This example shows that physical constants like α can
be modified by the presence of a complex environment,
in this case graphene’s honeycomb lattice. So perhaps
we should not be mystified by the seemingly arbitrary
value of the QED fine-structure constant after all.
"More is different." P.W. Anderson
What's good for QED (Quantum ElectroDynamics) is good for QGMD (Quantum GeometroDynamics).
QED is from the local gauging of the compact global U1 Lie group to U1(x) on some quantized matter fields.
QGMD is from the local gauging of the non-compact T4 Lie group to T4(x) on ALL quantized matter fields implementing Einstein's version of the Equivalence Principle (EEP).
Space-time fabric is the compensating gauge field from the largest non-compact universal symmetry group of the matter fields.
"Background independence" is simply gauge invariance of ALL matter fields under T4(x) i.e. 1916 Einstein GR.
This is a battle-tested organizing mainstream radically conservative idea for the TOE.
Einstein's attempt at unified field theory means, in post-modern times, enlarging the T4 group.
T4 --> Poincare ---> Conformal (Twistor)
Therefore, Karl Popper falsifiable prediction
1. in graphene sheets
emergent collective IR limit of QED coupling is (index of refraction)e^2/hcvacuum
2. in hypothetical graphene-based room temperature super-conducting meta-material - yet to be manufactured (except, perhaps, by the ET aliens or human time travelers from our future allegedly sabotaging our nuclear missile deterrent)
emergent collective IR limit of QGMD coupling is (index of refraction)^4GNewton/cvacuum^4
i.e. GMD "Ohm's law" (lumped parameter description)
induced curvature ~ (index of refraction)^4GNewton/cvacuum^4 applied stress-energy current density
I = V/R
V = applied stress-energy current density
I = induced curvature
Spacetime stiffness = G-string tension = R = cvacuum^4/ (index of refraction)^4GNewton
Maybe, as proposed recently by Xiao-Gang Wen at the
Massachusetts Institute of Technology, the electron
is not as elementary as one would think, but is instead
a consequence of interactions between more complex
degrees of freedom not yet experimentally accessible.
Physics World November 2006