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DOI: 10.6084/m9.figshare.13135163
Origin of Universal Gravitational constant, vacuum permittivity and permeability
Origin of Universal Gravitational constant, vacuum permittivity and permeability
Venkatram Nalla
Email: nallavram@gmail.com
Independent researcher, India and Singapore
We wonder the origin of Universal Gravitational constant and existence of vacuum permittivity and permeability in the space. These all seems, somehow related to the Space-time and physical dimensions of whole Universe. The relation between gravity and speed of light also reveals the origin of vacuum permittivity and permeability.
Recently there was a discussion on Young’s modulus Y of space-time [1, 2]. The question raised was, what is the Young’s modulus Y of space-time as experienced by a gravitational wave (GW), originally discussed at 2018 Hamilton Lecture at Princeton “Exploring the Universe with Gravitational Waves”. One response was that Yspace−time is frequency dependent and given by
where f is the frequency of the gravitational wave, and G the Newtonian Gravitational constant. Above equation reveals interesting relation between Gravitational constant and speed of light. In a way this is also clear explanation for the existence of vacuum permittivity and permeability in space. Using the same analogy of matching dimensions Newton’s gravitational constant is G = 6.67 × 10-11 Kg-1m3s-2, speed of light in vacuum is c = 3× 108 m/s, diameter of Universe Du = 8.8× 1026 m and total mass of the Universe Mu = 1.5 × 1053 Kg. Then, we can write (by dimensional analysis),
From equation 3 estimated mass of the Universe is 11.88 × 1053 Kg. This mass is eight times larger than our previous estimation of mass of the observable universe (1.5×1053 Kg), but previous estimation was not including dark matter and dark energy [3]. It is evident that, Universe has more than 90% of dark matter and dark energy [4]. All current estimations are limited to observable Universe only; this also can lead to discrepancy in calculations.
As squire of speed of light is equal to product of vacuum permittivity and permeability, equation 3 can be written as
Equation 4 clearly denotes that, vacuum permittivity and permeability are result of gravity of whole Universe. These vacuum permittivity and permeability are the result of space-time bending due to mass of the whole Universe.
Conclusions:
Universe is existing not because of universal constants but Universal constants are result of dimensions and properties of the Universe. Origin of universal constants such as Gravitational constant, vacuum permittivity and permeability in the space can be traced to space-time bending to mass of the whole Universe. Estimated Mass of the Universe in this method is eight times higher than the previous estimation, this estimation may be also accounting dark matter and dark energy.
References:
[1]. Kirk T. McDonald, “What is the Stiffness of Spacetime?”, (2018).
http://physics.princeton.edu/∼mcdonald/examples/stiffness.pdf
[2]. A. C. Melissinos, "Upper limit on the Stiffness of space-time", arXiv:1806.01133, (2018).
[3]. Paul Davies (2006). The Goldilocks Enigma, “Cosmic jackpot : why our universe is just right for life”, First Mariner Books. p. 43. ISBN 978-0-618-59226-5.
[4]. Dark Energy, Dark Matter, https://science.nasa.gov/astrophysics/focus-areas/what-is-dark-energy
[5]. The LIGO Scientific Collaboration and The Virgo Collaboration, The 1M2H Collaboration, The Dark Energy Camera GW-EM Collaboration and the DES Collaboration, The DLT40 Collaboration, The Las Cumbres Observatory Collaboration, The VINROUGE Collaboration & The MASTER Collaboration, “A gravitational-wave standard siren measurement of the Hubble constant”, Nature 551, 85–88 (2017).
Comments and notes:
Comments and notes:
There is an assumption that, space-time fabric has elasticity with Young’s modulus Yspace−time. But these assumptions cannot explain physical properties of Black holes and neutron stars. Here, we can think of other assumption, where universe is a three dimensional fluid, which has surface tension at the surface, object density higher than this surface tension will be submerged inside space-time, example of objects like black holes. Surface tension of space-time is
Where gammau is surface tension of the space-time, au acceleration of the Universe (70 kilometres per second per megaparsec) [5]. Estimated surface tension of space-time is 9.5 × 1023 N/m. By exploring this equation it is evident that surface tension of space-time is directly proportional to the Universe acceleration.
2. What if, space-time curvature of the whole Universe depends on its physical Mass. Mass converting to Energy will change the space-time curvature. Once space-time curvature becomes flat, the whole Universe will collapse into a single point, which will create a new Big-Bang to create new mass. This process is cyclic in Nature.
3. What if, total Mass-Energy equivalent of the Universe is constant. There is a continuous conversion of mass into energy, once the equilibrium between mass and energy breaks down, the Universe will become unstable and it will collapse. At the point of collapse, the Universe has less mass and more energy, this will prompt a Big-Bang, which will create new mass from the energy.
4. What if, space-time is curved because of the physical mass of the whole Universe, but dramatic conversion of mass into energy results in reduction of the curvature (Universe is flattening), this is giving us a feeling of expansion of the Universe. In a way, assumption of Universe expansion is due to reduction of space-time curvature, which is caused by conversion of mass into energy in the Universe.
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