- #1

arivero

Gold Member

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Plus c and h, of course.

The idea is to collect here in only a thread all the approximations voiced out during the summer. Surely this is to be quarantinised in TheoryDev, but it is interesting enough to be kept open as a thread (if closed, please be free to use my http://www.infoaragon.net/servicios/blogs/conjeturas/index.php?idarticulo=200410041 [Broken])

First we get Planck Mass, [tex]M_P[/tex], from G, c and h as usual.

Then we solve for [tex]\alpha[/tex], the fine structure constant, in HdV second equation (*),

[tex]

\alpha^{-1/2}+ (1+{\alpha \over 2 \pi }) \alpha^{1/2}=e^{\pi^2 \over 4}

[/tex]

The term in parenthesis, well, is sort of a first order correction.

Then we use http://wwwusr.obspm.fr/~nottale/ukmachar.htm to get the mass of the electron

[tex]

\ln (M_P/m_e) = \alpha^{-1} \sin^2 \theta_W

[/tex]

where the square sine of Weinberg angle [tex]\theta_W[/tex] is to be rather misteriously taken at the GUT value, 3/8. I have not checked if the need of Schwinger correction above counterweights this need of a value running up to GUT scale.

Now we use http://www.chip-architect.com/news/2004_07_27_The_Electron.html [Broken] to get in sequence the mass of the muon, via the rather strange

[tex]

\ln {m_\mu \over m_e}= 2\pi - 3 {1\over \pi}

[/tex]

and the mass of tau via the simpler

[tex]

\ln {m_\tau \over m_\mu}= \pi - {1\over \pi}

[/tex]

Alternatively HdV set of equations can be presented from a quotient [tex]m_e m_\tau^n / m_\mu^{n+1}[/tex], but the original presentation hints of a hyperbolic sine, or perhaps a q-group scent.

We could try to follow towards the full mass matrix, including neutrinos, via some empirical approximations collected by Mikanata and Smirnov.

----

(*) Update: HdV has uploaded to his webpage an indication of the origin of his formula, as a 3rd term truncation of a peculiar series.

The idea is to collect here in only a thread all the approximations voiced out during the summer. Surely this is to be quarantinised in TheoryDev, but it is interesting enough to be kept open as a thread (if closed, please be free to use my http://www.infoaragon.net/servicios/blogs/conjeturas/index.php?idarticulo=200410041 [Broken])

First we get Planck Mass, [tex]M_P[/tex], from G, c and h as usual.

Then we solve for [tex]\alpha[/tex], the fine structure constant, in HdV second equation (*),

[tex]

\alpha^{-1/2}+ (1+{\alpha \over 2 \pi }) \alpha^{1/2}=e^{\pi^2 \over 4}

[/tex]

The term in parenthesis, well, is sort of a first order correction.

Then we use http://wwwusr.obspm.fr/~nottale/ukmachar.htm to get the mass of the electron

[tex]

\ln (M_P/m_e) = \alpha^{-1} \sin^2 \theta_W

[/tex]

where the square sine of Weinberg angle [tex]\theta_W[/tex] is to be rather misteriously taken at the GUT value, 3/8. I have not checked if the need of Schwinger correction above counterweights this need of a value running up to GUT scale.

Now we use http://www.chip-architect.com/news/2004_07_27_The_Electron.html [Broken] to get in sequence the mass of the muon, via the rather strange

[tex]

\ln {m_\mu \over m_e}= 2\pi - 3 {1\over \pi}

[/tex]

and the mass of tau via the simpler

[tex]

\ln {m_\tau \over m_\mu}= \pi - {1\over \pi}

[/tex]

Alternatively HdV set of equations can be presented from a quotient [tex]m_e m_\tau^n / m_\mu^{n+1}[/tex], but the original presentation hints of a hyperbolic sine, or perhaps a q-group scent.

We could try to follow towards the full mass matrix, including neutrinos, via some empirical approximations collected by Mikanata and Smirnov.

----

(*) Update: HdV has uploaded to his webpage an indication of the origin of his formula, as a 3rd term truncation of a peculiar series.

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