Abstract
I suggest that stars introduce mass and density scales that lead to “naturalness” in the Universe. Namely, two ratios of order unity. 1) The combination of the stellar mass scale, M*(c, ℏ, G, mp, me, e, …), with the Planck mass, MPl, and the Chandrasekhar mass leads to a ratio of order unity that reads NPl*≡MPl/(M*mp2)1/3≃0.15−3, where mp is the proton mass. 2) A system with a dynamical time equals to the nuclear life times of stars, τnuc*, has a density of ρD*(c,ℏ,G,mp,me,e,…)≡(Gτnuc*2)−1. The ratio of the dark energy density to this density is Nλ* = ρΛ/ρD* ≈ 10−7−105. Although the range is large, it is critically much smaller than the 123 orders of magnitude usually referred to when ρΛ is compered to the Planck density. In the pure fundamental particles domain there is no naturalness; either naturalness does not exist or there is a need for a new physics or new particles. The “Astrophysical Naturalness” offers a third possibility: stars introduce the combinations of, or relations among, known fundamental quantities that lead to naturalness.
Highlights
The naturalness topic is nicely summarized by Natalie Wolchover in an article from May 2013 in Quanta Magazine.1 I here discuss two points as listed in the talk “Where are we heading?” given by Nathan Seiberg in 20132: 1) “Why doesn’t dimensional analysis work? All dimensionless numbers should be of order one”; 2) “The cosmological constant is quartically divergent—it is fine tuned to 120 decimal points.”My answer to the first point is that in astrophysics dimensional analysis does work when stars are considered as fundamental entities
The astrophysical naturalness approach, that holds that stars, despite being very complicated, serve as a basic entity in our Universe, makes the Universe simpler in both introducing naturalness and in arguing that fundamental constants, including the cosmological constant, do not vary with time
The naturalness question I studied here can be posed as follows: “What is the combination of the fundamental constants and particle properties that leads to a ratio of two values that is of order unity?” In the present essay I showed that stars introduce these combinations that give what might be termed “Astrophysical Naturalness.”
Summary
The naturalness topic is nicely summarized by Natalie Wolchover in an article from May 2013 in Quanta Magazine. I here discuss two points as listed in the talk “Where are we heading?” given by Nathan Seiberg in 20132: 1) “Why doesn’t dimensional analysis work? All dimensionless numbers should be of order one”; 2) “The cosmological constant is quartically divergent—it is fine tuned to 120 decimal points.”. My answer to the first point is that in astrophysics dimensional analysis does work when stars are considered as fundamental entities. This answers the second question as well. If the nuclear lifetime of stars is taken to be a dynamical time of the Universe, naturalness emerges from the observed cosmological constant. One might refer to relations introduced by stars as coincidental (e.g., Carr and Rees, 1979), but in the present essay I prefer to refer to these relations as naturalness. Many other relations and coincidences can be found in Carr and Rees (1979) and Burrows and Ostriker (2014). I will not touch the question of multiverse which is often connected to the values of fundamental quantities (e.g., Livio and Rees, 2005; Weinberg 2005; Livio and Rees, 2018; Adams 2019; AlonsoSerrano and Jannes, 2019)
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