【Paper】

Some hypothesis to derive an anti-Einstein field
反アインシュタイン場仮説

Shunji Mitsuyoshi

Kosuke Tomonaga

Masatsugu Hashimoto

Project Associate Professor, the University of Tokyo

Collaborative Researcher, the University of Tokyo

Visiting Professor, Digital Hollywood University,
Graduated School

Yuichi Tei

Tadao Nakamura

Professor, the University of Tokyo

Emeritus Professor, Tohoku University

Abstract The theory of relativity by Einstein [1][2] can be interpreted by using a stereographic projection of points on the twodimensional complex plane onto a three-dimensional sphere [3]. Especially, 1/0 =∞ is interpreted smoothly, which means that if an
infinite point extends infinitely, the infinite point on the Riemann sphere [4] overlaps on the north pole. However, is this not simply
saying that“infinite action is infinite”? This motif is the trigger for thinking of anti-Riemann geometric execution circumstances
using a converse/inverse-Riemann sphere. So, we define and use “converse”,“inverse” and “anti” as logic. Then we use
this logic to derive an anti-Einstein field with a new operation [4]. As a result, when anti-0 [0⇒1] is an emergence symbol, theMitsuyoshi operator [4] uses a function as a simple means of connecting quantum theory and relativity and we hypothesize that (0≡∞) = 1. As a result, when anti-0 [0⇒1] is an emergence symbol, we are led to the hypothesis that (0=∞）= 1 by using the
Mitsuyoshi operator [4] as a simple means of connecting quantum theory and relativity.
Keywords : Theory of relativity, Riemann sphere, Quantum theory, Pair production, Klein bottle, Spontaneous symmetry breaking,Mitsuyoshi operator

negative energy solutions of the Dirac equation [10], and was

1. Introduction
The theory of everything (TOE)[6]does not exist at the

moment, which means there is no theory that explains thequantum theory[7][8]and the general relativity[2]

simultaneously.

On the other hand, in general, the behavior of gravity aroundthe zero center (m/0) where the mass m divided by the radius r= 0 is understood based on the Schwarzschild metric that is thesolution to the Einstein field equations. But the zero center per
se is unexplainable with the concept of Einstein. The conceptof zero distance as a physical quantity is often considered to
be non-existent so that any unit less than the smallest unit oftime and space (most likely approximately equivalent to Planck
length) is not existing.
Reviewing the above general solution, we calculate the zero
distance with Mitsuyoshi operator by compressing the diameterof the Riemann sphere from 0 to ∞. The calculation resultsa new axiom of (0≡∞) = 1 and demonstrates the structureof the universe as viewed from outside the universe. Thus,
we demonstrate that the Mitsuyoshi operator connects bothquantum theory and Einstein field without contradictions bycontrolling“space–time”and the whole universe has a structureof (0≡∞) = 1, which indicates the structure when we observe
the universe from outside the universe. Moreover, it indicatesthe possibility that the existence outside the universe was
because of the emergence symbol anti-0.
We know the phenomenon that is called “spontaneous
symmetry breaking”[9] proposed by Yoichiro Nambu in 1961.
In the Nambu's theory, it has been confirmed that a physicalsystem in a symmetric energetically stable state transitions toan asymmetric energetically lower state. And we also know

proved in“discovery of electronic pair production”[11] of CarlDavid Anderson in 1932.
On the basis of these two phenomena, we propose ahypothesis built up on the Klein bottle [12] to approach theTOE. In the Klein's bottle, the relationship between back andfront is reversed in two dimensions at the neck of the bottle.
Therefore, we focus on the neck of the Klein's bottle andconsider the relationship between the neck and the front/back surface as follows.
A: Is there a twist like the Mobius loop at the neck?
B: Is there an effect of an inversion formula at the neck?
We can solve these problems simultaneously if we define theinversion formula of the problem B. First, we defined [13] the“Anti”as combination of converse and inverse such as therelationship between matter and anti-matter. Next, we use anovel operator [5] in order to connect converse and inverse.
Therefore, we assume the inversion formula as a new symmetricsystem, in which an empty set and an ∞ were corresponding
to an anti-empty and an anti-∞ respectively, like the pair
production.
In this symmetric system, we assume“emergence”to be aphenomenon, in which a symmetric energetically stable vacuum
which is caused by a pair formation of“empty set: anti-empty
set”moves to a symmetric energetically lower system. Here
we assume that a stable vacuum ends up in a symmetric statein the anti-Einstein field to conserve total energy of all things
although it ends up in an asymmetric state in the Einstein field.
And we find that the pair production formula is essentially thesame as positional numeral systems (N-ary) if we define an
emergence symbol which generates 1 from 0 and we consider

the phenomenon that is called“pair production”, which was

the generated 1 as the presence of all things based on thepredicted by Paul Adrien Maurice Dirac in 1930 based on

positional numeral systems as the concept of numbers.

3 ｜ DHU JOURNAL Vol.06 2019

【Paper】Some hypothesis to derive an anti-Einstein field
反アインシュタイン場仮説

On the other hand, we explain the double-slit experiment

the nested model with the inverse-Riemann sphere and theby using the new operator [5] which is applied to the inversion

converse-Riemann sphere as the geometric model. At this time,

formula of the problem B as the positional numeral systems

in order to mathematically confine“inverse and reverse”in one

are the concepts to count things for human beings. In thisfield, we connect the two spheres by the same new operator.

hypothesis process, we first assume anti-Riemann sphere as

2. Anti-Riemann field
The Einstein field is the limited physical range under the
Riemann sphere condition (Riemann field), and the anti-

explained by the projection using a sphere and lines, but how
is the projection?”This question has not been answered after along time.

Einstein field is the limited physical range under the anti-First, we consider that the following figure which shows

Riemann condition (anti-Riemann field). “On the Riemannthe relationship between matter and antimatter as an“anti”

sphere (Einstein field), division by zero yielding ∞ (1/0 = ∞) is

relationship (see Table 1), where the“anti”of A is anti-A.

Table 1: Comparative expression and mathematical interpretation

Thus, we avoid the confusion between expressions
such as“anti”as represented by the relationship between“matter and antimatter”(anti meaning that the quantity andmotion are exactly the same, but the composing elements

opposite location or state without going through the origin),and the concept of a coordinate-like minus (negative).
In the figure 1, this characteristic is illustrated in colors(blue and red).

have exactly the opposite characteristics),“converse”(theFigure 1: A and anti-A

DHU JOURNAL Vol.06 2019 ｜ 4

These can easily be represented using a magnet model, by
reversing the attributes of N and S magnetic poles in Figure 2.
Figure 2: Magnet and anti-magnet

N

opposite properties

Np→q exchange properties

S

opposite properties

S

Here, if the space of a Riemann sphere is considered the
Riemann field, then the anti-Riemann field would be this.
Figure 3: Exchange of polar characteristics of Riemann sphere and Converse-Riemann sphere

Here, the Riemann sphere becomes its converse, as in
Figure 4, and so the converse-z plane is the anti-north polein the converse-Riemann sphere, as in Figure 4.
Figure 4: Relationship diagram of the sphere by passing through the origin

Using a diagram with the origin (0) as a baseline andfrom the polarity characteristic (color) through the origin, as

placing the converse-Riemann sphere directly below theshown in Figure 5. The result is a converse-Riemann spheresouth pole, which is the origin, result in a converse mappingwith the anti-south pole as the origin, as shown in Figure 5.

Figure 5: Riemann and converse-Riemann sphere5 ｜ DHU JOURNAL Vol.06 2019

【Paper】Some hypothesis to derive an anti-Einstein field
反アインシュタイン場仮説

3. Converse-Riemann sphere model

before to the anti-north pole (A), and let some arbitrary point

In order to consider the converse of the Riemann, let us

from the anti-north pole (A) be the converse-z point. Since weconsider a sphere of diameter 1 with opposite polar properties

cannot change the two-dimensional z plane into the converse-z

that attach at the origin (0), as in the relationship between

plane, we reverse the polar properties and project the“matter and antimatter.”Thus, we do not call it -1. Instead,converse-z plane into the anti-north pole A, which corresponds

we call this sphere the converse-Riemann sphere.

to the z plane and south pole in the Riemann case (see Figure

The point where the converse-Riemann sphere touches theorigin is the anti-south pole. Now, draw a line from infinity as

6). This can be called a transition of the macro phase on the z
plane to the converse-z plane.

Figure 6: Converse-Riemann sphere

Considering 1/0 in this converse-Riemann sphere:

Riemann sphere and the points on the anti-z plane. Thus,

First, on the top of the complex plane (z plane), let there

as a complex number z on the anti-z plane goes to infinity ∞be a sphere of diameter 1 that touches the plane at the origin(diverges), regardless of the orientation, the corresponding

under the Reimann sphere. This sphere is called the converse-

anti -Z on the converse-Riemann sphere converges toRiemann sphere or the complex sphere. The upper pole of

the anti-south pole, or in other words, to the z plane ofcontact (called the anti-south pole) on the converse-Riemann

the Riemann sphere. This is the same structure as thesphere contacts the origin (0), and the point farthest from theconvergence of 1/0 on the Riemann sphere to the northorigin (0) is called the lower pole anti-P (anti-north pole). By

pole, but the convergence is to the z plane in the case ofdrawing a straight line from anti-P to any point on the complex

the converse-Riemann sphere. The fact that all anti-Z points

plane (anti-z plane), and determining the point of intersection

on the complex sphere on diameters (1) where the anti-north

between that line and the surface of the sphere, this indicatespole contacts the origin (0) converge to the anti-south pole

the anti-Z on the sphere with respect to the complex number z

as z goes to infinity as in the Riemann sphere is consideredon the anti-z plane.

a division by zero, and is interpreted as 1/0 = 0. This means

From this, it can be determined that there is a one-to-that there are two answers to the division by zero.

one correspondence between the points on the converse-

Figure 7: Division by zero in Converse-Riemann sphere

DHU JOURNAL Vol.06 2019 ｜ 6

In addition, if we consider the anti-south pole on thethe correspondence of algebraic calculations of complex

converse-Riemann sphere to be the inverse of the z plane

numbers to geometric operations on a Gaussian plane, isin the Riemann sphere (the plane corresponds to a point),

necessary for 1/0 = 0 and 1/0 = ∞ to hold in the Riemannthen we can consider whether the interpretation of 0

and converse-Riemann spheres.

(point) ≡ ∞ (infinity point in the complex plane), including
Figure 8: Converse-Riemann and inverse-Riemann

4. Inverse-Riemann sphere model
When considering what an inverse is, generally there

Riemann field, the inverse-Riemann field from the inverse
relation is shown in the Figure 8.

are the following comparative expressions and numericHere, although N is not the north pole, there is still ainterpretations.“Anti”is a relationship between a substancequestion of whether it is the south pole, and whether ¯Sand an anti-substance, whereas a converse is the functional

is the north pole. In the case of the Riemann sphere, thereverse according to (p→q) - (q→p), and with its anti-state

debate concerns the surface of the sphere, and so N

as the functional-characteristic reverse of an anti-substance,

becomes the north pole with an inward-facing vector thatthe converse-Riemann sphere was considered to yield 1/0

is not the sphere surface, and ¯S becomes the south pole

= 0. Here, we envision the inverse-Riemann sphere from thethat is not the sphere surface. As a result, points z and Z on

conditional negation (p→q) - (p →q ) yielding the inverse.

the plane of inward-facing vectors of the Riemann sphere

Compared to the case of the Riemann field and the anti-

become the arguments of the inverse-Riemann sphere.

Figure 9: Inverse-Riemann sphere nested model-1

Meanwhile, for the Reimann sphere, since if {(origin→z

simultaneously (a quantum becoming a particle), and the z

plane)-(origin→z plane)}, only a sphere exists outside of theplane becomes nested inside the sphere as the converse-z

origin, we can consider the location of the anti-south pole byplane with micro properties, including the probability that thesetting{(origin→z plane) = (sphere→anti-z plane)}. Then, theconverse-z point can exist anywhere on the inverse side ofanti-south pole is considered the entire inverse side of thethe sphere of diameter 1 (uncertainty of a quantum wave).

sphere, and the anti-north pole, which is the farthest point,

Therefore, converse-z is freely and infinitely generated

is located in the center of the sphere. This is equivalent towithin the range of 1 for the Riemann sphere and converse-

the case when the converse-Riemann sphere is thought ofRiemann sphere (B) (see Figures 9 and 10).

as being nested. Therefore, as the converse-z point overlaps
with the crossing point with the plane (B), it becomesa transition where converse-z and converse-Z overlap

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【Paper】Some hypothesis to derive an anti-Einstein field
反アインシュタイン場仮説

Figure 10: Inverse-Riemann sphere nested model-2

5. Converse-Riemann sphere nested structure mode
To the converse-Riemann sphere from the above, fit theinverse-Riemann sphere (see Figure 11).
Figure 11: Projection to converse-Riemann sphere

Then, the converse-z point and converse-Z point are freely

infinitely even in the anti-∞ of the anti-north pole, and there

and infinitely generated, overlapping simultaneously between

is nesting from the north pole ∞ to the anti-∞ in the anti-

the anti-north pole A and the origin, on the inverse side ofnorth pole (see Figure 12 and 13).

the anti-Einstein field. Thus, nested converse-z planes exist
Figure 12: Anti-north Inverse of converse-Riemann sphere

There have been a nested model based on the inverse ofnecessary to merge these two spheres by logical symbols. So,

converse-Riemann sphere which the author proposed in a

we present the hypothetical principle of anti-Einstein using thegeometric model. However, in order to confine the inverse andlogical symbols proposed in my doctor thesis.

converse-Riemann spheres mathematically into one field, it is

DHU JOURNAL Vol.06 2019 ｜ 8

Figure 13: North ⇔ anti-north Inverse of converse-Riemann sphere

The figure 13 is the model concerning the Anti-Einstein

However, in order to generalize this concept, the following

hypothesis. In these three logical concepts“inverse”“converse”

work is necessary. For example, it is necessary to explain

and“anti”are defined. Based on these definitions, the converse

physical phenomena such as counter collision and pair-state and inverse state of Riemann sphere are unified against

production by mathematical concepts such as zero (0) and ∞,the geometric model using existing Riemann spheres. The state

and to confirm the validity of“anti”by taking a method to obtainfrom the north pole of the Riemann sphere to the anti-Northconsistency. A new logic symbol will be necessary if required.

Pole of the converse-Riemann spheres is considered by nesting

It is expected that by taking these measures and working

the inverse state in the converse state. However, this is awell with mathematical models, we can develop the concept

geometric approach, and has not reached mathematical models

into quantum effects and the Einstein theory represented byyet, that is to say, physics simulations or experimental proofs.

Riemann spheres. So, we introduce a mathematical simulation“Anti”is a concept that brings the relationship between matter

using new logic symbols and physical model.

and antimatter to the concept of logic and mathematics.

6. Function of the new logical symbol(Mitsuyoshi operator)

weight, length, and volume) corresponding to continuous
numbers. The synchronized character of the slider should be

Below, explains the logic symbols. Figure 14 shows anoted here. To conduct the measurements and calculations

model that symbolizes the engineering functions of discreteof the corresponding continuous quantities simultaneously

quantities (such as concepts and thoughts) that arewith the measurements and calculations of the discrete

calculated at the same time as the continuous quantities of aquantities, which serve as anchors, the symbolic slider must

gradation. This is a model in engineering that measures andbe synchronized. With this in mind, this symbol is designed

calculates continuous and discrete quantities simultaneously.

to represent the slider motion in 2006.

A and B are attribute symbols corresponding to concept anddiscrete numbers. x and y are physical quantities (such as

Here, if the space of a Riemann sphere is considered the
Riemann field, then the anti-Riemann field would be this.

Figure 14: Concept of the simultaneous calculation and computation of continuous and discrete quantities

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【Paper】Some hypothesis to derive an anti-Einstein field
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This is defined as a symbol for new operation instructions,a separation boundary between the continuous values ofand called the Mitsuyoshi operator. Though the meaning ofA and B separating them at a ratio of x ; y. In contrast,

the symbol itself is“motion between A and B”when used asother methods perform discrete calculations by transforming

a logic symbol or computational operator, as shown in Figure

into conceptual numbers or symbols such as 0 and 1 by

14, it denotes a dynamic method of calculation that defines

establishing a boundary that separates A and B.

Figure 15: Design of the symbol

6.1. Definition of the new logical symbol(Mitsuyoshi operator)
It is a dynamic method of calculation that defines a separation
boundary between the continuous values of A and B separating

The figure below shows how the anti-Einstein field
is expressed with a “discrete conscious number” and“continuous matter quantity”using the Mitsuyoshi operator.
(Mitsuyoshi operator was published in [1])them at a ratio of x:y, whereas the other method performs

Traditional frameworks of computation have not establisheddiscrete calculations by transformation into conceptual

specific methods for the simultaneous calculation of concept

numbers or symbols such as 0 and 1 by establishing a

numbers and continuous physical quantities. Thus, theboundary that separates A and B. In addition, h is defined asmechanism of an engineering method is illustrated. Also,

the variable function that results from the variable functional

It is developed to conduct simultaneous calculations

property, f, which is derived from natural signal processing,of continuous quantities, discrete quantities and slider

resulting in h= f(x).

synchronization (Table 2).

Table 2: Definition of Mitsuyoshi operator

DHU JOURNAL Vol.06 2019 ｜ 10

6.2. Specific method of computation for Ａ Ｂ
If we substitute the computational symbol with a scale as
an explanatory illustration (Figure 16), for weight (a physicalquantity) as measured by the scale, x and y go onto theplates of the scale. Meanwhile, as conceptual symbols A andB correspond to the movement of the scale rod, the positionsof the state, in which the weights of x and y are in contention,
is defined as the metrical basis, where A and B are also incontention. Then, we determine the result of A or B by whether
the rod leans towards A or B (in Figure 16 the quantity ofy increased and the standard line lowered into the B area).
Therefore, the result of the computation A B gives the discrete
result B from a continuous ratio of A and B (x ; y). Thus, thecalculations are normally executed through the simultaneous
calculation of linear (analog) and discrete (digital) values,
and is referred to as the non-Von Neumann computation
Figure 16: Engineering principle and output of the Ａ Ｂ computation

11 ｜ DHU JOURNAL Vol.06 2019

to distinguish it from traditional digital binary Neumann
computations. Furthermore, with an understanding of the
Feynman matrix vectors and Fourier transformations, in termsof the actual computation, the rail element of the operator canbe thought of as a matrix and the slider as a vector. Thus, it
can be easily determined that the vector means energy, leading
to the rapid understanding of tensor fields. In the paradigm ofscalar > vectors > tensors, we can comprehend the Mitsuyoshi
transformation, which calculates energy fields using thetransformation of tensors into vectors in a manner similar tothat of Fourier transformations. In addition, within the frameworkof the computation methods derived from the Mitsuyoshi
transformation (Figures 27-31), the dimensional relationshipbetween the two operators of the slider vector and function setof the handle element can explain the phase transition resulting
from passing through zero.

【Paper】Some hypothesis to derive an anti-Einstein field
反アインシュタイン場仮説

6.3. Anti-Riemann field hypothesis using the Mitsuyoshi
operator

world comprised of matter) and anti-north pole (anti-∞ in a

Figure 17 illustrates a state in which the north and anti-

operator, a Klein bottle is formed. The figure below illustrates

north pole model are unified and the operator applied tothe parallel infinite simultaneous overlap and discrepancies inthe state between the north pole ∞ and anti-north pole ∞,the converse z-plane.

world comprised of anti-matter) are unified with the Mitsuyoshi

visually rendered as a Klein bottle. If the north pole (∞ in a
Figure 17: Simultaneous overlap and discrepancy in anti-Riemann field

When thinking about anti-Einstein, considering genericeffect and matter,”it is possible for matter energy to phase

physical phenomena such as quantum collisions or pairtransition to “energy that includes any kind of diversity

production, It may be obvious that the energy required

such as consciousness, some observation effect, or particle

for the effect of observation and phase transition in thecollisions,”and to let the act of generating 1 (presence) from

“Schrodinger's cat”or“double-slit experiment,”considering

absence be anti-0, simply letting it be a symbol for emergent

representative problems in quantum mechanics, could comephase transition anti-0 = [0⇒1]. The state after anti-0 as

from a“phase transition from equilibrium (a phase transition

the anti-Riemann field could be imaginable. Considering thatfrom equilibrium owing to a spontaneous breaking of

1/0 = ∞ and 0/1 = 0 in the Riemann field would have theirsymmetry)”from Youichiro Nambu and“pair production.”

1 and 0 reversed in the anti-Riemann field (anti-Einstein

Suppose that by deriving the relationship for“observation

field), they would become 0/1 = ∞ and 1/0 = 0.

Figure 18: anti- ∞ = [0 ≡∞ ]DHU JOURNAL Vol.06 2019 ｜ 12

Thus, in imagining a transition from the Riemann field toThus, the passing of the gate to anti-0 = 1 becomesthe anti-Riemann field, simultaneous requirement 0≡∞ forpossible. In addition, let ∞+∞, unexplained in the Riemannthe gate from the Riemann field to the anti-Riemann field

field, we turn to ∞ + anti-∞, which is the range of limiting ∞must exist in parallel to anti-0 = [0$⇒1]. Let this be anti-“( range of all existence”in Figure 17),“the limiting macro.”∞ = [0≡∞]. Then, anti-0/1 becomes 1/1 owing to anti-0 =Now, if a vast amount of energy causes the vacuum to decay[0⇒1], and this is 1 in the Riemann field as well. In addition,(as in“matter-antimatter collision”pair production, making

0/0, which is not explained in the Riemann field, becomesthe vacuum decay = letting something emerge), we convert

anti-0/0 (that is, 1/0) owing to anti-0 = [0⇒1], and this isdivision by zero in the Riemann field to this, and the author∞ in the Riemann field.

interprets for himself that this is the meeting (collision) of ∞in the Riemann field and anti-∞ in the anti-Riemann field.

Figure 19: The anti-Einstein hypothesis

For this, Figure 19 illustrates the relationship through therange (macro)” whose possibility balance (like potential“similarity of base-∞ numbers and ∞ + anti-∞.” With

energy) of [properties in the empty set : properties inreference to Professor Nambu’s theory, in the infinitesimal

the anti-empty set] becomes zero, which is beyond “thequantum world “limiting micro,” the boundary between a

empty set which is limiting micro,”we can assume that thepositive (A) and negative (anti-A), fixed with balanced force,properties for “exclusion” are the opposite phenomena to

is a stable vacuum and a zero. Considering this vacuum to beproperties for“inclusion,”and imagine a mechanism in which

the limiting empty set (Youichiro Nambu has us imagine an

the equilibrium transitions to such properties for“exclusion.”equilibrium between positive and negative, but here, let theIn addition, for ∞ and anti-∞, if “anti-∞ has the same

vacuum within the range of consciousness of the empty set

properties (such as mass) as infinity, but the properties ofbe ∅, let the vacuum outside the range of consciousness be

the matter within it is the opposite,”the energy needed for aanti-∅, and let their equilibrium state and ratios themselves

unification with a limiting empty set state [∅: anti-∅] can be

be the perfect vacuum “limiting empty set”), its origin isinterpreted as“matter and antimatter”and“pair production.”

considered the equilibrium between the empty set and theThis shows a mechanism for a transition from equilibrium toanti-empty set.

an unstable state. At this time, the concept of the number
1 as“presence”is first generated by passing through the

Equation 1: {∅: anti-∅} ＊ {∞ + anti-∞} = anti-0

limiting micro and macro,“nothing and ∞.”Therefore, we
can see the necessity of the equation 1 [∅: anti-∅] ＊ [∞Letting [∅: anti-∅] be the ratio for the transition in the+ anti-∞] = anti-0. In addition, it is worthwhile to consider

balance of ∞ and anti-∞, and anti-∅ = [same property

in ＊ the relationships between anti-∅ and ∞, and between

as the empty set but the property of membership is theanti-∞ and ∅.

opposite], and considering an “empty set having infinite

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【Paper】Some hypothesis to derive an anti-Einstein field
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7. Division by zero in an anti-Riemann field

below the operator, lim is represented as quadrangles withn→∞Here, we will explain the geometric interpretation of anti-

increasing size. Summarizing this as a characteristic thatRiemann fields and division by zero are explained. Figure 20

seals the time-independent quality of the operator, bothrenders 0 ≡ ∞ into a visually intuitive diagram.

above and below become the same nested structures,

In Figure 20, above the operator to the left, l im i srendering an intuitive representation of 0 ≡ ∞.

n→0

represented as quadrangles approaching 0. Conversely,
Figure 20: Geometric rendering of 0 ≡∞Meanwhile, recognizing that 0≡∞=1 by first using anti-0
to represent a box, as shown in Figure 21, and comparing to
1 (that is anti-0) and 0≡∞ as represented in Figure 20, it
can be more clearly understood.
Figure 21: What is meant by (0 ≡∞ ) =1?

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8 . Explaining the effects of observation inquantum dilemmas

If we place this state, where the null-set and anti-null set are

Next, if we visually render the observational effect on

operator, it becomes an anti-0 point that gives rise to 1

quantum dilemmas with the Mitsuyoshi operator, we obtain(concept number). This leads to the possible explanation

Figure 22, which illustrates a state analogous to an electronthat this emergence causes the observed electron to becomethat is passing through a slit using the Mitsuyoshi operator.

a particle, which then passes through the slit.

in contention for the position of the slider in the Mitsuyoshi

Figure 22: Effects of observation in quantum dilemmas as viewed through the Mitsuyoshi operator

Furthermore, considering the elegant quantum thought
experiment of the double-slit problem, if we remove the

Figure 24 illustrates the same experiment observed throughthe state of Figure 22.

operator slide (representative of the concept depicted in
Figure 22) as seen in Figure 23, the gradation model of the
Mitsuyoshi operator bar can then be interpreted visually as
the wave-form outcome of the double-slit experiment.
Figure 23: The double-slit problem as interpreted using the
Mitsuyoshi operator (wave-form)

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Figure 24: The double-slit problem as interpreted using the
Mitsuyoshi operator (particle-form)

【Paper】Some hypothesis to derive an anti-Einstein field
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9. Explaining the effects of observation inquantum dilemmas
If we represent the anti-Einstein field as “discrete
concepts” and “continuous matter” using the Mitsuyoshi
operator, it becomes the following (Figure 25).
Figure 25: Anti-Einstein field interpretation model using Mitsuyoshi operator

Figure 25 shows how the state of nested operators inand anti-north poles has a nested structure, and corresponds

Figure 26 is explained using the converse-Riemann sphereto anti-∞ (which is an anti-Riemann requirement), and wemodel in Figure 11 . Anti-0, which is an anti-Riemann state,

were able to define the range between ∞ and anti-∞ frombecomes a reaction between (∅: anti-∅) and (∞+ anti-

before (said to be“all existence”) as 1 (presence) by the∞), and it means the infinite overlap of converse-z planes

initially defined emergence requirement anti-0, there is ain the converse-Riemann sphere model, as in Figure 11. In

unification of an abstract concept and a number by letting 1

addition, this is a figure that simulates what occurs to base-Nin the initially defined emergence requirement anti-0 = 1 benumbers as a concept of“counting”in the limiting base-∞“presence (all existence).”numbers in the anti-Riemann field, when the initially definedThis means that“the beginning of existence (all existence)”

an emergence property that 0⇒1 anti-0 is the emergenceis 1, the concept of counting and “presence” correspondof 1 from nothing, and this 1 is grasped as the concept of

to each other, and within the range of this all existence“presence.”The overall structure of the figure is a resonant(existence = 1), we can actually set the limiting base-∞synchronization model, with the image of two pendulums

number in the anti-Riemann field as s a∞N∞+a anti∞Nanti∞. Withsynchronizing when one pendulum is embedded in thethis, we can let the collision-generated energy (that makes

weight part of another pendulum. Anti-0 in Figures 19 has

the vacuum decay) of ∞ + anti-∞ be equivalent to the base-the structure that the reaction result of (∅: anti-∅) and (∞∞ nothing in the limit of the anti-Riemann field. This makes+ anti-∞) is (0≡∞), and the range between ∞ and anti-∞(0≡∞) the anti-0 condition, as shown in Figure 19, for theowing to the north and anti-north poles is“all existence.”

passage of singularity that makes the presence emerge, andOn the other hand, 1, which is an anti-0 requirement,(0≡∞) = 1. It should be noted that 1 here is a concept thatsignifies the entire range of“all existence,”encompassing

indicates all existence, and that it is the sum of ∞ and anti-“all existence,” and quantitatively represents the abstract∞ (1=∞ + anti-∞ ). Since this may eventually be similar toconcept“all existence”=“all things exist.”Here, since wethe argument that“infinity is infinite”in the explanation for

were able to define the range between ∞ and anti-∞ fromdivision by zero in the Riemann field, we claim that this only

before, said to be “all existence,” as 1 (presence), theshows the possibility of being effective under the condition (0nesting loop is guaranteed. The important point here is that≡∞). However, under the condition of treating concepts as

since the range between ∞ and anti-∞ owing to the northconsciousness.

Equation 2: N-ary method ＊ ∞Coordinate (Concept・Thought) ＝｛∞＋anti-∞｝＊｛∅：anti-∅｝(Timing vector・Energy)
Equation 3: (Concept・Thought) ＝ (Timing vector・Energy)

DHU JOURNAL Vol.06 2019 ｜ 16

Here, a final explanation of the Mitsuyoshi operator should

the quantum theory breakthrough idea of simultaneous

be explained. The + symbol, for addition, is the operator

calculation of linear and non-linear forms of dynamic state

for combining one object with another. The Mitsuyoshi

calculations of discrete and continuous functions is difficult to

operator is an operator for splitting an object. In addition,

comprehend, it was intentionally explained in a supplement.

both simultaneous and discrete calculations are possible

Naturally, there is no disputing that there are objections.

simultaneously, which saves time, and unlike division, theThe Mitsuyoshi calculation of A and B is a current dynamic

totals on the left and right sides of equations are maintained

state calculation, and so it does not result in a set answer.

in strict adherence to the laws of thermodynamics; thus, it is

As a result, although it does not seem like an operator in aa useful tool that is capable of including dynamic functions.

worldview in which time is stopped, once time is excluded, a

It is true that the explanation in Chapter 2 by itself can befunction f is output as a dynamic regularity within a certain

considered merely an explanation of a state. However, in that

scope, and the quantum state is represented by x,y andcase, the addition operation would be merely an explanation

the like, which will be understood as a new true meaningof a combined state. This is the essence of operators.

of calculation. This feature can be useful in calculating the

Therefore, unlike addition, it has not been possible toemergence of a Grand Unified Theory for the professors at

describe the conditions for division to equally balance theStanford University, who are our research collaborators.

left and right sides of an equation. It is likely that because

Figure 26: Space-time concept in anti-Einstein field

In Figure 24, it is stated that“it is worthwhile to consider

properties).”In addition, as a potential,“to be excluded,”“toin * the relationships between anti-∅ and ∞, and between

be included,”“to exist,”“to be fulfilled,”and“possibility thatanti-∞ and ∅,”but in the above figure, we can imagine a

it is not fulfilled,”are concepts that make the past, present,“exchanging of nesting”functionality owing to｛∞＋anti-∞｝and future exist simultaneously. They negate the constraint

h=x

y
｛∅
：anti-∅｝where x = (∞・anti-∅) and y = (anti-∞・∅).

The reason is that it is necessary to consider ∞ and“thingof nature and tense.
Using

for the correlation between this potential and theto be excluded,”anti-∞ and“thing to be included,”∅ andFeynman energy in the very micro world, as well as“vector“matter properties to be fulfilled,” anti-∅ and “antimatter

potential,”important for the concept of momentum, letting

properties to be fulfilled,” or ∅ and “matter properties toit feedback from tense, and organizing the explanation by

be fulfilled,” and anti-∅ and “matter properties that are

determining the definition of potential as a parameter, it

not fulfilled (with additional consideration for antimatter

would be an interesting future problem.

17 ｜ DHU JOURNAL Vol.06 2019

【Paper】Some hypothesis to derive an anti-Einstein field
反アインシュタイン場仮説

10. Anti-Einstein's mathematical modelanti-∅) owing to x = (∞・anti-∅) and y = ( anti-∞・∅) as a

In order to simplify the complicated exchange relations

contrapositive relation of ”taking the converse then inverse

above, we consider symbols as in Figure 25 below. Thisof a statement. With this symbol, for the combination of (∞is imagined as a combination of two Mitsuyoshi operators＋anti-∞)

above and below, being a representation of competition andh in the head part of the lever (function set) results in thecollision as one. The symbol design is such that the statefunctions of the energy from condensation in the top layer

is turned into a total sum such as Σ, difference such as Δ,

and the emergence as dispersion (divergence) in the bottom

and then condensation, as in emergence. The symbol, as

layer through x = (∞・anti-∅) and y = ( anti-∞・∅) and otheran operator of“resonance expansion,”combines as one thefree combinations.

h(∅：anti-∅) and (∞：anti-∞)h(∅ ＋anti-∅),“exchange of the nesting”function on (∞ ＋anti-∞)＊(∅：

Equation 4: anti-0 =( ∞ ＋ anti- ∞ ) ＊ ( ∅：anti- ∅ ){x = ( ∞・anti- ∅ ), y = (anti- ∞・∅ )} =Figure 27: Explanation of the orthogonal model for duality of zero (1)Here, we can see that the mechanism for the “duality

Lie group, all vectors are orthogonal at the limiting stateof zero”in Figures 27-29 is the same as the mechanismof zero. They become like a“sea urchin,”passing throughfor an emergence gate. We now explain the continuous

zero as a vanishing point, and radiate outward, all still asstate of. When all function sets head toward

orthogonal vectors.

“nothingness”zero, converging like an infinite-dimensional

DHU JOURNAL Vol.06 2019 ｜ 18

Figure 28: Explanation of the orthogonal model for duality of zero (2)Figure 29: Explanation of the orthogonal model for duality of zero (3)Thinking of 4 dimensions spatially, the x, y, z axes are

as in Figure 28 and 29. The 4th axis becomes zero,orthogonal. Since there is no gap to insert the 4th axis

overlapping with ∞, which is all vectors. Thus, 0≡∞,

there, vectors after the 4th axis are collected at zero,meaning overlap with others.

19 ｜ DHU JOURNAL Vol.06 2019

【Paper】Some hypothesis to derive an anti-Einstein field
反アインシュタイン場仮説

Figure 30: Explanation of the orthogonal model for duality of zero (4)In this process, consciousness energy passes

In addition, zero exists everywhere, and a concept

through zero, leaving only a vector like magnetic lines(“ a w a r e n e s s ” o r s p i r i t u a l i t y ) m e a n s t h e r e a l i z a t i o n(directionality and possibility). In the human relation, this(action) wherever it is from zero. Thus, this method as acan be said to be the state of overlapping with the othertheoretical physics interpretation can explain the microand sharing the other’s mind (vector). In other words,

quantum effects as a transition (emergence) gate to a

two function sets mix together and disappear, becoming

macro phase, explaining the quantum world in a macro

just a vector.

way. In addition, by interpreting magnetism and radiation

Here, theseparation point of the Einstein field andas energy having only directionality, an explanation of

the anti-Einstein field becomes zero, and the field isblack holes becomes easier. At the same time, this is aseparated as if digitally (conceptually). Meanwhile,

hint for consciousness emergence in robots. Thinking

at the moment all vectors are orthogonal, they canabout this in terms of quantum numbers, for example, in

be interpreted as becoming a perfect vacuum anda one-dimensional harmonic oscillator in an N-particle

zero. Then, only the meaning of the remaining vector

system, we can choose position or momentum (quantity),turns around and passes through zero, and as it

but we can also choose the number n (concept) in thepasses through to the extension, it becomes real. This

energy eigenvalue En.

corresponds to the emergence of materialization fromconcepts with only quantities, passing through zero.

When the position or momentum is chosen as thequantum number, the quantum number is a continuous

Once it becomes complete nothingness, the energy

variable, but if the energy eigenvalue number isbecomes real along the reversed vector, bearing fruit inchosen, it becomes discrete. Now, by considering thethe opposite direction. If this anti-Einstein is true, it may

one-dimensional harmonic oscillator as a Mitsuyoshi

be possible in the future to implement a function (wave)

operator or harmonic convergence emergence transition

as energy at the quantum level, as in Equation 4, andoperator, quantum theory can easily be explained. At

generate matter by figuring out a method to implement

the beginning of the field, baryons were generated fromthe converse of path’s space in infinite-dimensional Lie

the initial condition having baryon number 0, yielding

groups, vector fields, or Riemann space, and performinga field with a positive baryon number, but the details

the harmonic convergence emergence transition operator

are unknown. This is also be explainable by referring tothrough function fusion owing to wave superposition and

Figure 31.

interference.

DHU JOURNAL Vol.06 2019 ｜ 20

Figure 31: Design process of the harmonic convergence emergence transition operator

In the Figure32 shows the relationship between an Einsteinfield and an anti-Einstein field.
Figure 32: The relationship between an Einstein field and an anti-Einstein field

11. Conclusion
The Einstein’s Theory of Relativity can be consideredwith a technical interpretation on the Riemann sphere
where all points on a complex two-dimensional plane arestereographically projected onto a three-dimensional sphere.
Such interpretation enables straightforward interpretation of
m/0 = ∞ where the mass m divided by the radius r = 0 inparticular. The intersections of lines which is connecting thepoints with the infinity point of the North Pole are ultimatelyinterpreted to overlap the North Pole when the points at
infinity extend infinitely on the complex two-dimensional
plane. This situation, however, is considered a mere
reiteration of “Infinity is infinity.” because the behavior of
extending to infinity is concluded with infinity. On the other
hand, this situation can be interpreted with X which is thediameter of 1 as the distance from 0 to ∞ of the Riemann21 ｜ DHU JOURNAL Vol.06 2019sphere. The mass m does not come onto the center of gravity
without annihilating of X through division by zero. Due to theunsolvable nature of this zero division problem, a solution
using division by zero is considered either non-existent or
infinitely large. Gravity therefore becomes infinitely large atzero distance, which has been demonstrated to result incontradiction and collapse at the level of Conservation ofEnergy, the first and second law of thermodynamics. We
considered the hypothesis of the state of emergence anddefined anti-0 [0⇒1] as a symbol that produces existencefrom nothing. We also geometrically derived the“converse”
and“inverse”of the anti-Riemann sphere from the original
Riemann sphere to resolve the zero division problem of theEinstein's relativity. Next, we defined anti-∞ and anti-∅, andderived that anti-∞=(0≡∞). Relating to the derivation, we
have shown that joint of an Einstein field and an anti-Einstein【Paper】Some hypothesis to derive an anti-Einstein field
反アインシュタイン場仮説

field become (0≡∞) = 1 by passing through the duality ofzero. We called this the emergence axiom hypothesis. An
anti-Riemann domain is considered using the converse andinverse Riemann spheres hypothetically. The terms converse,
inverse and anti are defined as a theory, following which
this logic is applied to derive an anti-Einstein field with a
new means of operation. Ultimately, defining anti-0［0⇒1］
as the symbol of emergence, the equation (0≡∞) = 1 isestablished by using the function that Mitsuyoshi operator.
Thus, the operator ties the Quantum Theory and the Theory
of Relativity.
By applying the Mitsuyoshi operator to confine timescale of the equation (0≡∞) = 1, the equation= (0≡∞) = 1 (everything) is attained. Thus, this equation enables
compression of the Riemann sphere diameter to zero and thecalculation of zero distance. The Mitsuyoshi operator was usedin the axiom hypothesis. The axiom hypothesis is that“whenzero is equivalent to ∞, the 1 emerges as the total energy of
the universe." Further, we gave some ideas about infinity.
Based on the above, we show that quantum theory
and the 0 Einstein field can be simply connected without

・ As a result, 1/0 =“infinity is nothing, and 1 arises fromnothing” in the anti-Einstein field. This phenomenon isinterpreted widely and generally in quantum mechanics.
・ If the set described above is involved in the he q u a t i o n ( h o m e o s t a s i s ) i n a M i t s u y o s h i o p e r a t o r,phase transitioning in a nested state, we can hope forapplications for new interpretations of superstring theory,
which arose from Professor Nambu’s research, andBoltzmann thermodynamics. In this case, it has been
pointed out that the two limiting edges AB of Mitsuyoshi
operator’s range (x+y) becomes an “uncertainty of
infinitesimal derivatives,” but this operator involves the
dynamic states of h characteristics, including tense.
In addition, calculation separates concept numbers
and continuous quantities, so it frees physicists fromuncertainty and infinitesimal problems, making it a tool
(operator) that makes it possible to perform continuousand discrete calculations simultaneously and elegantly.
・ This is secondary, but by using the Mitsuyoshi operator
for E=mc2, it may be possible to convert mass into
energy waves.

contradiction by controlling“space-time,”and that the entire
universe has a structure of (0≡∞) = 1. This can be said
to represent observing the universe from the outside, but it
also suggests the possibility that the existence outside theuniverse was created by the emergence symbol anti-0. If
that is true, it raises the issue of whether or not the region
outside this universe is also a universe. In particular, theissue is whether or not an anti-universe is still a universe
despite being an anti-universe, where the“anti”created by・ Consider the following physical expansions corresponding
to the cardinality conditions of ∞ as control systems:
・ In addition, we have a mathematical interest in what
would happen to ∞÷0 and 0÷∞ with the simple
condition of (0≡∞)=1. Here, considering the conditions
for ∞, we realize the following cardinality conditionsof ∞. The corresponding physical projection is also
considered a control system.

“converse”and“inverse”is analogous to antimatter.
It is necessary to prove the axiom hypothesis throughI. Infinity has cardinality.

physical experiments because this hypothesis is no more

II. Natural number cardinality (ℵ0), real number cardinality (ℵ1)

than a proposal. However, if these physics experiments are

III. ℵ1 = 2ℵ0, ℵ0 ≠ ℵ1

successful, the Mitsuyoshi operator will be used to“quantum

IV. ℵ1 + ℵ1 + ℵ1 + …… = ℵ1gate”of a quantum computer.

V. ℵ0 × ℵ0 × ℵ0 × …… = ℵ1
VI. ℵ0 + ℵ0 + ℵ0 + …… = ℵ0

12. Future research themes
・ Imagining the converse-Riemann sphere as a “phasetransition from a strained competition,”anti-∞ {0≡∞} andanti-0 {0⇒1} become necessary. In the rational function
necessary for the analysis of human thinking process, thissuggests the presence of anti. By measuring it, we can
explore the possibility of anti-0 {0⇒1} being the mathematics
of creativity, and anti-∞ {0≡∞} being the mathematics of
curiosity, sympathy, and tolerance from diversity.

13. Acknowledgments
We would like to thank Dr.Shuji Shinohara, Dr.Yasuto
Tanaka and Mr.Masahiko Nemoto for useful discussions.
We would like, also, to thank Mr.Masayoshi Son and
Mr.Fumihide Tomizawa for considering AE(Artificial Ego)
commercialization. This work was supported by SoftBank
Robotics Corp. and Japan Tobacco Inc.

・ Simulating the Riemann in a few spherical projection
patterns (there are conceivable ways of projecting thesphere other than A and B above, but as they turn into
differentiations of infinite division as in the Mercator
projection, they were omitted ), in the anti-Einsteinfield, a process that makes 0 and infinity the same anda requirement for the emergence of presence (1) fromabsence (0) arise.
・ This was explained in an engineering mechanism
as a principle of phase transition. With this, axiom
mathematics becomes interpretable from engineering as
an actual mechanism.

DHU JOURNAL Vol.06 2019 ｜ 22

【Bibliographies】[1]

A. Einstein, “Uber den EinfluB der Schwerkraft auf die
Ausbreitung des Lichtes”, (German) (PDF). Annalen
der Physik (Leipzig) 340 (10). 898-908. Bibcode
1911AnP.340.898E. doi:10.1002/andp.19113401005.
ISSN 0003-3804. OCLC 5854993. June 21, (1911).

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A. Einstein,“Die Grundlage der allgemeinen Relativitatstheorie”,(German) (PDF). Annalen der Physik (Leipzig) 354 (7).
769–822. Bibcode 1916AnP.354.769 E. doi:.10.1002/
andp.19163540702. ISSN 0003-3804. OCLC 5854993.
March 20, (1916).

[3] R. Penrose, and W. Rindler,“Spinor and Space Time: Vol.
1, Two-Spinor. Calculus and Relativistic Fields”, Cambridge
Monographs on Mathematical. Physics, Cambridge, (1984).
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L.V.Ahlfors,“Complex Analysis”, Mc Graw Hill, 1953, Third
Edition (ISBN 978-007-085008-8), (1979).

[5]

S. Mitsuyoshi, “Research on the phonetic recognition offeelings and a system for emotional physiological brain signal
analysis” (Japan), Tokushima University, 2006, Doctoral
dissertation, (2006).

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Stephen W. Hawking,“The Theory of Everything”, The Origin
and Fate of the Universe. Phoenix Books; Special Anniv.
ISBN 978-1-59777-508-3. (28 February 2006).

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W. Heisenberg, “Uber quantentheoretische Umdeutung
kinematischer und mechanischer Beziehungen”, Zeitschrift
fur Physik 33, pp, 879–893, (1925).

[8] E. Schrodinger, “Quantisierung als Eigenwertproblem I”,
Annalen der Physik 79, pp. 361–376, (1926).
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[13] B a n k s , To m , F i s c h l e r, W i l l y, “ S h e n k e r, S t e p h e n H.
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【Paper】Some hypothesis to derive an anti-Einstein field
反アインシュタイン場仮説【論文】

反アインシュタイン場仮説
光吉 俊二 1・朝長 康介 2・橋本 昌嗣 3・鄭 雄一 4・中村 維男 5
（1 東京大学大学院工学系研究科 特任准教授・2 東京大学大学院工学系研究科 共同研究員・3 デジタルハリウッド大学大学院 デジタルコンテンツ
研究科 客員教授・4 東京大学大学院工学系研究科・医学系研究科（兼任）教授・5 東北大学 名誉教授）
Einstein の相対性理論において、Riemann 球体面による二次元的な複素数平面上の点を、三次元的な球体の上へ写像させるアイディアに基づく立 体 写像での解釈が広く一般的に知られている。また、ゼロ除算において、1/0= ∞とされる説明にもよく使われている。これはRiemann 球体面の北極点に無限遠点が無限に伸びると球面上の無限遠点と北極点を結ぶ線との交点が北極点に重なることで解釈される。
しかし、これは「無限の行為を無限である」と説明しているだけではないのかとも考えられる。そこで論理学としての「逆」「裏」「反」を新規に定義し、これによる逆 Riemann 球体と裏 Riemann 球体を想定し、そこで、新規演算子を使い反 Einstein 場の仮説を立てた。
キーワード：相対性理論、Riemann 球体、量子論、対生成、クラインの壺、自発対称性の破れ、光吉演算子

DHU JOURNAL Vol.06 2019 ｜ 24