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SESSION:
MathematicsWedPM3-R3
Rowlands International Symposium (7th Intl. Symp. on Sustainable Mathematics Applications)
Wed. 23 Oct. 2024 / Room: Marika B2
Session Chairs: Peter Rowlands; James Watson; Student Monitors: TBA

16:25: [MathematicsWedPM310] OL
QUANTAL THEORY OF GRAVITY
Tolga Yarman1; Alexander L. Kholmetskii2; Christian Marchal3; Ozan Yarman4
1Istanbul Okan University, Istanbul, Turkey; 2Belarusian State University, Minsk, Belarus; 3Office National d'Etudes et de Recherches Aérospatiales, Paris, France; 4Istanbul University, Istanbul, Turkey
Paper ID: 443 [Abstract]

Quantal Theory of Gravity (QTG) describes interactions between masses based on a straightforward implementation of the law of energy conservation [1]. In a manner that right away brings about the de Broglie wavelength relationship λB=h/p, QTG remains in full symbiosis with Quantum Mechanics (QM), inasmuch as being equally applicable to either light or ordinary matter in both wave-like (quantal) and the particle-like (corpuscular) limits. Such a framework leads to all of the results that were historically considered to validate the General Theory of Relativity (GTR) of Einstein. All the same, the conformance between GTR and QTG amazingly transpires only in the latter’s quantal case. QTG normally consists in a two-entity formalism. This is where a wave-like behaving test object near a host massmust get torn apart into i) an accelerating wavepacket of energy hf=γm0∞c2 operating locally (this is precisely why the proper rest mass m0∞ appears in the given equality, which in turn constitutes de Broglie’s foundational premise), and ii) a necessarily recoiling corpuscular constituent of rest mass   m0∞e-awhich we call thecore or kernel, as tracked by the distant observerThe splitting occurs in accordance with the law of momentum conservation through a rest mass exchange, coming into play owing to the law of energy conservation, between the straggling core m0∞e-a and the throttled wavepacket hf. 

We further derive equations of motion for both the wavepacket hf and the core m0∞e-a vis-à-vis, respectively, a fixed local observer and a remote observer situated outside of gravity where i) both observers agree that hf accelerates, ii) there exists for the local observer just the wavepacket hf with regards to a wave-like mode of interaction, and iii) the distant observer can witness the recoiling of the core (while the local observer cannot). In such a way, and without introducing any metric at the outset, we are capable of not only explaining known astrophysical observations of the 20th century that were considered to support GTR, but also of providing an explanation for the lately reported anomalous precession of the perihelion of the orbit of Saturn [2]. 

If the test object at hand does not delineate any wave-like behavior in gravity, such as is the case of high-energy γ-quanta, QTG predicts the nullification of gravitational bending. This finding can be explained under neither GTR nor other purely metric theories of gravity, and delineates an important aspect in regards to experimentally testing QTG against metric theories including GTR. QTG is moreover applicable to all bound fields, and provides an answer to the dark energy quandary in conformance with the empirically ascertained accelerated expansion rate of the universe.

References:
[1] C. Marchal et al. Ann. Phys. 454, 169346, 2023.
[2] L. Iorio 2009 AJ 137, 3615.


17:25 POSTERS/EXHIBITION - Ballroom Foyer