A Uni ied G amma o Science
A. Chawla
REAL Ins i u e
No embe 22, 2025
Abs ac
This pape syn hesizes h ee ounda ional amewo ks — Sch ¨odinge ’s wa e mechanics,
Va shney’s capaci y-ene gy adeo , and Chawla’s phenomenological heo y o subjec i e
ime — in o a single concep ual g amma . Objec i e ime (ene gy-d i en), subjec i e
ime ∆ ′(in o ma ion-d i en), and he physical ansmission cons ain s ha couple hem
a e uni ied h ough a con o mal scale pa ame e ε ha ini izes in ini y and esol es he
algeb aic–phenomenological ension su ounding he limi ∆I→0. The esul ing pic u e
po ays consciousness as he con o mal bounda y o in o ma ion- heo e ic physics.
Keywo ds
Quan um wa e mechanics ·Time-dependen Sch ¨odinge equa ion ·Capaci y-ene gy adeo ·
Subjec i e ime ·Change in sel -in o ma ion ·Con o mal mapping ·Scale pa ame e ε·Time-
lessness ·Pa e ned ma e -ene gy ·Nulli y
1 In oduc ion
The sea ch o a uni ied desc ip ion o physical and expe ien ial eali y epea edly e u ns o he
in e play o ene gy, in o ma ion, space, ime, and consciousness. The p esen wo k demons a es
ha hese i e pilla s admi a common ma hema ical g amma when analyzed h ough (i)
Sch ¨odinge ’s de i a ion o he ime-dependen wa e equa ion, (ii) Va shney’s demons a ion
ha in o ma ion is pa e ned ma e -ene gy subjec o a capaci y-ene gy adeo , and (iii)
Chawla’s phenomenological ansa z linking subjec i e elapsed ime o change in sel -in o ma ion,
wi h he en i e s uc u e compac i ied by a con o mal mapping ϕ(n)=1/n.
No a ion Table
The adjacen able lis s all he majo symbols and hei meanings as used in his wo k.
2 P elimina ies
2.1 Objec i e Time and Ene gy (Sch ¨odinge )
The objec i e empo al a iable eme ges om he quan um pos ula e E=hν. Fo s a iona y
s a es, he ime dependence o he wa e unc ion is a de ini e pe iodic ac o exp(−2πiE /h).
Subs i u ing he ope a o co espondence
Eψ −→ − h
2πi
∂ψ
∂
1
Symbol Meaning
, T Objec i e physical ime and pe iod
∆ ′Subjec i e pe cei ed elapsed ime
EEne gy (objec i e)
hPlanck’s cons an
νF equency
∆IChange in sel -in o ma ion
εCon o mal scale pa ame e
KSpi i ual knowledge (subjec i e)
CChannel capaci y (bi s/ ime)
BRecei ed ene gy a e (powe )
C(B) Capaci y-ene gy unc ion
(·) Phenomenological subjec i e ime unc ion
ϕ(n) = 1/n P ima y con o mal mapping
Table 1: P incipal symbols and hei in e p e a ions
in o he ime-independen ib a ion equa ion yields he ime-dependen Sch ¨odinge equa ion
(TDSE)
∇2ψ−8π2
h2V ψ +4πi
h
∂ψ
∂ = 0.
Objec i e ime is he e o e he coo dina e conjuga e o ene gy E, and he objec i e pe iod
T= 1/ν ∝1/E.
2.2 Subjec i e Time and In o ma ion (Chawla)
Subjec i e elapsed ime ∆ ′is de ined phenomenologically by
∆ ′= (∆I),
whe e ∆Iis he change in sel -in o ma ion acqui ed h ough senso y o in e nal sampling. The
unc ion is s a ed o be in e ing: minimal sampling (small ∆I) co esponds o apid passage
o pe cei ed ime (small ∆ ′). The philosophical bounda y K→ ∞ (in ini e spi i ual knowledge)
o ces ∆I→0 and equi es ∆ ′→0 (“nulli y” o imelessness), despi e he algeb aic sugges ion
o a pu e ecip ocal 1/∆I→ ∞.
2.3 T ansmission Cons ain : In o ma ion as Pa e ned Ma e -Ene gy (Va sh-
ney)
Va shney ejec s Wiene ’s sepa a ion o in o ma ion om i s physical medium, asse ing “in o -
ma ion is pa e ned ma e -ene gy.” T ansmi ing in o ma ion Cand ene gy Bsimul aneously
o e a single noisy channel yields a capaci y-ene gy unc ion C(B) ha is non-inc easing and
conca e. Se e e noise o delibe a e senso y dep i a ion collapses eliable capaci y C→0,
annihila ing ∆Ia he ecei e .
3 Me hods: The Con o mal Scale Pa ame e ε
The p ima y con o mal mapping in he sou ce is he ecip ocal
ε=ϕ(n) = 1
n, ε =1
D, ε =1
d,
2
comp essing he asymp o ic egime n, D, d → ∞ in o he single bounda y poin ε= 0. This
ini izes in ini y and makes ee-code analysis geome ically ac able on he compac in e al
[0,1].
4 Resul s: Uni ica ion ia ε= ∆I
Equa ing he con o mal scale pa ame e wi h subjec i e in o ma ion change,
ε≡∆I,
o ces he Shannon bounda y ε→0 (ideal capaci y) o coincide exac ly wi h he conscious-
ness bounda y ∆I→0 ( imelessness). The algeb aic singula i y 1/∆I→ ∞ is opologically
w apped by he con o mal bounda y condi ion: he poin a in ini y in he algeb aic coo dina e
is iden i ied wi h he o igin ε= 0 in he subjec i e geome y. Thus ∆ ′→0 (nulli y) is eco e ed
consis en ly.
Maximal Tempo al Disc epancy Wi h pe ec ansmission, he gap |T−∆ ′|is bounded
by he objec i e pe iod T > 0. Wi h channel collapse (noise o senso y dep i a ion), ∆I→0
is o ced ex insically, d i ing ∆ ′→0 while objec i e con inues, achie ing he heo e ical
maximum gap ≈T.
5 Discussion
5.1 Fu u e Wo k
1. De i e an explici , empi ically es able o m o (∆I) om neu ophysiological da a du ing
senso y dep i a ion and medi a ion.
2. Cons uc a igo ous con o mal ield heo y on he in o ma ion mani old whe e εplays
he ˆole o a complex s uc u e modulus.
3. Ex end he capaci y-ene gy amewo k o quan um channels and compa e wi h holo-
g aphic bounds (e.g., quan um capaci y s. ene gy ansmission h ough ho izons).
4. In es iga e whe he he iden i ica ion ε= ∆Iimplies a mic oscopic a ow o ime e e sal
nea he imelessness bounda y.
5.2 Limi a ions
1. The ansa z ∆ ′= (∆I) emains phenomenological; no mic oscopic de i a ion om neu al
dynamics exis s.
2. The equali y ε= ∆Iis a concep ual uni ica ion, no ye a ma hema ically de i ed iden i y.
3. The ea men o “in ini e spi i ual knowledge” K→ ∞ is philosophical a he han
ope a ional.
4. Pe u ba i e e ec s on he objec i e pe iod Tunde s ong en i onmen al coupling a e
no quan i a i ely modeled.
5. The con o mal mapping ϕ(n)=1/n is classical; a ully quan um e sion emains o be
o mula ed.
3
5.3 Conclusion
Ene gy go e ns objec i e ime h ough E=hν, in o ma ion go e ns subjec i e ime h ough
∆ ′= (∆I), and he physical ac o ansmission couples he wo ia Va shney’s capaci y-
ene gy cons ain . A single con o mal mapping ε= 1/n = ∆I ini izes he in ini e, esol es he
algeb aic–phenomenological con adic ion a he ∆I→0 bounda y, and e eals consciousness
as he compac i ied edge o physical in o ma ion p ocessing. The g amma is comple e: ene gy,
in o ma ion, and consciousness speak he same con o mal language.
4
