Calculation of the Hubble Constant, the Minimum Mass and the Proton Charge Radius Using the Dirac&#039;s Hypothesis on the Ratio of the Electrostatic Force to the Gravitational Force

Paul Talbot

doi:10.3844/pisp.2023.1.5

Abstract

Currently, several physical constants are determined by observation. This is the case for the Hubble constant and the proton charge radius whose observed values involve large uncertainties. This publication suggests that these values could be calculated more precisely using algebraic equations involving other physical constants. To do so, some assumptions must be put forward, namely, the Dirac's hypothesis on the observed ratio of the electrostatic force to the gravitational force. The approach used also allows calculating the value of a minimum mass. The calculated value of the Hubble constant is: H ≈ 72.013 km s^‑1 Mpc^‑1, and that of the minimum mass: M_min ≈ 1.7206×10^‑68 kg. Recent observations suggest that the proton charge radius could also be calculated using an additional but related assumption: r_p ≈ 0.8264 fm.

References

Atoui, M., Barbaro, M. B., Hoballah, M., Keyrouz, C., Lassaut, M., Marchand, D., Quéméner, G., & Voutier, E. (2023). Determination of the Moments of the Proton Charge Density. ArXiv, 13521. https://doi.org/10.48550/arXiv.2304.13521

Berman, M. S. (1992). Large Number Hypothesis. International Journal of Theoretical Physics, 31, 1447–1450. https://doi.org/10.1007/bf00673977

Beyer, A., Maisenbacher, L., Matveev, A., Pohl, R., Khabarova, K., Grinin, A., Lamour, T., Yost, D. C., Hänsch, T. W., Kolachevsky, N., & Udem, T. (2017). The Rydberg Constant and Proton Size from Atomic Hydrogen. Science, 358(6359), 79–85. https://doi.org/10.1126/science.aah6677

Bezginov, N., Valdez, T., Horbatsch, M., Marsman, A., Vutha, A. C., & Hessels, E. A. (2019). A Measurement of the Atomic Hydrogen Lamb Shift and the Proton Charge Radius. Science, 365(6457), 1007–1012. https://doi.org/10.1126/science.aau7807

Cetto, A. M., Peña, L. D. la, & Santos, E. (1986). Dirac’s large-number hypothesis revised. Astronomy and Astrophysics, 164(1), 1–5.

Dirac, P. A. M. (1938). A new basis for cosmology. Proceedings of the Royal Society A, 165(921), 199–208. https://doi.org/10.1098/rspa.1938.0053

Dirac, P. A. M. (1974). Cosmological models and the Large Numbers hypothesis. Proceedings of the Royal Society A, 338(1615), 439–446. https://doi.org/10.1098/rspa.1974.0095

Dirac, P. A. M. (1979). The Large Numbers hypothesis and the Einstein theory of gravitation. Proceedings of the Royal Society A, 365(1720), 19–30. https://doi.org/10.1098/rspa.1979.0003

Djukanovic, D., Harris, T., Von Hippel, G., Junnarkar, P. M., Meyer, H. B., Mohler, D., Ottnad, K., Schulz, T., Wilhelm, J., & Wittig, H. (2021). Isovector electromagnetic form factors of the nucleon from lattice QCD and the proton radius puzzle. Physical Review D, 103(9), 094522. https://doi.org/10.1103/physrevd.103.094522

Freedman, W. L. (2021). Measurements of the Hubble Constant: Tensions in Perspective. The Astrophysical Journal, 919(1), 16. https://doi.org/10.3847/1538-4357/ac0e95

Gao, H., & Vanderhaeghen, M. (2022). The proton charge radius. Reviews of Modern Physics, 94(1), 015002. https://doi.org/10.1103/revmodphys.94.015002

Khetan, N., Izzo, L., Branchesi, M., Wojtak, R., Cantiello, M., Murugeshan, C., Agnello, A., Cappellaro, E., Della Valle, M., Gall, C., Hjorth, J., Benetti, S., Brocato, E., Burke, J., Hiramatsu, D., Howell, D. A., Tomasella, L., & Valenti, S. (2021). A new measurement of the Hubble constant using Type Ia supernovae calibrated with surface brightness fluctuations. Astronomy & Astrophysics, 647(A&A), A72. https://doi.org/10.1051/0004-6361/202039196

Kritov, A. (2021). Explicit Values for Gravitational and Hubble Constants from Cosmological Entropy Bound and Alpha-Quantization of Particle Masses. Progress in Physics, 17(2), 158–163.

Lau, Y. K., & Prokhovnik, S. J. (1986). The Large Numbers Hypothesis and a Relativistic Theory of Gravitation. Australian Journal of Physics, 39(3), 339–346. https://doi.org/10.1071/ph860339

Liao, K., Shafieloo, A., Keeley, R. E., & Linder, E. V. (2019). A Model-independent Determination of the Hubble Constant from Lensed Quasars and Supernovae Using Gaussian Process Regression. The Astrophysical Journal Letters, 886(1), L23. https://doi.org/10.3847/2041-8213/ab5308

Lusso, E., Piedipalumbo, E., Risaliti, G., Paolillo, M., Bisogni, S., Nardini, E., & Amati, L. (2019). Tension with the flat ΛCDM model from a high-redshift Hubble diagram of supernovae, quasars, and gamma-ray bursts. Astronomy & Astrophysics, 628(A&A), L4. https://doi.org/10.1051/0004-6361/201936223

Mercier, C. (2019). Calculation of the Universal Gravitational Constant, of the Hubble Constant, and of the Average CMB Temperature. Journal of Modern Physics, 10(6), 641–662. https://doi.org/10.4236/jmp.2019.106046

Perl, M. L., Lee, E. R., & Loomba, D. (2004). A Brief Review of the Search for Isolatable Fractional Charge Elementary Particles. Modern Physics Letters A, 19(35), 2595–2610. https://doi.org/10.1142/s0217732304016019

Pesce, D. W., Braatz, J. A., Reid, M. J., Riess, A. G., Scolnic, D., Condon, J. J., Gao, F., Henkel, C., Impellizzeri, C. M. V., Kuo, C. Y., & Lo, K. Y. (2020). The Megamaser Cosmology Project. XIII. Combined Hubble Constant Constraints. The Astrophysical Journal Letters, 891(1), L1. https://doi.org/10.3847/2041-8213/ab75f0

Ray, S., Mukhopadhyay, U., Ray, S., & Bhattacharjee, A. (2019). Dirac’s large number hypothesis: A journey from concept to implication. International Journal of Modern Physics D, 28(08), 1930014. https://doi.org/10.1142/s0218271819300143

Riess, A. G., Yuan, W., Macri, L. M., Scolnic, D., Brout, D., Casertano, S., Jones, D. O., Murakami, Y., Anand, G. S., & Breuval, L. (2022). A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−1 Mpc−1 Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters, 934(1), L7. https://doi.org/10.3847/2041-8213/ac5c5b

Rushdi, M. A., & Rushdi, A. M. (2016). On the Fundamental Masses Derivable by Dimensional Analysis. Journal of King Abdulaziz University: Engineering Sciences, 27(1), 35–42. https://doi.org/10.4197/eng.27-1.3

Shuntov, M. (2018). Unveiling the Concordance Model of Cosmology [Aix-Marseille Universit´e]. https://doi.org/10.13140/RG.2.2.30613.83688

Talbot, Paul. (2021). The Cosmospheric Principle: A Systemic Modeling of the Universe (pp. 97–100).

Valev, D. (2013). Three fundamental masses derived by dimensional analysis. Space Science International, 1(2), 145–149. https://doi.org/10.3844/ajssp.2013.145.149

Valev, D. T. (2015). Estimations of Neutrino and Graviton Masses by a Phenomenological Mass Relation for Stable Particles. Physics International, 6(2), 82–88. https://doi.org/10.3844/pisp.2015.82.88

Wesson, P. S. (2004). Is Mass Quantized? Modern Physics Letters A, 19(26), 1995–2000. https://doi.org/10.1142/S0217732304015270

Wilmot, R. G. (2021). Exact value of the hubble constant the most precise value of the hubble constant deduced from other constants of physics calculation of the hubble constant with an accuracy up to the tenth decimal figure deduced from known physics constants. Cosmic background radiation temperature and its calculation deduced from known physics constants. The large numbers hypotesis explained. Calculation of the change of the electromagnetic and gravitational fine structure constants, with the age of the universe. https://doi.org/10.13140/RG.2.2.25508.60802

Wolf, C. G. (2022). Hubble constant H0 is derived from Newtonian gravitational constant G, speed of light in vacuum c, electron mass me, classical electron radius re squared and fine structure constant α - all being primarily constants of quantum mechanics, while G is mostly associated to cosmology and speed of light c being omnipresent in both worlds - large and small. https://doi.org/10.13140/RG.2.2.15487.48801

Xiong, W., Gasparian, A., Gao, H., Dutta, D., Khandaker, M., Liyanage, N., Pasyuk, E., Peng, C., Bai, X., Ye, L., Gnanvo, K., Gu, C., Levillain, M., Yan, X., Higinbotham, D. W., Meziane, M., Ye, Z., Adhikari, K., Aljawrneh, B., … Zhao, Z. W. (2019). A small proton charge radius from an electron–proton scattering experiment. Nature, 575, 147–150. https://doi.org/10.1038/s41586-019-1721-2

Yang, T., Birrer, S., & Hu, B. (2020). The first simultaneous measurement of Hubble constant and post-Newtonian parameter from time-delay strong lensing. Monthly Notices of the Royal Astronomical Society: Letters, 497(1), L56–L61. https://doi.org/10.1093/mnrasl/slaa107

Calculation of the Hubble Constant, the Minimum Mass and the Proton Charge Radius Using the Dirac's Hypothesis on the Ratio of the Electrostatic Force to the Gravitational Force

Abstract

References

Download

Keywords