Sahni and Satsangi (2011) introduce graph theoretic quantum system modelling (GTQSM) which is facilitated by considering the fundamental unit of quantum computation and information, viz., a quantum bit or qubit as a basic building block. Unit directional vectors “ket 0” and “ket 1” constitute two distinct fundamental quantum across variable orthonormal basis vectors (for the Hilbert space) specifying direction of propagation, as it were, of information (or computation data) while complementary fundamental quantum through (flow-rate) variables specify probability parameters (or amplitudes) as surrogates for scalar quantum information measure (von Neumann entropy). Applications of GTQSM are presented for quantum information / computation processing circuits ranging from a simple qubit and superposition or product of two qubits through CNOT and Hadamard Gate Operations to a substantive case of 3-port, 5-stage circuit for quantum teleportation. An illustrative circuit for teleporting a qubit is modeled as a complex “system of systems” resulting in four probable transfer function models. It has the potential of extending the applications of GTQSM further to systems at the higher end of complexity scale too. Quantum Teleportation Quantum teleportation is a technique of moving quantum states around, even in the absence of a quantum communications channel linking the sender of the quantum bit to the recipient (Sahni 2007).

Figure 7 Circuit for teleporting a qubit

As an illustration, interconnection between quantum CNOT-processor and quantum-Hadamard Gate-processor at Stage 1 in Fig. 7 is captured in quantum subsystem representation by Fig. 8 and associated quantum subsystem graph vertex equation (7.1) and quantum subsystem graph circuit equations (7.2).


Figure 8

Quantum Subsystem Graph (Stage 1) as the union of QTGs i.e. ( ) ( )1 1 1 1, ,i iY X Y Xφ φ ∪ is given by Fig. 8(b) showing output graph in dotted lines and input graph in continuous lines. Quantum System Graph Vertex Equation is 1 1iY Y φ= i.e. 1 1 1 1 1 1

000 011 110 101

TiY Y Y Y Y Yφ ⎡ ⎤= ⎣ ⎦ (7.1); and Quantum System Graph Circuit Equation is 1 1 0iX X φ+ = . (7.2) Hopfield Neural Networks Inspired by Penrose-Hameroff Orch. OR theory, Behrman et. al. (2006) use an extremely simplified model of tubulin dimers, each represented simply as a qubit, a single quantum two-state system. In order to obtain the Quantum Hopfield Net (QHN), they consider an array of N qubits. Hamiltonian or energy function operator for each qubit j is given by

j x zH K Aσ σ= + (8)

where 0 11 0xσ⎡ ⎤

= ⎢ ⎥⎣ ⎦

and 1 00 1zσ⎡ ⎤

= ⎢ ⎥−⎣ ⎦ are respectively the Pauli X and Z matrices; and the full

Hamiltonian Operator 1

N

jj

H H=

= ∑

The first term in Equation (8) represents the flipping of the qubit from one state to the other, called “tunneling”, with amplitude K. Let 0 1ψ δ γ= + represent a qubit in terms of Quantum Terminal Graph (QTG) in Fig. 9

where 0 is the (+1) state 10⎡ ⎤⎢ ⎥⎣ ⎦

and 1 is the (-1) state 01⎡ ⎤⎢ ⎥⎣ ⎦

. Notice that x

δ γσ

γ δ⎡ ⎤ ⎡ ⎤

=⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎣ ⎦

which

flips the probability amplitudes. For example, the (+1) state 0 is flipped to the (-1) state 1 , and vice-versa.


Figure 9

The second term in Eq. 8 represents the energy-difference 2A between the two states. This difference can be the result of external fields or interaction with other qubits. The Pauli Matrix

zσ measures the state of the system; e.g. 0 0

( 1)1 1zσ⎡ ⎤ ⎡ ⎤

= −⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎣ ⎦

, telling us that the system is in the

(-1) state. Thus each qubit j may be visualized as a loop having n discretization points, propagating in imaginary time from 0 to β. [A discretization point at any instant of imaginary time is the instantaneous state of the qubit at that corresponding value of the inverse temperature]. Figure 10 shows a qubit with 4n = discretization points in a system of 3N = qubits.

δ γ

'1a

1b

'1b

1a

0 1

∪


Figure 10

i=3(3β/4)

i=1 (β/4)

i=3(3β/4)

i=1 (β/4)

121α

124α

234α

232α

311α

123α

313α

i=2 (β/2)

312α

122α

314α

i=2 (β/2)

i=1 (β/4)

i=2 (β/2)

231α23

3α

ζζ

ζζ

ζ ζ

ζζ

ζ

ζ

ζ

ζ

'jjiα α=

' 1,j j N∀ ≠ = and i=1,n

i=4 (0,β)

j=1

i=4 (0,β)

j=2

i=4 (0,β)

j=3 i=3

(3β/4)


Lyapunov (Energy) Function LQHN of Quantum Hopfield Network (QHN) LQHN for the simplest possible Quantum Hopfield Network model, considering N qubits each with n discretization points, propagating in imaginary time (inverse temperature) over 0 to β, (where each pair of qubits interacts only at equal imaginary discretized time n), is given by (Berhman et. al. 2006),

( )'11 1 ' 1 1

1 N n N nj j j j

QHN i i i ij i j j i

L S S S Sς αβ +

= = ≠ = =

⎡ ⎤⎛ ⎞ ⎛ ⎞= − +⎢ ⎥⎜ ⎟ ⎜ ⎟

⎢ ⎥⎝ ⎠ ⎝ ⎠⎣ ⎦∑∑ ∑ ∑ (7)

where the functions { }jiS refer to the instantaneous values (microstates) assumed by each of the

N qubits 1,1,

j Ni nψ == for each of its n “sub-qubits” corresponding to n discretization points (Notice

that 1 1N + = and 1 1n + = ); i.e. the eigenvalues of the operators ( ) ( ). .x zσ σ for each of the j

qubits (with discretization points of imaginary time) given by 1jiS = ± . Then 1j

iS = ± are the

microstates of the system; and the summation 1 1

N n

j i= =∑∑ in equation (7) gives the partition function

viz., LQHN in eq. (7).

ς = tunneling parameter = ( ){ }1 ln tanh2

K nβ− ; K being the tunneling amplitude

α = Coulombic interaction parameter = 2A β = Boltzmann’s constant As long as 1QHNL nβ , the discretization error should be small.


Interaction processes in QHN for Micro-Energy Function Generation may be represented graph-theoretically in generic terms for N qubits each with n discretization points, as follows : I. Tunneling interaction process for each qubit j, propagating in imaginary time (inverse temperature) between discretization points i and (i+1) from 0 to β , with a strength of ς .

Figure 11(a)

( )11j

xi iT ςσβ+ = −

Input Port 1

Input Port 2

Output Port

Tunneling Energy Function Generator Qubit j at

discretization point i

0i j

iψ

1i

1i

b

jiy

'

1ib

0i

a

jiδ

'

0ia

0 1

∪

Microstate 1j

iS = ±

Qubit discretization point i+1

( )01i +

( )1jiψ +

( )11i +

( )01ia +

1j

iδ +

( )'

01ia +

∪

0 1 ( )11ib +

1j

iy +

( )

'

1 1ib

+

Microstate

( )1 1jiS + = ±

Tunneling Hamiltonian Micro-Energy Function (or Micro Lyapunov Function)

( ) 111j j j

i iiH S Sςβ ++ = − 1, ; 1, ;j N i n∀ = =

(Nn micro-energy function)

Potentials 1 0 1

jiH +

1

0


II. Coulombic (bidirectional interaction process between the same discretization points i of each pair of different qubits j and 'j , with a strength of α

Figure 11(b)

( )' '

11 1 ' 1 1

N n N nj jj

QHN QHN ii ij i j j i

H L H H+= = ≠ = =

= = +∑∑ ∑ ∑

' 1jji zC ασ

β= −

Input Port 1

Input Port 2

Output Port

Bidirectional Coulombic Energy Function Generator Qubit j

0j

1j

1j

ib

jiy

'

ib

0i

a

jiδ

'0

i

ja

0 1

∪

Qubit j’

0

'j

'1j

10j

ia

'jiδ

( )0'jia

∪

0 1 1

iiib

'

'j

iy ( )1

'iiib

Coulombic Hamiltonian Micro Energy Function or Micro Lyapunov Function

' '1jj j ji i iH S Sα

β= − ' 1, ; 1, ;j j N i n∀ ≠ = =

( ( )1N N n− micro-energy function)

Potentials 1 0 'jj

iH

1

0


Toward Quantum Theoretic Model of Mind Von Neumann’s formulation of Quantum Theory fixes the essential quantum link between consciousness and neuroscience (Processes 1, 2 and 3 of von Neumann-Stapp approach). Mind and matter (brain) become dynamically linked in a way that is casually tied to the agents’ free choice of how he or she will act. Thus a casual dynamical connection is established between (1) a person’s conscious choices of how to act, (2) that person’s consciously experiential increments in knowledge and (3) the physical actualizations of the neural correlates (in the brain) of the experienced increments in knowledge. An increasing number of recent researchers since the dawn of the 21st century argue that the basic frame of quantum theory can find useful applications in the cognitive domain. For instance, Bltuner and Hochnadd [2009] report the application of quantum theoretic model to C.G. Jung’s theory of personality in psychodynamic field using a four-dimensional Hilbert-space for the representation of two qubits. In a nutshell, the two qubit model follows Jung in considering four psychological functions with the two basic attitudes extroversion and introversion. The four psychological functions consist of two opponent pairs : (1) sensing (S) and intuition (N), i.e. (irrational functions for perceiving information either directly by the senses or indirectly by the integration of the large amounts of information); (ii) thinking (T) and feeling (F), i.e. (rational functions for judging information either by reasoning or by evaluation). In the present model, the first qubit 0 1ψ α β= + represents the four psychological functions (as a quaternity) assuming the following correspondence in terms of Pauli operators (or spin matrices) :

xS σ= , xN σ= − s.t. 1 0 0 1xσ = +

zT σ= , zF σ= − s.t. 0 0 1 1zσ = − The aforesaid choice is the key for expressing Jung’s four psychological functions (in a quaternity) within a single qubit system and is primarily motivated by Jung’s idea of discriminating 8 basic personality types in dependence of one of the four dominant psychological functions as superior function and one of the complementary pairs, either S / Nor – T/F, as secondary function.

1. F > N > S > T 5. T > S > N > F 2. N > F > T > S 6. S > T > F > N 3. N > T > F > S 7. S > F > T > N 4. T > N > S > F 8. F > S > N > T


Figure 12 : Compass

Figure 13

The second qubit, 0 1θ δ γ= + is used for representing the different attributes of a personality (extroversion E vs. introversion I) also depicted respectively as the outer and inner sides of the compass in Fig. 12. It is assumed that the corresponding Pauli operator zσ is available with eigenvectors that represent the two opponent attitude states of extroversion and introversion. Hence, the two observables for extroversion and introversion are given by

zE σ= (for Extroversion) and zI σ= − (for Introversion) Also, XM σ= (for intermediate state with an equal superposition of pure extroversion and pure introversion states) For constructing the full Hilbert space of 4-dimensions, one may make use of the tensor product ⊗ of the two qubits as follows : If 0 1θ δ γ= + expresses a certain state of attitude (Extroversion, Introversion or superposition of both) :

Outer Side E

Inner Side I


and 0 1ψ α β= + expresses a certain psychological state reflecting a certain ranking of the four psychological functions (S, N, T, F), then θ ψΦ = ⊗ expresses a psychological state ψ with attitude θ In terms of type dynamics crucially involved in Carl Gustav Jung’s theory, it is claimed that each person realizes more than one psychological function, and the point is stressed that opponent psychological functions are realized with contrasting attitudes of Extroversion / Introversion. In the present model, this side is expressed by the notion of entanglement. It is therefore, claimed that the attitudes are entangled with the psychological functions. Formally, one can write such entangled states Φ in the following way :

θ ψ θ ψ⊥ ⊥Φ = ⊗ − ⊗ . . (8) where ⊥ is an operation that gives the orthogonal state of a certain qubit state. Conclusion Each scientific observer describes himself and his knowledge in a language that allows him to communicate to colleagues two kinds of information : how he has acted in order to prepare himself - - his mind, his body (including brain) and his devices - - to receive recognizable and reportable data and what he has learned from the data he thereby acquires. It is a description of his intentional probing actions and of the experiential feedbacks that he subsequently receives. Also, in actual scientific practice, the experimenters are free to choose which experiments they perform. The empirical procedures are determined by the protocols and aims of the experimenters. Given the aforesaid scientific practice emphasizing the elements of conscious freedom on the part of experimenting scientists as to how to act and what to learn from the experiments to be performed, and the recent success of brain-science (neuroscience) as well as the growing realization in the last decade of the aptness and applicability of quantum theoretic modelling to cognitive domain of mind science, it follows as a natural corollary to suggest extension of the quantum theory to the domain of spiritual-psychophysical dynamics. It would require separating the spiritual-self (or entity) of the observers (or experimenters), describing a stream of conscious experiences that are the experiential sides of a sequence of events, from the psychophysical sides of the observed system (including not only the physical bodies and brains of all observers but also their psychological minds as parts of the observed system described by quantum theory) which actualize the neural-correlates and cognitive-correlates of those experiences, respectively in the physical brains and psychological minds of the observers. It is expected that in due course of time, mind-science (i.e. cognitive science) together with already advanced brain-science will develop so as to bring up the empirical sides upto the level where the details of spirit-mind-brain inter-connections will be actively probed (through advancements in mind-science (via psychological test-scales) and brain-science) and intricate results will be explored that can be compared with the hypothesized spiritual-psychophysical quantum theory (e.g. Omni-quantum theory of consciousness, sketched out in rudimentary sense in the beginning of the presentation).


REFERENCES Bandopadhyay A. (2011), Direct experimental evidence for quantum states in microtubules and topological invariance, Abstracts : Towards a Science of Consciousness, 2011, Stockholm, Sweden, http://www.consciousness.arizona.edu/TSC2011MicroTub.htm. Behrman E.C. (2006), Gaddam K, Steck JE and Skinner SR, MTs as a Quantum Hopfield Network, The Emerging Physics of Consciousness, ed. J.A. Tuszynski, pp.351-370, Springer, New York, 2006. Bltuner and Hochnadd (2009), Two qubits for C.G. Jung’s theory of personality, Cognitive Systems Research 11 (2010) 243–259, Elsevier. Craddock TJA and Tuszynski J (2007), Information Processing in MTs and its Relation to Consciousness (MSc Thesis), University of Alberta, Edmonton, Canada, 2007. Hameroff S, Hagan S and Tuszynski JA (2002), Quantum computation in brain MTs: Decoherence and biological feasibility, Physical Review E 2002;65:061901 1-11. Stapp Henry (2006), “Quantum Interactive Dualism: Libet and Einstein-Podolsky-Rosen Causal Anomalies,” Invited contrib.. to Erekenntnis, Feb. 2006. Kumar and Satsangi (1992), “System Dynamics Simulation of Hopfield Neural Networks”, International Journal of Systems Science, Vol. 23, No. 9, pp. 1517-1525. Nielsen and Chuang (2000), Quantum Computation and Quantum Information, Cambridge University Press, 2000. Ochsner, K. N., Bunge, S. A., Gross, J. J., & Gabrieli, J. D. E. (2002). Rethinking feelings: An fMRI study of the cognitive regulation of emotion. Journal of Cognitive Neuroscience, 14, 1215-1299. Penrose and Hameroff (2011), Consciousness in the Universe: Neuroscience, Quantum Space-Time Geometry and Orch OR Theory, Journal of Cosmology, Vol. 14, April-May 2011. Sahni V., Lakshminarayanan V., Srivastava D.P. (2011), Quantum Information Systems, ISBN 9780070707078, Tata McGraw Hill, New Delhi, April 2011. Sahni V., Quantum Computing, ISBN 978-007062095-7, Tata McGraw Hill, New Delhi, 2007. Satsangi (2006), “Generalizing Physical Systems Through Applied Systems Research from “Real” Physical Systems through “Conceptual” Socio-Economic-Environmental Systems to “Complete” (Physical-Mental-Spiritual) Creational Systems”, International Journal of General Systems, Vol. 35, No. 2, 2006, pp. 127-167.


Satsangi (2010), Cosmology from the Twin Vantage Points of Radhasoami Faith and Systems Science, Vision Talk at International Seminar on Religion of Saints (‘Sants’) – Radhasoami Faith, Spiritual Consciousness Studies (SPIRCON 2010), Nov. 12-13, 2010. Schwartz, J. M., Stapp, H. P., and Beauregard, M. (2005). Quantum theory in neuroscience and psychology: A neurophysical model of mind-brain interaction. Philosophical Transactions of the Royal Society of London, Series B, 360(1458):1309-27. Srivastava, Sahni and Satsangi (2011), “Graph Theoretic Quantum System Modelling for Information / Computation Processing Circuits”, International Journal of General Systems, Taylor & Francis, iFirst article 2011, 1-28, D.O.I. 10.1080/03081079, 2011, 602016. http://www.informaworld.com Stapp (2007), Quantum Approaches to Consciousness, Chapter 31, Cambridge Handbook of Consciousness.

COSMOLOGY OF CONSCIOUSNESS : Towards Quantum-Theoretic ...qncvc.dei.ac.in/abstracts/106_Prof_PS_Satsangi.pdf · Spirit-mind-brain consciousness interactions are at the microscopic

Documents