The Holog aphic P inciple – Space ime as an In o ma ional P ojec ion
Alexande G ünbe g*
Independen Resea che , Ge many
Alumni, Uni e si y o Heidelbe g
ORCID: 0009-0009-7034-2202
*Co espondence: [email p o ec ed]
Abs ac
This pape o mula es a heo e ical amewo k in e p e ing space ime as an in o ma ional
p ojec ion. Building on holog aphic and he modynamic p inciples, i p oposes ha space ime
geome y ep esen s he mac oscopic equilib ium con igu a ion o an unde lying
in o ma ional ne wo k. In o ma ion is ea ed as a ounda ional physical quan i y om which
geome y and dynamics eme ge.
The model in eg a es insigh s om he modynamic g a i y, in o ma ion geome y, and
holog aphic duali y o es ablish a uni ied concep ual basis o eme gen space ime. The
Eins ein enso is in e p e ed as a measu e o in o ma ional imbalance, while cu a u e
quan i ies de ia ions om in o ma ional equilib ium. By in oducing a mapping be ween
in o ma ional and geome ic cu a u e on an in o ma ional mani old, he amewo k connec s
en opic, quan um, and geome ic desc ip ions unde a common in o ma ional on ology.
This in e p e a ion main ains consis ency wi h es ablished semiclassical esul s while
p o iding a cohe en on ological ounda ion o eme gen -space ime models. The pape o e s
a concep ual syn hesis cla i ying he in o ma ional basis o g a i a ional dynamics.
Keywo ds
Holog aphic p inciple; In o ma ional on ology; Eme gen space ime; In o ma ion geome y;
En opic g a i y; Quan um he modynamics.
1 In oduc ion
The p esen wo k ex ends p io he modynamic and en opic app oaches o g a i y [6–8] by
in oducing a geome ically s uc u ed in o ma ional on ology o space ime. Unlike p e ious
in e p e a ions ha ea in o ma ion as a me apho o en opy p oduc ion o ene gy lux, he
amewo k de ines i as a physically ins an ia ed pa e n o co ela ions among quan um deg ees
o eedom, embedded wi hin an in o ma ion-geome ic mani old ha ende s hese ela ions
explici .
Concep ually, he amewo k builds upon es ablished co espondences be ween
he modynamic, geome ic, and in o ma ional o malisms, bu aims o o malize he link
be ween in o ma ional lux—quan i ied as en opy low—and geome ic cu a u e using an
in o ma ional me ic on a s a is ical mani old de i ed om Fishe in o ma ion and Kullback–
Leible di e gence. This p o ides a uni ied in e p e i e s uc u e ha si ua es classical
cu a u e, ene gy, and en anglemen wi hin a common in o ma ional domain.
This app oach is nei he pu ely philosophical no me ely analogical; i p o ides ope a ional
de ini ions o in o ma ional quan i ies ha may, in p inciple, connec measu able en opy
g adien s and in o ma ion lows in quan um sys ems o analog-g a i y expe imen s.
The holog aphic p inciple, o iginally p oposed by ’ Hoo and e ined by Susskind and
Maldacena, asse s ha he in o ma ion con en o a spa ial egion – i s deg ees o eedom o
en opy con en – is encoded on i s bounda y [1–3]. I is oo ed in black-hole he modynamics,
whe e en opy scales wi h ho izon a ea a he han olume [4, 5], and was gi en conc e e o m
h ough he AdS/CFT co espondence. Ye , despi e i s echnical successes, he on ological
s a us o holog aphy – whe he i desc ibes a physical mechanism o me ely a dual desc ip ion
– emains unse led: i geome y and dynamics a e eme gen , om wha unde lying
in o ma ional s uc u e do hey a ise, and unde which cons ain s?
Recen de elopmen s in space ime–in o ma ion duali y, including wo k on la -space
holog aphy and cosmological ex ensions [17], ha e ex ended holog aphic easoning beyond
AdS con ex s, suppo ing he iew ha space ime s uc u e may e lec an unde lying
in o ma ion- heo e ic o ganiza ion.
Recen de elopmen s in ensi y he in o ma ion-cen ic iew – quan um en anglemen appea s
o build space ime connec i i y (ER = EPR, en anglemen wedge, RT/HRT) [11–13, 19]; enso -
ne wo k models model bulk geome y om bounda y co ela ions [14, 20]; and in o ma ion-
geome ic and complexi y-based app oaches ela e cu a u e o in o ma ional change [15, 16,
22, 23]. Founda ional he modynamic de i a ions o g a i a ional dynamics based on he
Clausius ela ion (Jacobson; Padmanabhan) and en opic g a i y p oposals (Ve linde) ein o ce
his end [5, 7, 8]. Howe e , wha emains missing is a cohe en on ological accoun ha
explains why in o ma ional o ganiza ion should yield s able geome ic laws and how Eins ein’s
equa ions can be ead as mac oscopic in o ma ional balance condi ions a he han p imi i e
geome ic pos ula es.
This pape de elops a concep ual amewo k ha in e p e s space ime as an in o ma ional
p ojec ion – he mac oscopic mani es a ion o an unde lying in o ma ional equilib ium be ween
bounda y and bulk deg ees o eedom. The con ibu ion is h ee old:
(C1) Syn hesis: I in eg a es black-hole he modynamics, AdS/CFT, and quan um-in o ma ion
insigh s in o a single in e p e i e on ology o space ime, whe e in o ma ion is on ologically
p ima y [3–5, 11–16, 19–23].
(C2) Rein e p e a ion o dynamics: I ecas s Eins ein’s equa ions, in he spi i o Jacobson’s
Clausius- ela ion app oach, as cons ain s en o cing in o ma ional consis ency, wi h δQ = T dS
ead as in o ma ion low ac oss local causal ho izons [5, 9].
(C3) P og amma ic implica ions: I ou lines empi ically mo i a ed di ec ions – in o ma ional
cu a u e and en opy low – as candida es o o maliza ion and u u e es s, connec ing o
con empo a y wo k in in o ma ion geome y and quan um e o co ec ion [12, 13, 15, 21, 22].
The amewo k is concep ual a he han de i a ional: no new undamen al ield equa ions a e
p oposed. Claims a e in e p e i e and p og amma ic; hey aim a cla i ying on ology and
mo i a ing u u e quan i a i e o mula ion. The accoun is backg ound-agnos ic – no es ic ed
o AdS – a he le el o in e p e a ion, while acknowledging ha many igo ous ools cu en ly
exis wi hin AdS/CFT. Whe e he pape ex apola es beyond p o en duali ies, i is explici ly
labeled as in e p e a ion.
In o ma ion deno es physically ins an ia ed, quan i iable deg ees o eedom and hei
co ela ions – o he Shannon o on Neumann ype – ope a ionally g ounded in quan um-
in o ma ion heo y a he han seman ic o ep esen a ional con en [6–8, 15]. P ojec ion e e s
o he mapping om bounda y in o ma ional s uc u e o e ec i e bulk desc ip o s, such as
me ic and cu a u e, consis en wi h holog aphic bounds [3, 19]. Eme gence indica es coa se-
g ained mac oscopic o de a ising om mic oscopic co ela ions, wi hou implying on ological
en i ies beyond in o ma ional ela ions [7, 9, 16].
The p esen in es iga ion add esses a ounda ional ques ion a he han a phenomenological
one: Can he geome ic s uc u e o space ime be in e p e ed in e ms o an in o ma ional
equilib ium s a e? This ques ion is explo ed in h ee logical s eps: (i) e iewing es ablished
holog aphic and he modynamic app oaches o g a i y, (ii) de ining a minimal in o ma ion-
geome ic o malism linking cu a u e and en opy, and (iii) discussing he on ological
implica ions o his iden i ica ion. Each s ep is concep ually mo i a ed and o mally delimi ed
o a oid con la ing physical law wi h in o ma ional analogy.
In con as o pu ely o mal eadings o holog aphy, he p esen accoun ea s holog aphy as an
on ological p inciple: geome y ep esen s he s a is ical egula i ies o in o ma ional
o ganiza ion, and g a i a ional dynamics ac o s abilize in o ma ional cohe ence ac oss scales.
This posi ion esona es wi h en anglemen -buil geome y [11–13, 19], ne wo k and
comp ession-based iews [14, 20], and in o ma ion-geome ic econs uc ions [15, 16, 22, 23],
while di e ing by ele a ing in o ma ional p imacy and by a icula ing explici p og amma ic
a iables, such as in o ma ional cu a u e and en opy low.
Sec ion 2 p o ides he ounda ional heo e ical backg ound linking en opy, en anglemen , and
holog aphy. Sec ion 3 in oduces he in o ma ional-p ojec ion amewo k and cla i ies i s
concep ual assump ions and implica ions. Sec ion 4 discusses he physical and philosophical
consequences and ou lines esea ch di ec ions owa d quan i a i e o mula ion, and Sec ion 5
concludes.
2 Theo e ical Backg ound
The holog aphic p inciple o igina es om black-hole he modynamics, in which Bekens ein
and Hawking showed ha he en opy 𝑆 o a black hole is p opo ional o he su ace a ea 𝐴 o
i s e en ho izon a he han i s olume [4, 5]. This ela ion is exp essed as
𝑆 = 𝑘B𝐴
4𝐿P2,
whe e 𝐿P deno es he Planck leng h. I implies ha he maximal in o ma ion capaci y (in en opy
uni s) o a spa ial egion scales wi h i s bounda y. ’ Hoo [1] and Susskind [2] gene alized his
esul o all physical sys ems, p oposing ha he comple e dynamical in o ma ion o a olume
can, in p inciple, be encoded on i s bounda y.
Maldacena’s AdS/CFT co espondence [3] p o ided he i s explici ealiza ion o he
holog aphic conjec u e, es ablishing a duali y be ween a g a i a ional heo y in (𝑑 +1)-
dimensional An i-de Si e space and a con o mal ield heo y on i s 𝑑-dimensional bounda y.
The co espondence showed ha bulk geome y and g a i a ional dynamics can, in p inciple,
be econs uc ed om lowe -dimensional quan um deg ees o eedom. Ex ensions — such as
he Ryu–Takayanagi o mula [19] and i s co a ian gene aliza ion, he Hubeny–Rangamani–
Takayanagi (HRT) p esc ip ion — quan i y en anglemen en opy in geome ic e ms,
demons a ing ha geome ic connec i i y is encoded in quan um en anglemen s uc u e.
While hese amewo ks a e well de ined in asymp o ically An i-de Si e (AdS) space imes,
hey do no di ec ly gene alize o cosmological (e.g., de Si e ) o non-con o mal se ings. The
p esen s udy he e o e ea s AdS/CFT as an exis ence p oo o he holog aphic p inciple a he
han as a uni e sal law. I uses i s in o ma ional s uc u e — speci ically bounda y encoding
and he en anglemen -geome y co espondence — as concep ual sca olding o an on ology
ha is no es ic ed o AdS symme y.
Jacobson’s de i a ion o Eins ein’s equa ions om he Clausius ela ion δ𝑄 = 𝑇 𝑑𝑆 [6]
in e p e s space ime cu a u e as he mac oscopic esponse o local ene gy–en opy exchange
ac oss causal ho izons. Padmanabhan [7] and Ve linde [8] ex ended his easoning by
desc ibing g a i y as an en opic–s a is ical phenomenon eme ging om coa se-g ained
mic oscopic deg ees o eedom. These app oaches con e ge on he iew ha g a i a ional
dynamics ac o en o ce in o ma ional balance — a co espondence be ween he modynamic
lux and space ime cu a u e.
The ecu ing ea u e o hese de i a ions is ha space ime dynamics eme ges om a ia ional
o ex emal p inciples in ol ing en opy o in o ma ion lux. This ecu en ole o
in o ma ional quan i ies sugges s ha geome y ep esen s no a undamen al en i y bu he
s a is ical equilib ium con igu a ion o an unde lying in o ma ional subs a e. The nex sec ion
o malizes his idea h ough he in oduc ion o a minimal ma hema ical s uc u e capable o
ep esen ing such in o ma ional cu a u e.
In con empo a y heo e ical physics, in o ma ion e e s o quan i iable co ela ions among
physical deg ees o eedom — ypically Shannon o on Neumann en opy — embedded in
Hilbe space s uc u e [6, 15]. En opy measu es in o ma ional unce ain y, while
en anglemen quan i ies he deg ee o non- ac o izabili y — ha is, he ex en o quan um
co ela ion — be ween subsys ems. Tenso -ne wo k models such as he mul i-scale
en anglemen eno maliza ion ansa z (MERA) ep oduce holog aphic scaling by encoding
coa se-g aining as eno maliza ion in en anglemen space [14, 20]. Quan um e o co ec ion
o mula ions [12, 13, 21] cla i y how local bulk ope a o s eme ge om edundan bounda y
encodings, ensu ing s abili y agains in o ma ion loss. Finally, in o ma ion-geome ic
app oaches [15, 22] ea cu a u e on s a is ical mani olds as a measu e o in o ma ional
change, hus p o iding a o mal b idge be ween he modynamics and geome y — and he
ma hema ical empla e de eloped in he nex sec ion.
In his amewo k, in o ma ion deno es physically ins an ia ed co ela ions among deg ees o
eedom, whe eas en opy quan i ies he s a is ical unce ain y o dis ibu ional sp ead o hose
co ela ions. The wo a e concep ually ela ed bu no in e changeable: in o ma ion ep esen s
s uc u e, en opy i s s a is ical measu e.
Collec i ely, hese de elopmen s sugges ha he undamen al a iables o space ime can be
unde s ood as in o ma ional a he han geome ic in o igin: cu a u e, ene gy, and causal
s uc u e eme ge om he la ge-scale o ganiza ion o unde lying co ela ions [23, 27]. G a i y,
in his in e p e a ion, a ises as a mac oscopic mani es a ion o in o ma ional g adien s ha end
o es o e in o ma ional equilib ium.
Wi hin his in o ma ional eading, geome y is no an independen on ological laye bu an
eme gen desc ip o o in o ma ional cohe ence. The in o ma ional ela ions hemsel es a e
physical, no me ely epis emic— hey co espond o ope a ionally measu able co ela ions.
On ologically, his mo es beyond subs ance me aphysics owa d a s uc u alis iew in which
in o ma ional ela ions cons i u e eali y [10, 25, 26]. Epis emically, obse a ion and in e ence
occu wi hin he same in o ma ional ne wo k—bo h a e physical p ocesses o co ela ion
ex ac ion, no ex e nal o i [25, 34].
The p esen amewo k is me hodologically ela ed o en opic app oaches ha de i e physical
dynamics om in o ma ional p inciples, such as Jaynes’s en opic in e ence, F ieden’s Ex eme
Physical In o ma ion, and Ca icha’s en opic dynamics. In con as o hese p ima ily in e en ial
models, howe e , he p esen accoun adop s an on ological s ance: in o ma ional ela ions a e
no me ely epis emic cons ain s on knowledge bu cons i u e he physical s uc u e om which
space ime geome y i sel eme ges.
Assump ions and Bounda ies
Fo concep ual cla i y and me hodological anspa ency, he amewo k ope a es unde he
ollowing explici assump ions and bounda ies:
(A1) The holog aphic bound 𝑆 ≤ 𝐴/4𝐿𝑃
2 is ea ed as an in o ma ional limi ing p inciple
cons aining he maximal in o ma ion densi y pe bounda y a ea, a he han as a pu ely
he modynamic ela ion.
(A2) All e e ences o “eme gence” e e o he coa se-g aining o physically ins an ia ed
in o ma ional s uc u e.
(A3) S a emen s ex ending beyond igo ously es ablished duali ies a e explici ly ma ked as
in e p e i e.
(A4) Dimensional quan i ies a e exp essed in Planck uni s unless o he wise s a ed.
These p emises delinea e he concep ual domain o he amewo k de eloped in Sec ion 3,
which in e p e s space ime as an in o ma ional-equilib ium p ojec ion o such ela ions.
3 Concep ual F amewo k: In o ma ional On ology o Space ime
Building on he assump ions ou lined abo e, he p esen amewo k de elops an in o ma ional
on ology o space ime. I es s on he p emise ha he physical uni e se can be desc ibed as a
ne wo k o quan i iable ela ions o in o ma ion a he han as a con inuum o subs ances o
ields. Each physical sys em co esponds o a s uc u ed ensemble o co ela ions cons ained
by he modynamic and quan um p inciples. The cen al hypo hesis is ha space ime geome y
eme ges as he mac oscopic equilib ium s a e o an in o ma ional ne wo k ha maximizes
consis ency among i s bounda y co ela ions.
The model gene alizes Jacobson’s he modynamic in e p e a ion o Eins ein’s equa ions [6]
and Padmanabhan’s eme gen -g a i y pic u e [7] by ea ing he ela ion
𝛿𝑄 = 𝑇 𝑑𝑆
as an ins ance o in o ma ional lux a he han o ene gy ans e alone. In his eading, he
Eins ein enso 𝐺μν quan i ies de ia ions om in o ma ional equilib ium. Local cu a u e
co esponds o a g adien o in o ma ional imbalance; la space ime ep esen s maximal
in o ma ional uni o mi y. The holog aphic en opy bound 𝑆 ≤ 𝐴/4𝐿P
2 [4, 19] he eby unc ions
as a cons ain on in o ma ion densi y, no me ely as a he modynamic limi . This in e p e a ion
p ese es compa ibili y wi h es ablished semiclassical esul s while o e ing a uni ying
in o ma ional language.
Th ee in o ma ional quan i ies unde lie he amewo k:
– In o ma ional densi y ρI: he en opy pe uni (Planck) a ea on a bounda y su ace,
dimensionless in Planck uni s;
– In o ma ional lux ΦI: he a e a which bounda y in o ma ion changes wi h espec o local
causal low, measu ed pe uni a ea and ime;
– In o ma ional cu a u e ℛℐ: a measu e o de ia ion om uni o m in o ma ional
dis ibu ion, o mally analogous o he geome ic scala cu a u e.
The co esponding in o ma ion-geome ic enso is 𝑅μν
(𝐼) [22, 32], and dimensionally [ℛℐ]=
𝐿−2.
In o ma ional mani old and dimensional consis ency
Ma hema ically, he in o ma ional s uc u e is ep esen ed as a s a is ical mani old ℳℐ endowed
wi h a Fishe in o ma ion me ic. To quan i y in o ma ional dis ances be ween p obabili y
dis ibu ions, we adop he amewo k o in o ma ion geome y, in which he Fishe in o ma ion
de ines a na u al Riemannian me ic on he space o s a is ical s a es.
Pa ame e iza ion and Fishe Me ic.
Le 𝑝(𝑥|𝜃)𝜃∈𝛩 be a smoo h s a is ical model wi h pa ame e mani old 𝛩 ⊂ ℝⁿ.
The Fishe in o ma ion me ic on 𝛩 is de ined as
𝑔𝑖𝑗
(𝐼)(𝜃)= 𝐸𝑥∼𝑝(⋅|𝜃)[∂𝑖log𝑝(𝑥|𝜃) 𝜕𝑗log𝑝(𝑥|𝜃)] = 𝜕𝑖𝜕𝑗𝐷KL(𝑝(⋅|𝜃)||𝑝(⋅|𝜃′))|𝜃′=𝜃. (1)
The associa ed Le i-Ci i a connec ion induces he in o ma ion-geome ic Ricci enso 𝑅𝑖𝑗
(𝐼)(𝜃)
and scala cu a u e
ℛ𝐼(𝜃)= 𝑔(𝐼)
𝑖𝑗 𝑅𝑖𝑗
(𝐼).
In equilib ium, ℛℐ→ 0 co esponds o anishing in o ma ional g adien s, ep oducing he
geome ic condi ion o la space ime, whe eas de ia ions gene a e non anishing cu a u e, in
analogy o he modynamic imbalance. This mapping p o ides an explici co espondence
be ween in o ma ional and geome ic cu a u e, o ming he ma hema ical ounda ion o he
p ojec ion o malism in oduced in he nex subsec ion. Since he Fishe me ic is de ined on a
dimensionless pa ame e mani old, physical dimensions en e only h ough he b idge leng h
ℓ𝐼, in oduced o ensu e dimensional consis ency wi h space ime cu a u e. This o mal
s uc u e p o ides he in o ma ional subs a e upon which he subsequen balance and
p ojec ion ela ions a e de ined.
No a ion
Al hough p ima ily concep ual, he in o ma ional amewo k can in p inciple be subjec ed o
empi ical o compu a ional sc u iny. Possible empi ical ancho s include analog g a i y sys ems,
black-hole he modynamics, and quan um-simula ion pla o ms which emula e en anglemen
geome y. In such con ex s, measu able co ela ions be ween in o ma ion low and cu a u e—
in e p e ed h ough en opic scaling laws—could p o ide indi ec es s o he in o ma ional-
p ojec ion hypo hesis. In o ma ional cu a u e κI could, in p inciple, be ope a ionally
app oxima ed h ough en opy–a ea scaling in quan um-simula ion sys ems, whe e
en anglemen co ela es wi h geome ic dis ance.
A key implica ion is ha he in o ma ional cu a u e ℛℐ may se e as a es able in a ian in
analog o simula ed quan um-g a i a ional sys ems, e.g., in enso -ne wo k models o op ical-
la ice simula o s. Mapping he mu ual-in o ma ion s uc u e o eme gen cu a u e enso s
p o ides a conc e e ou e owa d empi ical ope a ionaliza ion, aligning wi h he ounda ional
ye empi ically o ien ed scope o Founda ions o Physics [36].
In e disciplina y and P og amma ic Ou look
– Fo maliza ion: De elop igo ous and dimensionally consis en de ini ions o in o ma ional
cu a u e, en opy lux, and equilib ium s abili y using in o ma ion-geome y and complexi y
heo y [22, 23, 32].
– Simula ion and Tes ing: Explo e analog ealiza ions on enso -ne wo k and quan um-
simula ion pla o ms o es scaling ela ions be ween en anglemen and eme gen cu a u e
[20, 21].
– Cosmological Ex ension: Rela e in o ma ional-balance dynamics o la ge-scale s uc u e
o ma ion and en opic cosmology [31].
– Philosophical In eg a ion: Examine implica ions o a na u alized me aphysics o
in o ma ion and he ela ional ounda ions o law ulness [10, 34].
These di ec ions delinea e a esea ch p og am a he han a comple ed heo y. By iden i ying
in o ma ion as he on ological co e and equilib ium as he o ganizing p inciple, he amewo k
uni es quan um in o ma ion heo y, g a i a ional he modynamics, and he philosophy o
science unde a single concep ual ho izon.
I s success will ul ima ely depend on o mally and empi ically a icula ing in o ma ion as
geome y—a ask now wi hin each o bo h heo y and expe imen .
5 Conclusions
This s udy ein e p e s he holog aphic p inciple [1–3] wi hin a o mally de ined in o ma ional
on ology o space ime. By embedding he modynamic and en anglemen concep s in an explici
in o ma ion-geome ic mani old [14, 15, 32], he amewo k es ablishes a minimal
ma hema ical s uc u e ha exp esses Eins einian geome y as an in o ma ional balance
condi ion [5–9].
Unlike p e ious heu is ic ea men s, he p esen app oach speci ies how in o ma ional densi y,
lux, and cu a u e a e in e ela ed h ough he Fishe me ic and he Kullback–Leible
di e gence [14, 15, 32], he eby es ablishing a b idge be ween he modynamics, quan um
in o ma ion, and geome ic s uc u e [17, 19–21, 35]. While p ima ily p og amma ic, he model
p o ides a ma hema ically cohe en ounda ion o u u e de i a ions o es able in a ian s—
such as in o ma ional cu a u e o en opy- lux measu es— ha may be explo ed in analog-
g a i y and quan um-simula ion en i onmen s [20, 21, 27, 36].
The in o ma ional-p ojec ion model uni ies he modynamics, en anglemen heo y, and
geome y h ough a sha ed se o in o ma ional desc ip o s: densi y ρI, lux ΦI, and cu a u e
κI. Toge he , hese a iables o m a concep ual iad ha can be o mally embedded in
in o ma ion-geome ic me ics, o example as
𝑅I ∼ ∂2𝐷KL.
By linking cu a u e o in o ma ional di e gence, he amewo k mo i a es a ma hema ically
igo ous e o mula ion o g a i a ional equilib ium in pu ely in o ma ional e ms [15, 22, 32].
On ologically, in o ma ion is ea ed as he p imi i e s uc u e om which physical egula i ies
eme ge. Geome y, ene gy, and causali y a ise as s a is ical pa e ns o in o ma ional cohe ence,
while physical law exp esses he cons ain s ha main ain ha cohe ence [10, 25, 26, 34].
Epis emically, obse a ion and heo e ical ep esen a ion a e embedded wi hin he same
in o ma ional ne wo k; he e is no p i ileged ex e nal s andpoin beyond i . This s ance g ounds
he amewo k in s uc u al- ela ional ealism, acco ding o which eali y consis s in he o al
ela ional o de o in o ma ion physically ins an ia ed in quan um co ela ions.
Fu u e wo k should
– o malize in o ma ional cu a u e and en opy low wi hin gene ic cu ed space imes [22, 27,
32];
– de elop compu a ional models and quan um-simula ion analogs o es ing en anglemen –
cu a u e co ela ions [20, 21, 33]; and
– in eg a e in o ma ional and cosmological dynamics o explo e whe he la ge-scale s uc u e
o ma ion can be unde s ood as a p ocess o global en opy maximiza ion [31].
Philosophically, con inued in es iga ion o he in o ma ional ounda ions o physical law may
help cla i y how on ology, epis emology, and compu a ion a e in e connec ed wi hin a uni ied
concep ion o na u e.
In conclusion, his amewo k e ames he holog aphic p inciple as an in o ma ional
equilib ium condi ion unde lying space ime geome y. I p o ides a cohe en b idge be ween
he modynamics, quan um in o ma ion, and g a i a ion, while emaining open o o maliza ion
and empi ical alida ion. Whe he space ime is indeed an eme gen mani es a ion o
in o ma ional o de emains a ques ion o u u e heo y and expe imen —bu one ha can now
be posed wi h concep ual p ecision and es able in en .
Decla a ions
Con lic o In e es
The au ho decla es ha he e a e no con lic s o in e es ega ding he publica ion o his pape .
Funding
This esea ch ecei ed no speci ic g an om any unding agency in he public, comme cial, o
no - o -p o i sec o s.
Da a A ailabili y
No new da a we e c ea ed o analyzed in his s udy. Da a sha ing is no applicable o his a icle.
Acknowledgmen s
The au ho g a e ully acknowledges he b oade scien i ic communi y o open-access esea ch
and discussions ha ha e inspi ed his wo k.
Au ho Con ibu ion
The au ho con i ms sole esponsibili y o he s udy concep ion, heo e ical de elopmen , and
manusc ip p epa a ion.
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