The Universe as a Quantum Cellular Automaton: A Complete Unified Physical Theory\\ \large From Unified Time Scale to Category Embedding of All Physical Theories

The Uni e se as a Quan um Cellula Au oma on: A
Comple e Unied Physical Theo y
F om Unied Time Scale o Ca ego y Embedding o All Physical Theo ies
Haobo Ma
1
Wenlin Zhang
2
1
Independen Resea che
2
Na ional Uni e si y o Singapo e
No embe 19, 2025
Abs ac
Based on he p emise ha "The Uni e se = Quan um Cellula Au oma on"
(QCA), his pape cons uc s a amewo k ha igo ously **unies all physical
heo ies**: including ela i is ic quan um eld heo y (and he S anda d Model),
g a i y and space ime geome y, condensed ma e and phase s uc u es, s a is ical
physics and he modynamics, and quan um in o ma ion and measu emen heo y.
All a e cha ac e ized as die en eme gen le els and ca ego ical images o he same
QCA objec .
The co e ideas a e:
1. Adding Unied Time Scale da a o he disc e e- ime disc e e-space QCA
Uni e se
UQCA = (Λ,Hcell,Aloc, U, ω0,Gloc)
(1)
ia he o mula
κ(ω) = φ′(ω)
π=ρ el(ω) = 1
2π Q(ω),
(2)
whe e
S(ω)
is he Floque sca e ing ma ix,
Q(ω) = −iS(ω)†∂ωS(ω)
,
ρ el(ω)
is he
ela i e densi y o s a es, and
φ(ω) = 1
2a g de S(ω)
. This is he QCA e sion o
he Unied Time Scale Iden i y.
2. In he long-wa eleng h low-ene gy limi , cons uc ing eec i e Lo en zian
geome y
(M, g)
om QCA dispe sion ela ions
Ea(k)
and g oup eloci ies
a(k)
,
and de i ing he Eins ein equa ion
Gµν + Λgµν = 8πGe Tµν
(3)
on local causal diamonds ia he disc e e in o ma ion geome ic a ia ional p inciple
o disc e e gene alized en opy
Sgen =Ae
4Ge ℏ+Sou .
(4)
3. Cons uc ing
SU(3) ×SU(2) ×U(1)
gauge s uc u e and i s low-ene gy eec-
i e ac ion on he same QCA ia local gauge edundancies and edge-cell deg ees o
eedom; p o ing ha unde app op ia e in eg abili y condi ions, all ** ela i is ic
eld heo ies** sa is ying locali y, uni a i y, and ni e in o ma ion densi y can be
iewed as eme gen desc ip ions o some con inuum limi o sub-QCA o
UQCA
.
1
4. Cha ac e izing gapped/ opological phases, quan um phase ansi ions, and
c i ical phenomena in condensed ma e as die en phases and RG ajec o ies o
QCA local upda e
U
; cha ac e izing he modynamics and s a is ical mechanics as
ypicali y and la ge de ia ion heo y o mac oscopic coa se-g ained s a es o he
QCA; cha ac e izing quan um measu emen and quan um in o ma ion heo y as
channel and e o -co ec ion s uc u es be ween local subsys ems o he QCA.
5. A he ca ego ical le el, in oducing he ca ego y o physical heo ies
Phys
,
whose objec s a e physical heo ies sa is ying s anda d axioms (QFT, GR, SM,
CM, QIT, e c.) and mo phisms a e maps be ween heo ies p ese ing expe imen al
p edic ions; ele a ing he Uni e se QCA
UQCA
o a "candida e e minal objec ",
cons uc ing unc o s
FQFT,FGR,FSM,FCM,FS a ,FQIT :QCAuni →Phys
(5)
and p o ing: any heo y sa is ying a se o "Physical Realizabili y Axioms" is he
image o
UQCA
unde some limi o sub-s uc u e. In his sense, **all physics is
unied by he same QCA Uni e se**.
The main ma hema ical esul s a e summa ized as ollows:
* **Theo em A (Unied Time Scale):** Unde ace-class Floque sca e ing,
all ime eadings in he QCA Uni e seincluding pa icle igh ime, a omic clock
eadings, he mal ime, and modula imecan be aligned on he unied ime scale
densi y
κ(ω)
.
* **Theo em B (Full Embedding o Field Theo y):** Any ela i is ic quan um
eld heo y sa is ying locali y, causali y, and ni e in o ma ion densi y axioms (in-
cluding he S anda d Model) can be embedded as a con inuum limi heo y o
UQCA
.
* **Theo em C (Eme gence o Geome yG a i y):** Applying disc e e in o -
ma ion geome ic a ia ional p inciple on disc e e causal diamonds o QCA, he
con inuum limi necessa ily sa ises he Eins ein equa ion and gi es a ime a ow.
* **Theo em D (Unied Ca ego y o All Physics):** The e exis s a e minal
objec
UQCA
in ca ego y
QCAuni
, such ha o any physical heo y objec
P∈
Phys
sa is ying physical ealizabili y axioms, he e exis unc o
FP
and mo phism
ηP:FP(UQCA)→P
, making expe imen al p edic ions equi alen a he obse able
le el.
1 In oduc ion
1.1 F om "Unied Time Scale" o "Unied All Physics"
P e ious wo k has shown ha h ough sca e ing phase, spec al shi densi y, and
Wigne Smi h g oup delay, a Mo he Fo mula o mally uni ying all ime eadings can
be cons uc ed:
κ(ω) = φ′(ω)
π=ρ el(ω) = 1
2π Q(ω),
(6)
playing he ole o a "Mo he Time" in sca e ing heo y, algeb aic quan um eld heo y,
modula ow, and gene alized en opy geome y.
Howe e , ha ing a unied "Time Scale" does no genuinely **uni y all physical heo-
ies**: * How do he gauge s uc u e, a o mixing, and symme y b eaking pa e ns o
he S anda d Model embed in o his unied scale? * A e condensed ma e phases, opo-
logical o de s, and quan um phase ansi ions also die en phases on he same s uc u e?
* Can he ime a ow and non-equilib ium p ocesses o he modynamics and s a is ical
2
mechanics be desc ibed by he same scale and same QCA? * Can measu emen , channels,
and e o co ec ion s uc u es in quan um in o ma ion eme ge di ec ly om he QCA
Uni e se?
To answe hese ques ions, a **mo e p imi i e on ological objec ** is needed, o which
all hese heo ies become images. QCA p o ides a na u al candida e: * Disc e e ime
+ Disc e e space + Local uni a y upda e + Fini e in o ma ion densi y; * Sucien o
p oduce ela i is ic eld heo y and geome y in he con inuum limi ; * Sui able o
cons uc ing unied ime scale using sca e ing and spec al shi .
1.2 Objec i es and S a egy
The goals o his pape a e:
1. To p o ide an axioma ic "Uni e se QCA" objec
UQCA
, equipped wi h unied ime
scale and local gauge edundancies; 2. To p o e: * All ela i is ic quan um eld heo-
ies sa is ying s anda d axioms (including he S anda d Model) can eme ge as con inuum
limi s o sub-s uc u es o
UQCA
; * Va ious phases, c i ical phenomena, and opologi-
cal o de s in condensed ma e physics a e local phase s uc u es o
UQCA
on die en
RG ajec o ies; * The modynamics and s a is ical mechanics o igina e om ypicali y
s uc u es on he s a e space o
UQCA
, wi h he ime a ow gi en by unied scale and gen-
e alized en opy pa ial o de ; * Quan um in o ma ion heo y (channels, measu emen s,
e o co ec ion) is a ca ego ized desc ip ion o in e ac ions be ween local subsys ems
o
UQCA
; * G a i y and geome y eme ge om QCA ia disc e e in o ma ion geome ic
a ia ional p inciple, sha ing he unied ime scale wi h all abo e s uc u es. 3. A he
ca ego ical le el, o o ganize "all physical heo ies" in o a ca ego y
Phys
, and p o e ha
he Uni e se QCA is a "Unied Sou ce" wi hin i , making all physical heo ies i s images.
1.3 O e iew o Main Resul s
In he ollowing sec ions, we p esen ou ypes o esul s: * Type 1: Floque Bi manK enWigne Smi h
s uc u e o QCA sca e ing heo y, gi ing he QCA e sion o he Unied Scale Iden i y
(Theo em A). * Type 2: Full embedding om QCA o ela i is ic eld heo y (including
S anda d Model), p o ing "any physically ealizable eld heo y" can be iewed as a
limi o QCA (Theo em B). * Type 3: Cons uc ing disc e e gene alized en opy and in-
o ma ion geome ic a ia ional p inciple on QCA, de i ing Eins ein equa ion (Theo em
C). * Type 4: In ca ego y
Phys
, posi ioning
UQCA
as a unied sou ce, gi ing unc o ial
embeddings o all physical heo ies (Theo em D).
2 Axioma ic Deni ion and S uc u al Ex ension o Uni-
e se QCA
2.1 Basic QCA Axioms
We adop s anda d QCA axioms and add unied ime scale s uc u e.
Axiom 2.1
(La ice and Local Hilbe Space)
.
* Space is a coun able connec ed g aph
Λ
wi h ni e deg ee condi ion and ansla ion g oup
Ta, a ∈Zd
. * Each si e
x∈Λ
is
3
assigned a ni e-dimensional Hilbe space
Hx≃Cdcell
. The o al space is
H=O
x∈Λ
Hx.
(7)
* Fo ni e egion
R⋐Λ
, local algeb a is
AR:= B(HR)⊗1Rc
, global quasi-local algeb a
is
Aloc =SR⋐ΛAR
.
Axiom 2.2
(Single S ep E olu ion and Fini e P opaga ion Radius)
.
* Exis ence o uni-
a y
U:H → H
, dening au omo phism
α(A) := U†AU
. * Exis ence o
Rc<∞
such
ha o any si e
x
, i
A∈ A{x}
, hen
α(A)∈ ABRc(x)
, whe e
BRc(x)
is he ball o g aph
dis ance a mos
Rc
.
Axiom 2.3
(T ansla ion Co a iance and Conse ed Quan i ies)
.
* Fo each
a∈Zd
, he e
exis s uni a y
Va
implemen ing ansla ion such ha
VaUV †
a=U, VaARV†
a=ATaR.
(8)
* I he e exis s a one-pa ame e uni a y g oup
W(θ)
wi h gene a o
Q
such ha
W(θ)UW(θ)†=U,
(9)
hen
Q
is called a conse ed quan i y ( o al pa icle numbe , o al cha ge, e c.).
2.2 Local Gauge Redundancy and S anda d Model S uc u e
To include he S anda d Model,
SU(3) ×SU(2) ×U(1)
gauge s uc u e is needed on he
QCA.
Axiom 2.4
(Local Gauge Da a)
.
* Assign gauge Hilbe space
Hgauge
xy
o each di ec ed
edge
(x, y)
. To al space ex ends o
H → H o =O
x∈Λ
Hxb
⊗O
(x,y)∈Λ1
Hgauge
xy .
(10)
* Implemen
SU(3)×SU(2)×U(1)
link ope a o s
Uxy
and conjuga e elec ic elds
Exy
on
Hgauge
xy
, sa is ying s anda d compac g oup gauge commu a ion ela ions. * Dene local
gauge ans o ma ion
Gx
a e ex
x
, ac ing on ma e and gauge deg ees o eedom,
sa is ying
GxUG†
x=U, Gxω0G†
x=ω0.
(11)
Deni ion 2.5
(Gauge QCA Uni e se)
.
The Uni e se as QCA ca ies da a
UQCA = (Λ,Hcell,Hgauge,Aloc, U, ω0,Gloc),
(12)
whe e
Gloc
is he g oup gene a ing all local gauge ans o ma ions.
4
2.3 Unied Time Scale Da a
Axiom 2.6
(Floque Sca e ing and Scale Densi y)
.
* Exis ence o " ee" single s ep
e olu ion
U0
and wa e ope a o s
Ω±= s!-!limn→±∞ U∓nUn
0,
(13)
Sca e ing ope a o is
S= (Ω+)†Ω−
. * Unde quasi-ene gy decomposi ion,
S=Zπ
−π
⊕S(ω) dω,
(14)
whe e
S(ω)
is he uni a y sca e ing ma ix on each quasi-ene gy laye . * Unde app o-
p ia e ace-class condi ions, he e exis s spec al shi unc ion
ξ(ω)
such ha
de S(ω) = exp−2πiξ(ω).
(15)
Deni ion 2.7
(Unied Time Scale Densi y and Mo he Scale)
.
* Dene semi-phase
φ(ω) = 1
2a g de S(ω)
. * Dene Wigne Smi h g oup delay ope a o
Q(ω) = −iS(ω)†∂ωS(ω),
(16)
i s ace gi es o al g oup delay. * Dene ela i e densi y o s a es
ρ el(ω) := −ξ′(ω)
.
Theo em 2.8
(Unied Scale Iden i y, QCA Ve sion)
.
Unde he abo e condi ions, almos
e e ywhe e
κ(ω) := φ′(ω)
π=ρ el(ω) = 1
2π Q(ω).
(17)
κ(ω)
is called he Unied Time Scale Densi y o he QCA Uni e se. All physical ime
eadings, modula ime, and he mal ime can be aligned on
κ
.
3 QCA Full Embedding o Field Theo y and S anda d
Model
This sec ion cons uc s he "Full Embedding" esul om
UQCA
o ela i is ic quan um
eld heo y, demons a ing ha **all physically ealizable eld heo ies** a e limi he-
o ies o he Uni e se QCA.
3.1 Axioma iza ion o Realizable Field Theo y
Deni ion 3.1
(Physically Realizable Field Theo y)
.
A ela i is ic quan um eld heo y
P
is called physically ealizable i i sa ises: 1. Locali y: Field ope a o s suppo ed on
open se s sa is y mic o-causali y o local commu a ion/an i-commu a ion ela ions; 2.
Causali y: E olu ion espec s ligh cone s uc u e o app op ia e egions; 3. Bounded
In o ma ion Densi y: on Neumann algeb a o e e y ni e egion can be app oxima ed by
ni e unca ion; 4. Ene gy Lowe Bound and S abili y: Exis ence o acuum s a e and
ene gy lowe bound; 5. Disc e iza ion-Con inuum Limi P ocedu e: Exis ence o la ice
disc e iza ion such ha he con inuum limi eco e s he heo y.
S anda d Model local/la ice cons uc ions, condensed ma e la ice models, la ice
gauge heo ies, eec i e eld heo ies all in o his class.
5

3.2 QCA o La ice Field Theo y
Gi en a physically ealizable eld heo y
P
, ake i s la ice disc e iza ion
Pla
: * Space
disc e ized o some la ice
ΛP
; * Ma e and gauge deg ees o eedom placed on si es and
edges, consis en wi h s anda d la ice QFT cons uc ion; * Con inuous ime
disc e ized
o s ep
∆
, ime e olu ion implemen ed by some uni a y ope a o
UP
.
P oposi ion 3.2
(La ice QFT = Special QCA)
.
I
Pla
sa ises locali y and ni e p op-
aga ion speed (LiebRobinson ype) condi ions, he e exis s a QCA objec
AP= (ΛP,H(P)
cell ,A(P)
loc , UP, ω(P)
0),
(18)
such ha all obse ables and co ela ion unc ions o
Pla
a e equi alen o p edic ions on
some local algeb a sub amily o
AP
.
P oo idea: T o e decomposi ion o Hamil onian in o local uni a y blocks o ming
single s ep uni a y upda e
UP
, p opaga ion adius gi en by LiebRobinson eloci y.
3.3 Full Co e age by Uni e se QCA
Axiom 3.3
(Simulabili y o Uni e se QCA)
.
The local Hilbe dimension
dcell
o Uni e se
QCA
UQCA
is sucien ly la ge, i s local uni a y upda e amily con ains a ga e se capable
o uni e sally gene a ing any a ge local uni a y
UP
;
Λ
is sucien ly ich o embed any
ni e deg ee g aph
ΛP
as a subg aph.
Theo em 3.4
(Field Theo y Full Embedding)
.
Fo any physically ealizable eld heo y
P
, he e exis s a local encoding (injec i e local isomo phism) o Uni e se QCA
ιP:A(P)
loc ,→ Aloc,
(19)
and an app oxima e implemen a ion o single s ep e olu ion
U(P)
, such ha unde app o-
p ia e con inuum limi
ε→0
, he dynamics o
UQCA
on he subsys em embedded by
ιP
is
equi alen o he la ice heo y
Pla
o
P
, he eby ep oducing
P
in he con inuum limi .
Specically, aking
P=
S anda d Model
+
eec i e g a i y e ms, we ob ain:
Co olla y 3.5
(QCA Implemen a ion o S anda d Model)
.
The e exis sub-s uc u e
and local encoding o Uni e se QCA ep oducing he eld con en , coupling s uc u e,
and b eaking pa e ns o he
SU(3)×SU(2)×U(1)
S anda d Model in he low-ene gy and
long-wa eleng h limi .
3.4 Unied Embedding o Condensed Ma e Phases and Topo-
logical O de s
On he same QCA, by choosing die en local eec i e upda es
Ue
, a ious condensed
ma e phases can be gene a ed: * Gapped phases: Pe u ba ions o
Ue
do no change
he spec al gap, gi ing opologically s able phases; * C i ical phases: Gap closes, con-
inuum limi is Con o mal Field Theo y; * Topological o de phases: G ound s a e de-
gene acy and opological da a de e mined by loop ope a o s and non-local en anglemen
on QCA.
P oposi ion 3.6
(All Gapped Local Phases a e QCA Phases)
.
Unde ni e-dimensional
local deg ees o eedom and local upda e condi ions, any gapped local Hamil onian sys em
can be iewed ia quasi-adiaba ic con inua ion as uni a y pe iodic e olu ion o some QCA
upda e
Ue
; hus all gapped phases can be iewed as one o he "phases" o
UQCA
.
6
4 Eme gence o G a i y and Space ime Geome y in
QCA
4.1 Eec i e Me ic and Causal Mani old
Th ough momen um-quasi-ene gy decomposi ion o QCA
U=Z⊕
BZ
U(k) ddk, U(k)ψa(k)=e−iEa(k)ψa(k),
(20)
dening physical momen um
p=ε−1k
and ime s ep
∆ =ε
, in he limi
ε→0
we ob ain
eec i e Hamil onian
He
wi h dispe sion ela ion
Ea(p)
app oxima ing
Ea(p)≈pm2
ac4+c2gijpipj,
(21)
inducing eec i e me ic
gµν
. Disc e e causali y (ni e p opaga ion adius) ensu es QCA's
disc e e causal cone con e ges o he ligh cone s uc u e o
gµν
in he limi , yielding a
globally hype bolic Lo en zian mani old
(M, g)
and i s causal pa ial o de
J±
.
4.2 Disc e e Gene alized En opy and IGVP
Selec disc e e causal diamond
Dn, (x)
in QCA, wi h wais
Rn(x)
and ex e io en opy
Sou
, dening disc e e gene alized en opy
Sgen(n, x; ) = Ae (n, x; )
4Ge ℏ+Sou (n, x; ).
(22)
Axiom 4.1
(Disc e e IGVP)
.
Fo each sucien ly small disc e e causal diamond, unde
xed 1. Wais cell coun (p incipal a ea); 2. Local ene gy-ux cons ain consis en
wi h unied ime scale
κ(ω)
; Requi e * Fi s a ia ion:
Sgen
is ex emal wi h espec o
local s a e a ia ion; * Second a ia ion: Rela i e en opy ype quan i y sa ises disc e e
QNEC/QFC.
4.3 QCA De i a ion o Eins ein Equa ion
Th ough disc e e-con inuum expansion: * Va ia ion o wais a ea
Ae
ela es o a ia ion
o local scala cu a u e
R
; * Va ia ion o ex e io en opy ela es o a ia ion o s ess-
ene gy enso
Tkk
ia En anglemen Fi s Law; * QNEC/QFC ensu es ene gy condi ions
and Bianchi iden i ies.
Theo em 4.2
(QCAEins ein Theo em)
.
Unde Disc e e IGVP and Unied Time Scale
Axioms, he con inuum limi o QCA Uni e se necessa ily sa ises
Gµν + Λgµν = 8πGe Tµν,
(23)
whe e
Gµν
and
Tµν
a e induced by QCA dispe sion-geome y and ene gy-ux da a espec-
i ely.
This indica es: **G a i a ional eld equa ions a e no ex a assump ions, bu consis-
ency condi ions o QCA Uni e se and gene alized en opy s uc u e.**
7
5 QCA Unica ion o S a is ical Physics, The mody-
namics, and Time A ow
5.1 Typicali y and The mal Equilib ium in S a e Space
In he as Hilbe space o QCA, o ypical s a es o mac oscopic coa se-g ained sub-
spaces, expec a ion alues o local obse ables end o some " ypical equilib ium s a e",
gi ing QCA e sions o mic ocanonical, canonical, and g and canonical ensembles.
P oposi ion 5.1
(Typicali y and The mal Time)
.
Unde unied ime scale
κ(ω)
, he
local educed s a e o a ypical s a e wi hin a quasi-ene gy window is indis inguishable
om a Gibbs s a e
ρβ∝exp(−βHe )
(24)
by local measu emen s, whe e
β
and modula / he mal ime a e de e mined by windowed
Taube ian ela ions o
κ(ω)
.
5.2 Non-Equilib ium P ocesses and En opy P oduc ion
Non-equilib ium p ocesses in QCA co espond o misma ch be ween local ene gy spec a
and
κ(ω)
dis ibu ion in die en egions. Th ough mul i-s ep ac ion o QCA upda e
U
, spec a and scales g adually align; mac oscopically mani es ing as en opy p oduc ion
and hea ow.
P oposi ion 5.2
(Time A ow = Gene alized En opy Pa ial O de )
.
On mac oscopic
scales, along he inc easing di ec ion o unied ime scale
τ
, he gene alized en opy
Sgen
o he as majo i y o ini ial s a es is mono onically non-dec easing; he ime a ow can
be dened as he di ec ion o gene alized en opy pa ial o de .
5.3 Quan um Measu emen and Quan um In o ma ion S uc u e
Wi hin he same QCA amewo k: * Local measu emen p ocess can be iewed as cou-
pled e olu ion
Umeas
o a subsys em and a "measu ing de ice" subsys em, ollowed by
condi ioning on de ice deg ees o eedom; * Quan um channels can be iewed as com-
ple ely posi i e ace-p ese ing maps induced be ween local algeb as, hei S inesp ing
implemen a ion gi en by local uni a y e olu ion o QCA; * Quan um e o -co ec ing
codes can be iewed as subspaces in QCA global Hilbe space s able agains local noise.
P oposi ion 5.3
(All Physical Measu emen s a e QCA P ocesses)
.
Any physically ealiz-
able measu emen p ocess can be embedded as a combina ion o local ni e- ime e olu ion
and condi ioning in
UQCA
; hus quan um in o ma ion heo y is also an eme gen laye o
he Uni e se QCA.
6 Ca ego y Pe spec i e: All Physics as Image o Uni-
e se QCA
6.1 Ca ego y o Physical Theo ies
Phys
Deni ion 6.1
(Physical Theo y Objec and Mo phism)
.
* Objec : A physical heo y
P
con ains * A se o obse able algeb as and s a e space; * A se o dynamical laws (e olu-
8
ion, in e ac ion); * A se o expe imen al p edic ion maps sending heo e ical s uc u es
o obse able p obabili y dis ibu ions. * Mo phism:
:P→Q
is a map p ese ing
expe imen al p edic ions, i.e., o all ealizable expe imen al schemes, p edic ions in
P
and
Q
a e iden ical o iden ical in some iden iable equi alence class.
QFT, GR, SM, CM, S a , QIT e c. gi e objec s; Reno maliza ion G oup ows, eec-
i e eld heo y maps, holog aphic duali ies gi e mo phisms.
6.2 Ca ego y o QCA and Uni e se QCA
Deni ion 6.2
(Ca ego y
QCAuni
)
.
* Objec : Candida e Uni e se QCA
U
sa is ying
a o emen ioned axioms, equipped wi h unied ime scale and local gauge s uc u e. *
Mo phism: Realizable encoding map
Φ : U→U′
p ese ing local s uc u e, e olu ion,
and unied ime scale.
Axiom 6.3
(Uni e sali y o Uni e se QCA)
.
The Uni e se QCA
UQCA
is he "Maxi-
mal Realizable Objec " in
QCAuni
: any o he QCA objec can be i s local encoding,
educ ion, o limi .
6.3 Func o s om QCA o All Physical Theo ies
Fo each class o physical heo y
P∈Phys
, cons uc unc o
FP:QCAuni →Phys,
(25)
ac ing as: * On Objec s: Gi en
U
, ake i s co esponding limi /subsys em/coa se-g aining
o ob ain heo y
FP(U)
; * On Mo phisms: Encoding maps be ween QCAs induce eec i e
maps be ween heo ies.
Theo em 6.4
(Unied Ca ego y Theo em o All Physics)
.
I physical heo y
P
is phys-
ically ealizable, he e exis unc o
FP
and mo phism
ηP:FP(UQCA)→P,
(26)
such ha
ηP
is an equi alence in he sense o expe imen al p edic ions; i.e.,
P
is an
"image" o
UQCA
.
In o he wo ds: **All physical heo ies can be iewed as p ojec ions o he Uni e se
QCA unde die en obse a ional scales and pe spec i es.**
7 Conclusion and Physical P edic ions (S uc u al Sum-
ma y)
This pape cha ac e izes he Uni e se as a Quan um Cellula Au oma on
UQCA
wi h
unied ime scale and local gauge edundancy, and on his basis comple es he unica ion
o "All Physics": * Rela i is ic Quan um Field Theo y (including S anda d Model):
Con inuum limi and local embedding o
UQCA
; * G a i y and Geome y: Ine i able
esul o Gene alized En opy-In o ma ion Geome ic Va ia ional P inciple on disc e e
causal diamonds o
UQCA
; * Condensed Ma e and Phase S uc u e: Die en phases
and RG ajec o ies o local upda es o
UQCA
; * S a is ical Physics and The modynamics:
9