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In this paper, we rewrite the dimensionless gravitational coupling constant: αG, in a different form than has been shown before (without changing its value). We demonstrate that the dimensionless gravitational coupling constant is simply related to the Planck length squared, divided by the reduced Compton wavelength squared, of the mass in question. This could be useful for understanding how the ratio of the gravitational force versus the Coulomb force is linked to the quantum scale, which is linked to the Compton wavelength and the Planck length.

References

  1. Haug EG. A note on the dimensionless gravitational coupling constant. viXra, 2016. http://vixra.org/abs/1604.0198.
     Google Scholar
  2. Silk J. Cosmogony and the magnitude of the dimensionless gravitational coupling constant. Nature, 1977;265:710–711. https://doi.org/10.1038/265710a0.
     Google Scholar
  3. Rozental IL. On the numerical values of the fine-structure constant and the gravitational constant. Soviet Journal of Experimental and Theoretical Physics Letters, 1980;31(9):19–27.
     Google Scholar
  4. Neto MO. Using the dimensionless newton gravity constant ¯αg to estimate planetary orbits. Chaos, Solitons and Fractals, 2005;24(1):19–27. https://doi.org/10.1016/j.chaos.2004.07.032.
     Google Scholar
  5. Narimani A, Moss A, and Scott D. Dimensionless cosmology. Astrophys Space Science, 2012;341:617. https://doi.org/10.1007/s10509-012-1113-7.
     Google Scholar
  6. Burrows AS and Ostriker JP. Astronomical reach of fundamental physics. Proceedings of the National Academy of Sciences of the United States of America, 2013;111(7):31–36. https://doi.org/10.1073/pnas.1318003111.
     Google Scholar
  7. Jentschura UD. Fine-structure constant for gravitational and scalar interactions. Physical Review A, 2014;90:022112. https://doi.org/10.1103/PhysRevA.90.022112.
     Google Scholar
  8. Coulomb CA. Premier me´moire sur l’e´lectricite´ et le magne´tisme. Histoire de lO˜Acade´mie Royale des Sciences, 1785: 569–577.
     Google Scholar
  9. Compton AH. A quantum theory of the scattering of x-rays by light elements. Physical Review, 1923;21(5):483. https://doi.org/10.1103/PhysRev.21.483.
     Google Scholar
  10. Haug EG. Derivation of a relativistic Compton wave. European Journal of Applied Physics, 2022;4:24a. http://dx.doi.org/10.24018/ejphysics.2022.4.4.190.
     Google Scholar
  11. Cornu A. and Baille JB. D´etermination nouvelle de la constante de l’attraction et de la densit´e moyenne de la terre. C. R. Acad. Sci. Paris, 1873; 76.
     Google Scholar
  12. Haug EG. The gravitational constant and the Planck units. A simplification of the quantum realm. Physics Essays, 2016;29(4):558b. https://doi.org/10.4006/0836-1398-29.4.558.
     Google Scholar
  13. Planck M. Natuerliche Masseinheiten. Der K¨oniglich Preussischen Akademie Der Wissenschaften, 1899.
     Google Scholar
  14. Planck M. Vorlesungen ¨uber die Theorie der W¨armestrahlung. Leipzig: J.A. Barth, p. 163, see also the English translation “The Theory of Radiation” (1959) Dover, 1906.
     Google Scholar
  15. Haug EG. Progress on composite view of Newtonian gravitational constant and its link to the Planck scale. Universe, 2022;8(454)b. https://doi.org/10.3390/universe8090454.
     Google Scholar
  16. Cohen ER. Fundamental Physical Constants, in the book Gravitational Measurements, Fundamental Metrology and Constants. Edited by Sabbata, and Melniko, V. N., Netherland, Kluwer Academic Publishers, 1987.
     Google Scholar
  17. McCulloch ME. Quantised inertia from relativity and the uncertainty principle. Europhysics Letters (EPL), 2016;115(6):69001.
     Google Scholar
  18. https://doi.org/10.1209/0295-5075/115/69001.
     Google Scholar
  19. Haug EG. Can the Planck length be found independent of big G ? Applied Physics Research, 2017;9(6):58. https://doi.org/10.5539/apr.v9n6p58.
     Google Scholar
  20. Haug EG. Planck units measured totally independently of big G. Open Journal of Microphysics, 2022:55a. https://doi.org/10.4236/ojm.2022.122004.
     Google Scholar
  21. Haug EG. Measurements of the Planck length from a ball-clock without knowledge of Newton’s gravitational constant G or the Planck constant. European Journal of Applied Physics, 2021;3:15. https://www.ej-physics.org/index.php/ejphysics/article/view/133.
     Google Scholar
  22. Haug EG. Extraction of the Planck length from cosmological redshift without knowledge off G or ¯h. International Journal of Quantum Foundation, supplement series Quantum Speculations, 2022;4(2)c. https://ijqf.org/archives/6599.
     Google Scholar
  23. Haug EG. Newton and Einstein’s gravity in a new perspective for Planck masses and smaller sized objects. International Journal of Astronomy and Astrophysics, 2018;8. URL https://doi.org/10.4236/ijaa.2018.81002.
     Google Scholar
  24. Levitt LS. The proton Compton wavelength as the ‘quantum’ of length. Experientia, 1958;14:233. https://doi.org/10.1007/BF02159173.
     Google Scholar
  25. Trinhammer OL and Bohr HG. On proton charge radius definition. EPL,2019; 128:21001. https://doi.org/10.1209/0295-5075/128/21001.
     Google Scholar
  26. Haug EG. Demonstration that Newtonian gravity moves at the speed of light and not instantaneously (infinite speed) as thought! Journal of Physics Communication., 2021;5(2):1. https://doi.org/10.1088/2399-6528/abe4c8.
     Google Scholar
  27. Haug EG. Unified quantum gravity field equation describing the universe from the smallest to the cosmological scales. Physics Essays, 2022;35:61.d. https://doi.org/10.4006/0836-1398-35.1.61.
     Google Scholar