**Our external physical reality is a mathematical structure. That is, the physical universe is mathematics in a well-defined sense, and in those [worlds] complex enough to contain self-aware substructures SAS [they] will subjectively perceive themselves as existing in a physically 'real' world (- Max Tegmark's mathematical universe).**

# CODATA and alpha

There seems to be an extensive influence by the fine structure constant alpha on the values chosen by the CODATA committee. I note that to derive the CODATA 2002, 2006, 2010, 2014 values for the physical constants I need to use the CODATA 2002, 2006, 2010, 2014 values for alpha (the Rydberg changes little). Consequently the constants calculator (black hole electron) has alpha as the user input. An analysis of the results cannot therefore be separated from an analysis of alpha.

G: All results agree with experimental CODATA values except for G and and the Boltzmann constant k_{B}. As the CODATA m_{P} and l_{p} are calculated from G
(they are not experimental values), they also differ accordingly. There is however some controversy over the value of G as noted in
a recent Nature article
[G-whizzes disagree over gravity];
"...Faller and Harold Parks at Sandia National Laboratories measured G = 6.67234(21)e-11...".

Parks, H. V. & Faller, J. E. Phys. Rev. Lett. http://xxx.lanl.gov/abs/1008.3203 (2010).

The Newtonian constant of gravitation, a constant too difficult to measure? ...The Newtonian constant of gravitation, G, is the only fundamental constant of physics for which the uncertainty given in successive CODATA evaluations has increased. (http://royalsociety.org/events/2014/gravitation/)

k_{B} This value assumes idealized 'Planck' conditions. Accuracy is within 1.0008254 of the CODATA 2010 value. However when k_{B} is used to solve the Larmor frequency, precision improves to within experimental error.

Larmor frequency (calculated) f_L = 28\;024\;953\;555.403

free electron gyromagnetic ratio (CODATA 2010) gamma_e/(2pi) = 28\;024\;952\;66(62)

2. e:

The elementary charge is not an independently defined quantity. Instead, its value is derived
from the relation e^2 = 2.h.α/(mu_{0}.c).

Consequently the uncertainty in the value of e is therefore currently determined entirely by the uncertainty in the Planck constant. Likewise the electron mass is similarily inferred...

and so, apart from the Rydberg constant, the CODATA values should be considered more as a useful guideline and cannot be used as a tool for an independent verification of alpha.

3. von Klitzing:

As this constant reduces to alpha and c {R(K) = h/e^2 = pi*α*c/5000000}, it could be the most authoritative
of the alpha measurements. The
Tzalenchuk A et al
experimental value R(K) = 25,812.807557(18) using the QHE (Quantum Hall effect) gives a value for alpha;

α = 137.035 999 677(96) = 25,812.807557(18) *5000000/(pi.c)

This value is close to 2 proposed values for alpha;

α = 137.035 999 786 699 James Gilson; http://www.maths.qmul.ac.uk/~jgg/page5.html

α = (17^4+11)/(c*phi*mu0) = 137.0359997682931... where phi = (1+sqrt(5))/2 is the golden ratio
(golden mean) and the vacuum permeability mu_{0} = 4*pi/10000000 (exact) however the units appear not to match;

4. Atom-recoil measurements

Using h/rb=4.5913592729e-9,

87Rb=86.909180527amu,

me=0.000548579909067amu gives a value for

α = 1/sqrt((2*10973731.568539/c)*4.5913592729e-9*86.909180527/0.000548579909067);

α = 137.035 998 998

5. h/neutron ratio

Using E Kruger et al 1998 Metrologia 35 203;

h/mn=3.956033332e-7,

mn=1.00866491600amu,

me=0.000548579909067amu (Sturm et al 2014) gives a value for alpha;

α = 1/sqrt((2*10973731.568539/c)*3.956033332e-7*1.00866491600/(0.000548579909067));

α = 137.036 010 857

6. Eckart Schonfeld, Peter Wilde: A New Theoretical Derivation of the Fine Structure Constant

...The present paper is devoted to a new derivation of the expression given already earlier for the fine structure constant alpha.
This expression is exactly the same as that what we... http://www.ptep-online.com/index_files/2012/PP-28-01.PDF

Using the solution for the electron as a
magnetic monopole, the Schonfeld Wilde electron quantum mechanical fraction reduces to α = 137.035 999 252;

7. QED

Accepted values for alpha. These values are based on experimental results and QED theory. They assume that the QED theory used is correct.

1. α = 137.035 999 084(51) Gabrielse et al Phys. Rev. Lett. 100, 120801 (2008)

2. α = 137.035 999 074(44) CODATA 2010

3. α = 137.035 999 037(91) (2011) Bouchendira et al. http://arxiv.org/abs/1012.3627v1

8. h

The value for the (Planck constant) is still controversial. This video illustrates the problem.