The Planck Mass Density Radius of the Universe



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Submitted Mar 27, 2022
Published Apr 20, 2022
10.24018/ejphysics.2022.4.2.165

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What is the size of the universe if we take the estimated mass in the observable universe and compress it until we reach the Planck mass density? We will investigate this using both the Friedmann model and the recent Haug model of the universe that takes into account Lorentz relativistic mass. The resulting size is approximately that of a proton. We will also look at a hypothetical Planck mass size universe. In the Friedmann model one needs rapid expansion of mass to maintain the initial Planck mass density or, alternatively, only space expansion with the density decreasing from its initial conditions, while in the Haug model the Planck mass universe seems to cause no such “strange” predictions.

Keywords: Friedman model, Haug model, micro black holes, Planck density, Planck units, Planck mass universe

References

  1. M. Planck. Natuerliche Masseinheiten. Der Koniglich Preussischen Akademie Der Wissenschaften, 1899.
     Google Scholar
  2. M. Planck. 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
  3. R. J. Adler. Six easy roads to the Planck scale. American Journal of Physics, 78(9):925, 2010. URL https://doi.org/10.1119/1.3439650.
     Google Scholar
  4. S. Hossenfelder. Can we measure structures to a precision better than the Planck length? Classical and Quantum Gravity, 29, 2012. URL https://doi.org/10.1088/0264-9381/29/11/115011.
     Google Scholar
  5. S. Hossenfelder. Minimal length scale scenarios for quantum gravity. Living Reviews in Relativity, 16, 2013. URL https://doi.org/10.12942/lrr-2013-2.
     Google Scholar
  6. G. M. Obermair. Primordial Planck mass black holes (PPMBHS) as candidates for dark matter? Journal of Physics, Conference Series, 442, 2013. URL https://doi.org/10.1088/1742-6596/442/1/012066.
     Google Scholar
  7. G. E. Gorelik and L. M. Ozernoi. The cosmic background radiation as a possible product of the quantum era in the expansion of the universe. Soviet Astronomy Letters, 4:85, 1978.
     Google Scholar
  8. E. R. Caianiello. Is there a maximal acceleration? Letter Nuovo Cimento, 32:65, 1981. URL https://doi.org/10.1007/BF02745135.
     Google Scholar
  9. G. Scarpetta. Letter Nuovo Cimento, 51, 1984.
     Google Scholar
  10. E. R. Caianiello, S. D. Filippo, G. Marco, and Vilasi. G. Remarks on the maxlmal-acceleration hypothesis. Letter Nuovo Cimento, 34:112, 1982.
     Google Scholar
  11. E. R. Caianiello and Landi G. Maximal acceleration and Sakharov’s limiting temperature. Letter Nuovo Cimento, 42:70, 1985.
     Google Scholar
  12. D. F. Falla and P. T. Landsberg. Black holes and limits on some physical quantities. European Journal of Physics, 15, 1994. URL https://doi.org/10.1088/0143-0807/15/4/008.
     Google Scholar
  13. G. Spavieri, M. Rodriguez, and A. Sanchez. Thought experiment discriminating special relativity from preferred frame theories. Journal of Physics Communications, 8(2):1, 2018. URL https://doi.org/10.1088/2399-6528/aad5fa.
     Google Scholar
  14. G. Spavieri, G. Gillies, G. Haug, and A. Sanchez. Light propagation and local speed in the linear Sagnac effect. Journal of Modern Optics, 26(21): 2131, 2019. URL https://doi.org/10.1080/09500340.2019.1695005.
     Google Scholar
  15. E. T Kipreos and R. S Balachandran. Optical data implies a null simultaneity test theory parameter in rotating frames. Modern Physics Letters A, 36: 2150131, 2021. URL https://doi.org/10.1142/S0217732321501315.
     Google Scholar
  16. E. R. Harrison. Fluctuations at the threshold of classical cosmology. Physical Review D, 1:2726, 1970. URL https://doi.org/10.1103/PhysRevD.1.2726.
     Google Scholar
  17. A. Einstein. Naherungsweise integration der feldgleichungen der gravitation. ¨ Sitzungsberichte der Koniglich Preussischen Akademie der Wissenschaften ¨ Berlin, 1916.
     Google Scholar
  18. A. Friedmann. Uber die kr ¨ ung des raumes. ¨ Zeitschrift fur Physik ¨, 10:377, 1922. https://doi.org/10.1007/BF01332580.
     Google Scholar
  19. B. Schutz. Gravity from the Ground Up. Cambridge University Press, 2003.
     Google Scholar
  20. M. P. Hobson, G. Efstathiou, and A. N. Lasenby. General Relativity, An Introduction for Physicists. Cambridge, 2014.
     Google Scholar
  21. M. Guidry. Modern General Relativity. Cambridge University Press, 2019. [22] Hoyle F. Proceedings of 11th Solvay Conference in Physics, 1958.
     Google Scholar
  22. Valev. D. Estimations of total mass and energy of the universe. Physics International, 5:15, 2014. URL https://arxiv.org/abs/1004.1035.
     Google Scholar
  23. E. G. Haug. A new full relativistic escape velocity and a new Hubble related equation for the universe. Physics Essays, 34(4):502, 2021a. URL http://dx.doi.org/10.4006/0836-1398-34.4.502.
     Google Scholar
  24. E. G. Haug. Unified quantum gravity field equation describing the universe from the smallest to the cosmological scales. Physics Essays, 35:61, 2022a. URL https://doi.org/10.4006/0836-1398-35.1.61.
     Google Scholar
  25. H. A. Lorentz. Simplified theory of electrical and optical phenomena in moving systems. Proc. Acad. Scientific, Amsterdam, 1, 1899.
     Google Scholar
  26. F. E. Trinkein. Modern Physics, Teacher’s Edition. Holt, Reinhart and Winston Inc., 1992.
     Google Scholar
  27. R. D’Inverno. Introducing Einstein’s Relativity. Oxford University Press, 1992.
     Google Scholar
  28. D. C Giancoli. Physics for Scientists & Engineers. Pearson Prentice Hall, New Jersey, 2009.
     Google Scholar
  29. P. A. Tipler and R. A. Llewellyn. Introducing Einstein’s Relativity. W. H. Freeman and Company, New York, 2012.
     Google Scholar
  30. J. S. Walker. Physics, Fourth Edition. Addison-Wesley, 2010.
     Google Scholar
  31. A. Einstein. On the electrodynamics of moving bodies. Annalen der Physik, English translation by George Barker Jeffery 1923, (17), 1905. URL https://doi.org/10.1002/andp.19053221004.
     Google Scholar
  32. H. Minkowski. Space and time. A Translation of an Address delivered at the 80th Assembly of German Natural Scientists and Physicians, at Cologne, 21 September, in the book “The Principle of Relativity”, Dover 1923, 1908.
     Google Scholar
  33. C. G. Adler. Dose mass really depends on velocity dad? American Journal of Physics, 55:739, 1987. URL https://doi.org/10.1119/1.15314.
     Google Scholar
  34. L. B. Okun. The concept of mass. Physics Today, 42, 1989. URL https://doi.org/10.1063/1.881171.
     Google Scholar
  35. E. F. Taylor and J. A. Wheeler. Spacetime Physics, Introduction to Special Relativity. W. H. Freeman and Company, New York, 1992.
     Google Scholar
  36. E. Hecht. Einstein never approved the relativistic mass formula. The Physics Teacher, 47:336, 2009. URL https://doi.org/10.1119/1.3204111.
     Google Scholar
  37. W. Rindler. Putting to rest mass misconseptions. Physics Today, 43:13, 1990. URL https://doi.org/10.1063/1.2810555.
     Google Scholar
  38. W. Rindler. Relativity, Special, General and Cosmology, Second Edition. Oxford University Press, 2001.
     Google Scholar
  39. M. Jammer. Concepts of Mass in Contemporary Physics and Philosophy. Princeton University Press, 2000.
     Google Scholar
  40. E. G. Haug. The gravitational constant and the Planck units. A simplification of the quantum realm. Physics Essays, 29(4):558, 2016a. URL https://doi.org/10.4006/0836-1398-29.4.558.
     Google Scholar
  41. E. G. Haug. Progress on composite view of Newtonian gravitational constant and its link to the Planck scale. Hal Archives, 2022b. URL https://hal.archivesouvertes.fr/hal-03591779/document.
     Google Scholar
  42. S. Mukherjee and et al. First measurement of the Hubble parameter from bright binary black hole gw190521. Astrophys J.Lett. 908 (2021) 2, 908, 2021. URL https://doi.org/10.3847/2041-8213/abe388.
     Google Scholar
  43. J. Soltis, S. Casertano, and A. G. ARiess. The parallax of ω Centauri measured from Gaia EDR3 and a direct, geometric calibration of the tip of the red giant branch and the hubble constant. The Astrophysical Journal Letters, 908(1), 2021. URL https://doi.org/10.3847/2041-8213/abdbad.
     Google Scholar
  44. E. G. Haug. Can the Planck length be found independent of big G? Applied Physics Research, 9(6):58, 2017. URL https://doi.org/10.5539/apr.v9n6p58.
     Google Scholar
  45. E. G. Haug. Finding the Planck length multiplied by the speed of light without any knowledge of G, c, or h, using a Newton force spring. Journal Physics Communication, 4:075001, 2020a. URL https://doi.org/10.1088/2399-6528/ab9dd7.
     Google Scholar
  46. E. G. Haug. Collision space-time: Unified quantum gravity. Physics Essays, 33(1):46, 2020b. URL https://doi.org/10.4006/0836-1398-33.1.46.
     Google Scholar
  47. E. G. Haug. Using a grandfather pendulum clock to measure the world’s shortest time interval, the Planck time (with zero knowledge of G). Journal of Applied Mathematics and Physics, 9:1076, 2021b. URL https://doi.org/10.4236/jamp.2021.95074.
     Google Scholar
  48. E. G. Haug. 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, 3:15, 2021c. URL https://www.ej-physics.org/index.php/ejphysics/article/view/133.
     Google Scholar
  49. O. L. Trinhammer and H. G. Bohr. On proton charge radius definition. EPL, 128:21001, 2019. URL https://doi.org/10.1209/0295-5075/128/21001.
     Google Scholar
  50. E. G. Haug. Lorentz relativistic mass makes dark energy superfluous? SSRN archive, Elsivier, 2022c. URL https://papers.ssrn.com/sol3/papers.cfm?abstractid = 4040118.
     Google Scholar
  51. E. G. Haug. Wormholes do not exist, they are mathematical artifacts from an incomplete gravitational theory (?). HAL archive, 2021d. URL https://hal.archives-ouvertes.fr/hal-03325115/document.
     Google Scholar
  52. E. G. Haug. Light-speed acceleration radius. Working paper Norwegian University of Life Sciences, HAL archive, 2021e. URL https://hal.archivesouvertes.fr/hal-03405539/document.
     Google Scholar
  53. A. S. Eddington. Report on the Relativity Theory of Gravitation. The Physical Society of London, Fleetway Press, London, 1918.
     Google Scholar
  54. M.A. Markov. Elementary particles of maximally large masses (quarks and maximons). Soviet Physics JPT, 24(3), 1967.
     Google Scholar
  55. S. Hawking. Gravitationally collapsed objects of very low mass. Monthly Notices of the Royal Astronomical Society, 152, 1971.
     Google Scholar
  56. L. Motz and J. Epstein. The gravitational charge 1/2 √ ¯hc as a unifying principle in physics. Il Nuovo Cimento, 51(1), 1979. URL https://doi.org/10.1007/BF02822327.
     Google Scholar
  57. E. G. Haug. The Planck mass particle finally discovered! Working paper Norwegian University of Life Sciences http://vixra.org/abs/1607.0496, 2016b.
     Google Scholar
  58. V. Faraoni. Three new roads to the Planck scale. American Journal of Physics, 85, 2017. URL https://aapt.scitation.org/doi/pdf/10.1119/1.4994804.
     Google Scholar