Journal of Modern Physics, 2013, 4, 27-31
http://dx.doi.org/10.4236/jmp.2013.44A005 Published Online April 2013 (http://www.scirp.org/journal/jmp)
The Space Structure, Force Fields, and Dark Matter
Ding-Yu Chung1, Volodymyr Krasnoholovets2
1Utica, Michigan, USA
2Institute of Physics, National Academy of Sciences, Kyiv, Ukraine
Received January 28, 2013; revised March 1, 2013; accepted March 11, 2013
Copyright © 2013 Ding-Yu Chung, Volodymyr Krasnoholovets. This is an open access article distributed under the Creative Com-
mons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work
is properly cited.
ABSTRACT
It is proposed that the digital space structure consists of attachment space (denoted as 1) for rest mass and detachment
space (denoted as 0) for kinetic energy. Attachment space attaches to object permanently with zero speed, and detach-
ment space detaches from the object at the speed of light. The combination of attachment space and detachment space
brings about the three structures: binary lattice space, miscible space, and binary partition space. Binary lattice space, (1
0)n, consists of repetitive units of alternative attachment space and detachment space. In miscible space, attachment
space is miscible to detachment space without separation. Binary partition space, (1)n(0)n, consists of separated con-
tinuous phases of attachment space and detachment space. Binary lattice space, miscible space, and binary partition
space constitute quantum mechanics, special relativity, and the extreme force fields, respectively. Through the detach-
ment space, a higher dimensional particle in attachment space is sliced into infinitely surrounding a lower dimensional
core attachment space, resulting in a particle surrounding by gauge field in the form of binary lattice space. The 10d
particle can be sliced into 9d, 8d, 7d, 6d, 5d, and 4d particles equally by mass, corresponding to baryonic particle as 4d
and dark matter a s o ther 5 pa rticles , so the rati o bet ween ba ryonic matter and dark matter is 1 to 5, in agreement with the
observed ratio. At extreme conditions, such as extremely low temperature, the gauge force field in the form of binary
lattice space is transformed into the extreme force field in the form of binary partition space to explain extreme phe-
nomena, such as superconductivity.
Keywords: Space Structure; Quantum Mechanics; Force Fields; Dark Matter; Superconductivity
1. Introduction
The conventional explanation of the hidden extra space
dimensions is the compactization of the extra space di-
mensions. For example, six space dimensions become
hidden by the compactization, so space-time appears to
be four dimensional. Bounias and Krasnoholovets [1]
propose another explanation of the reduction of >4D
space-time into 4D space-time by slicing >4D space-
time into infinitely many 4D slices surrounding the 4D
core particle. Such slicing of >4D space-time is like slic-
ing 3D object into 2D object in the way stated by Michel
Bounias as follows: “You cannot put a pot into a sheet
without changing the shape of the 2D sheet into a 3D
dimensional packet. Only a 2D slice of the pot could be a
part of sheet”.
One way to describe the slicing of space dimension is
to have the space structure consisting of attachment
space and detachment space. Attachment space is the
space attaching to an object, such as 3D attachment space
attaching to a pot described above. Detachment space is
the space cutting attachment space into numerous at-
tachment space slices, such as detachment space cutting
3D attachment space into numerous 2D attachment space
slices. Such 2D attachment space slices with attached
objects, therefore, are separated by 2D detachment space
gaps without attached objects.
In this paper, the space structure consists of attachment
space and detachment space. This space structure ex-
plains the difference between quantum mechanics and
special relativity, the different force fields, the difference
between baryonic matter and dark matter, and the ratio
between baryonic matter and dark matter.
2. The Space Structure
The digital space structure [2-4] consists of attachment
space (denoted as 1) and detachment space (denoted as 0).
Attachment space attaches to object permanently with
zero speed. Detachment space detaches from the object at
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opyright © 2013 SciRes. JMP

D.-Y. CHUNG, V. KRASNOHOL OVETS 28
the speed of light. Attachment space relates to rest mass,
while detachment space relates to kinetic energy. Differ-
ent stages of our universe have differe nt space structures .
The transformation between mass (massive particle) in
attachment space and kinetic energy (massless particle)
in detachment space is through the scalar Goldstone
boson. For example, massive particles with n units of
attachment space, denoted as (1)n, are converted into
massless particles with n units of detachment space, de-
noted as (0)n through the Go ldstone bosons. The additio n
of the Goldstone bosons to massless particles in detach-
ment space results in massive particles in attachment
space, while the removal of removal of the Goldstone
bosons in attachment space leads to massless particles in
detachment space.


Goldstone boson
Goldstone boson
massive particles in1
massless part
massive particles in1
massless part
n
n






icles in0
icles in0
n
n
combination
pace,
or
n space

The Goldstone boson provides the longitudinal degree
of freedom for massive particle in attachment space. The
Goldstone boson itself is a zero-energy virtual particle by
taking energy from and returning energy to the object
transformed by the Goldstone boson. The Goldstone
boson in the Standard Model for electroweak interaction
is the Higgs boson.
The combination of attachment space (1) and detach-
ment space (0) brings about three different space struc-
tures: miscible space, binary partition space, and binary
lattice space for four-dimensional space-time as below.
 


 
attachment spacedetachmentspace
10
1 0binarylattice s
10miscible space,
10binarypartitio
nn
n
n
nn

Binary lattice space, (1 0)n, consists of repetitive units
of alternative attachment space and detachment space.
Thus, binary lattice space consists of multiple quantized
units of attachment space separated from one another by
detachment space. In miscible space, attachment space is
miscible to detachment space, and there is no separation
of attachment space and detachment space. Binary parti-
tion space, (1)n(0)n, consists of separated continuous
phases of attachment space and detachment space.
Binary lattice space consists of multiple quantized
units of attachment space separated from one another by
detachment space. An object exists in multiple quantum
states separated from one another by detachment space.
Binary lattice space is the space for wavefunction. In
wavefunction,
1
n
ii
i
c




Each individual basis element, i

, attaches to at-
tachment space, and separates from the adjacent basis
element by detachment space. Detachment space de-
taches from object. Binary lattice space with n units of
four-dimensional, (0 1)n, contains n units of basis ele-
ments.
Neither attachment space nor detachment space is zero
in binary lattice space. The measurement in the uncer-
tainty principle in quantum mechanics is essentially the
measurement of attachment space and momentum in bi-
nary lattice space: large momentum has small non-zero
attachment space, while large attachment space has low
non-zero momentum. In binary lattice space, an entity is
both in constant motions as wave for detachment space
and in stationary state as a particle for attachment space,
resulting in the wave-p article duality.
Detachment space contains no object that carries in-
formation. Without information, detachment space is
outside of the realm of causality. Without causality, dis-
tance (space) and time do not matter to detachment space,
resulting in non-localizable and non-countable space-
ime. The requirement for the system (binary lattice space)
containing non-localizable and non-countable detach-
ment space is the absence of net information by any
change in the space-time of detachment space. All
changes have to be coordinated to result in zero net in-
formation. This coordinated non-localized binary lattice
space corresponds to nilpotent space. All changes in en-
ergy, momentum, mass, time, space have to result in zero
as defined by the generalized nilpotent Dirac equation by
B. M. Diaz and P. Rowlands [5].

 

exp 0.
kt ijmikE ipjm
iEtpr
 


where E, p, m, t and r are respectively energy, momen-
tum, mass, time, space and the symbols ±1, ±i, ±i, ±j, ±k,
±i, ±j, ±k, are used to represent the respective units re-
quired by the scalar, pseudoscalar, quaternion and multi-
variate vector groups. The changes involve the sequential
iterative path from nothing (nilpotent) through conjuga-
tion, complexification, and dimensionalization. The non-
local property of binary lattice space for wavefunction
provides the v iolation of Bell inequalities [6] in quantum
mechanics in terms of faster-than-light influence and
indefinite property before measurement. The non- locality
in Bell inequalities does not result in net new informa-
tion.
In binary lattice space, for every detachment space,
there is its corresponding adjacent attachment space.
Thus, no part of the object can be irreversibly separated

D.-Y. CHUNG, V. KRASNOHOL OVETS 29
from binary lattice space, and no part of a different object
can be incorporated in binary lattice space. Binary lattice
space represents coherence as wavefunction. Binary lat-
tice space is for coherent system. Any destruction of the
coherence by the addition of a different object to the ob-
ject causes the collapse of binary lattice space into mis-
cible space. The collapse is a phase transition from bi-
nary lattice space to miscible space.








collap
binary latticespace
01n se
misciblespace
01
n
 
Another way to convert binary lattice space into mis-
cible space is gravity. Penrose [7] pointed out that the
gravity of a small object is not strong enough to pull dif-
ferent states into one location. On the other hand, the
gravity of large object pulls different quantum states into
one location to become miscible space. Therefore, a
small object without outside interference is always in
binary lattice space, while a large object is never in bi-
nary lattice space.
The information in miscible space is contributed by
the combination of both attachment space and detach-
ment space, so information can no longer be non-localize.
Any value in miscible space is definite. All observations
in terms of measurements bring about the collapse of
wavefunction, resulting in miscible space that leads to
eigenvalue as definite quantized value. Such collapse
corresponds to the appearance of eigenvalue, E, by a
measurement operator, H, on a wavefunction, .
H
E 
In miscible space, attachment space is miscible to de-
tachment space, and there is no separation of attachment
space and detachment space. In miscible space, attach-
ment space contributes zero speed, while detachment
space contributes the speed of light. A massless particle,
such as photon, is on detachment space continuously, and
detaches from its own space continuously. For a moving
massive particle consisting of a rest massive part and a
massless part, the massive part with rest mass, m0, is in
attachment space, and the massless part with kinetic en-
ergy, K, is in detachment space. The combination of the
massive part in attachment space and massless part in
detachment leads to the propagation speed in between
zero and the speed of light.
To maintain the speed of light constant for a moving
particle, the time (t) in moving particle has to be dilated,
and the length (L) has to be contracted relative to the rest
frame.
22
00
22
00
1,c t
mcmc
0,
tt
LL
EK









where 22 11 c   is the Lorentz factor for time
dilation and length contraction, E is the to tal energy, and
K is the kinetic energy.
Binary partition space, (1)n(0)n, consists of separated
continuous phases of attachment space and detachment
space. It is for extreme force fields under extreme condi-
tions such as near the absolute zero temperature. It will
be discussed in the Section 3 to explain extreme phe-
nomena such as superconductivity.
3. Baryonic Matter, Dark Matter, and
Gauge Force Fields
As described in Reference [2], at the beginning of the
current universe, the 10d particle universe was sliced into
six particles: 9d, 8d, 7d, 6d, 5d, and 4d equally by mass.
Baryonic matter is 4d, while dark matter consists of the
other five types of particles (9d, 8d, 7d, 6d, and 5d). The
mass ratio of dark matter to baryonic matter is 5 to 1 in
agreement with the observation [8] showing the universe
consists of 22.7% dark matter, 4.56% baryonic matter,
and 72.8% dark energy.
Detachment space (0) involves in the slicing of dimen-
sions. Attachment space is denoted as 1. For example,
the slicing of 10d particles into 4d particles is as follows.


  
slicing
46
4d attachmentspace
6
444
,6
1
4d core attachment space6 types of4dunits
1
101
i
i




j
The two products of the slicing are the 4d-core at-
tachment space and 6 types of 4d quantized units. The 4d
core attachment space surrounded by 6 types of many (j)
4d-quantized units corresponds to the core particle sur-
rounded by 6 types of many small 4d particles.
Therefore, the transformation from d to d – n involves
the slicing of a particle with d dimension into two parts:
the core particle with d – n dimension and the n dimen-
sions that are separable from the core particle. Such n
dimensions are denoted as n “dimensional orbitals”,
which become gauge force fields [9]. The sum of the
number of dimensions for a particle and the number of
dimensional orbitals (DO’s) is equal to 11 (including
gravity) for all particles with dimens i o ns . Therefore ,


11 DO's
ddn
FF dn


where 11 – d + n is the number of dimensional orbitals
(DO’s) for Fd–n. Thus, 10d particles can transformed into
9d, 8d, 7d, 6d, 5d, and 4d core particles, which have 2, 3,
4, 5, 6, and 7 separable dimensional orbitals, respectively.
Baryonic matter particle 4d has gravity and six other di-
mensional orbitals as gauge force fields
The dimensional orbitals of baryonic matter provide
the base for the periodic table of elementary particles to
calculate accurately the masses of all elementary parti-

D.-Y. CHUNG, V. KRASNOHOL OVETS 30
cles, including quarks, leptons, and gauge bosons [9].
The lowest dimensional orbital is for electromagnet-
ism. Baryonic matter is the only one with the lowest di-
mensional orbital for electromagnetism. With higher di-
mensional orbitals, dark matter does not have this lowest
dimensional orbital. Without electromagnetism, dark mat-
ter cannot emit light, and is incompatible to baryonic
matter, like the incompatibility between oil and water.
The incompatibility can be explained by the repulsive
part of the gravity from an elastic interaction between the
two matters [10,11]. The incompatibility between dark
matter and baryonic matter leads to the inhomogeneity
(like emulsion), resulting in the formation of galaxies,
clusters, and superclusters [11]. Dark matter has not been
found by direct detection because of the incompatibility
that does not allow the direct contact with dark matter by
baryonic matter.
4. Extreme Force Field
Under extreme conditions such as the absolute zero tem-
perature, binary lattice space for a gauge force field un-
dergoes a phase transition to become binary partition
space for the extreme force fields [4,11].
At zero temperature, binary lattice space for a gauge
force field undergoes a quantum space phase transition to
become binary partition space. In binary partition space,
detachment space and attachment space are in two sepa-
rate continuous regions as follows.
  
 
44
,
1
particle boson fieldin binary lattice
44
1
extreme particleextreme boson field
10
10
k
mnk
k
k
mn
k







4
space
4
,,
inbinary lattice space
1
1
k
nk

22
The force field in binary lattice space is gauge boson
force field, the force field in binary partition space is
denoted as “extreme boson force field”. The detachment
space in extreme boson field is the vacuum core, while
extreme bosons attached to attachment space form the
extreme boson shell. Gauge boson force field has no
boundary, while the attachment space in the bin ary parti-
tion space acts as the boundary for extreme boson force
field. Extreme boson field is like a bubble with core
vacuum surrounded by membrane where extreme bosons
locate.
The overlapping (connection) of two extreme bosons
from two different sites results in “extreme bond”. The
product is “extreme molecule”. An example of extreme
molecule is Cooper pair, consisting of two electrons
linked by extreme bond. Another example is superfluid,
consisting of molecules linked by extreme bonds. Ex-
treme bonds can be also formed among the sites in a lat-
tice, resulting in extreme lattice. Extreme lattice is su-
perconductor. Extreme boson force is incompatible to
gauge boson force field. The incompatibility of extreme
boson force field and gauge boson force field manifests
in the Meissner effect, where superconductor (extreme
lattice) repels external magnetism. The energy (stiffness)
of extreme boson force field can be determined by the
penetration of boson force field into extreme boson force
field as expressed by the London equation for the
Meissner effect.
H
H 

 ,
where H is an external boson field and λ is the depth of
the penetration of magnetism into extreme bos on shell.
5. Summary
It is proposed that the digital space structure consists of
attachment space (denoted as 1) for rest mass and de-
tachment space (denoted as 0) for kinetic energy. At-
tachment space attaches to object permanently with zero
speed, and detachment space detaches from the object at
the speed of light. The combination of attachment space
and detachment space brings about the three structures:
binary lattice space, miscible space, and binary partition
space. Binary lattice space, (1 0)n, consists of repetitive
units of alternative attachment space and detachment
space. In miscible space, attachment space is miscible to
detachment space without separation. Binary partition
space, (1)n(0)n, consists of separated continuous phases
of attachment space and detachment space. Binary lattice
space, miscible space, and binary partition space consti-
tute quantum mechanics, special relativity, and the ex-
treme force fields, respectively. Through the detachment
space, a higher dimensional particle in attachment space is
sliced into infinitely surrounding a lower dimensional
core attachment space, resulting in a particle surrounding
by gauge field in the form of bina ry lattice space. The 10d
particle can b e sliced into 9d, 8d, 7d , 6d, 5d, and 4d p ar-
ticles equally by mass, corresponding to b aryonic particle
as 4d and dark matter as other 5 particles, so the ratio
between baryonic matter and dark matter is 1 to 5, in
agreement with the observed ratio. At extreme conditions,
such as extremely low temperature, the gauge force field
in the form of binary lattice space is transformed into the
extreme force field in the form of binary partition space to
explain extreme phenomena, such as superconductivity.
REFERENCES
[1] M. Bounias and V. Krasnoholovets, “Scanning the Struc-
ture of Ill-Known Spaces: Part 1. Founding Principles
about Mathematical Constitution of Space,” The Interna-
tional Journal of Systems and Cybernetics, Vol. 32, No.
7/8, 2003. pp. 945-975.
doi:10.1108/03684920310483126

D.-Y. CHUNG, V. KRASNOHOL OVETS 31
[2] D. Chung and V. Krasnoholovets, “The Cosmic Organ-
ism Theory,” Scientific Inquiry, Vol. 8, 2007, pp. 165-182.
arXiv: physics/0512026
[3] V. Krasnoholovets and D. Y. Chung, “The Space Struc-
ture, Force Fields and Quantum Mechanics,” Interna-
tional Journal of Anticipatory Computing Systems, Vol.
839, 2006, pp. 191-197.
http://inerton.org/Inerton_Theory_-_Papers_-_Sub-micros
copic_Mechanics_files/30_Chung&Krasn_1.pdf
[4] D. Chung and V. Krasnoholovets, “The Quantum Space
Phase Transitions for Particles and Force Fields,” Pro-
gress in Physics, Vol. 4, 2006, pp. 74-77.
http://www.ptep-online.com/index_files/2006/PP-06-14.P
DF
[5] B. M. Diaz and P. Rowlands, “A Computational Path to
the Nilpotent Dirac Equation,” American Institute of
Physics Proceedings of the International Conference of
Computing Anticipatory Systems, 2003, pp. 203-218.
arXiv:cs/0209026
[6] J. S. Bell, “On the Einstein-Podolsky-Rosen Paradox,”
Physics, Vol. 1, 1964, pp. 195-199.
[7] R. Penrose, “Wavefunction Collapse as a Real Gravita-
tional Effect,” In: A. Fokas, A. Grigoryan, T. Kibble and
B. Zegarlinski, Eds., Mathematical Physics, Imperial
College, London, 2000, pp. 266-282.
[8] N. Jarosik, et al., “Seven-Year Wilson Microwave Ani-
sotropy Probe (WMAP) Observations: Sky Maps, Sys-
tematic Errors, and Basic Results,” 2010.
http://lambda.gsfc.nasa.gov/product/map/dr4/pub_papers/
sevenyear/basic_results/wmap_7yr_basic_results.pdf
[9] D. Chung, “The Periodic System of Elementary Particles
and the Composition of Hadrons,” Speculations in Sci-
ence and Technology, Vol. 20, 1997, pp. 259-268.
http://arxiv.org/ftp/hep-th/papers/0111/0111147.pdf
[10] V. Krasnoholovets, “Dark Matter as Seen from the Physi-
cal Point of View,” Astrophysics Space Science, Vol. 335,
No. 2, 2011, pp. 619-627.
doi:10.1007/s10509-011-0774-y
[11] D. Chung, “The Unified Theory of Physics,” 2012.
arXiv:hep-th/0201115