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Hu, H & Wu, M., Prespacetime-Premomentumenergy Model I: Generation of Elementary Particles & Quantum Theory for a Dual Universe Comprised of Spacetime & Momentum-energy Space

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Article

Prespacetime-Premomentumenergy Model I:

Generation of Elementary Particles & Quantum Theory for a Dual

Universe Comprised of Spacetime & Momentum-energy Space

Huping Hu* & Maoxin Wu

ABSTRACT

This article is a continuation of the Principle of Existence. A prespacetime-

premomentumenergy model of elementary particles, four forces and human consciousness is

formulated, which illustrate how the self-referential hierarchical spin structure of the

prespacetime-premomentumenergy (God) may provide a foundation for creating, sustaining

and causing evolution of elementary particles through matrixing processes embedded in said

prespacetime-premomentumenergy (God). This model generates elementary particles and

their governing matrix laws for a dual universe (quantum frame) comprised of an external

spacetime and an internal energy-momentum space. In contrast, the prespacetime model

described previously generates elementary particles and their governing matrix laws for a

dual universe (quantum frame) comprised of an external spacetime and an internal

spacetime. Then, the premomentumenergy model described recently generates elementary

particles and their governing matrix laws for a dual universe (quantum frame) comprised of

an external momentum-energy space and an internal momentum-energy space. These

quantum frames and their metamorphoses may be interconnected through quantum jumps as

demonstrated in forthcoming articles.

The prespacetime-premomentumenergy model may reveal the creation, sustenance and

evolution of fermions, bosons and spinless entities each of which is comprised of an external

wave function or external object in the external spacetime and an internal wave function or

internal object in the internal momentum-energy space. The model may provide a unified

causal structure in said dual universe (quantum frame) for weak interaction, strong

interaction, electromagnetic interaction, gravitational interaction, quantum entanglement,

human consciousness. The model may also provide a unique tool for teaching,

demonstration, rendering, and experimentation related to subatomic and atomic structures

and interactions, quantum entanglement generation, gravitational mechanisms in cosmology,

structures and mechanisms of human consciousness.

Key Words: prespacetime, premomentumenergy, four forces, consciousness, spin, existence.

*Corresponding author: Huping Hu, Ph.D., J.D., P.O. Box 267, Stony Brook, NY 11790, USA. E-mail: [email protected]

Note: This work was published in Scientific GOD Journal | November 2014 | Volume 5 | Issue 10 | pp. 885-964

mailto:[email protected]


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1. Introduction

In prespacetime-premomentumenergy we contemplate

As a continuation of the Principle of Existence, the beauty and awe of the possible

manifestations of prespacetime-premomentumenergy (God) are described in this article.

The prespacetime-premomentumenergy model generates elementary particles and their

governing matrix laws for a dual universe (quantum frame) comprised of an external

spacetime and an internal momentum-energy space, vice visa. This model generates a

quantum theory for said dual universe.

In contrast, the prespacetime model described previously [1-4] generates elementary

particles and their governing matrix laws for a dual spacetime universe comprised of an

external spacetime and an internal spacetime. The prespacetime model creates the usual

Relativistic Quantum Mechanics for the dual spacetime universe. Then, the

premomentumenergy model described recently [5-7] generates elementary particles and


momentum-energy space and an internal momentum-energy space. These quantum frames

and their metamorphoses may be interconnected through quantum jumps as illustrated

below and demonstrated in forthcoming articles.

Figure 1.1 Illustration of prespacetime model, premomentumenergy model

& prespacetime-premomentum model


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This work is organized as follows. In § 2, we shall use words and drawings to lay out the

ontology of the prespacetime-premomentumenergy model. In § 3, we shall express in

mathematics the prespacetime-premomentumenergy model in the order of: (1) scientific

genesis in a nutshell; (2) self-referential matrix law and its metamorphoses; (3) additional

forms of matrix law; (4) scientific genesis of primordial entities; and (5) scientific genesis

of composite entities. In § 4, we shall discuss within the context of prespacetime-

premomentumenergy model: (1) metamorphoses & the essence of spin; (2) the determinant

view & the meaning of Klein-Gordon-like equation; (3) the Schrodinger-like equation; and

(4) the third state of matter. In § 5 through § 8, we shall discuss, within the context of

prespacetime-premomentumenergy model, weak, electromagnetic, strong and gravitational

interactions respectively. In § 9, we shall discuss human consciousness within the context

of prespacetime-premomentumenergy model. In § 10, we shall pose and answer some

anticipated questions related to this work. Finally, in § 11, we shall conclude this work.

Readers are reminded that we can only strive for perfection, completeness and correctness

in our comprehensions and writings because we are limited and imperfect.

2. Ontology

In words and drawings we illustrate

In the beginning there was prespacetime-premomentumenergy (God) ei0

materially empty

but spiritually restless. And it began to imagine through primordial self-referential spin

1=ei0

=eiM-iM

=eiM

e-iM

=e-iM

/ e

-iM = e

iM/ e

iM…such that it created the external object to be

observed and internal object as observed, separated them into external spacetime and

internal momentum-energy space, caused them to interact through self-referential matrix

law and thus gave birth to the dual universe (quantum frame) comprised of said external

spacetime and internal momentum-energy space which it has since sustained and made to

evolve.

In this universe, the body of prespacetime-premomentumenergy (God), ether, represented

by Euler’s Number e, is the ground of existence and can form external wave functions as

external object and internal wave function as internal object (each pair forms an elementary

entity) and interaction fields between elementary entities which accompany the

imaginations of the prespacetime-premomentumenergy (God).

The prespacetime-premomentumenergy (God) can be self-acted on by self-referential

matrix law LM. The prespacetime-premomentumenergy (God) has imagining power i to

project external and internal objects by projecting, e.g., external and internal phase +M

=+(Et-p·x)/ħ at the power level of prespacetime-premomentumenergy (God). The universe

so created is a dual universe (quantum frame) comprising of the external spacetime with a

relativistic frame xμ=(t, x) and internal momentum-energy space with a relativistic frame

pμ=(E/c, p). The absolute frame of reference is the prespacetime-premomentumenergy


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(God) itself. Thus, if prespacetime-premomentumenergy (God) stops imagining (i0=0), the

dual universe (quantum frame) would disappear into materially nothingness ei0

=e0=1.

The accounting principle of the dual universe is conservation of total phase to zero, that is,

the total phase of an external object and its counterpart, the internal object, is zero. Also in

this dual universe, self-gravity is nonlocal self-interaction (wave mixing) between an

external object in the external spacetime and its negation/image in the internal momentum-

energy space, vice versa. Gravity in external spacetime is the nonlocal interaction (quantum

entanglement) between an external object with the internal momentum-energy space as a

whole.

Some other basic conclusions are: (1) the two spinors of the Dirac electron or positron in

this dual universe (quantum frame) are respectively the external and internal objects of the

electron or positron; and (2) the electric and magnetic fields of a linear photon in the dual

universe are respectively the external and internal objects of a photon which are always

self-entangled.

In this dual universe, prespacetime-premomentumenergy (God) has both transcendental

and immanent properties. The transcendental aspect of prespacetime-premomentumenergy

(God) is the origin of primordial self-referential spin (including the self-referential matrix

law) and it projects the external spacetime and internal momentum-energy space through

spin and, in turn, the immanent aspect of prespacetime-premomentumenergy (God)

observes the external spacetime through the internal momentum-energy space. Human

consciousness is a limited and particular version of this dual-aspect prespacetime-

premomentumenergy (God) such that we have limited free will and limited observation.

Before mathematical presentations, we draw below several diagrams to illustrate how

prespacetime-premomentumenergy (God) creates the dual universe (quantum frame)

comprising of the external spacetime and the internal momentum-energy space and how the

external object in the external spacetime and internal object in the internal momentum-

energy space interact.

Figure2.1. Illustration of primordial phase distinction


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As shown in Figure 2.1, a primordial phase distinction (dualization), e.g., +M=+(Et-p·x)/ħ,

was made at the power level of prespacetime-premomentumenergy (God) through

imagination i. At the ground level of prespacetime-premomentumenergy (God), this is

ei0

=e+iM-iM

=e+iM

e-iM

= e+iM

/ e

+iM….

The primordial phase distinction in Figure 2.1 is accompanied by matrixing of e into: (1)

external and internal wave functions as external and internal objects, (2) interaction fields

(e.g., gauge fields) for interacting with other elementary entities, and (3) self-acting and

self-referential matrix law, which accompany the imaginations of the prespacetime-

premomentumenergy (God) at the power level so as to enforce (maintain) the accounting

principle of conservation of total phase to zero, as illustrated in Figure 2.2.

Figure 2.2 Prespacetime-premomentumenergy (God) Equation

Figure 2.3 shows from another perspective of the relationship among external object in the

external spacetime, internal object in the internal energy-momentum space and the self-

acting and self-referential matrix law. According to the ontology of the Principle of

Existence, self-interactions (self-gravity) are quantum entanglement between the external

object in the external spacetime and the internal object in the internal energy-momentum

space.

Figure 2.3 Self-interaction between external and internal objects of a quantum

entity in a dual universe comprised of an external spacetime and an internal

energy-momentum space, vice versa.


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As shown in Figure 2.4, the external object in the spacetime and the internal object in the

internal energy-momentum space interact with each other through gravity or quantum

entanglement since gravity is an aspect of quantum entanglement (See, e.g., [1]). Please

note that, although in Figure 2.4 prespacetime-premomentumenergy (God) is shown as a

strip, both the dualized external spacetime and internal energy-momentum space are

embedded in prespacetime-premomentumenergy (God).

Figure2.4 Interactions in the dual universe comprised of the external spacetime

and internal energy-momentum space, vice versa.

3. Mathematics of the Prespacetime-premomentumenergy Model

In mathematics we express

3.1 Scientific Genesis in a Nutshell

It is our comprehension that:

God=Prespacetime-premomentumenergy

=Omnipotent, Omnipresent & Omniscient Being/State = ONE (3.1)


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Prespacetime-premomentumenergy (God) creates, sustains and causes evolution of

primordial entities (elementary particles) in prespacetime-premomentumenergy (God) by

self-referential spin as follows:

0

11

,,

11

1

00

M

i

e

M

iM

i

e

MiM

i

iM

e

iMeM

iMiM

ie

iMiMii

LLeA

AL

eA

eALL

eeLLeLee

(3.2)

In expression (3.2), e is Euler’s Number representing the body (ether) prespacetime-

premomentumenergy (God), i is imaginary unit representing the imagination of

prespacetime-premomentumenergy (God), ±M is content of imagination i, L1=1 is the Law

of One of prespacetime-premomentumenergy (God) before matrixization, Le is external

law, Li is internal law, LM,e is external matrix law, and LM,i is internal matrix law, LM is the

self-referential matrix law in prespacetime-premomentumenergy (God) comprised of the

external and internal matrix laws which governs elementary entities and conserves phase to

zero in the dual universe comprised of the external spacetime and the internal energy-

momentum space,

e

iM

eeA

is external wave function (external object),

i

iM

ieA

is internal wave function (internal object) and is the complete wave function

(object/entity in the dual universe as a whole).

Alternatively, prespacetime-premomentumenergy (God) creates, sustains and causes

evolution of primordial entities in prespacetime-premomentumenergy (God) by self-

referential spin as follows:

0

00

,,

1

0

0

M

i

e

M

iM

i

e

MiM

i

iM

e

iMeM

iMiM

pxmEt

iMiMi

LLeA

AL

eA

eALL

eeDetMDetMDetMeLe

(3.3)


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where L0 is the Law of Zero of the prespacetime-premomentumenergy (God) as defined by

fundamental relation (3.4) below, Det means determinant and MEt, Mm and Mpx are

respectively matrices with ±E & ±t (or ±iE & ±it ), ±m & ± (or ±im & ±i) and ±|p| & ±|x|

(or ±i|p| & ±i|x|) as elements respectively, and Et, -m and –p.x as determinant respectively.

Prespacetime-premomentumenergy (God) spins as ei0

=e+iM-iM

=e+iM

e-iM

= e+iM

/

e+iM

….before matrixization. Prespacetime-premomentumenergy (God) also spins through

self-acting and self-referential matrix law LM after matrixization which acts on the external

object and the internal object to cause them to interact with each other as further described

below.

3.2 Self-Referential Matrix Law and Its Metamorphoses

The matrix law

MiMeM LLL ,,

of the prespacetime-premomentumenergy (God) is derived from the following fundamental

relation through self-reference within this relation which accompanies the imagination

(spin i) in prespacetime-premomentumenergy (God):

0/ 0 LcmcctcE -xp

where time t and space x are continuous parameters in external spacetime but quantized

dynamical variables of an elementary particle in the internal energy-momentum space;

energy E and momentum p are quantized dynamical variables of said elementary particle in

the external spacetime but continuous parameters in internal energy-momentum space; and

is the intrinsic proper time of the elementary particle (e.g., defined as Compton

wavelength divided by speed of light =/c) and m is the mass of the elementary particle.

For simplicity, we will set c=ħ=1 throughout this work unless indicated otherwise, so that

we have from above equation:

00 LmEt -xp (3.4)

Expression (3.4) is based on the relation of four-momentum p = (E/c, p) and four-position

x = (ct, x) in special theory of relativity:

cmcctcE -xp /


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In the presence of an interacting field such as an electromagnetic potential (A(x,t), (x,t)) in

spacetime and its dual (A(p,E), (p,E)) in momentum-energy space, equation (3.4) may be

modified as follows for an elementary entity with charge e:

EtEt meteE ,,,, e-e- pxpx AxAp (3.5)

One form of the matrix law in prespacetime-premomentumenergy (God) is derived through

self-reference from (3.4) as follows whenx

p

m

t

E and p parallels to x:

0

1

1

t

mE

t

mE

t

mEmEtL

x

p

x

p

x

pxp (3.6)

where 2 pp and 2 xx . Matrixing left-land side of the last expression in (3.6) such

that 0Det mEtLM -xp so as to satisfy the fundamental relation (3.4) in the

determinant view, we have:

MiMeM LLLt

mE

,,

p

x (3.7)

Indeed, expression (3.7) can also be obtained from expression (3.4) through self-reference

as follows:

0

0

0

0

0

00

p

xxp

Det

mDet

t

EDetmEt

- (3.8)

Matrixing expression (3.8) by removing determinant sign Det, we have:

MiMeM LLLt

mEm

t

E

,,

0

0

0

0

0

0

p

x

p

x (3.9)


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After fermionic spinization:

pσ pσpp )(Det2 , xσ xσxx )(Det2

(3.10)

where σ = (σ1, σ2, σ3) are Pauli matrices:

01

101

0

02

i

i

10

013

(3.11)

expression (3.7) becomes:

MiMeM LLLt

mE

,,

pσ

xσ (3.12)

Expression (3.12) governs fermions in Dirac-like form such as Dirac electron and positron

in a dual universe (quantum frame) comprised of an external spacetime and an internal

energy-momentum space, and expression (3.7) governs unspinized or spinless

entity/particle with charge e and mass m (intrinsic proper time) such as a meson or a

meson-like particle in said dual universe. Bosonic spinization of expression (3.7)

pspp 2 and xsxx 2

shall be discussed later.

If we define:

pσxσpσ

xσ

tmE

t

mEDet (3.13)

wherex

p

m

t

E and p parallels to x,

We get:

02

ImEt

t

mEDet px

pσ

xσ

(3.14)

Thus, fundamental relation (3.4) is also satisfied under the determinant view of expression

(3.13). Indeed, we can also obtain the following conventional determinant:


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02

px

pσ

xσ

mEt

t

mEDet (3.15)

wherex

p

m

t

E and p parallels to x.

One kind of metamorphoses of (3.4)-(3.9) & (3.12-15) is respectively as follows when

p

x

mE

t and x parallels to p:

00 LmtE -px (3.4a)

tEtE meEet ,,,, e-e- xpxp ApAx (3.5a)

0

1

1

mE

t

mE

t

mE

tmtEL

p

x

p

x

p

x

px (3.6a)

MiMeM LLLmE

t

,,

x

p (3.7a)

0

0

0

0

0

00

x

ppx

Det

mDet

E

tDetmtE

- (3.8a)

MiMeM LLLmE

t

mE

t

,,

0

0

0

0

0

0

x

p

x

p (3.9a)

MiMeM LLLmE

t

,,

xσ

pσ (3.12a)

xσpσxσ

pσ

mEt

mE

tDet

(3.13a)


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02

ImtE

mE

tDet xp

xσ

pσ

(3.14a)

02

xp

xσ

pσmtE

mE

tDet

(3.15a)

Another kind of metamorphoses of expressions (3.6) – (3.14) is respectively as follows

whenx

p

m

t


0

1

1

x

p

x

p

x

pxp

tm

E

tm

E

tm

E

m

EtL

(3.16)

MiMeM LLLtm

E

,,

x

p (3.17)

x

ppx

0

0

0

0

0

00

Det

mDet

t

EDetmEt

(3.18)

x

p

x

p

tm

E

mt

E

0

0

0

0

0

0 (3.19)

LLLtm

EiMeM

,,

xσ

pσ (3.20)

mtEtm

EDet

xσpσ

xσ

pσ (3.21)

02

ImEt

tm

EDet

xp

xσ

pσ (3.22)


13

Expressions (3.16) – (3.22) have the following metamorphoses whenp

x

mE

t and x

parallels to p:

0

1

1

p

x

p

x

p

xpx

E

mt

E

mt

E

mt

m

tEL

(3.16a)

MiMeM LLLE

mt

,,

p

x

(3.17a)

p

xpx

0

0

0

0

0

00

Det

mDet

E

tDetmtE

(3.18a)

p

x

p

x

E

mtm

E

t

0

0

0

0

0

0 (3.19a)

LLLE

mtiMeM

,,

pσ

xσ

(3.20a)

mEt

E

mtDet pσxσ

pσ

xσ (3.21a)

02

ImtE

E

mtDet

px

pσ

xσ (3.22a)

Another kind of metamorphoses of expressions (3.6) - (3.14) is respectively as follows

whenx

p

m

t


0

1

1

t

i

im

E

t

i

im

E

t

i

im

E

m

EtL

x

p

x

p

x

pxp

(3.25)


14

MiMeM LLLtim

iE

,,

p

x (3.26)

0

0

0

0

0

00

p

xxp

i

iDet

mDet

t

EDetmEt

(3.27)

tim

iE

i

i

mt

E

p

x

p

x

0

0

0

0

0

0 (3.28)

MiMeM LLLtim

iE

,,

pσ

xσ (3.29)

pσxσpσ

xσ

imiEt

tim

iEDet

(3.30)

02

ImEt

tim

iEDet px

pσ

xσ

(3.31)

We can rewrite expression (3.29) as:

MiMeM

x

pLLL

tQ

Qt

,, (3.32)

where xσ iQp

is a quaternion and pσ imQx

is also a quaternion.


x

mE

t and x

parallels to p:

0

1

1

E

im

i

t

E

im

i

t

E

im

i

t

m

tEL

p

x

p

x

p

xpx

(3.25a)


15

MiMeM LLLEi

imt

,,

x

p

(3.26a)

0

0

0

0

0

00

x

ppx

i

iDet

mDet

E

tDetmtE

(3.27a)

Ei

imt

i

im

E

t

x

p

x

p

0

0

0

0

0

0 (3.28a)

MiMeM LLLEi

imt

,,

xσ

pσ

(3.29a)

xσpσxσ

pσ

iimtE

Ei

imtDet

(3.30a)

02

ImtE

Ei

imtDet xp

xσ

pσ

(3.31a)

Yet another kind of metamorphosis of expressions (3.6), (3.7) & (3.12) is respectively as

follows:

0

1

1

t

mE

t

mE

t

mEmEtL

x

p

x

p

x

pxp (3.35)

MiMeM LLLt

mE

,,

p

x (3.36)

MiMeM LLLt

mE

,,

pσ

xσ (3.37)


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If m==0, we have from expressions (3.6) - (3.14):

0

1

1

t

E

t

E

t

EEtL

x

p

x

p

x

pxp (3.38)

MiMeM LLLt

E

,,

p

x (3.39)

0

0

0

00

p

xxp

Det

t

EDetEt (3.40)

t

E

t

E

p

x

p

x

0

0

0

0 (3.41)

After fermionic spinization pσp and xσx , expression (3.39) becomes:

MiMeM LLLt

E

,,

pσ

xσ (3.42)

which governs massless fermion (neutrino) in Dirac-like form.

After bosonic spinization:

ps pspp 33 )( IDetIDet2 ,

xs xsxx 33 )( IDetIDet2 (3.43)

expression (3.39) becomes:

MiMeM LLLt

E

,,

ps

xs (3.44)

where s = (s1, s2, s3) are spin operators for spin 1 particle:


17

00

00

000

1

i

is

00

000

00

2

i

i

s

000

00

00

3 i

i

s (3.45)

If we define:

psxsps

xs

tE

t

EDets (3.46)

We get:

zyx

zyz

zyx

s

zpzpzp

ypypyp

xpxpxp

IEtt

EDet 3px

ps

xs (3.47)

To obey fundamental relation (3.4) in determinant view (3.46), we shall require the last

term in (3.47) acting on the external and internal wave functions respectively to produce

null result (zero) in source-free zone as discussed later. We propose that expression (3.39)

governs massless (intrinsic-proper-time-less) particle with unobservable spin (spinless).

After bosonic spinization, the spinless and massless particle gains its spin 1.


x

E

t & x parallels

to p:

0

1

1

E

t

E

t

E

ttEL

p

x

p

x

p

xpx (3.38a)

MiMeM LLLE

t

,,

x

p (3.39a)


18

0

0

0

00

x

ppx

Det

E

tDettE (3.40a)

E

t

E

t

x

p

x

p

0

0

0

0 (3.41a)

MiMeM LLLE

t

,,

xσ

pσ (3.42a)

MiMeM LLLE

t

,,

xs

ps (3.44a)

xspsxs

ps

tE

E

tDets (3.46a)

zpzpzp

ypypyp

xpxpxp

ItEE

tDet

zyx

zyz

zyx

s 3xpxs

ps (3.47a)

Another kind of metamorphosis of expressions (3.18) - (3.22) when m= = 0 is respectively

as follows:

x

pxp

0

0

0

00

Det

t

EDetEt (3.48)

MiMeM LLLt

E

t

E

,,

0

0

0

0

0

0

x

p

x

p (3.49)

MiMeM LLLt

E

,,

σ0

0σ

x

p (3.50)

MiMeM LLLt

E

,,

0

0

xs

ps (3.51)


19

xspsxs

ps

tE

t

EDets

0

0 (3.52)

zpzpzp

ypypyp

xpxpxp

IEtt

EDet

zyx

zyz

zyx

s 30

0xp

xs

ps (3.53)

Again, we shall require the last term in expression (3.53) acting on external and internal

wave functions respectively to produce null result (zero) in source-free zone in order to

satisfy fundamental relation (3.4) in the determinant view (3.52) as further discussed later.

Expressions (3.48)–(3.53) have the following metamorphoses whenp

x

E

t and x parallels

to p:

p

xpx

0

0

0

00

Det

E

tDettE (3.48a)

MiMeM LLLE

t

E

t

,,

0

0

0

0

0

0

p

x

p

x (3.49a)

MiMeM LLLE

t

,,

σ0

0σ

p

x (3.50a)

MiMeM LLLE

t

,,

0

0

ps

xs (3.51a)

psxsps

xs

tE

t

tDets

0

0 (3.52a)

zyx

zyz

zyx

s

zpzpzp

ypypyp

xpxpxp

ItEE

tDet 3

0

0px

ps

xs (3.53a)


20

Importantly, if t = 0, we have from expression (3.4):

0 xpm (3.54)

Thus, we can derive, for example, from (3.7) and (3.17) the following energy-less forms of

matrix law:

MiMeM LLLm

,,

p

x (3.55)

MiMeM LLLm

,,

x

p (3.56)

Further, if |p| = |x| = 0, we have from expression (3.4):

0 mEt (3.57)

Thus, we can derive, for example, from (3.7) and (3.17) the following spaceless forms of

matrix law:

MiMeM LLLt

mE

,,

0

0

(3.58)

MiMeM LLLtm

E

,,

(3.59)

The significance of these forms of matrix law shall be elucidated later. We suggest for now

that the timeless forms of matrix law govern external and internal wave functions (self-

fields) which play the roles of energy-less gravitons, that is, they mediate energy-

independent interactions through momentum space (position) quantum entanglement. On

the other hand, the momentum-less forms of matrix law govern the external and internal

wave functions (self-fields) which play the roles of momentum-less gravitons, that is, they

mediate momentum independent interactions through proper time (mass) entanglement.

The above metamorphoses of the self-referential matrix law of prespacetime-

premomentumenergy (God) are derived from one-tier matrixization (self-reference) and

two-tier matrixization (self-reference) based on the fundamental relation (3.4). The first-tier

matrixization makes distinctions in energy (time), mass (proper time) and total momentum

(undifferentiated space) that involve scalar unit 1 and imaginary unit (spin) i. Then the

second-tier matrixization makes distinction in three-dimensional momentum (three-

dimensional space) based on spin σ, s or other spin structure if it exists.


21

3.3 Additional Forms of Matrix Law

If prespacetime-premomentumenergy (God) allows partial distinction within first-tier self-

referential matrixization, we obtain, for example, the following additional forms of matrix

law MiMeM LLL ,, , whenx

p

m

t


mEt

mEt

p

x (3.60)

mEt

mEt

pσ

xσ (3.61)

x

p

mEt

mEt

0

0 (3.62)

σ

pσ

mEt

mEt

0

0 (3.63)

xp

xp

Etm

Et (3.64)

xp

xp

Et

mEt

0

0 (3.65)

tm

mE

xp

xp

(3.66)

xp

xp

mt

mE

0

0 (3.67)

xp

xp

mEt

mEt

0

0 (3.68)

Bosonic versions of expressions (3.61) and (3.63) are obtained by replacing σ with s.

Prespacetime-premomentumenergy (God) may create momentum-position self-

confinement of an elementary entity through imaginary momentum pi and imaginary

position xi (downward self-reference such that m >Et). We may write:

iiiziiyiixi iizpypxpEtm xp ,,,ii xp (3.69)

that is:

0 ii xpmEt (3.70)

Therefore, allowing imaginary momentum and imaginary position (downward self-


22

reference) for an elementary entity, we can derive the following matrix law in Dirac-like

form wheni

i

x

p

m

t

E and pi parallels to xi:

MiMeM

i

iLLL

t

mE

,,

p

x (3.71)

MiMeM

i

iLLL

m

,,

p

x

σ

σ (3.72)

Also, we can derive the following matrix law in Weyl-like (chiral-like) form:

MiMeM

i

iLLL

m

E

,,

x

p (3.73)

MiMeM

i

iLLL

tm

E

,,

x

p

σ

σ (3.74)

Bosonic versions of expressions (3.72) and (3.74) are obtained by replacing σ with s.

It is possible that the above additional forms of self-referential matrix law govern different

particles in the particle zoo as discussed later.

Expressions (3.70) can also be written as follows:

0 ii xpmtE (3.70a)

Expressions (3.71) – (3.74) have the following metamorphoses wheni

i

p

x

mE

t and xi

parallels to pi:

MiMeM

i

iLLL

mE

t

,,

x

p (3.71a)

MiMeM

i

iLLL

m

,,

x

p

σ

σ (3.72a)


23

MiMeM

i

iLLL

mt

,,

p

x

(3.73a)

MiMeM

i

iLLL

E

mt

,,

σ

σ

p

x

(3.74a)

3.4 Scientific Genesis of Primordial Entities in the Prespacetime-Premomentumenergy

Model

Prespacetime-premomentumenergy (God) creates, sustains and causes evolution of a free

plane-wave fermion such as an electron in Dirac-like form in a dual universe comprised of

an external spacetime and internal momentum-energy space as follows:

0

11

11

00

xipxipxipxip

xipxip

xipxipiMMii

et

emE

et

emE

eet

mE

emEt

Leee

x

p

x

p

x

p

xp

(3.75)

0

0

,

,

,,

,

,

,

,

,,

,

,

MLLL

eA

eA

t

mE

LLL

ea

ea

t

mE

i

e

iMeMxip

i

xip

e

Mi

e

iMeMxip

i

xip

e

pσ

xσ

p

x

where x

p

m

t

E; p parallels to x; E and p are only operators in spacetime acting on

external wave function (they are continuous parameters in momentum-energy space); and t

and x are only operators in momentum-energy space acting on internal wave function (they

are continuous parameters in spacetime),


24

that is:

,,

,,

ei

ie

t

mE

pσ

xσ or

,,,

,,,

exiiE

ipeet

ii

imi

σ

σ (3.76)

where substitutions tiE , xip in the external spacetime and Eit and

pix in the internal momentum-energy space have been made so that components of

LM can act on external and internal wave functions. Equation (3.76) may have free spherical

wave solution in the dual universe in the form:

iEti

iEte

i

e

eS

eS

,

,

,

,

(3.77)


evolution of a free plane-wave fermion such as the electron in Dirac-like form in the dual

universe as follows:

xipxipiMiMi emEteLe xp0

000 (3.78)

1

0

0

0

0

0

0

xipxipeeDet

mDet

t

EDet

p

x

00

0

0

0

0

0

,

,

,

,

xip

i

xip

e

xip

i

xip

e

ea

ea

t

mE

ea

eam

t

E

p

x

p

x

0,

,

,,

,

,

Mi

e

iMeMxip

i

xip

e LLL

eA

eA

t

mE

pσ

xσ

Expressions (3.75), (3.76) & (3.78) have the following metamorphoses, whenp

x

mE

t

and x parallels to p, for a dual universe comprised of an external momentum-energy space

and an internal spacetime:


25

0

11

11

00

xipxipxipxip

xipxip

xipxipiMMii

emE

et

emE

et

eemE

t

emtE

Leee

p

x

p

x

p

x

px

(3.75a)

0

0

,

,

,,

,

,

,

,

,,

,

,

MLLL

eA

eA

mE

t

LLL

ea

ea

mE

t

i

e

iMeMxip

i

xip

e

Mi

e

iMeMxip

i

xip

e

xσ

pσ

x

p

,,

,,

ei

ie

mE

t

xσ

pσ or

,,,

,,,

epiit

ixeeE

imi

ii

σ

σ (3.76a)

xipxipiMiMi emtEeLe px0

000 (3.78a)

1

0

0

0

0

0

0

xipxip

eeDetm

DetE

tDet

x

p

00

0

0

0

0

0

,

,

,

,

xip

i

xip

e

xip

i

xip

e

ea

ea

t

t

ea

ea

mE

t

x

p

x

p

0,

,

,,

,

,

Mi

e

iMeMxip

i

xip

e LLL

eA

eA

mE

t

xσ

pσ


plane-wave antifermion such as a positron in Dirac-like form in the dual universe

comprised of the external spacetime and the internal momentum-energy space as follows:


26

0

11

11

00

xipxipxipxip

xipxip

xipxipiMiMii

et

emE

et

emE

eet

mE

emEt

Leee

x

p

x

p

x

p

xp

(3.79)

0

0

,

,

,,

,

,

,

,

,,

,

,

Mi

e

iMeMxip

i

xip

e

Mi

e

iMeMxip

i

xip

e

LLL

eA

eA

t

mE

LLL

ea

ea

t

mE

pσ

xσ

p

x

or

xipxipiMiMi emEteLe xp0

000 (3.80)

00

0

0

0

0

0

0

0

0

0

0

0

,

,

,

,

1

xip

i

xip

e

xip

i

xip

e

xipxip

ea

ea

t

mE

ea

eam

t

E

eeDetm

Dett

EDet

p

x

p

x

p

x

0,

_,

,,

,

,

M

i

e

iMeMxip

i

xip

e LLL

eA

eA

t

mE

pσ

xσ

where x

p

m

t

E; p parallels to x; E and p are only operators in spacetime acting on


and x are operators only in momentum-energy space only acting on internal wave function

(they are continuous parameters in spacetime).

Expressions (3.79) & (3.80) have the following metamorphoses, whenp

x

mE

t and x

parallels to p, for the dual universe comprised of the external momentum-energy space and

the internal spacetime:


27

0

11

11

00

xipxipxipxip

xipxip

xipxipiMiMii

emE

et

emE

et

eemE

t

emtE

Leee

p

x

p

x

p

x

px

(3.79a)

0

0

,

,

,,

,

,

,

,

,,

,

,

Mi

e

iMeMxip

i

xip

e

Mi

e

iMeMxip

i

xip

e

LLL

eA

eA

mE

t

LLL

ea

ea

mE

t

xσ

pσ

x

p

xipxipiMiMi emtEeLe px0

000 (3.80a)

00

0

0

0

0

0

0

0

0

0

0

0

,

,

,

,

1

xip

i

xip

e

xip

i

xip

e

xipxip

ea

ea

mE

t

ea

ea

mE

t

eeDetm

DetE

tDet

x

p

x

p

x

p

0,

_,

,,

,

,

M

i

e

iMeMxip

i

xip

e LLL

eA

eA

mE

t

xσ

pσ

Similarly, prespacetime-premomentumenergy (God) creates, sustains and causes evolution

of a free plane-wave fermion in Weyl-like (chiral-like) form in the dual universe comprised

of the external spacetime and the internal momentum-energy space as follows:

0

11

11

00

xipxipxipxip

xipxip

xipxipiMiMii

et

em

Ee

te

m

E

eetm

E

em

EtLeee

x

p

x

p

x

p

xp

(3.81)


28

0

0

,

,

,,

,

,

,

,

,,

,

,

ML

ri

le

iMeMxip

ri

xip

le

ML

ri

le

iMeMxip

ri

xip

le

LL

eA

eA

tm

E

LL

ea

ea

tm

E

xσ

pσ

x

p

where x

p

m

t

E; p parallels to x; E and p are operators only in spacetime only acting on


and x are operators only in momentum-energy space only acting on internal wave function

(they are continuous parameters in spacetime),

that is:

leri

rile

mt

E

,,

,,

xσ

pσ or

leixriE

rileplet

mii

ii

,,,

,,,

σ

σ (3.82)


evolution of a free plane-wave fermion in Weyl-like (chiral-like) form in the dual universe

as follows:

00

0

0

0

0

0

0

0

0

0

0

0

00

,

,

,

,

1

0

0

xip

ri

xip

le

xip

ri

xip

le

xipxip

xipxipiMiMi

ea

ea

tm

E

ea

ea

mt

E

eeDetm

Dett

EDet

emEteLe

x

p

x

p

x

p

xp

(3.83)

0,

,

,,

,

,

ML

ri

le

iMeMxip

ri

xip

le LL

eA

eA

tm

E

xσ

pσ

where x

p

m

t

E, p parallels to x.

Expressions (3.81) - (3.83) have the following metamorphoses, whenp

x

mE

t and x



29


0

11

11

00

xipxipxipxip

xipxip

xipxipiMiMii

eE

me

te

E

me

t

eeE

mt

em

tELeee

p

x

p

x

p

x

px

(3.81a)

0

0

,

,

,,

,

,

,

,

,,

,

,

ML

ri

le

iMeMxip

ri

xip

le

ML

ri

le

iMeMxip

ri

xip

le

LL

eA

eA

E

mt

LL

ea

ea

E

mt

pσ

xσ

p

x

leri

rile

E

mt

,,

,,

pσ

xσ or

leiprit

rilexleE

ii

mii

,,,

,,,

σ

σ (3.82a)

00

0

0

0

0

0

0

0

0

0

0

0

00

,

,

,

,

1

0

0

xip

ri

xip

le

xip

ri

xip

le

xipxip

xipxipiMiMi

ea

ea

E

mt

ea

eam

E

t

eeDetm

DetE

tDet

emtEeLe

p

x

p

x

p

x

px

(3.83a)

0,

,

,,

,

,

ML

ri

le

iMeMxip

ri

xip

le LL

eA

eA

E

mt

pσ

xσ


plane-wave fermion in another form in the dual universe comprised of the external

spacetime and the internal momentum-energy space as follows:


30

0

11

11

00

xipxipxip

xipxipxip

xipxipiMiMii

et

ie

im

Ee

t

i

eim

Eee

t

i

im

E

em

EtLeee

p

p

x

p

x

p

xp

(3.84)

0,,

Mi

eiMeM

xip

i

xip

e LLL

eA

eA

tim

iE

pσ

xσ

0,,

M

i

e

iMeMxip

xip

x

pLLL

ei

A

ee

A

tQ

Qt

where x

p

m

t

E; p parallels to x; E and p are operators only in spacetime only acting on


and x are operators only in momentum-energy space acting on internal wave function (they

are continuous parameters in spacetime); xσ iQp

; and pσ imQx

, that is:

ei

ie

imt

iE

pσ

xσ or

ixeiE

ipiet

mi

i

σ

σ (3.85)


evolution of a free plane-wave fermion in another form in said dual universe as follows:

00

0

0

0

0

0

0

0

0

0

0

0

00

1

00

xip

i

xip

e

xip

i

xip

e

xipxip

xipxipiMiMi

ea

ea

tim

iE

ea

ea

i

i

mt

E

eei

iDet

mDet

t

EDet

emEteLe

p

x

p

x

p

x

px


31

0,,

Mi

eiMeM

xip

i

xip

e LLL

eA

eA

tim

iE

pσ

xσ

0,,

M

i

e

iMeMxip

xip

x

pLLL

ei

A

ee

A

tQ

Qt (3.86)

where x

p

m

t


Expressions (3.84) - (3.86) have the following metamorphoses, whenp

x

mE

t and x



0

11

11

00

xipxipxip

xipxipxip

xipxipiMiMii

eE

ime

i

te

E

im

ei

tee

E

im

i

t

em

tELeee

p

x

p

x

p

x

px

(3.84a)

0,,

Mi

eiMeM

xip

i

xip

e LLL

eA

eA

Ei

imt

xσ

pσ

0,,

M

i

e

iMeMxip

xip

p

xLLL

ei

A

ee

A

tQ

QE

where x

p

m

t

E, p parallels to x, xσ iQ

x , and xσ iQ

x ,

ei

ie

iE

imt

xσ

pσ or

ipeiE

ixieE

i

mi

σ

σ (3.85a)


32

00

0

0

0

0

0

0

0

0

0

0

0

00

1

00

xip

i

xip

e

xip

i

xip

e

xipxip

xipxipiMiMi

ea

ea

Ei

imt

ea

ea

i

im

E

t

eei

iDet

mDet

E

tDet

emtEeLe

x

p

x

p

x

p

xp

0,,

Mi

eiMeM

xip

i

xip

e LLL

eA

eA

Ei

imt

xσ

pσ

0,,

M

i

e

iMeMxip

xip

p

xLLL

ei

A

ee

A

EQ

Qt (3.86a)

Prespacetime-premomentumenergy (God) creates, sustains and causes evolution of a linear

plane-wave photon in the dual universe comprised of the external spacetime and the

internal momentum-energy space as follows:

0

11

11

00

xipxipxipxip

xipxip

xipxipiMiMii

et

eE

et

eE

eet

E

eEt

Leee

x

p

x

p

x

p

xp (3.87)

0

0

,

,

,,

0

,0

,

,

,,

,

,

photonMi

e

iMeMxip

i,-

xip

e

Mi

e

iMeMxip

i

xip

e

LLL

ei

e

t

E

LLL

ea

ea

t

E

B

E

p

x

ps

xs


evolution of the linear plane-wave photon in said dual universe as follows:


33

00

0

0

0

0

0

0

0

00

,

,

,

,

1

00

xip

i

xip

e

xip

i

xip

e

xipxip

xipxipiMiMi

ea

ea

t

E

ea

ea

t

E

eeDett

EDet

eEteLe

p

x

p

x

p

x

px (3.88)

0,

,

,,

0

,0

photonMi

e

iMeMxip

i,-

xip

e LLL

ei

e

t

E

B

E

ps

xs

This photon wave function in the dual universe may be written as:

)(

)(

)(

,

, xk

xk

xk

p

x

ti

ti

ti

i

e

photon eiei

e

i

0

0

0

0

B

E

B

E

B

E

(

(

E) ,

t) ,

(3.89)

After the substitutions tiE , xip and Eit , pix , we have from the

last expression in (3.87):

t) ,E) ,

E) ,t) ,

E) ,

t) ,

xp

px

p

x

((

((

(

(

EB

BE

B

E

xE

pt

Ex

pt

iii

ii0

ss

(3.90)

where we have used the relationship ppis to derive the latter equations which

together with 0 t) ,x(Ex and 0 E) ,p(Bp are the Maxwell-like equations in the

source-free vacuum in the dual universe comprised of the external spacetime and internal

momentum-energy space.

Prespacetime-premomentumenergy (God) creates a neutrino in Dirac-like form in the dual

universe comprised of the external spacetime and the internal momentum-energy space by

replacing the last step of expression (3.87) with the following:

0

,

,,,

,

,

σ

σ

MiMeMxip

i

xip

e Li

eLL

ea

ea

t

E

p

x (3.91)


34

Expressions (3.87) - (3.91) have the following metamorphoses for the dual universe

comprised of the external momentum-energy space and the internal spacetime:

0

11

11

00

xipxipxipxip

xipxip

xipxipiMiMii

eE

et

eE

et

eeE

t

etE

Leee

p

x

p

x

p

x

px (3.87a)

0

0

,

,

,,

0

,0

,

,

,,

,

,

photonMi

e

iMeMxip

i,-

xip

e

Mi

e

iMeMxip

i

xip

e

LLL

ei

e

E

t

LLL

ea

ea

E

t

B

E

x

p

xs

ps

00

0

0

0

0

0

0

0

00

,

,

,

,

1

00

xip

i

xip

e

xip

i

xip

e

xipxip

xipxipiMiMi

ea

ea

E

t

ea

ea

E

t

eeDetE

tDet

etEeLe

x

p

x

p

x

p

xp (3.88a)

0,

,

,,

0

,0

photonMi

e

iMeMxip

i,-

xip

e LLL

ei

e

E

t

B

E

xs

ps

)(

)(

)(

,

, xk

xk

xk

x

p

ti

ti

ti

i

e

photon eiei

e

i

0

0

0

0

B

E

B

E

B

E

(

(

t) ,

E) ,

(3.89a)

E) ,t) ,

t) ,E) ,

t) ,

E) ,

px

xp

x

p

((

((

(

(

EB

BE

B

E

pt

xE

tp

xE

iii

ii0

ss

(3.90a)


35

0

,

,,,

,

,

σ

σ

MiMeMxip

i

xip

e Li

eLL

ea

ea

E

t

x

p (3.91a)

Prespacetime-premomentumenergy (God) creates, sustains and causes evolution of a linear

plane-wave antiphoton in the dual universe comprised of the external spacetime and the


0

11

11

00

xipxipxipxip

xipxip

xipxipiMiMii

et

eE

et

eE

eet

E

eEt

Leee

x

p

x

p

x

p

xp

(3.92)

0

0

,

,

,,

,0

,0

,

,

,,,

,

antiphotonMi

e

iMeMxip

i

xip

e

Mi

e

iMeMi

e

LLL

e

ei

t

E

LLLt

E

E

B

p

x

ps

xs

This antiphoton wave function can also be written as:

)(

)(

)(

E) ,(

t),(

, E) ,(

t),(

E) ,(

t),(, xk

xk

xk

ti

ti

ti

i

antiphoton ei

e

eiie

p0

x0

p0

x0

E

B

E

B

E

B

p

x

(3.93)

Prespacetime-premomentumenergy (God) creates an antineutrino in Dirac-like in the dual

universe comprised of the external spacetime and the internal momentum-energy space

form by replacing the last step of expression (3.93) with the following:

0

,

,,,

,

,

σ

σ

MiMeMxip

i

xip

e Li

eLL

ea

ea

t

E

p

x (3.94)




36

0

11

11

00

xipxipxipxip

xipxip

xipxipiMiMii

eE

et

eE

et

eeE

t

etE

Leee

p

x

p

x

p

x

px

(3.92a)

0

0

,

,

,,

,0

,0

,

,

,,,

,

antiphotonMi

e

iMeMxip

i

xip

e

Mi

e

iMeMi

e

LLL

e

ei

E

t

LLLE

t

E

B

x

p

xs

ps

)(

)(

)(

t),(

E) ,(

, t),(

E) ,(

t),(

E) ,(, xk

xk

xk

ti

ti

ti

i

antiphoton ei

e

eiie

x0

p0

x0

p0

E

B

E

B

E

B

x

p

(3.93a)

0

,

,,,

,

,

σ

σ

MiMeMxip

i

xip

e Li

eLL

ea

ea

E

t

x

p (3.94a)

Prespacetime-premomentumenergy (God) creates, sustains and causes evolution of chiral

plane-wave photons in the dual universe comprised of the external spacetime and the


00

0

0

0

0

0

0

0

0

0

00

,

,

,

,

1

00

xip

ri

xip

le

xip

ri

xip

le

xipxip

xipxipiMiMi

ea

ea

t

E

ea

ea

t

E

eeDett

EDet

eEteLe

x

p

x

p

x

p

xp (3.95)

0

0

0

,

,

,,

,

,

Mri

le

iMeMxip

ri

xip

le LLL

eA

eA

t

E

xs

ps


37

where x

p

t

E and p parallels to x, that is,

le, and ri, are decoupled from each other

and satisfy the following equations respectively:

0

0

,

,

ri

le

t

E

xs

ps or

0

0

,,

,,

ripriE

lexlet

s

s (3.96)

which have the following respective solutions:

)(

)(

E) ,(E) ,(

t),( t),(

,

,

xk

xk

ti

ti

ri ei

ei

i

ile

E)0(p,0(p.E)

0(x.t)t)0(x,

BE

BE

BE

BE

pp

xx

(3.97)

0,, lexlet s produces Maxwell equations in external spacetime of the source-free

vacuum and 0,, ripriE s produce the Maxwell-like equations in internal

momentum-energy space of the source-free vacuum as shown in the second expression of

(3.90).

Prespacetime-premomentumenergy (God) creates neutrinos in Weyl-like (chiral-like) forms

in the dual universe comprised of the external spacetime and the internal momentum-

energy space by replacing the last step of expression (3.95) with the following:

00

0

,

,

,,

,

,

Mri

le

iMeMxip

ri

xip

le LLL

eA

eA

t

E

xσ

pσ (3.98)

that is, le, and

ri, are decoupled from each other and satisfy the following equations

respectively:

0

0

,

,

ri

le

t

E

x

p

σ

σ or

0

0

,,

,,

ripriE

lexlet

σ

σ (3.99)




38

00

0

0

0

0

0

0

0

0

0

00

,

,

,

,

1

00

xip

ri

xip

le

xip

ri

xip

le

xipxip

xipxipiMiMi

ea

ea

E

t

ea

ea

E

t

eeDetE

tDet

etEeLe

p

x

p

x

p

x

px (3.95a)

0

0

0

,

,

,,

,

,

Mri

le

iMeMxip

ri

xip

le LLL

eA

eA

E

t

ps

xs

0

0

,

,

ri

le

E

t

ps

xs or

0

0

,,

,,

rixrit

lepleE

s

s (3.96a)

)(

)(

t),( t),(

E) ,(E) ,(

,

,

xk

xk

ti

ti

ri ei

ei

i

ile

t)0(x,0(x.t)

0(p.E)E)0(p,

BE

BE

BE

BE

xx

pp

(3.97a)

00

0

,

,

,,

,

,

Mri

le

iMeMxip

ri

xip

le LLL

eA

eA

E

t

pσ

xσ (3.98a)

0

0

,

,

ri

le

E

t

p

x

σ

σ or

0

0

,,

,,

rixrit

lepleE

σ

σ (3.99a)

Prespacetime-premomentumenergy (God) creates and sustains timeless external wave

function (timeless graviton) and energy-less internal wave functions (energy-less graviton)

of an elementary particle in Dirac-like form as follows:

0

11

1

1

00

iMiMiMiM

iMiM

iMiMiMiMii

eem

eem

eem

em

Leee

x

p

x

p

xp

x

p (3.100)


39

0,

,

,,,

,

DMiD

eD

iMeMiMiD

iMeD VL

V

VLL

eg

egm

p

x

Alternatively, prespacetime-premomentumenergy (God) creates and sustains timeless

external wave function (timeless graviton) and energy-less internal wave functions (energy-

less graviton) of an elementary particle in Dirac-like form as follows:

00

0

0

0

0

0

0

0

00

,

,

,

,

1

00

iMiD

iMeD

iMiD

iMeD

iMiM

iMiMiMiMi

eg

egm

eg

egm

eeDetm

Det

emeLe

p

x

p

x

p

x

px (3.101)

Similarly, prespacetime-premomentumenergy (God) creates and sustains timeless external

wave function (timeless graviton) and energy-less internal wave functions (energy-less

graviton) of an elementary particle in Weyl-like (chiral-like) form as follows:

0

11

1

1

00

iMiMiMiM

iMiM

iMiMiMiMii

eem

eem

eem

em

Leee

x

p

x

p

xp

x

p

(3.102)

0,

,

,,

,

,

WMiW

eW

iMeMiMiW

iMeW VL

V

VLL

eg

eg

m x

p

Again, we will determine the form of the imaginary content M in expression (3.102) later.

Alternatively, prespacetime-premomentumenergy (God) creates and sustains timeless

external wave function (timeless graviton) and energy-less internal wave functions (energy-

less graviton) of an elementary particle in Weyl-like (chiral-like) form as follows:


40

00

0

0

0

0

0

0

0

00

,

,

,

,

1

00

iMiW

iMeW

iMiW

iMeW

iMiM

iMiMiMiMi

eg

eg

meg

eg

m

eem

DetDet

emeLe

x

p

x

p

x

p

xp

(3.103)



0

11

1

1

00

iMiMiMiM

iMiM

iMiMiMiMii

em

eem

e

eem

em

Leee

p

x

p

x

px

p

x (3.100a)

0,

,

,,,

,

DMiD

eD

iMeMiMiD

iMeD VL

V

VLL

eg

eg

mx

p

00

0

0

0

0

0

0

0

00

,

,

,

,

1

00

iMiD

iMeD

iMiD

iMeD

iMiM

iMiMiMiMi

eg

eg

meg

eg

m

eeDetm

Det

emeLe

x

p

x

p

x

p

xp

(3.101a)


41

0

11

1

1

00

iMiMiMiM

iMiM

iMiMiMiMii

em

eem

e

eem

em

Leee

p

x

p

x

px

p

x

(3.102a)

0,

,

,,

,

,

WMiW

eW

iMeMiMiW

iMeW VL

V

VLL

eg

egm

p

x

00

0

0

0

0

0

0

0

00

,

,

,

,

1

00

iMiW

iMeW

iMiW

iMeW

iMiM

iMiMiMiMi

eg

egm

eg

egm

eem

DetDet

emeLe

p

x

p

x

p

x

px

00

0

0

0

0

0

0

0

00

,

,

,

,

1

00

iMiW

iMeW

iMiW

iMeW

iMiM

iMiMiMiMi

eg

egm

eg

egm

eem

DetDet

emeLe

p

x

p

x

p

x

px

(3.103a)

Prespacetime-premomentumenergy (God) creates and sustains spaceless (momentum

independent) external wave function and momentumless (space independent) internal wave

functions of an elementary particle in Dirac-like form as follows:


42

00

0

0

0

0

0

0

0

0

0

00

,

,

,

,

1

00

iMiD

iMeD

iMiD

iMeD

iMiM

iMiMiMiM

eg

eg

t

mE

eg

egm

t

E

eem

Dett

EDet

emEteLe

(3.104)

Similarly, prespacetime-premomentumenergy (God) creates and sustains spaceless

(momentum independent) external wave function and momentumless (space independent

internal wave functions of an elementary particle in Weyl-like (chiral-like) form as follows:

0

11

11

00

iMiMiMiM

iMiM

iMiMiMiM

et

em

Ee

te

m

E

eetm

E

em

EtLeee

(3.105)

0,

,

,,

,

,

WMiW

eW

iMeMiMiW

iMeW VL

V

VLL

eg

eg

tm

E

Alternatively, prespacetime-premomentumenergy (God) creates and sustains spaceless

(momentum independent) external wave function and momentumless (space independent

internal wave functions of an elementary particle in Weyl-like (chiral-like) form as follows:

00

0

0

0

0

0

0

0

00

,

,

,

,

1

00

iMiw

iMeW

iMiW

iMeW

iMiM

iMiMiMiMi

eg

eg

tm

E

eg

eg

mt

E

eem

Dett

EDet

emEteLe

(3.106)




43

00

0

0

0

0

0

0

0

0

0

00

,

,

,

,

1

00

imtiD

imteD

iMiD

iMeD

iMiM

iMiMiMiM

eg

eg

mE

t

eg

eg

mE

t

eem

DetE

tDet

emtEeLe

(3.104a)

0

11

11

00

iMiMiMiM

iMiM

iMiMiMiM

eE

me

te

E

me

t

eeE

mt

em

tELeee

(3.105a)

0,

,

,,

,

,

WMiW

eW

iMeMiMiW

iMeW VL

V

VLL

eg

eg

E

mt

00

0

0

0

0

0

0

0

00

,

,

,

,

1

00

mtiw

imteW

iMiW

iMeW

iMiM

iMiMiMiMi

eg

eg

E

mt

eg

egm

E

t

eem

DetE

tDet

emtEeLe

(3.106a)

Prespacetime-premomentumenergy (God) may create, sustains and causes evolution of a

spatially and momentumly self-confined entity such as a proton through imaginary

momentum pi imaginary position xi (downward self-reference such that mτ>Et) in Dirac-

like form in the dual universe comprised of the external spacetime and the internal

momentum-energy space as follows:


44

0

11

11

00

xipixip

i

xipixip

i

xipxipi

i

xipxipiMiMii

et

emE

et

emE

eet

mE

emEt

Leee

x

p

x

p

x

p

px ii (3.107)

0

,

,

,,

,

,

Mi

e

iMeMiEti

iEte

i

iLLL

es

es

t

mE

p

x (3.108)

wherei

i

p

x

mE

t ; xi parallels to pi; E and pi are operators in spacetime only acting

external wave function (they are free parameters in momentum-energy space); and t and xi

are operators in momentum-energy space only acting on internal wave function (they are

free parameters in spacetime),After spinization of expression (3.108), we have:

0

,

,

,,

,

,

Mi

e

iMeMiEti

iEte

i

iLLL

eS

eS

t

mE

pσ

xσ (3.109)

It is plausible that expression (3.108) governs the confinement structure of the unspinized

proton in Dirac-like form through imaginary momentum ip and imaginary position ix and,

on the other hand, expression (3.109) governs the confinement structure of spinized proton

through ip and ix in the dual universe.

Alternatively, prespacetime-premomentumenergy (God) creates, sustain and cause

evolution of the spatially and momentumly self-confined entity such as a proton in Dirac-

like form in said dual universe as follows:

xipxip

ii

iMiMi emEteLe px0

000 (3.110)

00

0

0

0

0

0

0

0

0

0

0

0

,

,

,

,

1

iEti

iEte

i

i

iEti

iEte

i

i

xipxip

i

i

es

es

t

mE

es

esm

t

E

eeDetm

Dett

EDet

p

x

p

x

p

x


45

0,

,

,,

,

,

DMiD

eD

iMeMiEti

iEte

i

iLLL

es

es

t

mE

p

x

0,

,

,,

,

,

σ

σ

DMiD

eD

iMeMiEti

iEte

i

iLLL

eS

eS

t

mE

p

x

wherei

i

p

x

mE

t and xi parallels to pi.

Thus, an unspinized and spinized antiproton in Dirac-like form may be respectively

governed as follows:

0

,

,

,,

,

,

DMiD

eD

iMeMiEti

iEte

i

iLLL

es

es

t

mE

p

x (3.111)

0

,

,

,,

,

,

σ

σ

DMiD

eD

iMeMiEti

iEte

i

iLLL

eS

eS

t

mE

p

x (3.112)



0

11

11

00

xipixip

i

xipixip

i

xipxipi

i

xipxipiMiMii

emE

et

emE

et

eemE

t

emtE

Leee

p

x

p

x

p

x

xp ii (3.107a)

0

,

,

,,

,

,

M

i

e

iMeMiEti

iEte

i

iLLL

es

es

mE

t

x

p (3.108a)

0

,

,

,,

,

,

M

i

e

iMeMiEti

iEte

i

iLLL

eS

eS

t

t

xσ

xσ (3.109a)


46

xipxip

ii

iMiMi emtEeLe xp0

000 (3.110a)

00

0

0

0

0

0

0

0

0

0

0

0

,

,

,

,

1

iEti

iEte

i

i

iEti

iEte

i

i

xipxip

i

i

es

es

mE

t

es

es

mE

t

eeDetDetE

tDet

x

p

x

p

x

p

0,

,

,,

,

,

DMiD

eD

iMeMiEti

iEte

i

iLLL

es

es

mE

t

x

p

0,

,

,,

,

,

σ

σ

DMiD

eD

iMeMiEti

iEte

i

iLLL

eS

eS

mE

t

x

p

0

,

,

,,

,

,

DMiD

eD

iMeMiEti

iEte

i

iLLL

es

es

mE

t

x

p (3.111a)

0

,

,

,,

,

,

σ

σ

DMiD

eD

iMeMiEti

iEte

i

iLLL

eS

eS

mE

t

x

p (3.112a)

Similarly, prespacetime-premomentumenergy (God) may create, sustain and cause

evolution of a spatially and momentumly self-confined entity such as a proton through

imaginary momentum ip and imaginary position ix (downward self-reference) in Weyl-like

(chiral-like) form in the dual universe comprised of the external spacetime and the internal

momentum-energy space as follows:

0

11

11

00

xip

i

xipixip

i

xipi

xipxip

i

i

xipxipiiiMiMii

et

em

Ee

te

m

E

eetm

E

em

EtLeee

x

p

x

p

x

p

xp

(3.113)

0,

,

,,

,

,

M

li

re

iMeMiEtli

iEtre

i

iLLL

es

es

tm

E

x

p (3.114)


47

After spinization of expression (3.114), we have:

0

,

,

,,

,

,

σ

σ

M

li

re

iMeMiEtli

iEtre

i

iLLL

eS

eS

tm

E

x

p (3.115)

It is plausible that expression (3.114) governs the structure of the unspinized proton in Weyl

form and expression (3.115) governs the structure of spinized proton in Weyl form.


evolution of a spatially and momentumly self-confined entity such as a proton in Weyl

(chiral) form in said dual universe as follows:

xipxip

ii

iMiMi emEteLe xp0

000 (3.116)

0

,

,

,

,

1

0

0

0

0

0

0

0

0

0

0

0

0

iEtli

iEtre

i

i

iEtli

iEtre

i

i

xipxip

i

i

es

es

tm

E

es

es

mt

E

eem

DetDett

EDet

x

p

x

p

x

p

0

,

,

,,

,

,

M

li

re

iMeMiEtli

iEtre

i

iLLL

es

es

t

t

x

x (3.117)

0

,

,

,,

,

,

σ

σ

M

li

re

iMeMiEtli

iEtre

i

iLLL

eS

eS

tm

E

x

p (3.118)

Thus, an unspinized and spinized antiproton in Weyl-like form may be respectively

governed as follows:

0

,

,

,,

,

,

M

ri

le

iMeMiEtri

iEtle

i

iLLL

es

es

tm

E

x

p (3.119)

0

,

,

,,

,

,

σ

σ

M

ri

le

iMeMiEtri

iEtle

i

iLLL

eS

eS

tm

E

x

p (3.120)




48

0

11

11

00

xip

i

xipixip

i

xipi

xipxip

i

i

xipxipiiiMiMii

eE

me

te

E

me

t

eeE

mt

em

tELeee

p

x

p

x

p

x

px

(3.113a)

0,

,

,,

,

,

Mli

re

iMeMiEtli

iEtre

i

iLLL

es

es

E

mt

p

x (3.114a)

0

,

,

,,

,

,

σ

σ

Mli

re

iMeMiEtli

iEtre

i

iLLL

eS

eS

E

mt

p

x (3.115a)

xipxip

ii

iMiMi emtEeLe px0

000 (3.116a)

0

,

,

,

,

1

0

0

0

0

0

0

0

0

0

0

0

0

iEtli

iEtre

i

i

iEtli

iEtre

i

i

xipxip

i

i

es

es

E

mt

es

esm

E

t

eem

DetDetE

tDet

p

x

p

x

p

x

0

,

,

,,

,

,

Mli

re

iMeMiEtli

iEtre

i

iLLL

es

es

E

mt

p

x (3.117a)

0

,

,

,,

,

,

σ

σ

Mli

re

iMeMiEtli

iEtre

i

iLLL

eS

eS

E

mt

p

x (3.118a)

0

,

,

,,

,

,

Mri

le

iMeMiEtri

iEtle

i

iLLL

es

es

E

mt

p

x (3.119a)

0

,

,

,,

,

,

σ

σ

Mri

le

iMeMiEtri

iEtle

i

iLLL

eS

eS

E

mt

p

x (3.120a)


49

3.4 Scientific Genesis of Composite Entities in the Prespacetime-Premomentumenergy

Model

Then, prespacetime-premomentumenergy (God) may create, sustain and cause evolution of

a neutron in a dual universe comprised of an external spacetime and internal momentum-

energy space in Dirac-like form which is comprised of an unspinized proton:

p

iEti

iEte

Eti

Eit

es

es

ete

emeE

0

,

,

),(),(

),(),(

px

px

p

x

A

A (3.121)

where ),(

),(

),(

),(

ti

Ei

t

E

e

e

meE

et

x

p

x

p

p

x

A

A

, ),( Ei e px A parallels to ),( ti e xp A , E and pi are

operators only in spacetime acting on external wave function (they are continuous

parameters in momentum-energy space), and t and xi are operators only in momentum-

energy space acting on internal wavefunction (they are continuous parameters in

spacetime), and a spinized electron:

e

iEti

iEte

EEt

Ett

eS

eS

Vete

emVeE

0

,

,

),(),(),(

),(),(),(

ppx

pxx

Apσ

Axσ (3.122)

where ),(

),(

),(),(

),(),(

t

E

tt

EE

e

e

mVeE

Vet

x

p

xx

pp

p

x

A

A

, ),( Ee px A parallels to ),( te xp A , E and p are

operators in in spacetime acting on external wavefunction (they are continuous parameters

in momentum-energy space), and t and x are operators in momentum-energy space only

acting on internal wavefunction (they are free parameters in spacetime), as follows:

eiMiM

p

iMiMiii LeLeeee 000 111

e

xipxip

iip

xipxip

ii

emEt

emEt

pxpx

e

xipxip

p

xipxipi

i

eet

mEee

t

mE

1111

x

p

x

p

e

iEti

iEte

p

iEti

iEte

i

i

es

es

t

mE

es

es

t

mE

00

,

,

,

,

p

x

p

x


50

ne

iEti

iEte

EEt

Ett

p

iEti

iEte

Eti

Eit

eS

eS

Vete

emVeE

es

es

ete

emeE

0

0

,

,

,,,

,,,

,

,

,,

,,

ppx

pxx

px

px

Apσ

Axσ

p

x

A

A (3.123)

In expressions (3.121), (3.122) and (3.123), p,

e and

nindicate proton, electron

and neutron respectively. Further, unspinized proton has charge e, electron has charge –e,

pttA ),( ).,().,( xx A ,

pEEA ),( ).,().,( pp A and ettA ),( ).,().,( xx A ,

eEEA ),( ).,().,( pp A are

the electromagnetic potentials acting on unspinized proton and tightly bound spinized

electron respectively, and etV ),(x ,

eEV ),(p is a binding potential from the unspinized proton

acting on the spinized electron causing tight binding.

If pttA ),( ).,().,( xx A ,

pEEA ),( ).,().,( pp A is negligible due to the fast motion of the tightly

bound spinized electron, we have from the last expression in (3.123):

ne

iEti

iEte

EEt

Ett

p

iEti

iEte

i

i

eS

eS

Vete

emVeE

es

es

t

mE

0

0

,

,

,,,

,,,

,

,

ppx

pxx

Apσ

Axσ

p

x (3.124)

Experimental data on charge distribution and g-factor of neutron seem to support a neutron

comprising of an unspinized proton and a tightly bound spinized electron.

The Weyl-like (chiral-like) form of the last expression in (3.123) and expression (3.124)

are respectively as follows:

ne

iEtri

iEtle

EEE

ttt

p

iEtli

iEtre

Ei

tit

eS

eS

eVetm

eVeE

es

es

eetm

eeE

0

0

,

,

),(),(),(

),(),(),(

,

,

),(

),(),(

ppp

xxx

p

xx

pσ

pσ

x

p

A

A

A

A

(3.125)


51

ne

iEtri

iEtle

EEE

ttt

p

iEtli

iEtre

i

i

eS

eS

eVetm

eVeE

es

es

tm

E

0

0

,

,

),(),(),(

),(),(),(

,

,

ppp

xxx

Ax

Ap

x

p

σ

σ

(3.126)



p

iEti

iEte

tEi

tiE

es

es

ete

eet

0

,

,

),(),(

),(),(

xp

xp

x

p

A

A (3.121a)

e

iEti

iEte

ttE

tEE

eS

eS

mVeEe

eVet

0

,

,

),(),(),(

),(),(),(

xxp

xpp

Axσ

Apσ

(3.122a)

eiMiM

p


e

xipxip

iip

xipxip

ii

emtE

emtE

xpxp

e

xipxip

p

xipxipi

i

eemE

tee

mE

t

1111

p

x

p

x

e

iEti

iEte

p

iEti

iEte

i

i

es

es

mE

t

es

es

mE

t

00

,

,

,

,

x

p

x

p

ne

iEti

iEte

ttE

tEE

p

iEti

iEte

tEi

tiE

eS

eS

mVeEe

eVet

es

es

meEe

eet

0

0

,

,

,,,

,,,

,

,

,,

,,

xxp

xpp

xp

xp

Axσ

Apσ

x

p

A

A (3.123a)


52

ne

iEti

iEte

ttE

tEE

p

iEti

iEte

i

i

eS

eS

mVeEe

eVet

es

es

mE

t

0

0

,

,

,,,

,,,

,

,

xxp

xpp

Axσ

Apσ

x

p

(3.124a)

ne

iEtri

iEtle

ttt

EEE

p

iEtli

iEtre

tit

EiE

eS

eS

eVeE

meVet

es

es

eeE

meet

0

0

,

,

),(),(),(

),(),(),(

,

,

),(),(

),(),(

xxx

ppp

xx

pp

pσ

xσ

p

x

A

A

A

A

(3.125a)

ne

iEtri

iEtle

ttt

EEE

p

iEtli

iEtre

i

i

eS

eS

eVeE

meVet

es

es

E

mt

0

0

,

,

),(),(),(

),(),(),(

,

,

xxx

ppp

Ap

Ax

p

x

σ

σ

(3.126a)

Then, prespacetime-premomentumenergy (God) may create, sustain and cause evolution of

a hydrogen atom in a dual universe comprised of an external spacetime and internal

momentum-energy space in Dirac form comprising of a spinized proton:

p

iEti

iEte

Eti

Eit

eS

eS

ete

emeE

0

,

,

,,

,,

px

px

p

x

σ

σ

A

A (3.127)

where ),(

),(

),(

),(

ti

Ei

t

E

e

e

meE

et

x

p

x

p

p

x

A

A

, ),( Ei e px A parallels to ),( ti e xp A , E and pi are

operators in spacetime only acting on external wave function (they are free parameters in

momentum-energy space); and t and xi are operators in momentum-energy space only

acting on internal wavefunction (they are free parameters in spacetime), and a spinized

electron:

e

iEti

iEte

Et

Et

eS

eS

ete

emeE

0

,

,

,,

,,

px

px

Apσ

Axσ (3.128)


53

where ),(

),(

),(

),(

t

E

t

E

e

e

meE

et

x

p

x

p

p

x

A

A

,

),( Ee px A parallels to ),( te xp A , E and p are

operators in spacetime only (they are free parameters in momentum-energy space); and t

and x are operators in momentum-energy space only (they are free parameters in

spacetime), as follows:

eiMiM

p


e

xipxip

iip

xipxip

ii

emEt

emEt

pxpx

e

xipxipxipxipi

i

eet

mEee

t

mE

p

1111

x

p

x

p

e

iEti

iEte

p

iEti

iEte

i

i

es

es

t

mE

es

es

t

mE

00

,

,

,

,

p

x

p

x

he

iEti

iEte

Et

Et

p

iEti

iEte

Eti

Eit

eS

eS

ete

emeE

eS

eS

ete

emeE

0

0

,

,

,,

,,

,

,

,,

,,

px

px

px

px

Apσ

Axσ

p

x

σ

σ

A

A (3.129)

In expressions (3.127), (3.128) and (3.129), p , e and h indicate proton, electron

and hydrogen atom respectively. Again, proton has charge e, electron has charge –e, and

pttA ),( ).,().,( xx A ,

pEEA ),( ).,().,( pp A and ettA ),( ).,().,( xx A ,

eEEA ),( ).,().,( pp A are

the electromagnetic potentials acting on spinized proton and spinized electron respectively.

Again, if pttA ),( ).,().,( xx A ,

pEEA ),( ).,().,( pp A is negligible due to fast motion of the

orbiting spinized electron, we have from the last expression in (3.129):


54

he

iEti

iEte

Et

Et

p

iEti

iEte

i

i

eS

eS

ete

emeE

eS

eS

t

mE

0

0

,

,

),(),(

),(),(

,

,

px

px

Apσ

Axσ

p

x

σ

σ (1.130)

The Weyl-like (chiral-like) form of the last expression in (3.129) and expression (3.130)

are respectively as follows:

he

iEtri

iEtle

EE

tt

p

iEtli

iEtre

EiE

tit

eS

eS

eetm

eeE

eS

eS

eetm

eeE

0

0

,

,

),(),(

),(),(

,

,

),(),(

),(),(

pp

xx

pp

xx

Axσ

Apσ

Axσ

Apσ

(3.131)

he

iEtri

iEtle

EE

tt

p

iEtli

iEtre

i

i

eS

eS

eetm

eeE

eS

eS

tm

E

0

0

,

,

),(),(

),(),(

,

,

pp

xx

Axσ

Apσ

xσ

pσ

(3.132)



p

iEti

iEte

tEi

tiE

eS

eS

meEe

eet

0

A

,

,

),(),(

),(),(

σ

σ

xp

xp

x

p

A

(3.127a)

e

iEti

iEte

tE

tE

eS

eS

meEe

eet

0

,

,

),(),(

),(),(

xp

xp

Axσ

Apσ

(3.128a)

eiMiM

p



55

e

xipxip

iip

xipxip

ii

eEtE

eEtE

xpxp

e

xipxipxipxipi

i

eemE

tee

mE

t

p

1111

p

x

p

x

e

iEti

iEte

p

iEti

iEte

i

i

es

es

mE

t

es

es

mE

t

00

,

,

,

,

x

p

x

p

he

iEti

iEte

tE

tE

p

iEti

iEte

tEi

tiE

eS

eS

meEe

eet

eS

eS

meEe

eet

0

0

,

,

,,

,,

,

,

,,

,,

xp

xp

xp

xp

Axσ

Apσ

x

p

σ

σ

A

A (3.129a)

he

iEti

iEte

tE

tE

p

iEti

iEte

i

i

eS

eS

meEe

eet

eS

eS

mE

t

0

0

,

,

),(),(

),(),(

,

,

xp

xp

Axσ

Apσ

xσ

pσ

(1.130a)

he

iEtri

iEtle

tt

tt

p

iEtli

iEtre

tit

EiE

eS

eS

eeEm

eeE

eS

eS

eeE

meet

0

0

,

,

),(),(

),(),(

,

,

),(),(

),(),(

xx

xx

xx

pp

Apσ

Apσ

Apσ

Axσ

(3.131a)

he

iEtri

iEtle

EE

tt

p

iEtli

iEtre

i

i

eS

eS

eetm

eeE

eS

eS

tm

E

0

0

,

,

),(),(

),(),(

,

,

pp

xx

Axσ

Apσ

xσ

pσ

(3.132a)


56

4. Metamorphous Prespacetime-premomentumenergy (God) View

4.1 Metamorphoses & the Essence of Spin in the Prespacetime-premomentumenergy

Model

The preceding sections make it clear that the particle ei0

of prespacetime-

premomentumenergy (God) can take many different forms as different primordial entities

and, further, can have different manifestations as different wave functions and/or fields in

different contexts even as a single primordial entity. For example, the wave functions of an

electron can take the Dirac-like, Weyl-like, quaternion-like or determinant form

respectively in different contexts depending on the questions one asks and the answer one

seeks.

This work also makes it clear that primordial self-referential spin in prespacetime-

premomentumenergy (God) is hierarchical and that it is the cause of primordial distinctions

for creating the self-referential entities in the dual universe comprised of the external

spacetime and the internal momentum-energy space. There are several levels of spin: (1)

spin in the power level in prespacetime-premomentumenergy (God) making primordial

external and internal phase distinctions of external and internal wave functions; (2) spin of

the prespacetime-premomentumenergy (God) on the ground level making primordial

external and internal wave functions which accompanies the primordial phase distinctions;

(3) self-referential mixing of these wave functions through matrix law before spatial-

momentum spinization; (4) unconfining spatial-momemtum spin through spatial-

momentum spinization (electromagnetic and weak interaction) for creating bosonic and

fermionic entities in the dual universe; and (5) confining spatial-momentum spin (strong

interactions) creating the appearance of quarks through imaginary position-momentum

(downward self-reference) in the dual universe.

4.2 The Determinant view & the meaning of Klein-Gordon-like equation in the

Prespacetime-premomentumenergy Model

In the determinant view, the matrix law collapses into Klein-Gordon-like form as shown in

§ 3 but so far we have not defined the form of the wave function as a result of the said

collapse. Here, we propose that the external and internal wave functions (objects) form a

special product state

ie with

i containing the hidden variables, quantum potentials or

self-gravity as shown below, vice versa.

From the following equations for unspinized free particle in a dual universe comprised of

an external spacetime and internal momentum-energy space in Dirac-like and Weyl-like

form respectively:


57

0

,

,

DMi

eL

t

mE

p

x (4.1)

and

0

,

,

WM

ri

leL

tm

E

x

p (4.2)

we respectively obtained the following equations in the determinant view (Klein-Gordon-

like form):

0

0

0

,

,

,,,,

i

e

ieieM

mEt

mEt

mEtDetL

px

px

px

(4.3)

and

0

0

0

,

,

,,,,

ri

le

rilerileM

mEt

mEt

mEtDetL

xp

xp

xp

(4.4)

where x

p

m

t

E; p parallels to x, E and p are operators in spacetime only acting on

external wave function (they are free parameters in momentum-energy space); and t and x


free parameters in spacetime).

By way of an example, equation (4.1) has the following plane-wave solution:

xp

xp

Eti

ie

Eti

ee

ea

ea

,,

,,

(4.5)

from which we have:

i

Eti

ie

Eti

eie eaea xpxp

,,,, (4.6)

where

ii

ee

Et

Et

xp

xp (4.7)

are respectively the external and internal phase in the determinant view. The variables in


58

,i play the roles of hidden variables to ,e which would be annihilated, if

,i were

allowed to merged with,e . Indeed, if relativistic time in the external wave function

,e

is considered to be inertial time, then the relativistic time in the conjugate internal wave

function

,i plays the role of quantized gravitational time.

Similarly, from the following equations for spinized free fermion in Dirac-like and Weyl-

like form respectively:

0

,

,

Mi

eL

t

mE

pσ

xσ (4.8)

and

0

,

,

M

ri

leL

tm

E

xσ

pσ (4.9)

where ψD=(ψe,+, ψi,-)T=(ψ1,ψ2, ψ3, ψ4)

T and ψW=(ψe,l, ψi,r)

T=(ϕ1, ϕ2, ϕ3, ϕ4)

T, we respectively

obtained following equations in the determinant view (Klein-Gordon-like form):

0

0

0

0

0

4

3

2

1

,,2,,

px

px

px

px

px

mEt

mEt

mEt

mEt

ImEtLDet ieieM

(4.10)

and

0

0

0

0

0

4

3

2

1

,,2,,

mEt

mEt

mEt

mEt

ImEtLDet rilerileM

xp

xp

xp

xp

xp

(4.11)

where x

p

m

t

E; p parallels to x, E and p are operators in spacetime only acting on

external wave function (they are free parameters in momentum-energy space); and t and x


free parameters in spacetime).


59

Klein-Gordon-like equation in the presence of electromagnetic potential ),(),( , ttA xx A

in spacetime and ),(),( , EEA pp A in momentum-energy space will be treated in future

articles.

4.3 Schrodinger-like Equation in the Prespacetime-premomentumenergy Model

From equation (4.3), we can obtain the following Schrodinger-like Equations:

eeet

m

tHE

p

xˆ (4.12)

that is,

exeett

mc

tiHi

2

ˆ x (4.13)

and

iiiE

m

ETt

x

pˆ (4.12)

that is,

ipiiEE

mc

EiTi

2

ˆ p (4.13)

4.4 The Third State of Matter in the Prespacetime-premomentumenergy Model

In this work we have suggested that Kein-Gordon-like equation is a determinant view of a

fermion, boson or an unspinized entity (spinlesson) in which the external and internal wave

functions (objects) form a special product state

ie with

i as the origin of hidden

variable, quantum potentials or self-gravity. The unspinized entity (spinlesson) is neither a

boson nor a fermion but may be classified as a third state of matter described by the

unspinized equation in Dirac-like or Weyl-like (chiral-like) form, for example:

0

,

,

,,

,

,

Mi

e

iMeMxip

i

xip

e LLL

ea

ea

t

mE

p

x (4.14)


60

0

,

,

,,

,

,

Mri

le

iMeMxip

ri

xip

le LLL

ea

ea

tm

E

x

p (4.15)

where x

p

m

t


The hadronized versions of the above equations in which the position is imaginary are

respectively as follows:

0

,

,

,,

,

,

Mi

e

iMeMiEti

iEte

i

iLLL

es

es

t

mE

p

x (4.16)

0

,

,

,,

,

,

ML

ri

le

iMeMiEtri

iEtle

i

iLL

es

es

tm

E

x

p (4.17)

wherei

i

p

x

mE

t and xi parallels to pi.

The wave functions of a fermion and boson are respectively a bispinor and bi-vector but

that of the third state (spinlesson) is two-component complex scalar field. The third state of

matter is the precursor of both fermionic and bosonic matters/fields before fermionic or

bosonic spinization. Thus, it may step into the shoes played by the Higgs field in the

standard model. Further, in this scenario, intrinsic proper time is created by the self-

referential spin (imagination) of premomentumenergy.

5. Weak Interaction in the Prespacetime-premomentumenergy Model

Weak interaction is an expressive process (emission or radiation) through fermionic

spinization with or without intermediary bosonic spinization and the associated reverse

process (capture or absorption). There are two possible kinds of mechanisms at play. One

kind is the direct fermionic spinization of an unspinized massive particle as shown in § 3:

pσ pσpp )(Det2 , xσ xσxx )(Det2 (5.1)

that is, for example:


61

00

i

e

i

e

t

mE

t

mE

pσ

xσ

p

x (5.2)

and the following reverse process:

pp pσpσ 2)(Det , xx xσxσ 2)(Det (5.3)


00

i

e

i

e

t

mE

t

mE

p

x

σ.p

xσ (5.4)

Processes (5.1) and (5.3) only conserve spin in the dual universe as a whole. There is no

exchange particle involved in process (1) or (2). In neutron synthesis from proton and

electron, if it exists, the reverse process (5.3) may occur during which a spinized proton (or

electron) loses its spin and free electron becomes tightly bound to proton.

We suggest that the following equation governs free unspinized particles having mass m in

external spacetime, intrinsic proper time in momentum-energy space, and charge e

respectively but spinless:

0

i

e

t

mE

p

x or

ei

ie

t

mE

p

x (5.5)

After spinization through (5.1), we arrive at Dirac-like equation:

0

i

e

t

mE

p

x or

ei

ie

t

mE

pσ

xσ (5.6)

Assuming a plane wave

xip

e e

, exists for equation (5.5), we obtain the following

solution for said equation:

xip

xip

xip

i

ee

t

Ne

t

eN

pp

1

,

, (5.7)

where N is a normalization factor and where we have utilized the following relation for an

time eigenstate:

,,,, eieit

t

p

p (5.8)

After spinization of solution (5.7):


62

t

p

t

ippt

ipp

t

p

t

tzyx

yxz

10

01

σ

10

011

p

p (5.9)

we arrive at the free plane-wave electron solution for Dirac-like equation (5.6) in the dual

universe comprised of the external spacetime and the internal momentum-energy space:

xip

yz

z

i

e e

t

ippt

pN

0

1

,

, and

xip

z

yx

i

e e

t

pt

ippN

1

0

,

, (5.10)

Prespacetime-premomentumenergy (God) may allow the following bosonic spinization of

massive spinless particle:

ps pspp 33 )( IDetIDet2,



0

s

s0

i

e

i

e

t

mE

t

mE

p

x

p

x (5.12)

and/or

2133 σσ)( ppps pspp IDetIDet2

2133 σσ)( xxxs xsxx IDetIDet2 (5.13)


00

s

i

e

i

e

t

mE

t

mE

p

x

p

x

s

(5.14)

21

00

i

e

i

e

t

E

t

mE

pσ

xσ

pσ

xσ


63

The spinized equation in expression (5.12) for a free massive spin 1 particle may take the

following Dirac-like form:

0

E) ,(

t),(

_,

,

_,

,

s

s

MMi

e

Mi

eL

iLL

t

mE

p

x

B

E

p

p (5.15)

or

0

E) ,(

t),(

,

_,

,

,

s

s

MMi

e

Mi

eL

iLL

t

mE

p

x

E

B

p

x (5.16)

After calculating the determinant:

psxs

ps

xs

tmE

t

mEDet

s

(5.17)

We obtain the following:

T

zyx

zyz

zyx

s

MImEt

zpzpzp

ypypyp

xpxpxp

ImEtt

mEDet

3

3

px

pxps

xs

(5.18)

As mentioned in § 3, the last term MT in expression (5.18) makes fundamental relation

0 pxmEt not to hold in the determinant view (5.17) unless the action of MT on

the external and internal components of the wave function produces null result, that is:

0)( t),(

xExzyx

E

E

E

M

z

y

x

T (5.19)

and


64

0)( E) ,(

pBpzyx

z

y

x

T ppp

B

B

B

M (5.20)

6. EM Interaction in the Prespacetime-momentumenergy Model

Electromagnetic interaction is an expressive process (radiation or emission) through

bosonic spinization of a massless and spinless entity and the associated reverse process

(absorption). There are possibly two kinds of mechanisms at play. One kind is the direct

bosonic spinization (spinizing radiation):

ps pspp 33 )( IDetIDet2 ,



00

i

e

i

e

t

t

t

E

s.x

xs

p

x (6.2)

and the following reverse process (unspinizing absorption):

pp psps 2

33 )( IDetIDet ,

xx xsxs 2

33 )( IDetIDet (6.3)


00

i

e

i

e

t

E

t

E

p

x

ps

xs (6.4)

Assuming a plane wave

xip

e e

, exists for the spinless and massless particle:

0

i

e

t

E

p

x or

ei

ie

t

E

p

x (6.5)

we obtain the following solution for this equation:

xip

xip

xip

i

ee

t

Ne

t

e

pp

1

2

1

,

, (6.6)


65

where we have utilized the following relation for an energy eigenstate and N is the

normalization factor :

,,,, eieit

t p

p (6.7)

After spinization:

0

0

0

t

ip

t

ipt

p

t

ipt

ip

t

ip

tt

xy

xz

yz

pp s (6.8)

We arrive at the plane-wave solution:

xip

y

zi

xe e

t

ipt

ip

0

0

0

1

2

1

,

,

xip

x

z

i

ye e

t

ip

t

ip

0

0

1

0

2

1

,

,

xip

x

y

i

ze e

t

ipt

ip

0

1

0

0

2

1

,

,

(6.9)

for the spinized photon equation:

0

i

e

t

E

p

x

s

s or

ei

ie

t

E

p

x

s

s (6.10)

For bosonic spinization pspp 2 and xsxx 2 , the Maxwell-like equations in

the vacuum in the spacetime-momentumenergy unverse may be written as follows:

0

0

0

E) ,(

t),(

E) ,(

t),(

p

x

p

x

B

E

Bx

Ep

ps

xs

it

E

,

0

0

0

E) ,(

t),(

E) ,(

t),(

p

x

p

x

B

E

B

E

p

x

Ex

pt

ii

i


66

or

0

0

E) ,(

t),(

t),(E) ,(

E) ,( t),(

p

x

xp

px

B

E

EB

BE

p

x

xE

pt

(6.11)

If we calculate the determinant:

psxs

ps

xsEt

t

EDet

s

(6.12)

We obtain the following:

T

zyx

zyz

zyx

s MIEt

zpzpzp

ypypyp

xpxpxp

IEtt

EDet

33 pxpx

ps

xs (6.13)

The last term MT in expression (6.13) makes fundamental relation 0 pxEt not hold

in the determinant view (6.12) unless the action of MT on the external and internal

components of the wave function produces null result, since equations (5.20) and (5.21)

only hold in the source-free region of the dual momentum-energy universe.

If source 0, ),(),( tE xp j in the spacetime-momentumenergy universe, we may have

instead:

0

0

E) ,(

p) ,( t),(

t),(

E) ,(

t),(

p

Ex

x

p

x j

B

E

Bx

Ep

ps

xs

i

i

it

E

,

0

0

E) ,(

E) ,( t),(

t),(

E) ,(

t),(

p

px

x

p

x j

B

E

B

E

p

x

Ep

pt i

ii

i

or

0E) ,(

E) ,( t),(

t),(E) ,(

t),(E) ,( t),(

p

px

xp

xpx

B

E

EB

jBE

p

x

xE

pt

(6.14)


67

Importantly, we can also choose to use fermionic spinization scheme pσpp 2and

xσxx 2 to describe Maxwell-like equations. In this case, the Maxwell-like

equation in the vacuum may have the form:

0-

-

E) ,(

t),(

p

x

Bσ

Eσ

pσ

xσ

it

E (6.15)

which gives:

0

0

0

E) ,(

t),(

E) ,(

t),(

p

x

p

x

B

E

B

E

p

x

Ex

pt

(6.16)

If source 0, ),(),( tE xp j , we may have:

E) ,(

t),(

E) ,(

t),(

-

-

p

x

p

x

i

i

it

E jσ

Bσ

Eσ

pσ

xσ (6.17)

which gives:

0E) ,(

E) ,( t),(

t),(E) ,(

t),(E) ,( t),(

p

px

xp

xpx

B

E

EB

jBE

p

x

xE

pt

(6.18)

Therefore, in the fermionic spinization scheme, we have in place of the bi-vector wave

function a 4x4 tensor comprising of two bi-spinors (instead of the bi-vector itself)

generated by projecting the bi-vector comprised of E(x, t) and iB(p, E) to spin σ.

Further, we point out here that for a linear photon its electric field E(x, t) is the external wave

function (external object) and its magnetic field B(p, E) is the internal wave function (internal

object). These two fields are always self-entangled and their entanglement is their self-

gravity. Therefore, the relation between E(x, t) and B(p, E) in a propagating electromagnetic

wave is not that change in E(x, t) induces B(p, E) vice versa but that change in E(x, t) is always

accompanied by change in B(p, E) vice versa due to their entanglement (self-gravity). That

is, the relationship between E(x, t) and B(p, E) are gravitational and instantaneous.


68

7. Strong Interaction in the Prespacetime-momentumenergy Model

While weak and electromagnetic interactions are expressive processes involving fermionic

and bosonic spinizations of spinless entities (the third state of matter) and their respective

reverse processes, strong interaction does not involve spinization, that is, strong force is a

confining process.

In order to achieve confinement of a nucleon or stability of the nucleus, we suggest that, in

the dual universe comprised of the external spacetime and internal momentum-energy

space, strong interaction may involve imaginary momentum and imaginary position

respectively in the confinement zone as illustrated below. We have suggested in § 3 that the

proton may be considered as an elementary particle that accomplishes spatial and

momentum self-confinement through downward self-reference (imaginary momentum and

imaginary position).

8. Gravity in the Prespacetime-momentumenergy Model

Gravity in the spacetime-momentumenergy universe is quantum entanglement

(instantaneous interaction) across the dual universe comprised of the external spacetime

and internal momentum-energy space. There are two types of gravity at play. One is self-

gravity (self-interaction) between the external object (external wave function) and internal

object (internal wave function) of an entity (wave function) governed by the metamorphous

matrix law described in this work and the other is the quantum entanglement (instantaneous

interaction) between two entities or one entity and the external or internal universe as a

whole. As further shown below, gravitational field (graviton) is just the wave function itself

which expresses the intensity distribution and dynamics of self-quantum-entanglement

(nonlocality) of an entity. We focus here on three particular forms of gravitational fields.

When E=t=0, we have from fundamental relationship (3.4):

0 pxm or 0 pxm (8.1)

As shown in § 3, the timeless and energy-less matrix law in Dirac-like and Weyl-like form

is respectively the following:

MiMeM LLLm

,,

p

x (8.2)

MiMeM LLLm

,,

x

p (8.3)

Thus, the equations of the timeless and energy-less wave functions (self-fields) are

respectively as follows:


69

0

,

,

,,

,

,

DMiD

eD

iMeMiMiD

iMeD VL

V

VLL

eg

egm

p

x (8.4)

and

0

,

,

,,

,

,

WMiW

eW

iMeMiMiW

iMeW VL

V

VLL

eg

eg

m x

p (8.5)

Equation (8.4) and (8.5) can be respectively rewritten as:

eDiD

iDeD

VV

VmV

,,

,,

p

x

or

eDiD

iDeD

VV

Vm

V

,,

,,

p

x

(8.6)

and

eWiW

iWeW

VV

VmV

,,

,,

p

x

or

eWiW

iWeW

VV

Vm

V

,,

,,

p

x

(8.7)

When |p|=|x|=0, we have from fundamental relationship (3.4):

0 mEt (8.18)

As shown in § 3, the spaceless and momemtumless matrix law in Dirac-like and Weyl-like

form is respectively the following:

MiMeM LLL

t

mE

,,

0

0

(8.19)

and

MiMeM LLL

tm

E

,,

(8.20)

and the equation of spaceless and momemtumless wave functions (self-fields) are

respectively the follows:

0

0

0

,

,

,,

,

,

DMiD

eD

iMeMiMiD

iMeD VL

V

VLL

eg

eg

t

mE

(8.21)

and


70

0

,

,

,,

,

,

WMiW

eW

iMeMiMiW

iMeW VL

V

VLL

eg

eg

tm

E (8.22)

The external and internal (momentum-less) wave functions VD,e and VD,i in equation (8.21)

are decoupled from each other, but those in equation (8.22),VW,e and VW,i, are coupled to

each other:

iDiD

eDeD

VtV

mVEV

,,

,,

but

eWiW

iWeW

mVtV

VEV

,,

,, (8.23)

It can be verified that the solutions to equation (8.21) are in forms of:

imt

imt

iD

eD

D eNe

NV

VV

0

1

0,

,

(8.24)

or

Ei

EiiD

eD

D eNe

NV

VV

1

00

,

,

(8.25)

but the solutions to equation (8.22) are in the forms of:

itEmi

itEmi

itEmi

iW

eW

W eNe

eN

V

VV

1

1

,

,

(8.26)

When m==0, we have from fundamental relationship (3.4):

0 pxEt (8.31)

We can regard expression (8.31) as a relationship governing the massless and intrinsic-

proper-time-less dual universe in which the total mass and intrinsic-proper-time are both

zero. As shown in § 3, the intrinsic-proper-time-less matrix law in Dirac-like and Weyl-like

form is respectively the following:

MiMeM LLLt

E

,,

p

x (8.32)

and

MiMeM LLLt

E

,,

0

0

x

p (8.33)

and the equations of massless and intrinsic-proper-time-less wave functions (self-fields) are


71

respectively the following:

0

,

,

,,

,

,

DMiD

eD

iMeMiMiD

iMeD VL

V

VLL

eg

eg

t

E

p

x (8.34)

and

0

0

0

,

,

,,

,

,

WMiW

eW

iMeMiMiW

iMeW VL

V

VLL

eg

eg

t

E

x

p (8.35)

The external and internal (masssless) wave functions VD,e and VD,i in equation (8.34) are

coupled with each other, but those in equations (8.35),VW,e and VW,i, are decoupled from

each other:

eDiD

iDeD

VtV

VEV

,,

,,

p

x but

iWiW

eWeW

VtV

VEV

,,

,,

x

p (8.36)

The solutions to equation (8.34) are in the forms of:

)(

)(

)(

,

,11

xkxk

xk

ti

ti

ti

iD

eD

D e

t

Ne

t

eN

V

VV

pp (8.37)

or

)(

)(

)(

,

,

11

xk

xk

xk

ti

ti

ti

iD

eD

D eEN

e

eEN

V

VV

xx

(8.38)

but the solutions to equation (8.35) are in the forms of:

)(

)(

,

,

0

1

0

xkxk

ti

ti

iw

eW

W eNe

NV

VV

(8.39)

or

)(

)(,

,

1

00xk

xk

ti

tiiW

eW

W eNe

NV

VV

(8.40)

Equations (8.34) and (8.35) describe the self-interaction of external and internal spinless

wave functions (self-fields).


72

9. Human Consciousness in the Spacetime-momentumenergy Universe

We now briefly discuss human consciousness in the prespacetime-premomentumenergy

(God) model. Detailed treatment will be given in forthcoming articles.

Our experimental results on quantum entanglement of the brain with external substances

(See, e.g., Refs, in [1]) suggest that Consciousness is not located in the brain but associated

with prespacetime-premomentumenergy (God) or simply is prespacetime-

premomentumenergy (God). Thus, Consciousness as prespacetime-premomentumenergy

(God) has both transcendental and immanent properties. The transcendental aspect of

Consciousness as prespacetime-premomentumenergy (God) is the origin of primordial self-

referential spin (including the self-referential matrix law) and it projects the external and

internal objects (wavefunctions) in the dual universe through spin and, in turn, the

immanent aspect of Consciousness as prespacetime-premomentumenergy (God) observes

the external object (wavefunction) in the external spacetime through the internal object

(wavefunction) in the internal momentum-energy space.

Human consciousness in the dual universe comprised of the external spacetime and the

internal momentum-energy space is a limited and particular version of this dual-aspect

Consciousness as prespacetime-premomentumenergy (God) such that we have limited free

will and limited observation.

Figure 9.1 Interaction between an object and the brain (body) in the dual universe

As illustrated in Figure 9.1, there are two kinds of interactions between an object (entity)

outside the brain (body) and the brain (body) in the prespacetime-premomentumenergy

model. The first kind is the direct physical and/or chemical interactions such as sensory

input through the eyes. The second and lesser-known but experimentally proven to be true


73

kind is the instantaneous interactions through quantum entanglement. The entire world

outside our brain (body) is associated with our brain (body) through quantum entanglement

thus influencing and/or generating not only our feelings, emotions and dreams but also the

physical, chemical and physiological states of our brain and body.

In the prespacetime-premomentumenergy model, we may write the following Hodgkin-

Huxley equation in the external spacetime and Hodgkin-Huxley-like like equation in the

internal momentum-energy space respectively:

i

iim

m

mt gEVC

V1

(9.1)

where Vm is the electric potential across the neural membranes, Cm is the capacitance of the

membranes and gi is the ith voltage-gated or constant-leak ion channel; and

i

EiEiEm

Em

EmE gEVC

V ).().().(

).(

).(

1ppp

p

p (9.1a)

where Vm(p,E) is the electric potential across the neural membranes, Cm(p,E) is the capacitance

of the membranes, gi(p,E) is the ith voltage-gated or constant-leak ion channel.

Microscopically, in the dual universe comprised of the external spacetime and the internal

momentum-energy space, electromagnetic fields E(x, t) and B(x, t) or their four-poential

),(),(),( , tttA xxx A in the external spacetime:

),(),(

),(),(),(

tt

tttt

xx

xxx

AB

AE (9.2)

and electromagnetic fields E(p, E) and B(p, E) or their four-potential

),(),(),( , EEEA ppp A in the internal momentum-energy space:

),(),(

),(),(),(

EE

EEEE

pp

ppp

AB

AE (9.2a)

interact with proton of charge e and unpaired electron of charge –e respectively as the

following Dirac-Maxwell-like systems:


74

pi

e

Et

Et

ete

emeE

0

,

,

,,

,,

px

px

p

x

Aσ

Aσ

i

i (9.3)

p

E

t

E

t

ii

ii

it

E

,

†

,

†

,

,

)(

)(

-

-

p

x

p

xj

Bσ

Eσ

pσ

xσ

σασ (9.4)

and

e

ete

emeE

i

e

Et

Et

0

,

,

,,

,,

px

px

Apσ

Axσ (9.5)

e

ii

ii

it

E

E

t

E

t

,

†

,

†

,

,

)(

)(

-

-

p

x

p

xj

Bσ

Eσ

pσ

xσ

σασ (9.6)

where β and α are Dirac matrices and ),(),( , tE xp j is the electric density in the internal

momentum-energy space and current in external spacetime respectively.

10. Some Questions & Answers

1. Do the uncertainty principle and commutation relations among energy, momentum, time

and position hold in the prespacetime-premomentumenergy model? Yes, they hold

separately in the external spacetime and the internal momentum-energy space. In

external spacetime, time and position are continuous parameters and energy and

momentum are quantized dynamical variables. In the internal momentum-energy space,

time and position are quantized dynamical variables and energy and momentum are

continuous parameters.

2. How are prespacetime model, premomentumenergy model and prespacetime-

premomentumenergy (God) connected to each other? The elementary particle in

prespacetime model is transformed into that in prespacetime-premomentumenergy

and/or premomentumenergy model through quantum jump as demonstrated in forth

coming articles.

3. What is the foundation of the dual universe comprised of the external spacetime and the

internal momentum-energy space? The foundation is prespacetime-premomentumenergy

(God) which is omnipotent, omniscient and omnipresent.

4. Was there something before the dual universe comprised of the external spacetime and

the internal momentum-energy space was born (if there was such birth)? Yes,


75

prespacetime-premomentumenergy (God) alone (1=ei0

) without differentiation or

dualization. So, it may be said that 1= ei0

is the primordial particle.

5. How does prespacetime-premomentumenergy (God) create, sustain and cause evolution

of the dual universe comprised of the external spacetime and the internal momentum-

energy space and all entities in it? Prespacetime-premomentumenergy (God) does these

things by hierarchical self-referential spin of itself at its free will.

6. Why is there materially something instead of nothing? Prespacetime-

premomentumenergy (God) is restless and tends to create, sustain and make evolutions

of different entities.

7. How does prespacetime-premomentumenergy (God) govern the dual universe

comprised of the external spacetime and the internal momentum-energy space?

Prespacetime-premomentumenergy (God) governs through metamorphous self-

referential matrix law.

8. What is matter in the prespacetime-premomentumenergy model? Matter is a dualized

entity (created through hierarchical self-referential spin of prespacetime-

premomentumenergy (God)) comprised of an external wave function (external object)

having positive energy by convention and an internal wave function (internal object)

having negative time by convention.

9. What is antimatter in the prespacetime-premomentumenergy model? Antimatter is a

dualized entity (created through hierarchical self-referential spin of prespacetime-

premomentumenergy (God)) comprised of an external wave function (external object)

having negative energy by convention and an internal wave function (internal object)

having positive time by convention.

10. What is quantum entanglement in the prespacetime-premomentumenergy model? It is

the interaction and/or connections between the external and internal wave functions

(objects) of a single dualized entity or among different dualized entities through the

prespacetime-premomentumenergy model which is outside spacetime and momentum-

energy.

11. What is self-interaction, self-gravity or self-quantum entanglement in the the

prespacetime-premomentumenergy model? Self-interaction is the interaction between

the external and internal wave functions (objects) according to the the prespacetime-

premomentumenergy (God) equation governed by the self-referential matrix law.

12. What is strong force in the prespacetime-premomentumenergy model? It is downward

self-reference through imaginary momentum in the external spacetime and imaginary

position in the internal momentum-energy space.


76

13. What is weak force in the prespacetime-premomentumenergy model? It is fermionic

spinization and unspinization of spinless entities with or without bosonic intermediary

spinization.

14. What is electromagnetic force in the prespacetime-premomentumenergy model? It is

bosonic spinization and unspinization of intrinsic-proper-time-less (massless) and

spinless entity.

15. What is gravity in the prespacetime-premomentumenergy model? It is quantum

entanglement across the dual universe comprised of the external spacetime and the

internal momentum-energy space which includes self-gravity or self-quantum-

entanglement between the external and internal wave functions (objects) of a single

dualized entity and gravity or quantum entanglement among different entities.

16. What is the origin of the quantum effect in the prespacetime-premomentumenergy

model? The origin is primordial hierarchical self-referential spin of prespacetime-

premomentumenergy (God).

17. What is information in the prespacetime-premomentumenergy model? It is a distinction

(either quantitative or qualitative) experienced or perceived by a particular

consciousness.

18. What is quantum information in the prespacetime-premomentumenergy model? It is a

distinction or a state of distinction (either quantitative or qualitative) experienced or

perceived by a particular consciousness which is due to a quantum effect such as

quantum entanglement.

19. What is the meaning of imaginary unit i in the prespacetime-premomentumenergy

model? It is the most elementary self-referential process. As imagination of

prespacetime-premomentumenergy (God), it makes phase distinction of an elementary

entity and, as an element in the matrix law, it plays a crucial role in self-referential

matrixing creation of prespacetime-premomentumenergy (God).

20. What is Consciousness? Consciousness is prespacetime-premomentumenergy (God)

which is omnipotent, omniscient and omnipresent.

21. What is human consciousness? It is a limited or individualized Consciousness

associated with a particular human brain/body.

22. Does human consciousness reside in human brain? No, the human brain is the interface

for human consciousness to experience and interact with the external universe.

23. What are spirit, soul and/or mind? They are different aspects or properties of

prespacetime-premomentumenergy (God) which is transcendent, immanent and eternal.


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24. Where did we come from? Physically/biologically, we came from prespacetime-

premomentumenergy (God) as its creation. Spiritually, we are an inseparable part of

prespacetime-premomentumenergy (God) and our consciousness is limited and/or

individualized version of unlimited Consciousness.

25. Where are we going? Physically/biologically, we disintegrate or die unless we advance

our science to the point where death of our biological body becomes a choice, not

unavoidability. Also, we are of the opinion that advancement in science will eventually

enable us to transfer or preserve our individual consciousness associated with our ailing or

diseased bodies to another biological or artificial host. Spiritually, we may go back to

prespacetime-premomentumenergy (God) or reincarnate into a different form of individual

consciousness that may be able to recall its past.

26. How does the mind influence the brain? Mind influences the brain through free will

which acts on subjective entities (internal objects), which in turn effect objective entities

(external objects) through the prespacetime-premomentumenergy (God) equation.

27. What is the origin of the uncertainty principle? The origin is self-referential spin or

zitterbewegung.

28. What is the origin of quantum jump? The free will of prespacetime-

premomentumenergy (God) or unlimited transcendental Consciousness. Remember that our

limited free will is part of the unlimted free will of prespacetime-premomentumenergy

(God) since we are part of prespacetime-premomentumenergy (God).

29. Is information conserved? It is our opinion that information is conserved to zero in the

dual universe since each distinction in the external space is accompanied by its negation in

the internal space. However, information is not conserved in each space alone.

30. What is a graviton? There is no graviton in the sense of a quantum (particle) which

mediated gravitational interaction at the speed of light. However, since gravity is quantum

entanglement, the wave function of each entity may be treated as a graviton.

31. Is there an absolute reference frame? Yes, it is simply prespacetime-

premomentumenergy (God).

11. Conclusion

This article is a continuation of the Principle of Existence. A prespacetime-

premomentumenergy model of elementary particles, four forces and human consciousness is

formulated, which may illustrate how the self-referential hierarchical spin structure of the

prespacetime-premomentumenergy (God) provides a foundation for creating, sustaining and


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causing evolution of elementary particles through matrixing processes embedded in said

prespacetime-premomentumenergy (God). This model generates elementary particles and


spacetime and an internal energy-momentum of a dual universe. In contrast, the

prespacetime model described previously generates elementary particles and their governing

matrix laws for a dual universe (quantum frame) comprised of an external spacetime and an

internal spacetime. Then, the premomentumenergy model described recently generates

elementary particles and their governing matrix laws for a dual universe (quantum frame)

comprised of an external momentum-energy space and an internal momentum-energy space.

These quantum frames and their metamorphoses may be interconnected through quantum

jumps as demonstrated in forthcoming articles.

The prespacetime-premomentumenergy model may reveal the creation, sustenance and

evolution of fermions, bosons and spinless entities each of which is comprised of an

external wave function or external object in the spacetime and an internal wave function or

internal object in the internal momentum-energy space. The model may provide a unified

causal structure in said dual universe (quantum frame) for weak interaction, strong

interaction, electromagnetic interaction, gravitational interaction, quantum entanglement,

human consciousness. The model may also provide a unique tool for teaching,

demonstration, rendering, and experimentation related to subatomic and atomic structures

and interactions, quantum entanglement generation, gravitational mechanisms in

cosmology, structures and mechanisms of human consciousness.

In the beginning there was prespacetime-premomentumenergy (God) ei0

materially empty

but restless. And it began to imagine through primordial self-referential spin 1=ei0

=eiM-

iM=e

iM e

-iM=e

-iM/ e

-iM = e

iM/ e

iM…such that it created the external object to be observed and

internal object as observed, separated them into external spacetime and internal

momentum-energy space, caused them to interact through self-referential matrix law and

thus gave birth to the dual universe (quantum frame) comprised of said external spacetime

and internal momentum-energy space which it has since sustained and made to evolve.

In this universe, the body (ether) of prespacetime-premomentumenergy (God), represented

by Euler’s Number e, is the ground of existence and can form external wave functions as

external object and internal wave function as internal object (each pair forms an elementary

entity) and interaction fields between elementary entities which accompany the

imaginations of the prespacetime-premomentumenergy (God).

The prespacetime-premomentumenergy (God) can be self-acted on by self-referential

matrix law LM. The prespacetime-premomentumenergy (God) has imagining power i to

project external and internal objects by projecting, e.g., external and internal phase +M

=+(Et-p·x)/ħ at the power level of prespacetime-premomentumenergy (God). The universe

so created is a dual universe (quantum frame) comprising of the external spacetime with a

relativistic frame xμ=(t, x) and internal momentum-energy space with a relativistic frame

pμ=(E/c, p). The absolute frame of reference is the prespacetime-premomentumenergy


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(God) itself. Thus, if prespacetime-premomentumenergy (God) stops imagining (i0=0), the

dual universe (quantum frame) would disappear into materially nothingness ei0

=e0=1.

The accounting principle of the dual universe is conservation of total phase to zero, that is,

the total phase of an external object and its counterpart, the internal object, is zero. Also in

this dual universe, self-gravity is nonlocal self-interaction (wave mixing) between an

external object in the external spacetime and its negation/image in the internal momentum-

energy space, vice versa. Gravity in external spacetime is the nonlocal interaction (quantum

entanglement) between an external object with the internal momentum-energy space as a

whole.

Some other basic conclusions are: (1) the two spinors of the Dirac electron or positron in

this dual universe (quantum frame) are respectively the external and internal objects of the

electron or positron; and (2) the electric and magnetic fields of a linear photon in the dual

universe are respectively the external and internal objects of a photon which are always

self-entangled.

In this dual universe, prespacetime-premomentumenergy (God) has both transcendental and

immanent properties. The transcendental aspect of prespacetime-premomentumenergy

(God) is the origin of primordial self-referential spin (including the self-referential matrix

law) and it projects the external spacetime and internal momentum-energy space through

spin and, in turn, the immanent aspect of prespacetime-premomentumenergy (God)

observes the external spacetime through the internal momentum-energy space. Human

consciousness is a limited and particular version of this dual-aspect prespacetime-

premomentumenergy (God) such that we have limited free will and limited observation.

References

1. Hu, H. & Wu, M. (2010), The Principle of Existence: Toward a Scientific Theory of Everything.

Scientific GOD Journal 1:1, pp. 8-77. Also see: http://vixra.org/abs/0912.0047

2. Hu, H. & Wu, M. (2010), The Principle of Existence II: Genesis of Self-Referential Matrix Law,

& the Ontology & Mathematics of Ether. Scientific GOD Journal 1:8, pp. 520-550. Also see:

http://vixra.org/abs/1012.0042

3. Hu, H. & Wu, M. (2013), Application of Prespacetime Model I. Prespacetime journal 4:6, pp.

641-660.

4. Hu, H. & Wu, M. (2013), Application of Prespacetime Model II. Prespacetime journal 4:6, pp.

661-680.




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5. Hu, H. & Wu, M. (2014), Premomentumenergy Model I: Genesis of Elementary Particles &

Relativistic QM for a Dual Momentum-Energy Universe. Scientific GOD Journal 5:9, pp. 763-

831.

6. Hu, H. & Wu, M. (2014), Premomentumenergy Model II: Genesis of Self-Referential Matrix

Law & Mathematics of Ether. Scientific GOD Journal 5:9, pp. 832-863.

7. Hu, H. & Wu, M. (2014), Modeling Methods Based on Premomentumenergy Model. Scientific

GOD Journal 5:9, pp. 864-884.

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