Jupyter-Notebook Practice Physical Constants Ratios.ipynb

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    "# ***Jupyter-Notebook to Practice Physical Constants Ratios***\n",
    "\n",
    "## Dr Francis M. Sanchez's Physical Constants Ratios in Cosmology and MicroPhysics\n",
    "\n",
    "### Physical Constants Ratios\n",
    "\n",
    "Introduction\n",
    "------------\n",
    "\n",
    "`Jupyter-Notebook Practice Physical Constants Ratios` provides common physical constants ratios.\n",
    "\n",
    "\n",
    "Installation\n",
    "------------\n",
    "\n",
    "Run the Jupyter-notebook in [Mybinder.org](https://mybinder.org/v2/gh/LaGuer/Jupyter-Notebook-Practice-Physical-Constants-Ratios/master) will be available for Julia 0.7 and later versions, and can be\n",
    "installed with\n",
    "[Github.com source code](https://github.com/LaGuer/Jupyter-Notebook-Practice-Physical-Constants-Ratios/blob/master/Jupyter-Notebook%20Practice%20Physical%20Constants%20Ratios.ipynb).\n",
    "In a terminal session run the command\n",
    "\n",
    "```\n",
    "jupyter-notebook\n",
    "    \n",
    "```\n",
    "\n",
    "### Updated universal constants and particle properties ( thanks to Jean Maruani / Francis M. Sanchez)\n",
    "* [The_Dirac_Electron_From_Quantum_Chemistry_to_Holistic_Cosmology @ researchgate](https://www.researchgate.net/publication/287808070_The_Dirac_Electron_From_Quantum_Chemistry_to_Holistic_Cosmology)\n",
    "* [Dirac_Electron_From_Quantum_Chemistry_to_Holistic_Cosmology @ Wiley](https://onlinelibrary.wiley.com/doi/abs/10.1002/jccs.201500374)\n",
    "\n",
    "| Symbol  | Name                                | Formula                  | Dimension      | Value              | Unit            |\n",
    "| ------  | ----                                | -------                  | ---------      | -----              | ----            |\n",
    "| `π`     | pi                                  | -                        | -              | 3.1415926535897932 | `pure number`   |\n",
    "| `e`     | e                                   | -                        | -              | 2.7182817284590452 | `pure number`   |\n",
    "| `γ`     | gamma                               | -                        | -              | 0.5772156649015329 | `pure number`   |\n",
    "| `26SGP` | 26 sporadic group Product           | -                        | -              | exp(841.2869278)   | `pure number`   |\n",
    "| `HFP`   | Happy Family product                | -                        | -              | exp(674.5210288)   | `pure number`   |\n",
    "| `O_M`   | Monster Group Cardinal              | -                        | -              | 8.080174248 × 1053 | `pure number`   |\n",
    "| `O_B`   | Baby Monster Group Cardinal         | -                        | -              | 4.15478148 × 1033  | `pure number`   |\n",
    "| `c`     | Speed of light in vacuum            | -                        | -              | 2.99792458e8       | `m.s^-1`        |\n",
    "| `ħ`     | Reduced Planck constant             | ħ=h/2pi                  | -              | 1.054571800e-34    | `m^2 kg s^-1`   |\n",
    "| `G'`    | constant of gravitation CODATA2014  | -                        | M^-1L^3T^-2    | 6.67408(31)e-11    | `m^3 kg^-1 s^-2`|\n",
    "| `G`     | F.M.Sanchez constant of gravitation | F_gr=Gmm'/ d^2           | M^-1L^3T^-2    | 6.675453818e-11    | `m^3 kg^-1 s^-2`|\n",
    "| `a`     | Electric constant                   | a=α^-1  F_qq=ħc/ad^2     | dimensionless  | 137.035999139^-1   | `pure number`   |\n",
    "| `R_U`   | Universe Hubble radius (Sz)         | R_U=2G.M_U/c)^2          | L              | 1.3065e26          | `m`             |\n",
    "| `G_F`   | Fermi Coupling Constant (Sz)        | G_F=(ħc)^3/E_F^2         |   ML^5T^-2     | 1.4358509(7)e-62   | `J.m^3`         |\n",
    "| `a_G`   |Gravit Sanchez Coupling Constant     | a_G=ħc/Gm_pm_H           | -              | 1.691936465e38     | `pure number`   |\n",
    "| `M_U`   | Universe Sanchez Mass               | M_U=(ħc/G)^2/m_e.m_p.m_H | M              | 8.7936e52          | `kg`            |\n",
    "| `t_cc`  | Kotov Cosmic Periodicity            | -                        | s              | 9600.061(2)        | `s`             |\n",
    "|`r_H(0)` | Bare Hydrogen radius                |    aħ/m_ec               | L              | 5.291772103e-11    | `m`             |\n",
    "| `H`     |Hydrogen-electron mass ratio         |    m_H/m_e               | dimensionless  | 1837.152645        | `pure number`   |\n",
    "| `p`     |Proton-electron mass ratio           |    m_p/m_e               | dimensionless  | 1836.152672        | `pure number`   |\n",
    "| `n`     |Neutron-electron mass ratio          |    m_n/m_e               | dimensionless  | 1838.683659        | `pure number`   |\n",
    "| `m_e`   |electron mass                        | -                        | M              |9.10938356(11)e-31  | `kg`            |\n",
    "| `μ'`    |Muon electron mass ratio CODATA2014  | -                        | dimensionless  |206.7682826(41)     | `pure number`   |\n",
    "| `μ`     |Muon mass F.M.SANCHEZ  (Sz)          | -                        | dimensionless  |206.7682869         | `pure number`   |\n",
    "| `f'`    |Strg Nuc Coupling Constant CODATA2014| -                        | dimensionless  |1/0.1181(11)        | `pure number`   |\n",
    "| `f`     |Strg Nuc Coupling Constant C.Bizouard|    F^2/2pi(pH)^3/2       | dimensionless  |8.434502892         | `pure number`   |\n",
    "| `F'`    |Fermi Constant reduced mass CODAT2014|   E_F / m_ec^2           | dimensionless  |573007.33(25)       | `pure number`   |\n",
    "| `F`     |Fermi Constant reduc mass F.M.SANCHEZ| -                        | dimensionless  |573007.3652         | `pure number`   |\n",
    "| `d_e`   | electron magnetic moment excess     | -                        | dimensionless  |1.00115965218091(26)| `pure number`   |\n",
    "| `θ'`    |Cosmic Temperature CODATA2014        | -                        | -              |  2.7255(6) K       | `K`             |\n",
    "| `θ`     |Cosmic Temperature F.M.Sanchez       | -                        | -              |  2.725820831 K     | `K`             |\n",
    "| `k_B`   |Boltzman Energy-temperature Convers° | -                        | -              | 1.3806488e10-23    | `J K^-1`        |\n",
    "| `W`     |Intermediate vector boson Red. Mass  | -                        | dimensionless  | 157298(23)         | `pure number`   |\n",
    "| `Z`     |Intermediate vector boson Red. Mass  | -                        | dimensionless  | 178450.0(41)       | `pure number`   |\n",
    "| `Π±`    |Intermediate vector boson Red. Mass  | -                        | dimensionless  | 273.13203(68)      | `pure number`   |\n",
    "| `Π0`    |Intermediate vector boson Red. Mass  | -                        | dimensionless  | 264.1426(18)       | `pure number`   |\n",
    "\n",
    "## Latex and notations\n",
    "\n",
    "- Put your LaTeX math inside ```$$ $$```\n",
    "\n",
    "- Example of notation for: \n",
    "    \n",
    "- $$\\sqrt{a_W} = \\frac{E_F}{m_e \\cdot c^2}$$ type ```$$\\sqrt{a_W} = \\frac{E_F}{m_e \\cdot c^2}$$```\n",
    "\n",
    "- Write your equation in a dedicated cell with latex\n",
    "\n",
    "Exercice of notation for:\n",
    "\n",
    "- $$\\sqrt{G'G_F} = \\frac{\\frac{ƛ_e^2}{t_cc} \\cdot ħ}{\\sqrt{m_p \\cdot m_H}}$$ ```$$\\sqrt{G'G_F} = \\frac{\\frac{ƛ_e^2}{t_cc} \\cdot ħ}{\\sqrt{m_p \\cdot m_H}}$$```\n",
    "\n",
    "- This translates ```\\begin{equation}\n",
    "  \\frac{\\pi_Pt}{\\pi_Bb}\\ = 6\\cdot\\frac{\\pi^5}{p_H^9}\n",
    "  \\label{eq:sample}\n",
    "\\end{equation}\n",
    "```\n",
    "\n",
    "- to this:\n",
    "    \\begin{equation}\n",
    "  \\frac{\\pi_Pt}{\\pi_Bb}\\ = 6\\cdot\\frac{\\pi^5}{p_H^9}\n",
    "  \\label{eq:sample}\n",
    "\\end{equation}\n",
    "\n",
    "```\n",
    "%%latex\n",
    "\\begin{align}\n",
    "\\R_U = \\frac{2\\cdot G\\cdot M_U}{c^2} \\\\\n",
    "\\M_U = \\frac{({ħc}{G})^2}{m_em_pm_h} \\\\\n",
    "\\r_H/ƛ_e = frac{\\sum\\frac{1}{n}{\\sum(\\frac{1}{n^2})}\\\\\n",
    "\\end{align}\n",
    "```\n",
    "\n",
    "- $$\\e^{i\\pi} = -1$$ type ```$$\\e^{i\\pi} = -1$$```\n",
    "```\n",
    "\n",
    "- to this:\n",
    "- $$\\sum{n}(\\frac{1}{n})\\ = \\frac{137}{60} = 2 \\times (\\pi-2)$$ type ```$$\\sum{n}(\\frac{1}{n})\\ = \\frac{137}{60} = 2 \\times (\\pi-2)$$```\n",
    "    \n",
    "\n",
    "\n",
    "\n",
    "##"
   ]
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    "%%timeit\n",
    "# %matplotlib inline\n",
    "%matplotlib notebook\n",
    "import matplotlib\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# using PhysicalConstants.CODATA2014\n",
    "## m_p/m_e\n",
    "## R_U=2G.M_U/c)^2"
   ]
  },
  {
   "cell_type": "code",
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    {
     "data": {
      "text/latex": [
       "\\begin{align}\n",
       "\\frac{π_P_t}{π_B_b} = {6π^5}{p_H^9} \\\\\n",
       "\\frac{\\pi_Pt}{\\pi_Bb} = 6 \\cdot \\frac{\\pi^5}{p_H^9}\n",
       "\\end{align}"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
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    }
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   "source": [
    "%%latex\n",
    "\\begin{align}\n",
    "\\frac{m_p^4}{m_p\\cdot m_H\\cdot\\ m_e} = M \\\\\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Starting CosmHology...\n",
      "a/137\tpg\tpK\tH\tp\tn\t1sH-p\td\tZeros\tPrecision\n",
      "1\t2\t2\t1\t-3\t-2\t-1\t0\t1\t-16\n",
      "0\t0\t0\t0\t0\t0\t0\t0\t8\t0\n",
      "-1\t-2\t-2\t-1\t3\t2\t1\t0\t1\t16\n",
      "All results lead to nbSolutions = 3\n",
      "Precision 2e-08\n",
      "Used Values are: [['a/137', 0.00026273263604270625], ['pg', 7.51290767625786], ['pK', 7.518935136442214], ['H', 7.515972176482602], ['p', 7.515427722407373], ['n', 7.5168051918630026], ['1sH-p', 2.7000364506560378e-05], ['d', 0.0011589801229981887]]\n"
     ]
    }
   ],
   "source": [
    "# %%timeit\n",
    "# Inclusions\n",
    "from math import *\n",
    "values = []\n",
    "exponents = []\n",
    "\n",
    "########################################################\n",
    "#     Physical Constants Ratios                        #\n",
    "########################################################\n",
    "\n",
    "progression_display = True # True / False\n",
    "exponent_minmax = 3\n",
    "precision = 0.00000001 # add or remove 0 for precision's accuracy\n",
    "number_min_Zero = 1\n",
    "\n",
    "# exercice 2\n",
    "#exponent_minmax = 4\n",
    "#precision = 0.00000002\n",
    "#values.append(['a/137',log(137.0359991)-log(137)])\n",
    "#values.append(['pg',log(1831.531308)-log(1836.152672)*0])\n",
    "#values.append(['pK',log(1842.604127)-log(1836.118109)*0])\n",
    "#values.append(['H',log(1837.152645)-log(1836.118109)*0])\n",
    "#values.append(['p',log(1836.152672)+log(1836.118109)*0])\n",
    "#values.append(['n',log(1838.683659)])\n",
    "#values.append(['1sH-p',-log(0.999973)])\n",
    "#values.append(['d',log(1.001159652)])\n",
    "\n",
    "# exercice 2\n",
    "values.append(['pi',1.144729886])\n",
    "values.append(['a',4.920243658])\n",
    "values.append(['137',4.919980926])\n",
    "values.append(['F',13.25865385])\n",
    "values.append(['H/p',0.00054445428])\n",
    "values.append(['x',0.002792343634])\n",
    "values.append(['n',7.516805193])\n",
    "values.append(['8',2.079441542])\n",
    "values.append(['d',0.001158980123])\n",
    "values.append(['Ggamma',3.22597446])\n",
    "\n",
    "########################################################\n",
    "#     The Program itself                               #\n",
    "########################################################\n",
    "\n",
    "print (\"Starting CosmHology...\")\n",
    "length = len(values)\n",
    "precedent=-exponent_minmax\n",
    "\n",
    "# Min exponent set for each value \n",
    "for i in range (0,length):\n",
    "    exponents.append(-exponent_minmax)\n",
    "    print(values[i][0],end='\\t')\n",
    "\n",
    "print(\"Zeros\",end='\\t');\n",
    "print(\"Precision\");\n",
    "\n",
    "\n",
    "nbSolutions = 0\n",
    "#<= 0 Do not make twice the same calculation with the inverses\n",
    "while exponents[length-1]<=0:\n",
    "    # Calculate and process the result\n",
    "    result= 0\n",
    "    j=0\n",
    "    while j<length:\n",
    "        result=result + (values[j][1])*(exponents[j])\n",
    "        j+=1\n",
    "    #if result<0:\n",
    "    #    result*=(-1)\n",
    "\n",
    "    # Display or not the results\n",
    "    if result<=precision and result>=-precision:\n",
    "        # counting zeros\n",
    "        nbzero=0\n",
    "        for j in range (0,length):\n",
    "            if (exponents[j] == 0):\n",
    "                nbzero+=1\n",
    "        if nbzero >= number_min_Zero:\n",
    "            for j in range (0,length):\n",
    "                print(exponents[j],end='\\t')\n",
    "            print(nbzero,end='\\t')\n",
    "            print(int(result*1000000000))\n",
    "            nbSolutions = nbSolutions + 1\n",
    "    \n",
    "    # Add + Exponents Rotation\n",
    "    exponents[0]+=1\n",
    "    for j in range (0,length-1):\n",
    "        if exponents[j]>exponent_minmax:\n",
    "            exponents[j]=-exponent_minmax\n",
    "            exponents[j+1]+=1\n",
    "    if (progression_display):\n",
    "        if (exponents[length-2]!=precedent):\n",
    "            precedent=exponents[length-2]\n",
    "            #print(\"Status:\",end=' ')\n",
    "\n",
    "print(exponents[j+1]);\n",
    "print (\"All results lead to nbSolutions =\", nbSolutions)\n",
    "print(\"Precision\", precision)\n",
    "print(\"Used Values are:\", values)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the following example, one can write the equation with Latex:"
   ]
  },
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     "data": {
      "text/latex": [
       "\\begin{eqnarray}\n",
       "\\frac{m_p^4}{m_p\\cdot m_H\\cdot\\ m_e} = M  \\\\\n",
       "\\R_U = \\frac{2\\cdot G\\cdot M_U}{c^2} \\\\\n",
       "\\M_U = \\frac{({ħc}{G})^2}{m_em_pm_h} \\\\\n",
       "\\frac{r_H}{ƛ_e} = \\frac{\\sum\\frac{1}{n}}{\\sum\\frac{1}{n^2}}\\\\\n",
       "\\end{eqnarray}"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.display import Latex\n",
    "Latex(r\"\"\"\\begin{eqnarray}\n",
    "\\frac{m_p^4}{m_p\\cdot m_H\\cdot\\ m_e} = M  \\\\\n",
    "\\R_U = \\frac{2\\cdot G\\cdot M_U}{c^2} \\\\\n",
    "\\M_U = \\frac{({ħc}{G})^2}{m_em_pm_h} \\\\\n",
    "\\frac{r_H}{ƛ_e} = \\frac{\\sum\\frac{1}{n}}{\\sum\\frac{1}{n^2}}\\\\\n",
    "\\end{eqnarray}\"\"\")\n"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    ":star:\n",
    "\n",
    "# Docs\n",
    "\n",
    "This project aims at providing a repository dedicated to Dr Francis Michel Sanchez' work in holography and cosmology; it is just a mere continuation of what was initiated and published on a couple of other blogs.\n",
    "\n",
    "## Blog\n",
    "* [cosmhology blog in english](https://cosmhology.blogspot.com/)\n",
    "* [cosmhologie blog in french](https://cosmhologie.blogspot.com/)\n",
    "* [Concorde Physiques in russian ](http://concorde-physiques.blogspot.com/)\n",
    "\n",
    "## Publications\n",
    "* Please, cite this paper (http://vixra.org/pdf/1811.0146v8.pdf) if you employ this package in your research work.\n",
    "* [Vixra Publications](https://vixra.org/author/francis_m_sanchez)\n",
    "* [A coherent resonant cosmology approach and its implications in microphysics and Biophysics Pages 375-407 of Quantum Systems in Physics, Chemistry](https://www.springer.com/fr/book/9783319502540?token=gbgen&wt_mc=GoogleBooks.GoogleBooks.3.EN#)\n",
    "* [From Coherent Cosmic Oscillations to the Steady-State Cyclic Ultrafast](https://rxiv.org/abs/1401.0228)\n",
    "* [Evidence for a Steady-State, Holographic, Tachyonic and Super-Symmetric Cosmology](https://www.researchgate.net/publication/267430152_Evidence_for_a_Steady-State_Holographic_Tachyonic_and_Super-Symmetric_Cosmology)\n",
    "* [academia.edu Correcting Five Historical Faults in Modern Cosmology](https://www.academia.edu/30843365/Correcting_Five_Historical_Faults_in_Modern_Cosmology)\n",
    "\n",
    "## Videos\n",
    "\n",
    "* [L'enigme des grands nombres Part1](https://www.youtube.com/watch?v=ev_eIqLtK8s)\n",
    "* [L'enigme des grands nombres Part2](https://www.youtube.com/watch?v=i4w392nYqns)\n",
    "* [L'enigme des grands nombres Part3](https://www.youtube.com/watch?v=b4WvI0yVXnE)\n",
    "* [Exposés de Francis Sanchez](https://www.youtube.com/playlist?list=PLQXUNrzoAeFbmfHo3jgWzzExlVoBn2JUw)\n",
    "* [Khelif/Torgoz/Sanchez' Debate on LE FORMALISME EN PHYSIQUE ET EN SCIENCE](https://www.youtube.com/watch?v=TEK2hCI2we0)\n",
    "\n",
    "* https://www.youtube.com/watch?v=dyUlUahgHGg\n",
    "* https://www.youtube.com/watch?v=NmvvIQjxBw8\n",
    "* https://www.youtube.com/watch?v=dyUlUahgHGg\n",
    "* https://www.youtube.com/watch?v=zUt1hxTdiuA\n",
    "* https://www.youtube.com/watch?v=05g416VWjnw\n",
    "\n",
    "## Books\n",
    "\n",
    "* [Quantum Systems in Physics, Chemistry, Springer Ed](https://www.amazon.com/gp/search?index=books&linkCode=qs&keywords=9783319502557)\n",
    "* [The Worldwide List of Alternative Theories and Critics](https://books.google.com/books?isbn=2902425171)\n",
    "* [The Dirac Electron: From Quantum Chemistry to Holistic Cosmology by J.Maruani](https://onlinelibrary.wiley.com/doi/abs/10.1002/jccs.201500374#)\n",
    "* [solar 22 years cycle](https://link.springer.com/article/10.1007%2Fs10509-016-2985-8)\n",
    "* [Current Issues in Cosmology](https://www.cambridge.org/gb/academic/subjects/physics/cosmology-relativity-and-gravitation/current-issues-cosmology?format=HB&isbn=9780521858984)\n",
    "* ```@inproceedings{Sanchez2015RemarkablePO,\n",
    "  title=Remarkable Properties of the Eddington Number 137 and Electric Parameter 137 . 036 excluding the Multiverse Hypothesis},\n",
    "  author={Francis M. Sanchez and Valery A. Kotov,\n",
    "  year=2015```\n",
    "\n",
    "## Papers\n",
    "\n",
    "* [Discussions sur les oscillations cosmiques, les nombres sans dimension et les periodicites en microphysique et cosmologie - College de France 2004](https://lempel.pagesperso-orange.fr/occ_cdf.pdf)\n",
    "\n",
    "More to come soon stay tuned.../.:stars:."
   ]
  },
  {
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   "source": [
    "\n",
    "\n",
    "    #Write your equation in a dedicated cell with latex\n",
    "\n",
    "from IPython.display import Latex\n",
    "Latex(r\"\"\"\\begin{eqnarray}\n",
    "\\frac{m_p^4}{m_p\\cdot m_H\\cdot\\ m_e} = M \\\\\n",
    "\\frac{\\pi_Pt}{\\pi_Bb} = 6 \\cdot \\frac{\\pi^5}{p_H^9} \\\\\n",
    "\\end{eqnarray}\"\"\")\n",
    "\n",
    "\n"
   ]
  }
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