Challenging Randomness and P obabili y in a
Symme ic Uni e se Based on he G oup
(nZ,+)
Benchek oun Mounssi
Abs ac
This a icle p oposes a adical ques ioning o he concep o an-
domness and p obabili y, based on a undamen al hypo hesis: he
obse able uni e se is he symme ic coun e pa o a p io uni e se,
acco ding o a ma hema ical s uc u e ounded on he disc e e g oup
(nZ,+). In his ision, e e y e en ha seems unce ain o p obabilis-
ic oday is in ac he de e minis ic mani es a ion o an e en al eady
accomplished in he symme ic uni e se be o e ze o. This amewo k
o e s a new in e p e a ion o quan um phenomena, pa icula ly en-
anglemen and measu emen , wi hou eso ing o p obabilis ic ap-
p oxima ion.
1 In oduc ion
Mode n physics elies hea ily on p obabilis ic no ions, especially in quan um
mechanics, whe e p obabili y is pe cei ed as in insic. He e, we p opose an
al e na i e: he wo ld we pe cei e does no con ain eal inde e minacy, since
e en s a e al eady de e mined, being e lec ions o a symme ic uni e se.
2 Ma hema ical Founda ion: The G oup (nZ,+)
We conside he disc e e Abelian g oup (nZ,+), which con ains all in ege s
ha a e mul iples o a gi en in ege n. He e, ze o ep esen s he ipping
poin , he bounda y be ween wo s a es o exis ence:
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•Nega i e elemen s o nZ ep esen pas e en s o a p io uni e se (be o e
0).
•Posi i e elemen s a e he symme ic e lec ions o hese e en s in he
cu en uni e se.
Thus, e e y e en occu ing in ou wo ld is seen as he p ojec ion o sym-
me ic epe i ion o an e en al eady ealized.
3 Ques ioning Randomness
Wi hin his amewo k, andomness does no exis . The appa en igno ance
o he obse e is due no o undamen al inde e minacy, bu o a lack o
knowledge o he p io symme ic s a e. P obabili ies a e he e o e s a is ical
app oxima ion ools, bu do no e lec any on ological eali y.
3.1 Applica ion o Quan um Mechanics
Conside a classic example: he measu emen o a pa icle’s s a e in supe po-
si ion. In he s anda d model, a p obabili y is associa ed wi h each ou come.
Bu in his amewo k:
•The inal measu ed s a e co esponds o an e en al eady accomplished
in he symme ic uni e se.
•En anglemen is no an ins an aneous ansmission o in o ma ion, bu
he simul aneous mani es a ion o a single symme ic e en sha ed be-
ween wo en i ies.
Thus, he wa e unc ion and i s collapse a e no longe necessa y. The ole o
he obse e is simply o e eal an al eady ealized s a e.
4 P obabili y as a Human Tool
Wha we call p obabili y is he e o e a human ool, use ul o deal wi h ig-
no ance. Bu in a pe ec ly symme ic and de e minis ic wo ld, p obabili y
loses any undamen al meaning.
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5 Conclusion
We p opose a adically de e minis ic in e p e a ion o he physical wo ld,
based on a symme y a ound ze o in a disc e e g oup. This app oach abol-
ishes andomness and es o es logical cohe ence o so-called andom phe-
nomena. I is no me ely a philosophy, bu a ma hema izable amewo k
ha may be ex ended o o he physical quan i ies.
Pe spec i es
A nex s ep would be o ex end his amewo k o phenomena such as deco-
he ence, he a ow o ime, o he wa e-pa icle duali y, and o in es iga e
whe he he known laws o physics can be eco e ed om his undamen al
p inciple.
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