The Ci cula Logic o G a i a ional Time Dila ion
Max Ka son
No embe 21, 2025
Abs ac
Gene al ela i i y ope a ionally de ines ime as “wha a clock measu es.” This de ini ion
conceals a logical ci cula i y. Any physical clock mus ha e ini e spa ial ex en and ine i ably
unde goes de o ma ion due o idal o ces and p ope accele a ion. De ining his de o ma ion
as ” ime dila ion” implici ly assigns he clock a pe sis en physical iden i y, e i iable only ia
p e-exis ing knowledge o he space ime me ic. Howe e , he me ic i sel is ope a ionally
cons uc ed using clocks. We demons a e ha he concep o a alid clock in a g a i a ional
ield is logically impossible wi hou assuming a hidden, absolu e New onian backg ound o
e mina e he in ini e eg ess o calib a ion.
1 The Physical Reali y o Clock De o ma ion
A clock is no a dimensionless poin ; i is a composi e assembly (e.g., wo mi o s and a pho on)
wi h ini e spa ial ex en . In any eal space ime, hese mi o s ollow dis inc geodesics, o cing
he pho on o a e se a changing gap. S anda d physics labels he esul ing measu emen a i-
ance ” ime dila ion,” he eby simul aneously acknowledging he clock’s de o ma ion and ce i ying
i s con inued accu acy. This dual asse ion, in which he clock is bo h al e ed and unal e ed,
p esupposes p io knowledge o he geome y.
2 The Logical Ci cula i y
The claim ha an accele a ed clock e ains i s iden i y c ea es a a al ci cula i y in he ope a ional
logic o gene al ela i i y:
1. To measu e he geome y, we mus use alid clocks.
2. To alida e a clock, we mus al eady know he geome y.
I he clock de o ms, a ibu ing he obse ed a iance ei he o space ime geome y o mechan-
ical dis o ion becomes a bi a y. Thus, he accu acy o bo h clocks and geome ic maps educes
o pu e con en ion, as ela i i y p o ides no ancho o calib a ion.
3 Poin Clocks Smuggle in a New onian Backg ound
By employing he poin -clock idealiza ion [1], s anda d ea men s implici ly g an clocks pe sis en
iden i ies and absolu e accu acy, p esupposing ha he geome ies hey inhabi a e al eady cha ed.
This assump ion ea s cu a u e as me ely a dis o ion o e laid on a Minkowski backg ound—
a baseline which, al hough ope a ionally inaccessible, is p esumed knowable. Connec ing hese
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idealiza ions o eal-wo ld ins umen s (e.g., GPS o a omic clocks) u he asse s ha Ea h’s
space ime geome y is empi ically known and e i ied. This claim es s on a logical impossibili y:
he p edic able beha io o a clock canno simul aneously se e as e idence o bo h he clock’s
accu acy and he geome y i pu po edly measu es.
4 Conclusion
The concep o g a i a ional ime dila ion elies on a ci cula chain o non-ope a ional asse ions.
By in e p e ing he measu emen s o a physically s e ched clock as accu a e eadings o space-
ime geome y, s anda d ea men s implici ly g an obse e s ei he independen knowledge o he
space ime me ic o an ideal calib a ion clock immune o de o ma ion. Ei he condi ion co e ly
ein oduces he absolu e backg ound ha ela i i y ejec s.
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] Misne , C. W., Tho ne, K. S., and Wheele , J. A., G a i a ion (W. H. F eeman, 1973).
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