jeudi 10 octobre 2024

Relative mass Proton / Electron

A Surprising Way to Calculate the Proton/Electron Mass Ratio

     There are things in the Universe that we do not know how to calculate, we only measure them.
One of them is the mass of the proton. Why does the proton have this mass exactly? Nobody knows. But today I propose to show you a calculation that deduces the mass of the proton from that of the electron.

    Behind this calculation is an old theory, which I will not show you now, because the purpose of this article is only to draw attention to it.

What is remarkable on this calculation is that it only uses physical constants and does not seem to cheat to obtain the expected result.
And even more remarkable: it obtains the first 7 significant digits!

The variables used are:
.Electron mass
.Speed ​​of light
.Fine Structure Constant
.Permeability of Space
.Electron charge
.Electron magnetic moment
.Compton wavelength
.Planck constant

 These constants are used respecting the balance of their SI units.

Calculated proton/electron mass ratio (CODATA 2020)  : 1836.15220 

Official proton/electron mass ratio (CODATA 2020)        : 1836.15267

The script also calculates the neutron/electron mass ratio. 

The calculation correctly gives the first seven significant digits. It is impossible that this is a coincidence. Analysis of the program shows that no number is added to make the calculations correct. The program works as an iterative loop whose first level is the mass of the electron and then each level contributes with a higher mass.


    As giving the algorithm is worth a thousand words, here is the program written in basic javascript, just copy it into a text file and save it under a name like myscript.html. Then open it with your favorite browser. This program is the exact translation of the Lockyer's program written in BASIC many years ago..

<html><body><head>
<style>
table, th, td {
  border: 1px solid black;
  border-collapse: collapse;
  padding: 3px;
  text-align : right;
}
</style>
<script>
// You can check these values on the internet :
c = 299792458;               // Light speed    m/s
alpha = 0.00729735257  // fine structure constant 
pi = Math.PI;      
vp = 4*pi/Math.pow(10,7);      // Magnetic vacuum permeability  : Henry per meter : H/m  [N/A^2]
e0 = 1 / (c*c*vp);                     // vacuum permittivity                   : = 8.8541878176 * 10^-12 F/m
e = 1.60217733 * Math.pow(10,-19);       // charge of electron                        : Ampere*second
cwl = 2.42631058 * Math.pow(10,-12);   // Compton wave length                  : meters 
rcwl = cwl/(2*pi);                     // rationalized Compton wavelength electron  : meters 
me = 9.10938972 * Math.pow(10,-31);    // mass of electron                           : Kilograms 
ElectronMass = 1;                     // Relative electron mass; 
SquareRootTwo = Math.sqrt(2); 
signif = 1000000;                     // To avoid displaying too many unnecessary decimals

// Rationalized fine structure constant
alpha_e = alpha/(2*pi);
a_u = 2 * (Math.sqrt(1 + alpha_e) - 1);
d = (1-(SquareRootTwo/2))/2 - a_u/SquareRootTwo;     // The radius of each level is slightly smaller. The Fine Structure Constant intervenes

m = (d*d)/(me*4*pi*c*c*rcwl*d*e0);     // m being smaller than 1, the fine structure constant increases the mass contribution of each calculated level
m = (e*e)/(me*Math.pow(10,7)*rcwl*d);  // equivalent formula with less rounding errors

document.write ("<table>");
document.write ("<th colspan=5 style='text-align:center;'> &nbsp &nbsp &nbsp _-_ &nbsp Calculation of the proton/electron mass ratio &nbsp _-_ &nbsp &nbsp &nbsp </th>");
document.write ("<tr><td>Level</td><td>m1</td><td>m2</td><td>m1+m2</td><td>Sum</td></tr>");

var m1 = new Array(); var m2 = new Array();
m1[1] = ElectronMass; m2[1] = m;    
t1=0; t2=0;
for(i=1;i<=19;i++){
m1[i+1]= ElectronMass * Math.pow(SquareRootTwo,i) / (1-SquareRootTwo*a_u);
m2[i+1]= m * Math.pow(SquareRootTwo,i) / (1-SquareRootTwo*a_u);
t1 += m1[i];
t2 += m2[i];
document.write ("<tr><td>" + i + "</td><td>" + Math.round(m1[i]*signif)/signif + "</td><td>" + Math.round(m2[i]*signif)/signif + "</td><td>" + Math.round(eval(m1[i]+m2[i])*signif)/signif + "</td><td>" + Math.round(eval(t1+t2)*signif)/signif + "</td></tr>");
}
document.write ("</table>");
signif = 100000000;   // To avoid displaying too many unnecessary decimals
document.write ("<br>Calculated proton/electron mass ratio : "+ Math.round((t1+t2)*signif)/signif+ " <br>--- Official proton/electron mass ratio : 1836.15267343  &nbsp (CODATA 2020)"); 
mr = Math.round((eval((t1+t2-1836.15267343)/1836.15267343)*signif))/signif;
document.write ("<br>Relative error = " + mr + " = " + mr.toFixed(8) + " = " + (100*mr).toFixed(6) + "%");

document.write ("<br><br>Calculated neutron/electron mass ratio : "+ Math.round(eval(t1+t2+m1[1]+m2[1]+m1[2]+m2[2])*signif)/signif+ " <br>--- Official neutron/electron mass ratio : 1838.683662 &nbsp (CODATA 2020)");
mr = eval((t1+t2+m1[1]+m2[1]+m1[2]+m2[2]-1838.683662)/1838.683662);
document.write ("<br>Relative error = " + Number.parseFloat(mr).toExponential(2) + " = " + mr.toFixed(8) + " = " + (100*mr).toFixed(6) + "%");
</script></body></html>


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Masse relative Proton / Electron