This is a very short post and it is just a couple of things I've stumbled upon in my latest Physics Journey. Check these out.
The first one is related to the title of this post. This is straight from Wiki
"The one-loop contribution to the anomalous magnetic moment—corresponding to the first and largest quantum mechanical correction—of the electron is found by calculating the vertex function .... The calculation is relatively straightforward and the one-loop result is:
$ a = \frac{\alpha}{2 \pi} \approx 0.0011614 $
where α is the fine structure constant. This result was first found by Julian Schwinger in 1948"
now, how about this
$ \frac {Z_P} {R_k} = $$\frac {\hbar} {q_p^2} / \frac {h} {e^2} = \frac {e^2} {2\pi q_p^2} = \frac{\alpha}{2 \pi}$$ \approx 0.0011614 $
where
$Z_P$ - Planck impedance = $\frac {\hbar} {q_p^2}$
$R_k$ - von Klitzing Constant = $\frac {h} {e^2}$
$q_p$ - Planck Charge
$e$ - charge on an electron
$\alpha$ - fine structure constant
how cool is that, they are the same! Though the calculation for this second version is considerably easier! Is there some sort of equivalence thing going on here? will do more on this later. It's also equal to the classic electron radius divided by the Compton wavelength of the electron!
The second is just a bit of minor number crunching
have a look at this. It is the rest mass of the electron multiplied by the speed of light divided by the Boltzmann constant,
$\frac {m_e c} { 2 \pi^2 k_b}$ $= 1.002 $
$m_e = 9.1093829 10^{-31} kg $
$c = 299 792 458 ms^{-1}$
$k_b$ - Boltzmann constant = $1.3806488 10^{-23} m^2 kg s^{-2} K^{-1}$
That is so close to unity it has to mean something, then again!
Note ,the units of 1.002 is $\frac {K s} {m}$ Temperature / velocity, but this is not as odd as you might think.
Anyway, that is it for now, more on both of these later
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