En opy-Induced Collapse (EIC) and he
In o ma ion Th eshold:
A Philosophical Memo andum — O igins o
he F amewo k
Takao Koizumi
Independen Resea che , Japan
[email p o ec ed]
Oc obe 9, 2025
Abs ac
The collapse o he wa e unc ion emains one o he mos un esol ed aspec s
o quan um mechanics. While many in e p e a ions ha e in oked obse a ion, con-
sciousness, o hidden a iables, none ha e achie ed uni e sal consis ency. This
memo andum e isi s he p oblem om he pe spec i e o he En opy-Induced
Collapse (EIC) amewo k, emphasizing wo cen al ideas: i e e sible in o ma-
ion leakage and h eshold- igge ed ac i a ion. I seeks o e o mula e wa e unc ion
collapse as an in insic p ocess o he uni e se’s in o ma ional sel -consis ency, in-
dependen o subjec i e obse a ion.
I. In oduc ion — The Cen al P oblem
The collapse o he wa e unc ion lies a he co e o quan um mechanics, ye i s unde lying
mechanism emains obscu e. Classical in e p e a ions ha e o en asc ibed collapse o an
ac o measu emen o obse a ion, sugges ing ha consciousness plays an ac i e ole in
de e mining physical eali y. Howe e , such in e p e a ions in oduce mo e me aphysical
di icul ies han hey esol e.
In his wo k, we ejec he necessi y o any obse e -dependen o consciousness-based
mechanism. Ins ead, he phenomenon is econside ed as a h eshold p ocess oo ed in
he beha io o in o ma ion i sel . Speci ically, we p opose ha he wa e unc ion collapse
occu s when in o ma ion abou a sys em becomes i e e sibly encoded in he en i onmen
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and app oaches he c i ical bounda y a which he p e-collapse s a e would become e-
cons uc able. This iew implies ha collapse is nei he a p oduc o obse a ion no a
me e decohe ence e ec , bu a sel -consis ency condi ion imposed by he in o ma ional
s uc u e o he uni e se.
II. O igin o he Idea
The inspi a ion o his concep eme ged om he well-known quan um e ase expe imen .
In ha se up, in e e ence inges eappea when he which-pa h in o ma ion, p e iously
eco ded, is subsequen ly “e ased.” This beha io sugges s ha he key a iable is no
he ac o measu emen i sel , bu a he whe he in o ma ion abou he sys em emains
accessible wi hin he en i onmen .
This obse a ion led o he hypo hesis ha collapse is go e ned by he balance be ween
in o ma ion leakage and he limi s o econs uc abili y. When in o ma ion is con ined
o ende ed un eco e able, cohe ence eappea s; when i sp eads i e e sibly and eaches
a h eshold o econs uc i e po en ial, collapse becomes ine i able. Thus, he quan um
e ase is no me ely a e e sal o measu emen , bu a window in o he in o ma ional
bounda y ha go e ns physical eali y.
III. Theo e ical Di ec ion
A he heo e ical le el, wo main app oaches we e conside ed o desc ibing he EIC
amewo k. The i s in ol ed in oducing a nonlinea educ ion equa ion o model col-
lapse dynamically. The second was a hyb id app oach, combining he p obabilis ic e o-
lu ion o he wa e unc ion wi h a de e minis ic collapse h eshold. While he nonlinea
o mula ion ca ies aes he ic appeal, i isks b eaking he o mal consis ency o s an-
da d quan um mechanics. The hyb id model, by con as , e ains compa ibili y while
in oducing a well-de ined bounda y o collapse.
In he EIC in e p e a ion, he wa e unc ion e ol es con inuously and p obabilis i-
cally unde he s anda d Sch ¨odinge dynamics. Howe e , as he sys em in e ac s wi h
i s en i onmen , in o ma ion g adually leaks ou and accumula es. When his leakage
eaches a c i ical le el—whe e he p e-collapse s a e could, in p inciple, be uniquely e-
cons uc ed— he sys em unde goes an i e e sible con ac ion. This p ocess is nei he
andom no obse e -induced, bu a he an eme gen consequence o he uni e se’s in-
o ma ional sel -consis ency. I is his h eshold de e minism ha dis inguishes EIC om
bo h s ochas ic collapse models and con en ional decohe ence heo ies.
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IV. Re ision and In eg a ion
The e ined iew o he En opy-Induced Collapse model can be summa ized as ollows:
1. In o ma ion leaks i e e sibly in o he en i onmen and is ne e comple ely los .
2. Collapse does no equi e any econs uc i e ac o he in e en ion o an obse e .
3. The wa e unc ion collapses immedia ely be o e he p e-collapse s a e becomes e-
cons uc able om en i onmen al in o ma ion.
In o he wo ds, collapse occu s jus p io o he momen when he en i onmen al
in o ma ion eaches he h eshold o econs uc abili y. The igge is no an ex e nal
ac ion bu an in insic in o ma ional cons ain : a sel -consis ency sa egua d wo en in o
he ab ic o he uni e se.
This aming allows he collapse phenomenon o be in e p e ed no as a discon inui y
in physical law, bu as a na u al ansi ion wi hin he in o ma ional domain— a poin
whe e he en opy o in o ma ion low mee s a uni e sal cons ain o e e sibili y.
V. Conclusion
Wi hin he EIC (En opy-Induced Collapse) amewo k, wa e unc ion collapse is unde -
s ood as an in o ma ion- heo e ic h eshold phenomenon:
An i e e sible con ac ion occu s jus be o e he p e-collapse s a e becomes
econs uc able ( om en i onmen al eco ds) in p inciple.
Ope a ionally, le E deno e he (e e -g owing) en i onmen al eco d up o ime and
conside al e na i e p e-collapse his o ies {Hi}. When he en i onmen -encoded s a es
{ρ(i)
E( )}become su icien ly dis inguishable (e.g., hei pai wise ace dis ances app oach
uni y so ha he Hels om bound on disc imina ion e o ends o ze o), he sys em ap-
p oaches a econs uc abili y bounda y. EIC asse s ha collapse is igge ed immedia ely
p io o his bounda y, p ese ing global consis ency wi hou equi ing any obse e , ac
o measu emen , o explici nonlinea i y in he uni a y dynamics.
This iew is nei he me e decohe ence (a con inuous di usion p ocess) no an obse e -
dependen pos ula e. Ra he , i ea s collapse as a sel -consis ency sa egua d in he
in o ma ional s uc u e o he uni e se.
VI. Implica ions and Ou look
1. Obse e -independence. Collapse does no ely on obse a ion o unde s and-
ing. The igge is de ined by an in o ma ion h eshold ied o econs uc abili y,
no by epis emic access o conscious app aisal.
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2. Compa ibili y wi h uni a y e olu ion. Be ween h esholds, e olu ion emains
s anda d and p obabilis ic (Sch ¨odinge dynamics). EIC in oduces a de e minis-
ic igge a a well-de ined bounda y, a oiding ad hoc nonlinea educ ions while
explaining i e e sibili y.
3. Rela ion o decohe ence. Decohe ence d i es he en i onmen s a es {ρ(i)
E( )}
owa d mu ual o hogonali y. EIC supplemen s his by posi ing a p e-o hogonali y
collapse h eshold: con ac ion occu s be o e pe ec dis inguishabili y would allow
unique econs uc ion o he pas .
4. No- e ocons uc ion p inciple. In EIC, a ully unique e ocons uc ion o he
p e-collapse s a e is ne e ealized in physical his o y; collapse in e enes jus sho
o ha possibili y. This en o ces an in o ma ional a ow o ime wi hou in oking
obse e s.
5. Falsi iable di ec ion (concep ual). I an in o ma ion- h eshold mechanism is
co ec , sys ems in which en i onmen al leakage and econs uc abili y can be pa a-
me ically uned should exhibi sha p ansi ions in collapse-associa ed s a is ics
nea a c i ical egime (as opposed o a pu ely smoo h, dis ance-like end expec ed
om decohe ence alone).
VII. Scope, Limi a ions, and Open P oblems
•Th eshold unc ional. This memo andum lea es abs ac he p ecise unc ional
ha se s he h eshold (e.g., ace-dis ance s uc u e, Bayesian e o bounds, al-
go i hmic econs uc abili y, o mu ual-in o ma ion c i e ia). Fo malizing a basis-
independen , ope a ional de ini ion emains an open ask.
•Locali y and causali y. Any h eshold mus be cons ained o locally a ailable
classical eco ds (e.g., wi hin pas ligh -cones) o a oid supe luminal signaling. A
igo ous s a emen o hese cons ain s in ela i is ic se ings is equi ed.
•The modynamic linkage. While “en opy” mo i a es he EIC nomencla u e,
connec ing he h eshold o conc e e he modynamic o en opic quan i ies (and
dis inguishing hem om gene ic decohe ence a es) dese es u he analysis.
•In e ace wi h expe imen s. Concep ual signa u es o a h eshold (as dis inc
om smoo h decohe ence) should be a icula ed in expe imen ally accessible e ms
wi hou elying on obse e -cen ic language o de ice-speci ic nonlinea i y.
•Founda ional uni ica ion. Cla i ying how EIC ela es o, o di e s om, s ochas ic-
collapse models and many-wo lds/decohe ence accoun s—especially ega ding e-
cons uc abili y and i e e sibili y— is an open heo e ical p og am.
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