What Does the Central Limit Theorem
Have to Say About General Relativity?
Réjean Plamondon
Abstract In this paper, we speculate on a possible connection between the
Bayes’s law and the Einstein’s general relativity equation to support the use of a
metric based on an erfc gravitational potential that has been recently proposed to
provide some cues to open problems in the solar systems. Starting from a basic
interdependence premise, an analogy between Einstein’s equation and Bayes’s law
is used to analyze the linear case of a weak field static symmetric massive object,
providing a probabilistic context that takes into account the probability of presence
of a given energy density in its corresponding 4D curved space-time manifold.
Using the Central Limit Theorem to model globally the very slow process of star
formation and mathematically express the corresponding probability density, the
new framework provides a rationale for the emergence of a weighted Newton’s law
of gravitation. One key feature of this modified gravity model is that it relies on the
existence of an intrinsic emergent physical constant σ , a star-specific proper length
that scales all its surroundings.
Keywords Modified gravity · Weighted Newton’s law · Central limit theorem ·
Bayes’s law · Star proper length · erfc potential · Emergence · Self-organization
In its most general configuration, a complex system is a network of heterogeneous
and usually simpler subsystems that interact among each other to give rise to
emergent features that guides its self-organization into a more complex system.
The description of the whole process simplifies at a given level of representation,
leading to some emergent properties [1]. These emergent systems are omnipresent
in physics, chemistry, and biology [2].
Among the tools that can be used to study such systems and their convergence
is the Central Limit Theorem [3]. This theorem has been developed over four
centuries in the context of searching for the asymptotic probabilistic behavior of a
R. Plamondon ()
Département de génie électrique, Polytechnique Montréal, Montréal, QC, Canada
e-mail: rejean.plamondon@polymtl.ca
© Springer Nature Switzerland AG 2021
M. B. Paranjape et al. (eds.), Quantum Theory and Symmetries, CRM Series in
Mathematical Physics, https://doi.org/10.1007/978-3-030-55777-5_47
503
Have to Say About General Relativity?
Réjean Plamondon
Abstract In this paper, we speculate on a possible connection between the
Bayes’s law and the Einstein’s general relativity equation to support the use of a
metric based on an erfc gravitational potential that has been recently proposed to
provide some cues to open problems in the solar systems. Starting from a basic
interdependence premise, an analogy between Einstein’s equation and Bayes’s law
is used to analyze the linear case of a weak field static symmetric massive object,
providing a probabilistic context that takes into account the probability of presence
of a given energy density in its corresponding 4D curved space-time manifold.
Using the Central Limit Theorem to model globally the very slow process of star
formation and mathematically express the corresponding probability density, the
new framework provides a rationale for the emergence of a weighted Newton’s law
of gravitation. One key feature of this modified gravity model is that it relies on the
existence of an intrinsic emergent physical constant σ , a star-specific proper length
that scales all its surroundings.
Keywords Modified gravity · Weighted Newton’s law · Central limit theorem ·
Bayes’s law · Star proper length · erfc potential · Emergence · Self-organization
In its most general configuration, a complex system is a network of heterogeneous
and usually simpler subsystems that interact among each other to give rise to
emergent features that guides its self-organization into a more complex system.
The description of the whole process simplifies at a given level of representation,
leading to some emergent properties [1]. These emergent systems are omnipresent
in physics, chemistry, and biology [2].
Among the tools that can be used to study such systems and their convergence
is the Central Limit Theorem [3]. This theorem has been developed over four
centuries in the context of searching for the asymptotic probabilistic behavior of a
R. Plamondon ()
Département de génie électrique, Polytechnique Montréal, Montréal, QC, Canada
e-mail: rejean.plamondon@polymtl.ca
© Springer Nature Switzerland AG 2021
M. B. Paranjape et al. (eds.), Quantum Theory and Symmetries, CRM Series in
Mathematical Physics, https://doi.org/10.1007/978-3-030-55777-5_47
503