{"id":31823035,"url":"https://github.com/laguer/hubble-radius","last_synced_at":"2026-03-08T16:33:13.708Z","repository":{"id":106680767,"uuid":"233860723","full_name":"LaGuer/hubble-radius","owner":"LaGuer","description":"48 Methods exhibiting the Hubble radius (distance estimates) mistakenly known as the age of the universe","archived":false,"fork":false,"pushed_at":"2025-03-30T14:15:23.000Z","size":1867,"stargazers_count":3,"open_issues_count":0,"forks_count":0,"subscribers_count":1,"default_branch":"master","last_synced_at":"2025-03-30T14:28:47.400Z","etag":null,"topics":["age","astrophysics","bondi","calculation","calculus","constant","cosmology","eddington","gravitational","jupyter","kotov","nambu","notebook","planck","radius","sanchez","schwarzschild","steady-state","theory","universe"],"latest_commit_sha":null,"homepage":"","language":"Jupyter 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Notebook","funding_links":[],"categories":[],"sub_categories":[],"readme":"# Hubble radius distance estimates\n\n[![Cite ptep](https://img.shields.io/badge/PP-57-12-yellow.svg?style=flat)](http://www.ptep-online.com/2019/PP-57-12.PDF)\n[![Latest PDF](https://img.shields.io/badge/PDF-latest-red.svg?style=flat)](http://www.ptep-online.com/2019/PP-57-12.PDF)\n[![Cite rXiv](https://img.shields.io/badge/rXiv-1904.0218-orange.svg?style=flat)](http://rxiv.org/abs/1904.0218)\n[![Cite viXra](https://img.shields.io/badge/viXra-1811.0146-green.svg?style=flat)](http://vixra.org/pdf/1811.0146v8.pdf)\n[![Build Status](https://travis-ci.org/LaGuer/hubble-radius.svg?branch=master)](https://travis-ci.org/LaGuer/hubble-radius) \n[![codecov](https://codecov.io/gh/LaGuer/hubble-radius/branch/master/graph/badge.svg)](https://codecov.io/gh/LaGuer/hubble-radius)\n[![Binder](https://mybinder.org/badge_logo.svg)](https://mybinder.org/v2/gh/LaGuer/hubble-radius/master)\n[![Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/laguer/universe-age/blob/master/universe-age.ipynb)\n[![nbviewer](https://img.shields.io/badge/view%20on-nbviewer-brightgreen.svg)](https://nbviewer.jupyter.org/github/LaGuer/hubble-radius/blob/master/hubble-radius.ipynb)\n[![Binder](https://mybinder.org/badge.svg)](https://mybinder.org/v2/gh/LaGuer/hubble-radius/master?urlpath=lab%2Ftree%2Fhubble-radius-new.ipynb)\n\nThis repository contains python code and Jupyter notebooks presenting 48 Methods exhibiting the age of the universe (Hubble radius distance) using 3 physical constants excluding the speed of light.\n\nSource Context:\n\nThe formula **$R_H= ℏ^2/G m_e m_n m_p$** is derived via dimensional analysis, inspired by approaches in natural units and large-number hypotheses.\n\n\nDimensional Relationships\nThe quantity for length (𝐿) can be derived from the Planck constants. Using dimensional analysis:\n$𝐿 ∝ ℏ𝐺 / 𝑀$\nWhere:\nℏ has dimensions of $ML^2T^{-1}$,\n𝐺 has dimensions of $L^3M^{-1}T^{-2}$,\n𝑀 represents mass.\n\nTo incorporate the masses of fundamental particles, we treat \n𝑀 as the combination of \n$𝑚_𝑝$, $𝑚_𝑛$, and $𝑚_𝑒$ in relevant proportions (to represent universal characteristics).\n\nThese 48 formulas illustrate how one can “compute” a cosmic length scale using only ℏ, 𝐺, and the masses $𝑚_𝑒$, $𝑚_𝑛$, and $𝑚_𝑝$\n – all without an explicit appearance of the speed of light. They serve as a playground for exploring how dimensional analysis and natural unit ideas may (or may not) reflect deep physics.\n\nPhysical Interpretation: In a standard cosmological setting the Hubble radius is defined by \n$𝑅_𝐻 = 𝑐/𝐻_0$\n (which explicitly uses the speed of light). Recasting it in terms of other fundamental constants—and in particular not introducing \n𝑐\n—is an approach that appears in attempts (such as those by Francis Michel Sanchez) to “derive” cosmic scales from quantum–gravitational considerations. The fact that one can match the observational scale (within a few percent, under a suitable choice of \n𝑘\n) is a point of considerable debate and interest.\n \n```\nimport scipy.constants as const\nimport numpy as np\n\n# Constants (CODATA 2018/2022 values for consistency)\nhbar = const.hbar  # Reduced Planck constant (J·s)\nG = const.G        # Gravitational constant (m^3·kg^−1·s^−2)\nm_e = const.electron_mass  # Electron mass (kg)\nm_p = const.proton_mass    # Proton mass (kg)\nm_n = const.neutron_mass   # Neutron mass (kg)\nalpha = const.alpha        # Fine-structure constant (dimensionless)\n\n# Conversion constants\nmeters_per_lightyear = 9.461e15  # Approximate meters in one light-year\nmeters_to_gly = 1 / (meters_per_lightyear * 1e9)  # Convert meters to gigalight-years\n\n# JWST measured value (placeholder, in meters)\njwst_measured_value = 1.308e+26  # Approximate JWST value (corresponding to 13.81 Gly)\n\n# Ratio of Compton wavelength to Planck length\nlambda_e = hbar / (m_e * const.c)  # Electron Compton wavelength (m)\nL_planck = np.sqrt(hbar * G / const.c**3)  # Planck length (m)\nP = lambda_e / L_planck\n\n# Precision formula\ndef precision_formula(P, alpha, lambdabare):\n    \"\"\"\n    Precision theory formula for calculation.\n    P: Ratio of Compton wavelength to Planck length\n    alpha: Fine-structure constant\n    lambdabare: Bare constant input\n    \"\"\"\n    term1 = np.e**(4 * np.e - 1 / alpha)\n    term2 = np.log(P**4 / alpha**3)**2\n    exponent = np.sqrt((term1 - term2) / 2)\n    return np.exp(exponent) * lambdabare\n\n# Corrected formula: R = 2 * hbar^2 / (G * m_e * m_n * m_p)\ndef corrected_formula(hbar, G, m_e, m_p, m_n):\n    \"\"\"\n    Calculates the Hubble radius using the corrected formula.\n    \"\"\"\n    return 2 * hbar**2 / (G * m_e * m_n * m_p)\n\n# Adjusted lambdabare value for scaling\nlambdabare = 1e-5  # Example value in meters\n\n# Calculate corrected formula result\ncorrected_result = corrected_formula(hbar, G, m_e, m_p, m_n)\ncorrected_result_gly = corrected_result * meters_to_gly  # Convert to gigalight-years\n\n# Calculate precision formula result\nprecision_result = precision_formula(P, alpha, lambdabare)\nprecision_result_gly = precision_result * meters_to_gly  # Convert to gigalight-years\n\n# Calculate precision difference (JWST deviation)\nprecision_difference = abs(corrected_result_gly - 13.81) / 13.81\n\n# Output results\nprint(\"Hubble Radius Calculation:\")\nprint(f\"Corrected Formula:\")\nprint(f\"R (meters) = {corrected_result:.3e} m\")\nprint(f\"R (gigalight-years) = {corrected_result_gly:.3f} Gly\")\n\nprint(\"\\nPrecision Formula Calculation:\")\nprint(f\"R (meters) = {precision_result:.3e} m\")\nprint(f\"R (gigalight-years) = {precision_result_gly:.3f} Gly\")\n\nprint(\"\\nJWST Measured Value:\")\nprint(f\"JWST Value (meters) = {jwst_measured_value:.3e} m\")\nprint(f\"JWST Value (gigalight-years) = {jwst_measured_value * meters_to_gly:.3f} Gly\")\n\nprint(f\"\\nPrecision Difference (Relative Error): {precision_difference:.5%}\")\n\n\n```\n\n\nIn addition we used Python modules such as: scipy, sympy, pandas and numpy\n\nFixed Constants used are:\n\n* 𝜋=3.141592653589793... https://oeis.org/A000796\n* Euler Mascheroni  𝛾=0.5772156649015329... https://oeis.org/A001620\n* Atiyah's  Γ=25.178097241906... \n* Feigenbaum constant δ=4.669201609102990671853... https://oeis.org/A006890\n* 2nd Feigenbaum constant α=2.50290787509589282228390287321... https://oeis.org/A006891\n* Eddington Electric Constant  𝑎=137.0359990836958  also known as the inversed fine structure constant CODATA2018\n* 𝑐=299792458.0  m/s CODATA2018\n* ℎ=6.62607015.10−34   𝐽.𝐻𝑧−1  CODATA2018\n* ℏ=1.0545718176461565.10−34   𝐽.𝑠  CODATA2018\n* 𝑙𝑃=1.616255.10−35  m Planck length\n* 𝑚𝑃=2.176434.10−8  kg Planck mass\n* ƛ𝑒 =3.8615926796.10−13 m Reduced (Electron) Compton Wavelength CODATA2018\n* ƛ𝑝 =2.10308910336.10−16 m Reduced (Proton) Compton Wavelength CODATA2018\n* Mass of the electron  𝑚𝑒=9.1093837015.10−31  kg CODATA2018\n* Mass of the proton  𝑚𝑝=1.67262192369.10−27  kg CODATA2018\n* Boson  𝑊=80.379𝐺𝑒𝑉  ± 0.012 Particle Data Group Bosons M. Tanabashi et al. (Particle Data Group), Phys. Rev. D 98, 030001 (2018) and 2019\n* Boson  𝑍=91.1876𝐺𝑒𝑉  ± 0.0023 Particle Data Group Bosons M. Tanabashi et al. (Particle Data Group), Phys. Rev. D 98, 030001 (2018) and 2019\n* Lepton  𝑒=0.5109989461𝑀𝑒𝑉  Particle Data Group Leptons M. Tanabashi et al. (Particle Data Group), Phys. Rev. D 98, 030001 (2018) and 2019\n* Baryon  𝑝=938.272081𝑀𝑒𝑉  Particle Data Group Baryons M. Tanabashi et al. (Particle Data Group), Phys. Rev. D 98, 030001 (2018) and 2019\n* Baryon  𝑛=939.565413𝑀𝑒𝑉  Particle Data Group Baryons M. Tanabashi et al. (Particle Data Group), Phys. Rev. D 98, 030001 (2018) and 2019\n* 𝐺=6.6743.10−11   𝑚3.𝑘𝑔−1.𝑠−2  Newtonian constant of gravitation CODATA2018\n* 𝐺𝑞=6.6755.10−11   𝑚3.𝑘𝑔−1.𝑠−2  Newtonian constant of gravitation measured by T.Quinn et al. (2013) BIPM Sevres Improved determination of G using two methods\n* 𝐺𝑏2𝑐=6.6754552.10−11   𝑚3.𝑘𝑔−1.𝑠−2  Newtonian constant of gravitation estimated by Francis M. Sanchez et al. (2019) in Back to Cosmos\n* 𝐺𝑠=6.67545372.10−11   𝑚3.𝑘𝑔−1.𝑠−2  Newtonian constant of gravitation estimate by Francis M. Sanchez (Jan 2020)\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Flaguer%2Fhubble-radius","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Flaguer%2Fhubble-radius","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Flaguer%2Fhubble-radius/lists"}