PSYCHO-PHYSICAL MATHEMATICAL THEORY OF THE PSI PHENOMENON
ABRAP – IPRJ - NIAC
Dedicated to Dean Radin,
PhD, Psi researcher of the
Institute of Noetic Sciences
The aim is
to express physically and mathematically the mind as the
universal element that gives meaning to matter and its
phenomenon is the most immediate application as a form
of expression of the pure consciousness and it was about
it that we used our formulation to describe the
processes that were didactically separated into Extra
sensorial Perceptions, (instantaneous) Telepathy,
Precognition and Psychokinesis. The Psi phenomenon can
be complex, involving combinations extra sensorial and
telepathic events, cognitions out of real time and
is expressed as plane wave free of interactions with
real potentials, stretching itself into the continuous
and infinite harmonic oscillatory spectrum.
aggregated and detached from the
represent specific geometric and oscillatory concepts,
characteristics that allow their identification in the
plane wave, with the use of the de Broglie’s
expressions, can be wholly equaled to the free particle
of the transformation equations by Lorentz. Unlike
Schroedinger, Einstein took these equations to find the
mass. The first is Newton's and second Relativistic.
be necessary to establish an additional transformation
that made Lorentz’s particle equations as periodical as
the free complex wave.
Four ways have open up:
1. De Moivre’s
application to the free wave.
of the logarithm to the free wave.
case, one would reach the entropy and the syntactic
information of the matter. The application of the
logarithm in the wave, converts it in the imaginary
oscillation of Lorentz’s equations through the quantum
commutation of the free wave and consequent elimination
of Heisenberg’s uncertainty allow the approximation of
the quantum theory to the special relativity.
attempt was also to give the free plane wave the
simplifying characteristic that drew Einstein’s
attention in the EPR paradox as the missing element in
the physical theory for its completeness. Thus, the
subjectivity inherent to consciousness comes to be part
of the physical theory.
4. The fourth
way would be the passage of the geometrical expressions
of the free particles and free waves to the matter.
The use of
a matter creator operator applied to the plane wave
function would be a solution that would remain unknown.
we shall take advantage of Einstein’s own passage of
Lorentz’s free particle to matter without the use of
speed, aiming to put an end to the implicit unknown of
matter creator operator.
case, Lorentz’s correction factor plays a fundamental
expression of metric interval in special relativity,
which is obtained directly from Lorentz’s time
transformations, is assumed to be essential to the
multidimensional formulation of waves and free particles
(PSICONS), involving necessarily imaginary speeds and
greater than the speed of light with reference to
matter. The multidimensional formulation of PSICONS is
implicit in the development of our work and differs from
the 4-space by Minkowsky.
or helical multidimensional cosmology can be obtained as
an infinite sequence of PSICONS of the continuous
spectrum for each inner multiple of the speed of light,
as if multiple universes of consciousness separated from
their only origin or “zero point”, without the need of
“loop” (a universe in a continuously rising spiral with
multiple hyper-dimensional universes). By the geometric
negligence of acceleration in the isotropic cosmological
solution by Friedman, the use of general relativity
seems not to
the result of such a cosmology that has been presented
and initially obtained in other studies of this same
the physical equality between the drawing of reality,
matter, and the drawing of consciousness, thought, can
be psychologically expressed as ‘link”, given the total
absence of physical interaction between mind and matter.
This conceptual element of signification of the mass, I
believe it to be what Freud and, in general, Jung,
called the unconscious and that it cannot be accepted
completely by individuals under penalty of sticking the
real (Lacan) or loss of identity or disorganization.
resistance to the “link’ points out the greater or
lesser detachment of matter and the concept is thus the
necessary condition to the progressive separation of
matter with the increase in the resistance to the “real”
(case of concept projected on matter: “resistance” 1,
minimum zero speed).
phenomenon moves between this state itself and the
universal states of ESP which are only interconnected
semantic information or entangled minds (Radin).
To the reader:
THE SYMBOLS USED ARE THE CONVENTIONAL ONES OF PHYSICS –
1 - THE TWO QUANTUM EXPRESSIONS OF THE THOUGHT
Initially one sets out from the plane wave function.
= ei (kx - wt).
The exponent in (k x - w t), as it is about a periodical
wave, can be simply reverted to (x - v t).
Observe that its division by k, where k can take any
value although constant to a wave, that is,
makes it identical to
(x - v t)
This occurs because
= ei (kx - wt) = ei (x - v t) .
2- 1st COMMUTATION of
: p x to
Back to the function
= ei (kx - wt), its application to the
operator commutator [ Pop xop - xop
replacing the quantum operators, comes:
It must be verified that p and x, are quantities that do
not commute, this is, there is no simultaneous wave
function for both quantities, so that they attend to
Heisenberg’s Principle of Uncertainty.
Developing the above operation and zeroing the result,
one obtains undoubtedly
3 - 2nd COMMUTATION of
E t to
Doing the same to the pair energy - time will lead to:
[ Eop top - top Eop
With the operators, will come
This operation will also result in
E t = - i
4 - LINEARIZATION OF
AND CONJUNCTION OF THE HYPER-DIMENSION
The results obtained in (3) and (4) will immediately
As p =
k and E = ħ w, the expression becomes:
i ( k x - w t) which, as seen, is identical to
i (x - v t).
Alternatively, supposing Lorentz’s formulation,
in the numerator of Lorentz’s expression for time:
v t' = v t - x = - (x - v t).
It is as if the movement of the particle happened in the
opposite direction to (x - vt), which, for this analysis
is irrelevant (it must be seen that v is constant).
comes from the fact that
so the free plane wave moves in hyper-space, x2,
at the speed ic just like
being t naturally an imaginary temporal factor, if x2
5 – APPEARANCE OF THE FREE MATTER (PSICON- PARTICLE)
Introducing Lorentz’s the correction factor,
it is obtained from the expressions of (4):
This transformation by Einstein forms the mass
To v = 0, one
simply has im0.
Between v = 0 and v = i c one has a series of v = i v,
for the values between 0 and c.
6 - THE EQUALITY
The only way to make real the expression
is by introducing into the denominator the rotation i,
or the rotation - i into the numerator just like
As the 1st term in root can vary from 1 to
the corresponding values of the 2nd term in
the denominator will also be between 1 and
The mass M is real so that it establishes a link between
the imaginary and the real just like
We translate this fact from the wave function
we associate to the mind, saying that im0, is
“the concept” established by the mass and its
hyper-dimensional and imaginary form (semantic
informational vacuum) corrected by the real factor which
varies in the interval
which we call, in a general way, “Resistance”.
Thus, one has a new formulation of the Freudian
It must be considered that matter in the Freudian case
is the Nervous System (NS) and its neurological
configurations, while the resistance is the obstacle to
the mixing or sticking the concept in reality.
Psychologically speaking this factor might be compared
to the Freudian repression or to the archaic human
tendency, “culpability” associated to the hero, it
means, Oedipus. Woman is the lack, only the hero.
This aspect becomes evident if one suppose the concept
as EGO (Freud), I (Lacan) or even SELF (Jung).
Biologically, how projections of the evolutionary
psychological concepts itself , we have that……..……..,
adults, children, animals, plants, gens, viruses and
particles would have resistance from infinite to 1, when
would be mixed to reality (matter).
Beyond “Culpability”, out of the “nucleus of hurt”, in
the recognition of the Other, or more, when the own
individual concept disappears, the moving away from
reality process also increases, consequently, the
resistance. In this circumstance the matter tends to
zero. Here one has spontaneous or inducted states of
mind that are close to this extreme, such as:
Altered(Amplified) state of consciousness-ASC………..Tart
Delta-wave sleep………………..Rechtschaffen and Kales
All this proposition can be imagined if one suppose the
3D+T3 dimension like the sea or the ether projecting
itself on the 2D+T2 dimension, like its shadow or reflex
creating and interfering in it. Analogous to this, one
observes 3D+T3 matter immersed in 4D+T4 or i(3D+T3),
mind. Now, it’s the mind that creates and interferes on
the matter . There is a hierarchical and mobile
structure, a spiral universe on a cylinder, a helix.
Dimensions can only exist once the hyper- dimensions had
create them.. The opposite is mathematically impossible:
dimension does not create hyper-dimension.
ESP and PK are public proof and consequence that this
conception is possible as the general model mind-matter.
7 - INTRODUCTION TO THE PSI FUNCTIONS AND SPIRAL
The resistance to the sticking of the concept to reality
is divided into two resistances, the resistance to
PSYCHOKINESIS, called RHO function and the resistance to
TELEPATHY and CLAIRVOYANCE, called PHi.
The very existence of an imaginary speed allows for the
mind that the imaginary time means absence of time.
Supposing a speed faster than light, be it v, we will
have the following picture:
The rotation i of 90 ° of this speed v > c will
inevitably result in:
Effectively, the speed i v will be able to reach values
∞, always occupying regions permeated between 0 and inv,
n the number of dimensions considered.
One initially verifies, in the first figure that,
< 45°, c t g
> 1 until ∞.
The rotation of 90°, ( i ), does
not alter this situation, except for what concerns the
axis t. The new axis i t points out to neither the past
nor the future. Conclusively, mental time does not exist
past or future.
This agrees with the timelessness of the Freudian
a structure that does not move in the classical sense
and allows the mental perception of past time
(retrocognition) and of future time (Precognition).
The free movement of the
Freudian unconscious is here translated mathematically,
accepting the same movement of every kind towards the
future or the past.
In the case in which
= 90 °,
the speed goes to zero, as mentioned, reflecting a total
lack of resistance in relation to PHi as well as RHO, a
fusion occurring between concept and reality (resistance
equals to 1).
Negative real time occur for another rotation of 900.
The picture would be approximately:
In this other dimension, the mind would have a real
sense of the future to the past. The mental logic would
be inverted in relation to the material logic (eg,
decreasing entropy). In this linear dimensional
conception the transition in
However, considering the spatial dimensions, the speed
which is the one we adopt in our studies. In this case,
the universe would be represented as a spiral:
This is a space of speeds or world lines
n = 1, 2, 3, 4 ..... ∞.
this case, shadows and bi-dimensional reflexes would be
related to space R3, in
the same way that the
latest would in relation to R4 etc.
The relativist - quantum energy E = m v2,
would have its expression written as:
The antiparticle appears as E = - m c2
And a universe could only be represented by the
hyper-dimensional universe (s).
Each universe, therefore, would have a mind that
A version of the “spiral universe" represented here,
and referred to the operation
is the octadimensional version in which 3 + 1 spatial
dimensions and time are rotated from 90 °, 180 °, 270 °
and 360 ° (i, i2, i3, i4).
According to the parapsychologist at the Institute of
Noetic Sciences - IONS, Dean Radin, in “Entangled Minds,
Ed. Aleph, 2008, the model (proposed by physicists and
parapsychologists Elizabeth Rauscher and Russell Targ)
assumes that minds have the capacity of navigating
through this octadimensional space and it is useful to
point out how in principle one can explain the required
non-local properties for the functioning of PSi without
causing damage to the known physics. However, it does
not provide an explanation for the way the required
mental navigation can be performed or the way
psychokinesis works. (This is a non literal version
of the original idea.)
One can observe the similarities between the point of
view commented by Dean Radin, in his book, and the
physic-mathematic development in this text.
The Spiral Cosmology suggests the appearance of a
helical universe by gathering the rotation of space-time
with the rotation of the space around the time.
8 - TELEPATHY and CLAIRVOYANCE (RELATIVISTIC ANALYSIS)
So far, one has the relation Ψ
Second, following algebraic operations, one reaches the
In this case, the resistance numerically varies between
is divided into two types:
PHi Resistance to the extra-sensorial perception and RHO
Resistance, to psychokinesis.
The cognition phenomena that exclusively involve time,
PRECOGNITION and RETROCOGNITION, are imbued in all Psi
phenomena that happen independently of the real time:
mental time is imaginary.
The mind can be called im0 = Ψ, in such a way
that the previous expression should be written in words
The validity (Matter x Resistance) 1
(im0) 1 = Ψ1, should be stressed,
a special case of the concept Ψ1 after the
special real product (M R) 1.
It should be understood that it equals the continuous
spectrum of states that sets out from zero and reaches
To an isolated individual, the resistance, when it
reaches its lowest level, will make the infinite mind
project itself on matter in such a way that
This not occurs, when all consciousness is banned
(Einstein) and the (human) individual in sensorial
regression does not receive loads of universal
signifying thought. As
in this case M still exists, the human individual dies,
and his nervous system is diluted in other system,
depending on the degree of sensorial regression.
PSi Phenomena of information, such as TELEPATHY and
CLAIRPERCEPTION are the same previous phenomena except
that they arise with no apparent external influence.
Probably the genetic mapping of the paranormal will
present resemblances in the genetic code of these
Observe the TELEPATHY among individuals, whether or not
they have a nervous system. The figures below may give a
clearer idea of what has been said:
Individuals 1 and 2 separated spatially and temporally
We can assume the following decoherence:ψa,b,c,d
A= Man B= Dog C= vegetable D=Particle
If the real general state M x R = im0 is the
same, that is, if (MR) A = (MR) B = (MR) C = (MR) D, the
mind will signify the same. Obviously, for identical
particles, if one takes, E and F, we will have (MR) E =
(MR) F and they will have identical behaviors, that is,
the real state of E = the real state of F = Ψ.
For human beings A and B the situation is the same,
involving instead of M, the nervous system and its
states of resistance so that
If (SN x R) A = (SN x R) B, one has real equality A and
B among individuals, naturally keeping the levels
previously established for only one individual.
The meaning of A and B separately will be the same, as
in this case A = B, just like it occurs with identical
In this last case, telepathy among particles violates
the Pauli`s principle of exclusion and instantaneously
results in a same real state.
Other typical examples are the identical twins in
identical states (sleeping, for instance), dogs and
owners with similar emotional neurological states, men
in the same emotional-neural situation etc.
The situation can be generalized for all kind of
telepathic contact and clairvoyant among beings.
Individuals in situations of normality, although also
under the meaningful pressure of Ψ, tend to act
independently (local and discontinuous):
As (M x R) A ≠ (M x R) B, then the meaning will be
The massification introduced by the means of
communication can be seen in this aspect:
(M R) A = (M R) B = M R (C) = M R (D).....,
where M is the Nervous System.
In this case, the meanings of real nervous receptacles
of PSI with the same resistance will be the same as the
known ideas – forces (Roger Martin du Gard) which have
been leading human behavior arise. It must be considered
that this phenomenon differs from the one of pure
telepathy among equal individuals, since massifying
equality is obtained through such external means like
harmful drugs noxious, alienating and freedom-taking
The merely sensorial communication would only be an
exchange of physical energy without any sense that might
give meaning susceptible of intelligible communication.
In case, there was no “hierarchically superior” Ψ. But Ψ
is the element (psicon) that can define matter. And
matter is a creative representation of PSI.
9 – PSYCHOKINESIS (RELATIVISTIC ANALYSIS)
Again we have the equality Ψ = im0.
As seen, with the Einstein’s equality
a speed higher than the light, one can have
Taking advantage of only
its interaction with matter is obvious that it becomes a
modification of the speed state of the later
action of energy or acceleration.
Or, which is the same, in order to simplify, albeit not
necessarily, as im0 can be any,
v2 = 0,8 and v1 = 0,3, that is,
that the body mass equivalent to the
speed 0,3 jumps to the state speed 0,8, without real
Naturally it is expected that v >1.
Effectively, making the substitutions of the speeds, we
that is, it is found, as wished, that the mind, at
speeds higher than the one of light in psychokinesis
over matter, alters its speed.
Naturally, if an object is still, it will leave the
state of rest under mental action and will be in motion.
It is what I called "outsourcing" of the neurotic
defense mechanism on the part of the epicenter of
psychokinesis. It must be emphasized that the
compositions of various speeds and diverse objects may
be able to suffer the same psychokinetic effect, being
the simplest POLTERGEIST.
However, the mental ascendency over the object allows us
to understand more conceptually that the mind would not
have any limitations whatsoever in the production of
kinetic effects. There is no implicit prohibition so
that conceptual mind cannot manifest its LINK neurotic
in the most varied possible ways.
I should stress that possible changes of energy levels
in Qantum Physics may be attributed to Psychokinesis in
explicit violation of the maximum limit of the speed of
light of restrict relativity. The choice of formalism
cannot alter the absolute value of certain scalar
quantities such as mass.
10 – PRECOGNITION (RELATIVISTIC ANALYSIS)
Observe initially that
One obtains Lorentz’s known expression:
Dividing it by t one obtains:
as mentioned at the beginning of this item.
Squaring it, we will have:
the known metric interval of Special Relativity.
Now we will introduce a 2nd dimension x2:
to a new dimension, keeping the speed, will come the
same kind of expression for the metrical interval:
Adding to the expression of the metric interval in one
dimension we have:
However, the basic principle that the sum of two speeds
cannot be higher than the speed of light which is c, one
then one has
this is, assuming x as real, the metrical interval will
By calculating this interval as a metrical interval of
the first dimension, one will obtain:
As seen previously,
By doing as before
that only speeds equal to or higher than the speed of
light are admitted.
In this case, instead of what the Special Relativity
predicts, the introduction of new coordinate or a new
dimension (hyper-dimension) results in the developments
of the 1st dimension as if the effect came
before the cause, that is, PRECOGNITION, and the mental
observer who, due to being hyper-dimensional, has the
speed already calculated,
be apt in the first dimension to violate the basic
principle that the cause comes before the effect.
Our general expression
can be written as:
In other terms, exceeding the speed of light, clocks
that measured the time of the mental observer moving at
speeds higher than light would be measuring a time
higher than the time measured by the fixed observer,
which means that the clock hands will mark lower and
lower time intervals with the increase in the
hyperdimensional mental speed.
This is exactly the opposite of what the Special
In other terms, mental time projected as projected
imaginary hyperdimension would allow one to know the
real effect before the real cause: PRECOGNITION. The
mind knows the future!
The reader may find strange the apparent paradox with
what was said in item 7 about the inexistence of mental
time. Yet, it must be remembered that a second rotation
of both spatial and temporal axes leads to real negative
This was exactly what we have done at this item 10, when
we returned to the expression of hyperdimension of
The reader, in this last case, will be able to imagine a
determined piece of information departing from another
source at two different speeds: take the “thunder”.
Obviously, the luminous information of the “thunder”
will come before the same information “thunder” brought
to the receiver by the sound.
Evidently, the receiver of the concept “thunder” will be
predicting that it will happen again. By imagining now
an issuing source of “thunder” travelling at a speed
higher than the speed of the light, the mentalreceiver
will already have developed the concept “thunder” before
the luminous lightning and will interpret such a fact as
non-causal mere coincidence (Jung).
Effectively, what the receiver font they thought really
happened "afterwards". A “double temporal connection” is
However, above the speed of light, there is only
thought. Thus, the term "thunder" moves at a speed above
the light and is mearly a signifying concept of what
will come next. This is by definition what can be called
semantic information: the one that will give meaning to
the material element when this occurs. We have seen in
telepathy that mental concepts can be equal between
different persons in altered neurological states. In
these situations, resistance cames close to 1, times
approach from the hyperdimension and the concept
projects itself on matter although the mind is beyond
time, without any time. To the paranormal individual,
the Psi agent, the mind is joined to matter and the
mental and material times can be inverted. In case of
higher resistance, they disconnect and the concept
escapes reality (psicons) reaching the maximum of
disconnection when LINK disappears and the concept comes
to exist as an isolated entity: vacuum.
The same expression, now to another dimension:
valid. For PSi agent, perhaps due to its genetic
information, the state of resistance reflects the entire
informational mental totality without damage
The states of normal sensoriality happen to us because
the sources are very close to receivers and high speeds
of syntactic information transmission do not allow
individuals to think that their formation of signifying
concepts prevails over simple material transmissions
that have the speed of light as a limit.