The Equi alence P inciple In alida es I sel
Max Ka son
No embe 21, 2025
Abs ac
The Eins ein Equi alence P inciple (EEP) asse s ha locally, a g a i a ional ield is indis-
inguishable om uni o m accele a ion, p o ided he labo a o y is su icien ly small. We iden i y
wo undamen al con adic ions ha ende his compa ison logically oid. Fi s , i g a i a ional
cu a u e is small enough o be unde ec able, i is insu icien o cause ee all; he p inciple hus
demands an e ec wi hou a cause. Second, he “uni o mly accele a ing labo a o y” equi ed
o compa ison is a physical impossibili y: a body mus ei he de o m ( iola ing he ixed- ame
equi emen ) o emain Bo n- igid (making accele a ion ope a ionally indis inguishable om
es ). The EEP he e o e does no de ine a alid ine ial ame, bu ins ead p o ides a ci cula
a ionaliza ion o app oxima ing poin -limi locali y.
The Negligibili y Con adic ion
The s anda d de ense o he EEP [1] is ha idal o ces anish in he limi o locali y, bu g a i y
i sel is he idal g adien .
•I cu a u e is unde ec able, no ee all occu s.
•I ee all occu s, cu a u e is de ec able.
Thus he EEP simul aneously demands and o bids g a i y.
The Rigidi y Dilemma
The p inciple in okes a labo a o y ame ha is bo h locally la and accele a ing; his is a con a-
dic ion in e ms.
•I he lab ame accele a es wi h Bo n igidi y, local la ness is p ese ed bu accele a ion is
unde ec able.
•I he lab ame accele a es non- igidly, accele a ion is de ec able bu local la ness is iola ed.
Thus, he EEP con as s a g a i a ional case in which he cause (cu a u e) is o bidden wi h
a kinema ic case in which he s a e ( igid accele a ion) is impossible.
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Conclusion
The Equi alence P inciple demands bo h ee all in la space and Bo n- igid accele a ion. Because
hese condi ions a e impossible, he p inciple is bes unde s ood as a educ io ad absu dum in ali-
da ing he concep o locali y in ela i i y. Ins ead, he EP unc ions as a ci cula dec ee abou how
o do physics—namely, i s ipula es ha poin app oxima ions a e alid. Tha assump ion disca ds
ela i i y’s ull geome ic pic u e in a o o a la New onian backg ound ha is me ely wa ped
by cu a u e, he signi icance o negligibili y o which is decided by adi ion and con en ion.
AI Disclosu e
The au ho used AI language models o assis wi h d a ing, de i a ions, and logical checks.
Re e ences
[1] A. Eins ein, Ҭ
Ube das Rela i i ¨a sp inzip und die aus demselben gezogenen Folge ungen,”
Jah buch de Radioak i i ¨a und Elek onik 4, 411–462 (1907).
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