### M Theory Lesson 289

The rest mass of the electron appears in the formula for the Rydberg constant $R$:

$m = \frac{2 h R}{c \alpha^{2}}$

Describing $m$ as the eigenvalue of a Koide matrix with angle parameter $\theta = \delta + 2 \pi /3$, we find that

$\textrm{cos} \theta = \frac{1}{\sqrt{2}} (( \frac{2 \times 13.6056923}{7.29735254^{2} \times 313.85949})^{0.5} - 1)$

in terms of $R$ and $\alpha$, and in agreement with the value $\delta = 2/9$ for Brannen's natural scale $313.86$ MeV. Since both $R$ and $\alpha$ have been measured extremely accurately, the first relation shows that errors in the known electron mass are related to errors in Planck's constant. Conversely, an exact value for $\delta$, along with an accurate value of the natural scale, could be used to predict more accurate values of $\hbar$.

$m = \frac{2 h R}{c \alpha^{2}}$

Describing $m$ as the eigenvalue of a Koide matrix with angle parameter $\theta = \delta + 2 \pi /3$, we find that

$\textrm{cos} \theta = \frac{1}{\sqrt{2}} (( \frac{2 \times 13.6056923}{7.29735254^{2} \times 313.85949})^{0.5} - 1)$

in terms of $R$ and $\alpha$, and in agreement with the value $\delta = 2/9$ for Brannen's natural scale $313.86$ MeV. Since both $R$ and $\alpha$ have been measured extremely accurately, the first relation shows that errors in the known electron mass are related to errors in Planck's constant. Conversely, an exact value for $\delta$, along with an accurate value of the natural scale, could be used to predict more accurate values of $\hbar$.

## 5 Comments:

Now see this paper of Carl's for fairly accurate values of delta and the scale.

Carl's paper about hadron masses completely disregards SU(3) colour symmetry (check out equation 16 and the surrounding discussion, which seems to be foundational to the paper). I left a comment on his blog to the same effect.

Marni,

My new paper is out, and Lubos is already improving it. See his facebook page: http://www.facebook.com/home.php#/lubos.motl?ref=nf

He notes that tripled Pauli statistics involves only one of the two Pauli states being tripled. This is compatible with only the left handed fields carrying mass charge. It would make the right handed fields ride along for free (be malleable with regard to the mass interaction). This might give another explanation of the square root.

Carl

Oh, I should link to the new paper, "Emergent Spin".

typo found on p. 20

"around 2/9 and give sthe mixing"

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