Mind and Tachyons
Mind and Tachyons
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Mind and Tachyons: How Tachyon Changes Quantum Potential and Brain
Creates Mind
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Original Article
                   Key Words: quantum potential, mind field, tachyon, exocytosis, computer and brain,
                   artificial intelligence, temporal anomalies
                                                                   NeuroQuantology 2011; 2: 255-270
          quantum theory and at least some                      do the task of the psychon; that is, interact
          mathematical tools exist for use in                   with the bouton and increase the probability
          theoretical investigations.                           of the exocytosis state. We introduce the
        For quite some time, the author                         interaction into the same quantum tunneling
(Hari, 2002; Vishnubhatla, 1985) has held                       model of Beck and Eccles.            Since the
the view that thought processes in a brain                      Schrödinger equation is not invariant under
involve tachyons defined by physicists                          Lorentz transformations, we will not require
sometime ago. Some intuitive rationale for                      our description to be invariant under Lorentz
this hypothesis may be found in the stated                      transformations either (like e.g., usually,
references. It is interesting that Fred Alan                    descriptions of electromagnetic interactions
Wolf (2008) recently stated some quantum                        with nonrelativistic matter are not Lorentz-
field    theoretical   concepts    associating                  invariant). As Recami (1986; 9(6):36) points
tachyons to mind. In the past, there has                        out, “Given a phenomenon ph, the principle
been at least one theoretical physicist, Late                   of relativity requires that two different
Regis Dutheil, a quantum physicist and a                        inertial observers O1, O2 find that ph is
consciousness researcher, who proposed a                        ruled by the same physical laws but it does
model in which mind is a field of tachyonic                     not require O1, O2 to give the same
or superluminal matter4.                                        description of ph”. However, if we assume
                                                                that local observers of the brain do not move
        In section 2, we present a part of the                  relative to the observed brain with speeds
theory of the earlier paper (Hari, 2008) for                    comparable to the light speed c in vacuum,
convenience of reading. Using the quantum                       then tachyons whose speeds are much
tunneling model of Beck and Eccles (1992),                      greater than c may be regarded as close to
and Bohmian model of quantum mechanics,                         infinity when compared to speeds of the
we describe how a ZET when absorbed                             nonrelativistic matter in the brain. Hence,
collectively by the multiple boutons of a                       although a tachyon with infinite speed in one
dendron, changes their quantum potential                        frame of reference may have a finite speed in
and triggers exocytosis simultaneously in all                   another frame, the speed could still be much
of them. In this section, we compare ZET                        greater than c, if the relative speed of the two
features with those of mind fields proposed                     frames is much lower than c5. The energy of
by Eccles, Libet, Bohm, and Hiley.                              a ZET in one frame would be close to zero in
                                                                the other frame also; but in all local frames
Assumptions                                                     tachyons will be found to exchange a finite
Since the Beck-Eccles model of exocytosis                       and non-zero momentum with the brain’s
uses     the    nonrelativistic  Schrödinger                    matter. Moreover, as already mentioned,
equation, obviously they assumed exocytosis                     they would not be found as particles flying
to be a nonrelativistic process. Hence we                       around with faster-than-light speeds but
make the same assumption in our                                 they would be fields spread over regions of
discussion. Eccles also assumed that for                        the brain.
exocytosis to occur, a certain nonmaterial                              Similarly, in Section 4, where we
psychon should intervene and increase the                       describe ZET production as the reaction of
probability of the required brain state which                   the system of nonrelativistic material
is a solution of the Schrödinger equation. In                   particles on a ZET which acts upon the
what follows, we will describe how a tachyon                    particles, again, we do not require the
having zero energy in the laboratory frame of                   description to be relativistically invariant
reference in which a bouton is observed, can                    because one participant of the interaction,
4
   Dutheil, M.D. considered that the mind, though of
tachyonic nature, belongs to the true fundamental universe      5
                                                                 The velocity transformation law relating velocities v and v′
and that our world is merely a subluminal holographic           of a particle relative to Lorentz frames moving with relative
projection. He taught physics and biophysics at "Poitiers"      velocity u gives the following relation between the speeds:
Faculty of Medicine. He dedicated himself to research in        v=|v|, v′=|v′|, u=|u|.
fundamental physics from 1973 on. He was the author of
"Superluminous Man" & "Superluminous Medicine". He                                (         )
                                                                v′2 / c 2 = 1 + [ v 2 / c 2 − 1][1 − u2 / c 2 ]/[ 1 − u.v / c 2 ]2
was a joint Director in "Louis de Broglie" Physics Foundation   (Feinberg, 1967; 159) so that v′>c if v>c. If v = ∞ then v′=
in Paris (Evellyn Elsaesser Valarino 1997).                     c2/u; therefore v′>>c if u<<c.
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NeuroQuantology | June 2011 | Vol 9 | Issue 2 | Page 255-270                                                                 258
Hari SD., Mind and tachyons
       Hence the frequency ω is real only for                      would only transfer momentum to a charged
k ≥m. In the frame of reference in which the                       particle but no energy.
energy of a tachyon vanishes, the magnitude                                    Beck and Eccles (1992) modeled
of the momentum is equal to m0c and the                            exocytosis as a quantum tunneling process of
tachyon has infinite speed. The interaction of                     a two-state quasiparticle governed by a one-
such a tachyon with ordinary matter would                          dimensional Schrödinger equation:
be to instantaneously transfer momentum
but no energy in a manner analogous to a                           iћ∂ t ψ ( q,t ) = − ( ћ 2 / 2M ) ( ∂ q 2 + V ( q ) ) ψ ( q,t ) (2.5)
rigid    body’s     transferring     impulses                      where q is the quasiparticle’s degree of
instantaneously in a collision without                             freedom, M is the mass of the particle, V(q)
exchanging energy (Sudarshan, 1970).                               the external potential energy, and ћ is the
Sudarshan (1969) further describes: “In a
                                                                   Plank’s constant. Writing the quasiparticle
sense,    then,     tachyons      reintroduce
                                                                   wave-function ψ ( q,t ) of equation (2.5) as
instantaneous            action-at-a-distance
                                                                                    iS ( q,t ) / ћ
characteristic in a relativistic theory. An                        ψ ( q,t ) = Re  , where R and S are real
event interpreted as instantaneous action-                         valued functions and equating the real and
at-a-distance in one Lorentz frame will                            imaginary parts on both sides of we obtain
appear to be a propagated action in another                        the following two equations:
frame.”
                                                                   ∂ t S + ( ∂ q S ) / 2M + Q + V ( q ) = 0
                                                                                    2
                                                                                                                                (2.6)
       A zero-energy solution of (2.2)
corresponds to frequency ω = 0 and k2 = m2
and satisfies the Helmholtz equation:
                                                                                (
                                                                   ∂ tR 2 + ∂q R 2∂q S / M = 0   )                              (2.7)
      Equation (2.3) has multiple linearly                         called the quantum potential; the particle’s
                                                                   total energy E = −∂tS, and ∂qS is the
independent solutions Φ ( x ) ) corresponding                      particle’s momentum. Once (2.5) is solved
to a given value of m. Each solution                               for the wavefunction ψ ( q,t ) , the particle’s
represents a field with zero energy and                            trajectories can be computed classically from
capable of exchanging momentum with a
                                                                   Mdq / dt = ∂ q S             or
particle of matter. We take Φ ( x ) to be real.                                                                                 (2.8)
                                                                   Md 2 q / dt 2 = −∂ q ( Q + V )
To describe the interaction of a field
satisfying equation (2.3) with a particle                          by prescribing initial conditions (see Holland
whose motion is governed by a Schrödinger                          1993: equations 3.2.19 and 3.2.24 on pages
equation, we associate with Φ ( x ) the                            73 and 74 respectively). Just before
electromagnetic field defined by the four-                         tunneling begins motion is classical and E =
potential:                                                         V and Q = 0; hence in equation (2.6) the
                                                                   particle’s kinetic energy (∂qS)2 /2M = 0 at
à = ( ∂ ν φm ( x, t ) ) = ( U,A )                          (2.4)   this time. As the potential V increases and
                                                                   becomes > E, motion is classically forbidden.
where
                                                                   As long as the particle remains in the state of
φm ( x ,t ) = e imct Φ ( x ) ,                                     no exocytosis, it has not crossed the barrier
U = ∂ 0φm ( x ,t ) = ime imct Φ ( x )                              V> E, the particle’s momentum ∂qS remains
                                                                   zero and the quantum potential Q adjusts
and A = −(∂ 1, ∂ 2, ∂ 3)φm ( x ,t ) = −e imct ∇Φ ( x ) .           itself so that Q+V = E; Q+V cannot be > E
                                                                   because (∂qS)2 cannot be negative. On the
Note that the potentials A and U give rise                         other hand, Q+V can be < E although V > E;
to zero electric and magnetic fields.                              if so, the second of equations (2.8) gives
According to Eccles (1992), the interaction of                     trajectories penetrating the barrier (Holland
psychon and dendron is momentary and                               1993, p 199) and equation (2.6) gives a
hence we take t = 0 as the time of interaction                     nonzero kinetic energy.
of the tachyon with the dendron. We find
                                                                            The electromagnetic interaction with
that at t=0, the scalar potential is purely
                                                                   the tachyon field changes the equation (2.5)
imaginary whereas the vector potential is
                                                                   to:
real and therefore, the zero-energy tachyon
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NeuroQuantology | June 2011 | Vol 9 | Issue 2 | Page 255-270                                                                                    260
Hari SD., Mind and tachyons
From the analysis in the above section, it is                  field Φ does exactly what Hiley and
clear that the field Φ does exactly what                       Pylkkanen are hoping for a mind-field to do;
Eccles proposed that a psychon would do:                       it changes the quantum potential of
     •    Φ      alters  quantum       transition              quasiparticles to effectively reduce the height
          probabilities as seen from equation                  of their barriers and thereby increases the
          (2.11) where the right hand side is not              probability of exocytosis. In the footnote
          zero after interaction with the                      accompanying the above quote, Hiley and
          field Φ whereas the right of hand side               Pylkkanen say:
          of equation (2.7) is zero and implies                       “However, different doctrines in the
          conservation of probability.                                philosophy of mind might interpret the
                                                                      idea of a “mind-field” in their own way
     •     Φ increases probability of exocytosis                      (in case they would accept such an idea).
          in all boutons of the interacting                           E.g., a property dualist could see it as a
          dendron simultaneously. Φ gives a                           mental property; a functionalist would
          little push as it were, to all the                          focus on the functional role it plays; an
          boutons at the same time leading to                         eliminative materialist could see it as a
          simultaneous exocytosis in those                            new scientific (physicalist) concept of
          which are ready for it.         Eccles’s                    mind,     replacing    traditional   folk-
                                                                      psychological categories.”
          rationale (Eccles, 1990) for the
          hypothesis of mental interaction                             From what we have presented about
          includes the argument that mental                    our tachyon field Φ so far, it meets the
          intention must be neurally effective                 criteria of all the three doctrines. It performs
          by momentarily increasing the                        the function of the mental property volition
          probabilities for exocytosis in a whole              proposed by Eccles and plays the functional
          dendron and coupling the large                       role of changing the quantum potential of a
          number of probability amplitudes to                  Schrödinger equation; the field Φ should
          produce coherent action because in                   satisfy a materialist as well because a branch
          the absence of mental activity these                 of theoretical physics already describes it
          probability amplitudes would act                     although experimental verification of the
          independently, causing fluctuating                   theory is not available so far.
          EPSPs      (excitatory    postsynaptic
          potentials) in the pyramidal cell.                   The Field Φ Produces Back-Action in
     •    The interaction conserves total                      the Continuity Equation
          momentum because Φ is absorbed                       Sarfatti (1996), another associate of Bohm
          collectively by the boutons and the                  calls any function F(r(t)) ≠ 0 (not necessarily
          momentum of Φ is shared by them.                     a solution of the Helmholtz equation) that
          The      four-momentum        of    all              depends upon the actual position r(t) of the
          interacting boutons together is also                 particle at time t, on the right-hand side of
          conserved because the mass of each                   equation (2.7), as back-action. He interprets
          bouton is reduced by spilling its                    that such an F(r(t)) implies that the
          contents (neurotransmitters) into a                  quantum wave field is directly affected by the
          postsynaptic cleft (a body at rest can               conditions of the particles and therefore
          absorb a zero energy tachyon only if                 completes a feed-back control loop between
          its rest mass decreases during the                   the particle and its wave-function.
          interaction [Recami, 1986] and this                  Probability current is not locally conserved
          condition is satisfied here).                        and maximal uncontrollable randomness is
                                                               not possible if this term is present. He thinks
                                                               that all forms of life must have back-action in
The Field Φ               Contributes to Active
                                                               the sense that if mind-like quantum
Information
                                                               potential acts on the material particle to
Hiley and Pylkkanen (2005) say “Let us                         guide it into an eigenstate then the particle
assume that the ‘mind-field’ can be seen as                    should also impact the mind-like quantum
containing    active  information     which                    wave. He thinks that back-action is a
contributes to the quantum potential.” As                      necessary condition for describing any form
already seen in the previous sections, the                     of living matter using quantum theory.
Clearly, equation (2.11) is the same as                        field makes a “two-way traffic” between the
equation (2.7) except for the function Φ on                    two levels possible. However, as Sarfatti
its right-hand side. Therefore a living brain                  (1996) points out, Bohm and Hiley
which includes Φ satisfies Sarfatti’s criterion                themselves write “the Schrödinger equation
for a quantum-theoretical description.                         for the quantum field does not have sources,
                                                               nor does it have any other way by which the
3. How Tachyon Field Relates to                                field could be directly affected by the
Quantum Potential                                              condition of the particles...". Hence their
Bohm’s quantum potential for a system of                       proposal includes only the action of mind on
particles is an intrinsic property of the                      matter but not the action of matter on mind.
system. It depends only on the form of the                     Sarfatti emphasizes that the existence of the
Schrödinger wave function of the system, but                   “reverse traffic” is a necessary condition for
not on the wave’s intensity. It acts as it were,               matter to be living matter.
as a common pool of “active information”,                              Eccles, on the other hand, proposed
which provides a nonlocal connection and                       explicit dualist-interactionism. For him mind
guides them as an “internal” force into                        is a nonmaterial field carrying little or no
organized movement. Bohm (1990) views the                      energy, which nevertheless can trigger neural
quantum potential as a mind-like quality of                    processes. He did not elaborate on the
matter which reveals itself strongly at the                    interaction in the reverse direction, that is,
quantum level, in the movements of the                         how the brain acts upon the mind field
particles. He extends this notion of “mind-                    though. Our proposal that the mind may
like” active information to processes of                       include zero-energy tachyon fields is
thought and says (Bohm, 1990);                                 compatible with Eccles’s proposal in the
          “There is a kind of active information               sense that tachyons are nonmaterial and can
          that is simultaneously physical and                  have no energy unlike matter fields, but they
          mental in nature. Active information can             can interact with material particles such as
          thus serve as a kind of 'bridge' between             neurons. Further, our proposal has the
          these two sides of reality as a whole.
                                                               advantage that tachyons are mathematically
          These two sides are inseparable, in the
          sense that information contained in                  defined and therefore the proposal makes it
          thought, which we feel to be on the                  possible to develop a mathematical theory of
          'mental' side, is at the same time a related         action of the brain’s material on the tachyon
          neurophysiological,        chemical,    and          part of the mind (see section 4).
          physical activity (which is clearly what is                 Our proposal may not be compatible
          meant by the 'material' side of this                 with the Bohm-Hiley proposal that mind
          thought).”
                                                               consists of superquantum potentials of the
        Like Bohm. Hiley and Pylkkanen                         brain at various levels in the hierarchy of
(2005) see the “mind-field” as a fairly subtle                 quantum potentials described by them (e.g.,
level of reality, which has both a physical                    Bohm, 1990); or at least the compatibility is
aspect and a more subtle mental aspect.                        not obvious and requires a mathematical
They assume that the mind-field’s physical                     proof. On the other hand, we believe that
aspect, though subtle, allows it to influence                  there is a relationship between the tachyon
other physical levels (e.g., the known neural                  field and the quantum potential; it is similar
levels) and be influenced by them. They                        to the relationship between an algorithm and
claim that such assumptions imply avoiding                     its representation stored in a computer
dualism or idealism without falling into                       (digital or quantum). We will explain this
reductive materialism. They say “mind” acts                    relationship in the next section.
on “matter” but not in the sense of a
mechanical interaction of two separate                         An     algorithm       in     a    computer
substances. Rather, mind is to be understood                   programmer’s head is not the same as
as a new level containing active information,                  its representation stored in a
which affects the quantum potential, which                     computer (digital or quantum)
in turn affects the physical processes in the                  Nowadays, computers can perform many
brain. Hiley and Pylkkanen state that the                      tasks which in earlier days, were supposed to
dual role (mental and physical) of the mind-                   require a high level of intelligence and
education. E.g., today’s Artificial Intelligence               program in this series are not identical with
(AI) programs can simulate several thought                     the meaning in the programmer’s or user’s
processes such as learning and problem                         head; they are merely representations of
solving. This is all possible because the                      some meaning that exists only in a human
human brain is in some ways, similar to a                      being’s head. Actually, each of the programs
computer.     Indeed, many consciousness                       is an algorithm in the programmer’s head
researchers have used the computer                             and already exists in the computer memory
metaphor in their scientific explanations of                   as a representation in terms of SSHUs before
consciousness     (e.g.,   Pribram,      2004).                the process begins. Thus the entire process
Computer users frequently use expressions                      of execution of these programs is a material
like "the computer knows", "it does not                        physical process to which meaning is
understand", "it thinks", and so on. In fact,                  assigned by a human being. In other words,
we can precisely define what we mean when                      we have just reiterated Pribram’s theme that
we say "the computer knows the object".                        the medium is not the message (Pribram,
                                                               2004). However I do not agree with the
Definition 1. A computer behaves as if it                      other theme of Pribram that communication
knows an object (a data item or a program                      is mental (Pribram, 2000) where he assumes
instruction), when a representation of that                    that communication is necessarily mental.
object as bytes of "0"s and "1"s in a digital                          We hold the view that all
computer or qubit states in a quantum                          communication known to us so far is
computer, in other words, as a sequence of                     physical and we are struggling to
states of some hardware units (SSHU),                          understand mental communication. The
exists in its memory.                                          same meaning may be conveyed by different
        Once such a representation is entered                  words in different languages. Hence the
into a computer's memory, it can perform                       meaning is different from any of the words
any number of operations with that                             which are used to convey the meaning.
representation. The computer can compare                       Meaning exists only in the brain but not in
the object with other objects also known to it                 the words nor in the paper on which the
similarly. It can add, subtract, compute                       words are written. Sometimes language is
functions of it, draw a picture of it, and so                  not even used to communicate information.
on. The computer can do almost anything                        E.g., a right signal flashing from a car is an
that a person can do with that object and                      indication to others that the car is about to
behave as though it "knows" the object                         make a right turn. The same piece of
without really knowing anything! Our use of                    information can be conveyed in many ways
the word representation is intended to                         and the means of communication always
convey that meaning is assigned to the                         uses a representation. The representation
computer’s SSHUs by the programmer. The                        may be in the form of words, sounds,
computer, whether digital or quantum, does                     electrical signals, and so on. A language is a
not know the meaning of its memory                             mapping of information into words
contents.      Even when an AI program                         (symbols) which become sound energy when
produces a new intelligent formula, first it                   pronounced, and particles of matter when
produces a new pattern of SSHUs at the                         written on a paper, and become electrical
hardware level; the new hardware pattern is                    energy when transmitted over a telephone
then input to a machine level program which                    line. Yet information exists only in the brain
translates it into a pattern of numbers, the                   and is different from the language or signals
number pattern in its turn is input to a                       that are used for its communication just like
compiler or an interpreter and the output fed                  water is different from its container without
into a higher level language program, and so                   which it cannot be taken from place to
on, until finally after executing a few                        place. We are so accustomed to using
programs in succession, the formula appears                    material representations to store or
in English language or in some other                           communicate our thoughts (because we
written-and-spoken language, which the                         cannot help it), that we do not even
programmer has designed the computer to                        recognize the fact that information and its
output. The point to note is that both the                     mapping are different.             Thus all
input to and output of each computer                           communication that we use and know in the
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NeuroQuantology | June 2011 | Vol 9 | Issue 2 | Page 255-270                                                           264
Hari SD., Mind and tachyons
world outside the brain is physical. Mental                    recognized only when it executes on a piece
communication exists only in the human                         of hardware by receiving some inputs and
brain and probably inside other living beings                  producing some outputs. It is not that
too.                                                           materialists (those who argue that
       Bohm identified the mind field with                     consciousness is a state of matter) think that
superquantum potentials when he said that a                    a computer knows the meaning of its
quantum potential is mind-like. Bohm                           memory contents but they believe that the
(1989) says:                                                   biological matter in a living brain somehow
                                                               creates the meaning although any matter
          “I would like to suggest then that the
                                                               outside the brain does not. However, they
          activity, virtual or actual, in the energy
          and in the soma is the meaning of the                have yet to explain how biological matter
          information, rather than to say that the             creates meaning.
          information affects an entity called the                     We propose that the brain is similar
          mind which in turn operates somehow on               to a computer in the sense that it has a
          the matter of the body. So the                       physical component and some information;
          relationship between active information              but unlike the computer, the brain carries
          and its meaning is basically similar to
          that between form and content, which we
                                                               some “real information” along with a
          know is a distinction without a real                 representation of that information stored in
          difference or separation between the                 its physical memory. We propose that the
          elements distinguished.” Again in an                 relation between the tachyon field and the
          interview with Weber (1986) Bohm                     change it produces in the quantum potential
          expressed; "It has been commonly                     of the system with which the tachyon
          accepted, especially in the West, that the           interacts is the relation between an
          mental and physical are quite different              algorithm and its representation stored in a
          but somehow are related but the theory               computer (digital or quantum). We agree
          of their relationship has never been                 with Bohm and Hiley (1984) in the sense
          satisfactorily developed. I suggest that
          they are not actually separated; that the
                                                               that quantum potential is software-like5
          mental and physical are two aspects, like            because it causes change in the system
          the form and content of something which              dynamics. The quantum potential which is
          is only separable in thought, not in                 software-like, and the holographic memory
          reality."                                            which is database-like, both provide
The last sentence shows that Bohm                              representations in the hardware-like brain
dismissed thought as not part of reality;                      for the “real information” or the “meaning”
when he said that both mind and matter are                     which consists of zero-energy tachyon fields.
two aspects of one reality. We differ from
Bohm and believe that the content is just as                   4. The Biological Matter in a Living
real as the form that contains it. We believe                  Brain Creates Meaning Although Any
that the content has an identity of its own                    Matter outside the Brain Does Not
and different from all forms containing it                     In the case of a lifeless computer, we know
although content is generated in the brain by                  that AI (artificial intelligence) programs can
means of forms and although content cannot                     learn; they can even discover new formulas
be communicated without being separated                        and theories from the data input to them.
from the form. This is particularly because                    When a computer program learns, it actually
the same content can be communicated or                        creates in its memory, some new patterns of
stored using different forms.                                  hardware units, which were not stored in the
        Again considering the computer                         computer prior to the program execution.
analogy, if the computer is broken, we can                     The new information that the program is
still run the software on another computer                     said to have discovered is obtained only by
provided we have saved a copy of the                           the programmer’s assigning meaning to the
software on a storage device such as a
compact disc. The point is that information                    5
                                                                 The notion of active information clearly finds an analogue
contained in software exists independent of                    in the field of computer science, for example, in the fact
any computer hardware although the                             that a program contains not only passive memory but also
software existence and features can be                         instructions that actively guide the computer (Bohm and
                                                               Hiley, 1984).
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NeuroQuantology | June 2011 | Vol 9 | Issue 2 | Page 255-270                                                                     265
Hari SD., Mind and tachyons
computer’s output consisting of numbers                        when absorbed by brain’s matter can trigger
and       letters   (a    certain     language)                exocytosis. Let us now consider what the
corresponding to the newly created hardware                    brain’s action, rather in general, material
patterns. Meanings of words in any language                    particles’ action upon the tachyon-field
once again, are in the head of the                             would be without going into the physiology
programmer/user but not in the symbols of                      of the brain.
the language itself. So, the computer does                            We write a Lagrangian for the free
not create new “real information” but it does                  tachyon field governed by equation (2.1) as
create new patterns of hardware units to
                                                               Lfield = ∫ £d 3x = ∫ d 3x ⎡ ( ∂ t Ψ / c ) + ( ∇Ψ ) + m 2 Ψ 2 ⎤ / 2
                                                                                                        2        2
which the programmer assigns meaning                                                     ⎣                                  ⎦
according to the original rules adopted for                    For the jth nonrelativistic particle interacting
information storage. An important point to                     with the field Ψ , the equation of motion can
note here is that to create even such a                        be derived from the Lagrangian:
hardware mapping of new information
though not new information itself, a certain                   L particle − j = ∫ d 3 x ⎡⎣ M j v j2 − ε j Ψ ⎤⎦ δ ( x − x j )
piece of software is required to be already
                                                               where Mj is the particle’s mass, vj is its
present and complete execution in the
                                                               velocity, and εj is a coupling constant. Then
computer; a machine cannot learn if it has
                                                               the Lagrangian for the system of particles
no software or cannot execute software; in
                                                               and the field together is
AI terms, such a machine cannot exhibit
“intelligence”.                                                                             ⎧ ⎡( ∂ Ψ/c)2 + ( ∇Ψ)2 + m2Ψ2 ⎤ /2⎫
                                                                                            ⎪⎣ t                            ⎦ ⎪
         As to the living brain, it starts                     Lfield +∑Lparticle−j = ∫ d x ⎨    3
                                                                                                                                  ⎬
                                                                                            ⎪+ ⎡∑ Mj vj − εjΨ⎤⎦δ( x − xj ( t) ) ⎤ ⎪
                                                                                                       2
                                                                                                         (
learning from the moment it is born. Even if                                                ⎩   ⎣                               ⎦ ⎭
it does not learn new techniques of how to
respond to situations, it constantly interacts                 where the sum ∑ is over interacting particles
with the environment and stores the                            at positions xj j = 1,2,…. The action for the
experience and thereby creates new memory                      system of particles and the field together is
both physical and mental. Like Eccles we
think that the physical and mental memory                      S = ∫(L field + ∑ L particle − j ) dt
structures are not the same. The physical
                                                               The Euler-Lagrange equations derived by
memory         may   consist    of    Pribram’s
                                                               minimizing the above action S alter the field
holograms; but we do not think that the
                                                               equation (2.1) to:
“meaning” associated with a holographic
structure is identical with it. What brain                     (∂   t
                                                                        2
                                                                                             )
                                                                            / c2 − Δ − m2 Ψ ( x, t ) =∑ εjδ(x − x j ( t )) (4.1)
scientists can observe today are structures in
the physical memory. Since the computer                        To find how the momentary interaction with
analogy suggests that new memory cannot be                     the particles at time t = t0 changes the zero-
created from hardware alone without some                       energy tachyon field, we may minimize
code already entered in it, probably, the                       S subject to the conditions: t = t0 and
physical body alone cannot create mind                         ∂ t Ψ = 0. Substituting these conditions in
when there is no mind already in it (no mind                   (4.1), we find that after the interaction, the
means no life! Interestingly, after failures of                ZET field equation (2.3) changes to:
experiments to create tachyons in bubble
chambers Feinberg conjectured (1970) that                      (Δ                  )
                                                                            + m 2 Ψ ( x ) = ∑ ε j δ ( x − x j ( t 0 ))         (4.2)
tachyons probably cannot be produced from                      Now, recall that the effect of the ZET,
matter although Feinberg never associated                      Φ m ( x ) = Φ ( x ) which satisfies equation (2.3),
mind with tachyons). However, again just
like in a computer, it is possible for the body                on the Schrödinger equation of quantum
and the mind to interact with each other                       particles was introduced via the four-
producing more mind and creating physical                      potential               {∂ ν φm ( x ,t )} , where
memories to represent the newly created                        φm ( x ,t ) = e imct Φm ( x ) . To find the effect vice
mind.
                                                               versa of the particles on φm ( x,t ) , we may
         In section 2, we showed that a zero-                  apply similar analysis to the massless scalar
energy tachyon emitted by a mind field,                        wave equation:
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Hari SD., Mind and tachyons
∂ ν ∂ ν φ( x, t) = 0                                            (4.3)
                                                                        5. Libet’s Delay-and-Antedating
for which φm ( x,t ) is a solution. In this case,                       Paradox
we find that the field φ continues to satisfy                           Considering the explanation of a computer's
equation (4.3) even after interaction. Since                            knowing an object stated in Definition 1 in
 Φ m ( x ) does change after interaction as seen                        section 3, a similar definition applies to a
                                                                        human brain with the following difference:
from equation (4.2), it follows that after
interaction, the field φm ( x,t ) with a definite                       Definition 2. A brain knows an object if
                                                                        and only if a representation of that object
value for m changes to a general linear                                 together with the "real information" in the
superposition:                                                          form of ZETs regarding the object already
ф ( x , t ) = ∑ k e imkct Φ mk ( x ) dmk                        (4.4)   exists in its memory. Hence we anticipate
                                                                        that awareness of an object (which may be
If one defines the mass operator as −(i/c)∂t                            an experience) occurs when and only when
then the wavefunction φm ( x,t ) is the                                 a physical record of that object and its
eigenfunction of this operator with the                                 associated mental record consisting of
eigenvalue m, the mass of the ZET (strictly                             ZETs, are created in the brain.
speaking m0 = mћ / c is the ZET proper                                         We will see that this definition of
mass). For different values of m these                                  occurrence of consciousness in the brain (as
eigenfunctions     represent    free    non-                            involving both a neural record and mental
interacting ZETs with definite masses. A                                record consisting of ZETs), is consistent with
linear superposition such as (4.4) is                                   the quantum-physical explanation of Libet’s
associated with a tachyon with non-definite                             delay-and-antedating hypothesis, by Wolf
mass. Fourier analysis of (4.4) leads to the                            (1998) and adds further clarity to his
uncertainty relation between the spread of                              explanation.
ZET mass and spread of time given below:                                         Libet's work on stimulus and
( Δmc )( Δt )     ≥ 1                                        (4.5)      sensation and the theory of "human mind
                                                                        antedating stimulus sensation" have been
In a momentary interaction the inequality                               subject to much debate. Libet (1979)
(4.5) implies that the spread Δm >> m and                               proposed the well-known hypothesis that a
suggests creation of new ZETs.                                          subject’s experience of any peripheral
Clearly, a superposition of green’s functions:                          sensation appears to be referred backwards
∑ ε jG ( x − x j ( t 0 ) ) is a solution of equation                    in time approximately to the instant of
                                                                        stimulation although the neural processes
(4.2) when G ( x − x j ( t 0 ) ) is a green’s function                  associated with the sensation take some
of the Helmholtz equation and satisfies;                                finite period of time to attain “neuronal
                                                                        adequacy” which is required for awareness of
(Δ           )
     + m 2 Ψ ( x ) = ε j δ( x − x j ( t 0 ))                            the sensation. Because no neural process
along with specified boundary conditions.                               was found (actually not found as yet) that
                                                                        would account for such backwards in time
Expressing G ( x − x j ( t 0 ) ) for each j, as a
                                                                        subjective referrals, Libet concluded that
superposition of functions            Φmk ( x )                         subjective referrals and corrections take
associated with eigenvalues mk, a solution of                           place at the mental level but not in the
equation would look like                                                activities at neural levels. Dualist John
                                                                        Eccles interpreted Libet's work as implying
Φ ΄ ( x ) = ∑ j ε j ∑ m k Φ m k ( x ) Φ m k ( x j ) / ( m 2 − mk 2 )    that a non-physical mind is the one
                                                                        responsible for the backward step in time.
where x j = x j ( t 0 ) . The field Φ ΄ ( x ) is thus a
                                                                                 In support of Libet’s hypothesis, Wolf
superposition of ZETs of masses mk which                                (1998)      offered    a     quantum-physical
are in general, different from m, the mass of                           explanation based on the so called two-time
the interacting field Φ m ( x ) . Thus, because of                      observable       (TTO)     quantum       theory
interaction with material particles new zero-                           (Aharonov, 1990) and the transactional
energy tachyons may have been created.                                  interpretation (TI) (Cramer, 1983) of
                                                                        quantum mechanics. He proposed a model
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NeuroQuantology | June 2011 | Vol 9 | Issue 2 | Page 255-270                                                           267
Hari SD., Mind and tachyons
based on TTO and TI wherein two neural                         a quantum system is still an assumption but
events lead to backwards-through-time wave                     not an already proven scientific fact.
function collapse in the intervening space-                            Wolf (1998) talks about two
time interval. Wolf (1998) states:                             situations involving this correspondence
            “A conscious experience occurs if and              between mental and neural events. One is
            only if two events occur. If one assumes           exocytosis regarding which Eccles (Beck and
            that consciousness arises with a single            Eccles, 1992) postulated that a mental event,
            event, paradoxes like the ones indicated           namely volition, causes the collapse of the
            by Libet’s experiments occur. Neuronal
                                                               wavefunctions of vesicles; Wolf seems to
            adequacy and subjective experience are
            not one and the same events. Neither               agree. The other is awareness of the
            are     peripheral   stimulation     and           peripheral sensation. In this case, Wolf
            subjective experience one and the same             assumes that awareness occurs along with
            even though they seem to be. The truth             the     collapse    of    brain’s     quantum
            actually lies somewhere in-between.                wavefunction. As regards exocytosis, we
            Both the stimulation and neuronal                  showed in section 2 (Hari, 2008) that a zero-
            adequacy (two events) are needed for               energy tachyon can precisely play the role of
            the apparent conscious (one event)                 volition. In the case of awareness of the
            experience...”                                     peripheral sensation, we will see below that
The last observation is not at all surprising                  besides a neural record whose creation is
when one considers the computer-like                           reflected by neuronal adequacy, a mental
behavior of the brain.          A peripheral                   record consisting of ZETs and associated
stimulation is an input to the brain (a neural                 with the new neural record is also created in
computer) and the corresponding neuronal                       the brain thus satisfying Definition 2.
adequacy state is the one that contains a                              Wolf’s model explains temporal
neural record of the input. The computer                       anomalies in Libet’s experiments dealing
cannot know an input (in the sense described                   with sensory experiences generated by real
in section 3) unless it receives the input to                  sensory stimuli as well as imagined sensory
begin with, and then creates a record of the                   experiences generated by cortical stimuli.
input in its memory. But something else also                   New predictions of Wolf about the timings of
happens in the brain besides what happens                      occurrence of the experience have some
in a lifeless mechanical computer.           In                experimental evidence. In each of the
addition to receiving the input and creating a                 scenarios which he discussed, the TTOTI
physical (neural) record, the brain creates a                  model determines the time interval in which
mental record which we call conscious                          the quantum wavefunction collapses. TTOTI
experience and which does not seem to exist                    does not say that consciousness occurs along
in any lifeless computer, at least not yet.                    with the collapse. That is Wolf’s assumption.
Wolf (1998) states “quantum mechanical                         However, in each scenario, the time of
descriptions are relevant to neural                            occurrence of the experience in the Libet’s
behavior. Consequently the brain and                           experiment does fall within the time interval
nervous system can be treated as a quantum                     of the wavefunction collapse predicted by the
system. This shows that mental events do                       TTOTI model thus justifying Wolf’s
correspond with neural events through the                      hypothesis.
action of the collapse of the probability field
of the quantum wavefunction.” But does                                 In our ZET model, the brain is a
collapse of the wavefunction of a quantum                      system consisting of some neurons and
system necessarily imply that some mental                      ZETs.      In previous sections, we have
event occurs in the system along with the                      obtained the equations governing the action
collapse? Of course not. There are no                          of a ZET on neurons as well as the action of
mental events in many lifeless quantum                         neurons on a ZET. The former action is
systems that we currently know, e.g., no                       described by the Schrödinger equation:
consciousness occurs in the Wheeler’s                                       ⎧ 1/2M ⎡( ћ /i) ∂ − ε A x ,t /c⎤2 ⎫
                                                                            ⎪(      j)⎣              j j ( j ) ⎦ ⎪Ψ (5.1)
delayed choice machine, which is the model                     iћ∂t Ψ = ∑j ⎨                                      ⎬
for Wolf’s analysis. Hence this concept of                                 ⎩⎪+εjU( x j ,t ) + V( x j )           ⎭⎪
“correspondence” in the case of the brain as
where the suffix j describes quantities                         neuronal adequacy are simultaneous events
belonging to the jth particle and the                           and definition 2 is satisfied in this frame. So,
electromagnetic potentials U, A are given                       the ZETs, which are the mental contents of
by equation (2.4). Conversely, the action of                    the person experiencing the sensation, report
neurons on the ZET is described by equation                     the time of experience as the time of the
(4.4) and governed by the inequality:                           birth of the ZETs. So, the ZET hypothesis
                                                                agrees with both the Wolf hypothesis
( Δmc )( Δt )    ≥ 1
                                                                concerning the timing of conscious
If the wavefunction collapse is assumed to be                   experience and
                                                               instantaneous  as Snyder’s  hypothesis interpretation,
                                                                                 in the Copenhagen      (Snyder,      the abov
instantaneous as in the Copenhagen                              1987) concerning the difference in
interpretation, the above inequality implies                    temporality of the experiential and
that ∆m>>m and hence creation of new                            neurophysiological reference frames; the
ZETs. In Bohm’s interpretation, there is no                     ZET hypothesis does not see a conflict
collapse but an effective collapse is arrived at                between the Wolf and Snyder hypotheses.
by the system in a continuous manner. The
above Heisenberg inequality holds for                           6. Why Tachyons and Further Work
arbitrarily small intervals around the time of                  The proposal that memory and thought in
the effective collapse. On the other hand, the                  the brain involve tachyons is based mainly
TI used by Wolf determines the timing of                        on some observed fundamental differences
collapse up to an interval. In this case, the                   in the behaviors of living beings and lifeless
inequality ∆m>>m holds if the energy m0c2                       systems (Hari, 2002). These behavioral
of the tachyon, which is its energy in the                      differences include the following:
frame of reference fixed in it, is sufficiently
                                                                        The first observation is well-known
small. If so, the effect of collapse of the
                                                                and discussed by Searle (1980) and may be
wavefunction Ψ in (5.1) is to create new
                                                                briefly stated as “Information in a living
ZETs. Since in TI, the collapse depends
                                                                brain is different from any of its
upon the information pertaining to the initial
                                                                representations used for its storage or
and final states before and after the collapse,
                                                                communication”. Whenever we refer to
and the information pertaining to the
                                                                “information” in physical sciences, it consist
stimulus that caused the collapse, the ZETs
                                                                some form of matter or material energy and
created by the collapse also depend upon all
                                                                is merely a representation of some “real
that information. Thus experience of the
                                                                information” stored in a living brain. The
peripheral sensation occurs because the
                                                                meaning exists only in the brain and not in
relevant ZETs are created.
                                                                any representation of it outside the brain. It
        Recalling the role of a ZET in                          is possible that the meaning which is known
exocytosis, where the proper mass of the ZET                    to be carried nonlocally by systems of
is required to be sufficiently small (Hari,                     neurons may consist of tachyons which have
2008) for the ZET to have a non-zero                            imaginary masses and nonlocal and thus
gradient across the whole dendron, it                           different from the ordinary matter and
appears that tachyons (and therefore mind)                      energy obtained from matter.
need only very small energies to work with
                                                                        Another observation is that our
the brain.
                                                                actions almost always have a desire, urge,
         In the laboratory frame of reference,                  purpose, motive, etc. as their basis. We act in
awareness of the sensory stimulus is                            the present not only because what we are at
reported to the experimenter even before the                    present or what we were in the past but also
required neuronal adequacy is observed and                      because what or where we want to be in the
that is the paradox. Wolf’s resolution is that                  future. So, our reasoning is inductive as well
in this frame, the brain’s wavefunction                         as deductive. The causality associated with
collapse indeed occurs earlier than neuronal                    inductive reasoning is called circular
adequacy. What we showed above is that                          causality. If desires, motives, etc consist of
ZETs which carry the collapse information                       tachyons, then it would be possible for an
are also created when the collapse occurs.                      action in the present to have a future state as
Now, in the frame of reference of any created                   a cause. Among the several papers written on
ZET, the birth of the ZETs and attainment of                    causality of or its violation by tachyons, the