occasional meanderings in physics' brave new world

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Location: New Zealand

Marni D. Sheppeard

Monday, July 27, 2009

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 $\hbar$.

Kea said...

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

July 27, 2009 3:55 AM
Rhys said...

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.

July 27, 2009 6:58 PM
CarlBrannen said...

Marni,

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

July 28, 2009 10:52 AM
CarlBrannen said...

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

July 28, 2009 10:53 AM
Stuffy said...

typo found on p. 20
"around 2/9 and give sthe mixing"

July 29, 2009 7:21 AM