ws0">is the total energy of M;
5) the energy subtotal for row i of M is denoted

*
0
M
n
iij
j
;
6) the energy subtotal for column j of M is denoted

*
0
M
k
j
ij
i
;
7)



imb
11 11
M
kn kn
imp ijijij
ij ij
mmm


 

 
,ee

,mm
is
the YinYang imbalance of M;
8) balance or harmony or stability of M is defined as
Harmony(M) = Balance(M) = Stability(M) = (|ε|(M)
|εimb(M)|)/|ε|(M);
9) the average energy of M is measured as h =
(ε(M)/(kn), ε+(M)/(kn)) where kn = k n is the total
number of elements in M.
Law 1. Elementary Energy Equilibrium Law. (x,y)
B
= [–, 0] [0, +] and (u,v) B
F = [–1,0]
[0,1], we have
a) [|
|(u,v) 1.0] [|
|((x,y) (u,v)) |
|(x,y) ];
b) [|
|(u,v)<1.0] [|
|((x,y) (u,v)) < |
|(x,y) ];
c) [|
|(u,v)>1.0] [|
|((x,y) (u,v)) > |
|(x,y) ].
Equilibrium/Non-Equilibrium System. A bipolar
dynamic system S is said an equilibrium system if the
system’s total energy |
|S remains in an equilibrium state
or d(|
|S)/dt = 0 without external disturbance. Otherwise
it is said a non-equilibrium system. A non-equilibrium
system is said a strengthening system if d(|
|S)/dt > 0; it
is said a weakening system if d(|
|S)/dt < 0.
Law 2. Energy Transfer Equilibrium Law. Given an
n n input bipolar matrix E = [eik] = [(ikik )], 0 < i, k
n, an n n bipolar connectivity matrix M = [mkj] =
[( kj kj
v)], 0 < k, j n, and V = E M = [Vij] = [(ij
,
ij
v
)], k, j, let |ε|(Mk*) be the k-th row energy subtotal
and let |ε|(M*j) be the j-th column energy subtotal, we
have, k, j,
a) [|ε|(Mk*) |ε|(M*j) 1.0 ] [|
|(V) |
|(E)];
b) [|ε|(Mk*) |ε|(M*j) 1.0 ] [|
|(V) < |
|(E)];
c) [|ε|(Mk*) |ε|(M*j) > 1.0 ] [|
|(V) > |
|(E)].
From the above, it is clear that without YinYang bipo-
larity, classical linear algebra cannot deal with the coex-
istence of the Yin and the Yang of nature and their causal
interactions in bipolar quantum entanglement.
Law 3. Law of Energy Symmetry. Let t = 0, 1, 2,,
Y(t+1) = Y(t) M(t), |ε|Y(t) be the total energy of an
YinYang-N-Element vector Y(t), |ε|M(t) be the total en-
ergy of the connectivity matrix M(t), |ε|Mi*(t) be the en-
ergy subtotal of row i of M(t), |ε|M*j(t) be the energy
subtotal of column j of M(t).
1) Regardless of the local YinYang balance or imbal-
ance of the elements at any time point t, the system will
remain a global energy equilibrium if, t, d(|ε|Y(t))/dt
0, or (a)i,j, [|ε|(Mi*) |ε|(M*j) 1.0] and (b) no external
disturbance to the system occurs after the initial vector
Y(0) is given.
2) Under the same conditions of (1), if, t, |ε(M*j)| >
0 and |ε+(M*j))| > 0, all bipolar elements connected by M
will eventually reach a local YinYang balance
(–|ε|Y(t)/(2N), |ε|Y(t)/(2N)) at time t.
Law 4. Law of Broken Symmetry (Growing). For
the same system with Law 3, if, i, j, |ε|(Mi*) |ε|(M*j) >
1.0, regardless of the local YinYang balance or imba-
lance of the elements at any time point t, the system en-
ergy will increase and eventually reach a bipolar infinite
W.-R. ZHANG 1265
(–,) or fission state without external disturbance or we
have,t, d(|ε|Y(t))/dt 0.
Law 5. Law of Broken Symmetry (Weakening). For
the same system as for Law 3, if, i, j, |ε|(Mi*) |ε|(M*j)
< 1.0, regardless of the local YinYang balance or imba-
lance of the elements at any time point t, the system en-
ergy will decrease and eventually reach a (0,0) or decay-
ed state without external disturbance or we have, t,
d(|ε|Y(t))/dt < 0, until |ε|Y(t) = 0.
3. Bipolar Strings and Bipolar Atom
3.1. YinYang Bi pol ar Stri n g s
Fundamentally different from the mainstream string the-
ory or “theory of everything”, BDL and BQLA provide
the logical and physical bipolar bindings for the “strings”
of reality but retain the open-world non-linear dynamic
property of nature tailored for open-ended exploratory
scientific discovery. While strings are far from observable
reality, the non-linear dynamic property of BDL and
BQLA do not compromise the law of excluded middle—a
unique basis for a scalable and observable alternative bi-
polar string theory.
Since (–1,0) (–1,0) = (–1,0)2 = (0,1) and (–1,1)
(–1,1) = (–1,1)2 = (–1,1), (–1,0)n defines an oscillatory
non-equilibrium and (–1,1)n defines a non-linear dynamic
equilibrium. Such properties provide a unifying logical
representation for particle-wave duality. For instances,
(P)(f) = (–1,0)n (3 1012) can denote that “particle P
changes polarity three trillion times per second”; (P)(f) =
(–1,1)n (3 1012) can denote that “The two poles of P in-
teract three trillion times per second.”
As strings can be one-dimensional oscillating lines or
points, a bipolar string can be defined as an elementary
bipolar variable or quantum agent e = (–e,+e) and char-
acterized as (e)(f)(m) where (e)B1 or B, f is the fre-
quency of bipolar interaction or oscillation, and m is
mass. If e is massless we have m = 0. The two poles of e
as negative and positive strings are non-exclusive, recip-
rocal, entangled, and inseparable. Thus, bipolar strings
cannot be dichotomous and bipolar string theory is a
non-linear dynamic unification of singularity, bipolarity,
and particle-wave duality.
3.2. YinYang Bipolar Atom
Figure 4 shows a YinYang-n-element bipolar quantum
cellular automaton (BQCA), where each link and each
element is characterized with a bipolar value (n,p). A
negative side n can indicate output of an element or re-
pression of a link weight; a positive side p can indicate
input of an element or activation of a link weight. A set
of dynamic equations have been derived based BQLA for
characterizing the cellular structure in Figure 4. The set
Figure 4. A YinYang-n-element cellular structure.
of equations can be simplified as Y(t+1) = Y(t) M(t),
where Y(t) is a bipolar vector at time t and M(t) a con-
nection matrix at time t. Now, our questions are:
1) How to use a YinYang-n-element cellular structure
to describe and unify matter and antimatter atoms?
2) How to use a YinYang-n-element cellular structure
to unify particle and wave?
3) How to use a YinYang-n-element cellular structure
to describe and unify quantum theory and relativity?
4) How to integrate multiple YinYang-n-element cel-
lular structures together?
5) How to use BDL, BQLA and BQCA to unify big
bang and black hole as well as space and time?
Dramatically, BQLA and BQCA can be used for rep-
resenting both matter and antimatter atoms as well as
particles and waves. Figure 5(a) shows the bipolar rep-
resentation of a hydrogen atom. Figure 5(b) is a redrawn
of Figure 4 by omitting connectivity. The positrons can
be regrouped to the nucleus of a matter atom as shown in
Figure 5(c), where the negative signs can character elec-
trons or electron cloud. Similarly, an antimatter atom is
shown in Figure 5(d). Thus, both matter and antimatter
atoms can be characterized using Equation (15) in BQLA.
It is evident from Figure 5 that YinYang bipolar atom
has the potential to bridge a gap between black hole and
big bang in a cyclic process model because it allows par-
ticles and antiparticles emitted from a black hole [2,3] to
form matter and antimatter again. While Laws 1 - 5 pro-
vide the axiomatic conditions for energy equilibrium,
growing, and degenerating, we introduce a new law of
oscillation [1] in the following:
Law 6. Law of Oscillation. Let t = 0, 1, 2, , Y(t+1)
= Y(t) M(t), |ε|Y(t) be the total energy of an YinYang-
n-element vector Y(t), |ε|M(t) be the total energy of the
connectivity matrix M(t), if, i, j, |ε|(Mi*)(tk) |ε|(M*j) (tk)
> 1.0 and |ε|(Mi*)(tk+1) |ε|(M*j) (tk+1) < 1.0, the system’s
total energy will be alternatively increasing at time k and
decreasing at time k + 1.
Evidently, any particle or wave form can be repre-
sented with Yin energy, Yang energy, or unified Yin-
Yang form. But without YinYang, the bipolar coexis-
tence and interaction of the two poles can’t be visualized.
The four cases of equilibrium, growing, degeneration and
oscillation are simulated in Figures 6-9.
W.-R. ZHANG
1266
‐
+
‐ +
‐
‐
+‐ ‐+
‐
‐
‐
‐
‐
‐
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
‐
‐
(a) (b)
‐ ‐
‐
‐
‐
‐
‐
‐
‐
‐
‐
‐
‐
‐
‐
‐
‐
‐
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
‐
‐
‐
‐
‐
‐
‐
‐
‐
‐
(c) (d)
Figure 5. (a) Bipolar representation of a hydrogen; (b) Bi-
polar representation of YinYang-n-elements; (c) Matter
atom; (d) Antimatter atom.
Figure 6. Bipolar energy rebalancing wave forms after a
disturbance to one element [8].
Figure 7. YinYang bipolar energy growing [8].
Figure 8. YinYang bipolar energy decreasing [8].
4. Bipolar Quantum Cellular Automata
YinYang bipolar atom leads to bipolar quantum cellular
automata (BQCA) for advancing research in cosmolo-
gical and molecular interactions. YinYang as the basis of
Figure 9. YinYang bipolar energy oscillation [8].
traditional Chinese medicine (TCM) has been in the di-
lemma of lacking a formal logical, mathematical, physi-
cal, and biological foundation. On the other hand, despite
one insightful surprise after another the genome has
yielded to biologists, the primary goal of the Human Ge-
nome Project—to ferret out the genetic roots of common
diseases like cancer and Alzheimer’s and then generate
treatments—has been largely elusive. Although quantum
mechanics provides a basis for chemistry and molecular
stein’s relativity theory. This situation provides an oppor-
tunity for YinYang to enter modern science and play a
unifying role. For instance, given the cellular structures
in Figure 10, we have the question: “How to model the
integration, interaction, and equilibrium conditions?”
Law 7 (Following Law 3). Law of Integrated En-
ergy Symmetry. Given Figure 10, let t = 0, 1, 2, ,
Y(t+1) = Y(t) M(t), |ε|Y( t) be the total energy of the
integrated BQCA vector Y(t), |ε|M(t) be the total energy
of the integrated connectivity matrix M(t), |ε|Mi*(t) be the
energy subtotal of row i of M(t), |ε|M*j(t) be the energy
subtotal of column j of M(t), the integrated BQCA can
satisfy the following two global conditions:
1) Regardless of the local YinYang balance/imbalance
of the subsystems at any time point t, the integrated sys-
tem will remain a global energy equilibrium if, t,
d(|ε|Y(t))/dt 0, or
(a) i,j, [|ε|(Mi*) |ε|(M*j) 1.0];
(b) no external disturbance or input/output to/from the
system after the initial vector Y(0) is given;
(c) no internal disturbance or energy creation and con-
sumption in the system after the initial vector Y(0) is
given. That is, all the k component BQCA satisfy the
condition, t, d(|ε|Yk(t))/dt 0, or, equivalently, i, j,
[|εk|(Mi*) |εk|(M*j) 1.0]. Otherwise, there will be in-
ternal disturbance.
2) Under the conditions of (1), if, t, |ε(M*j)| > 0 and
|ε+(M*j))| > 0, all components connected by M will even-
tually reach a local YinYang balance (–|ε|Y(t)/(2K),
|ε|Y(t)/(2K)) at certain time point t.
Law 8 (Following Law 4). Law of Integrated En-
ergy Broken Symmetry (Growing). For the same inte-
grated BQCA as for Law 7, if, (a) i, j, |ε|(Mi*) |ε|(M*j)
> 1.0; (b) no external disturbance after the initial vector
W.-R. ZHANG 1267
Figure 10. Integration of bipolar cellular subsystems.
Y(0) is given; (c) no internal disturbance or energy crea-
tion and consummation after the initial vector Y(0), re-
gardless of the local YinYang balance or imbalance of its
local component BQCAs at any time t, the system energy
will increase and eventually reach a bipolar infinite
(–,) or t, d(|ε|Y(t))/d t 0.
Law 9 (Following Law 5). Law of Integrated En-
ergy Broken Symmetry (Weakening). For the same
system as for Law 7, if, (a) i,j, |ε|(Mi*) |ε|(M*j) < 1.0;
(b) no external disturbance to the system after the initial
vector Y(0) is given; (c) no internal disturbance or en-
ergy creation and energy consumption after the initial
vector Y(0) is given, regardless of the local YinYang
balance/imbalance of its local component BQCAs at any
time t, the system energy will decrease and eventually
reach an eternal equilibrium (–0,+0) state or, equivalently,
t, d(|ε|Y(t))/dt < 0, until |ε|Y(t) = 0.
Law 10 (Following Laws 3-9). Necessary and Suffi-
cient Conditions for Collect ive Bipolar Adaptivity. The
two conditions of Law 3 are necessary for collective bi-
polar adaptivity of any simple or integrated BQCA into
equilibrium and symmetry; the two conditions are suffi-
cient for collective bipolar adaptivity of any simple
BQCA but not for integrated BQCAs; the two conditions
in Law 7 are both necessary and sufficient for collective
bipolar adaptivity of any simple BQCA or integrated
BQCA into equilibrium and symmetry.
5. An Eastern Road to Quantum Gravity
Since acceleration is equivalent to gravitation under gene-
ral relativity, any physical, socioeconomic, mental, and
biological acceleration, growth, degeneration or aging
are qualified to be a kind of quantum gravity. It can be
further argued that as a most fundamental scientific uni-
fication not only can quantum gravity be applied in phy-
sical science, but also in computing science, social sci-
ence, brain science, and life sciences as well. This argu-
quantum gravities: physical quantum gravity, logical
quantum gravity, mental quantum gravity, biological
quantum gravity, and social quantum gravity [8]. In the
Q5 paradigm, the theory of physical quantum gravity is
concerned with quantum physics; logical quantum gra-
vity is focused on quantum computing; mental quantum
gravity is focused on the interplay of quantum mechanics
and brain dynamics; biological quantum gravity is focus-
ed on life sciences; social quantum gravity spans social
sciences.
The Q5 paradigm may sound like a mission impossible.
It actually follows a single undisputable observation and
a single condition: 1) bipolar equilibrium or non-equili-
brium is a generic form of any multidimensional equili-
brium from which nothing can escape; 2) bipolar quan-
tum entanglement is logically definable with BUMP that
unifies truth, being and dynamic equilibrium with logi-
cally definable causality.
Roger Penrose described two mysteries of quantum
entanglement [14, p. 591]. The first mystery is the phe-
nomenon itself; the second one is: “Why do these ubi-
quitous effects of entanglement not confront us at every
turn?” Penrose remarked: “I do not believe that this sec-
ond mystery has received nearly the attention that it de-
serves.” It is contended that YinYang bipolar quantum
entanglement provides a resolution to the first mystery
and the Q5 paradigm provides a resolution to the second.
Since the Yin and the Yang are two reciprocal oppo-
site poles or energies that are completely background in-
dependent, YinYang bipolar geometry is fundamentally
different from Euclidian, Hilbert, and spacetime geome-
tries. With the background independent property, the new
geometry makes quadrants irrelevant because bipolar iden-
tity, interaction, fusion, separation, and equilibrium can
be accounted for in it even without quadrants (Figure
11).
Defined in YinYang bipolar geometry, BDL and
BUMP make quantum causality logically definable as
equilibrium-based quantum entanglement. It simply states:
For all bipolar equilibrium functions
,
, ψ, and
, IF
(
) & (ψ
), THEN the bipolar interaction (
ψ)
implies that of (
). With the emergence of space and
time, BUMP leads to a completely background inde-
pendent theory of YinYang bipolar relativity defined by
Equation (16) [8]. a,b,c,d,













x1 y3
x2 y4
12
34
,,&
,,
,,
,,
xx
yy
at pct p
bt pdt p
at pbtp
ct pdt p








(16)
In Equation (16), a(t1,p1), b(t1,p2), c(t2,p3), d(t2,p4) are
any bipolar agents where a(t,p) stands for “agent a at
time t and space p” (tx, ty, px and py can be the same or
different points in time and space). An agent without
time and space is assumed at any time t and space p. An
agent at time t and space p is therefore more specific.
The symmetrical property of YinYang bipolar geome-
W.-R. ZHANG
JMP
1268
(a) (b) (c)
Figure 11. Background-Independent YinYang bipolar geometry: (a) Magnitudes of Yin and Yang; (b) Growing curve; (c)
try enables information to be passed through large or
small scale quantum entanglement with or without pass-
ing observable energy or mass. When photon or electron
is passed the speed is limited by the speed of light that
has been proven in physics. Physicists have so far failed
to experimentally verify the existence of graviton and the
speed of gravity. If all action-reaction forces are funda-
mentally equilibrium-based and bipolar quantum entan-
gled in nature, gravity would be logically unified with
quantum mechanics in the form of Equation (16) [8].


 


12
12
,0.0499,
, 0,00.0499,0,0
fStp fEtp
fStpfEt p



For instance, based on general relativity, gravity “tra-
vels” at the speed of light and the effect of a disturbance
to the Sun (S) could take 499 seconds to reach the Earth
(E). Let f(S) = f(E) = (–f,f)(S) = (–f,f)(E) be the gravita-
tional (reaction, action) forces between S and E; let time
t be in second; let p1 and p2 be points for S and E, respec-
tively; let (0,0) (S) be the hypothetical Sun’s vanishment
or eternal equilibrium; we have






12
2
, 499,
99,0,0
fStp fEtp
p






1
,0
,04fStp fEt

(17a)
If f() is normalized to a bipolar predicate, can be re-
placed with , and the binding of &, &, , , , or
to in Equation (17a) would lead to the vanishment of
the Sun and then the disappearing of the Earth from its
orbit after 499 seconds. Thus, bipolar quantum entan-
glement and general relativity are logically unified under
equilibrium-based YinYang bipolar relativity [8]. Here
bipolar relativity can host space and time emergence fol-
lowing agents’ arrivals.
Equation (17a) assumes that the speed of gravity
equals the speed of light based on general relativity. This
assumption is actually questionable. If we assume gravi-
tation is a kind of large scale quantum entanglement of
action and reaction forces, gravity could have a minimum
lower bound of 10,000 times the speed of light [15] and
would travel from the sun to the Earth in less than 0.0499
second and we would have Equation (17b).

◆◆
(17b)
A comparison of Equations (17b) with (17a) reveals an
equilibrium-based logical “bridge” from relativity to
quantum mechanics—a bridge toward quantum gravity.
Why cannot other logical and statistical systems be used
for the above unification? The answer is that without bi-
polarity a truth value in {0,1} or a probability p [0,1] is
incapable of carrying any shred of direct physical syntax
or semantics such as equilibrium (–1,+1), non-equili-
brium (–1,0) or (0,+1), quasi-equilibrium (–0.9, +0.9),
eternal equilibrium (0,0) and, therefore, unable to repre-
sent non-linear bipolar dynamic interactions such as bi-
polar fusion, fission, oscillation, quantum entanglement,
and annihilation.
Bipolar relativity can also support causal reasoning
with time reversal because the premise of Equation (16)
could be a future event and the consequent a past one.
Although time travel in physics and cosmology is highly
speculative in nature, time reversal analysis has been pro-
ven very useful in many other scientific, technological,
and engineering research and development.
The equilibrium-based interpretation leads to a number
unifying features for particle-wave, matter-antimatter,
strings and atom as well as black hole and big bang. Evi-
dently, Law 6 provides the basic condition for both
waves and particles; YinYang bipolar atom provides the
unification for matter and antimatter. Since Figures 5(a)-
(d) are redrawing of a bipolar representation like Figure
8 (different only in the number of elements), BQLA,
BQCA, and Laws 1 - 6 all apply to the unipolar repre-
sentations of Figures 5(c) and (d). Thus, BQCA presents
a unifying mathematical model for matter and antimatter
atoms as well as particles and waves. In turn, it makes
the unification of black hole and big bang possible be-
cause the theory allows particles and antiparticles emitted
from a black hole [2,3] to form matter and antimatter
W.-R. ZHANG 1269
again. Thus, it bridges a major gap in quantum cosmo-
logy and set the stage for another cycle of a cyclic pro-
cess model of the universe. The unifying features are
made possible by the complete background independent
property of YinYang bipolar geometry (Figure 11).
YinYang bipolar elements and sets [8] provide an al-
ternative interpretation for strings as well. Different from
mainstream string theory, bipolar strings are scalable and
can be the makings of bipolar atoms (Figure 5). Thus,
the alternative interpretatio YinYang Bipolar Atom—An Eastern Road toward Quantum Gravity