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Abstract
A theory of special inconstancy, in which some fundamental physical constants such
as the fine-structure and gravitational constants may vary, is proposed in pregeometry.
In the special theory of inconstancy, the \alpha-G relation of \alpha=3\pi/[16ln(4\pi/5GM_W^2)]
between the varying fine-structure and gravitaional constants (where M_W is the charged
weak boson mass) is derived from the hypothesis that both of these constants are related
to the same fundamental length scale in nature. Furthermore, it leads to the prediction
of dot{{\alpha}}/\alpha=(-0.8\pm2.5)\times10^{-14}yr^{-1} from the most precise limit
of dot{G}/G=(-0.6\pm2.0)\times10^{-12}yr^{-1} by Thorsett, which is not only consistent
with the recent observation of dot{{\alpha}}/\alpha=(0.5\pm0.5)\times10^{-14}yr^{-1}
by Webb et al. but also feasible for future experimental tests. Also a theory of general
inconstancy, in which any fundamental physical constants may vary, is proposed in
"more general relativity", by assuming that the space-time is "environment-dependent".
In the general theory of inconstancy, the G-\Lambda\ relation between the varying
gravitational and cosmological constants is derived from the hypothesis that the space-time
metric is a function of \tau, the "environment-coodinate", in addition to x^{\mu},
the ordinary space-time coodinates. Furthermore, it leads to the prediction of the
varying cosmological constant, which is consistent with the present observations.
In addition, the latest observation of spatial variation in the fine-structure constant
from VLT/UVES of (1.1\pm 0.2)\times 10^{-6}GLyr^{-1} by King et al. is suggested to
be taken as a clear evidence for environment-dependent fundamental physical constants
Report No CAOS-Report-005(CAOS,Tokyo,2012), February 4, 2012
Comments 15 pages, a reduced and up-dated version of the contribution
presented at the Eighth Bolyai-Gauss-Lobachevsky International Conference on
Non-Euclidean Geometry in Modern Physics and Mathematics, Uzhgorod, Ukraine,
May 22-25, 2012