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Matheology § 171
Posted:
Dec 5, 2012 1:37 AM
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Matheology § 171
Does the infinitely small exist in reality?
Quarks are the smallest elementary particles presently known. Down
to 10^-19 m there is no structure detectable. Many physicists
including the late W. Heisenberg are convinced that there is no deeper
structure of matter. On the other hand, the experience with molecules,
atoms, and elementary particles suggests that these physicists may be
in error and that matter may be further divisible. However, it is not
divisible in infinity. There is a clear-cut limit.
Lengths which are too small to be handled by material meter sticks
can be measured in terms of wavelengths lambda of electromagnetic
waves, for instance.
lambda = c/f (c = 3*10^8 m/s)
The frequency f is given by the energy E of the photon
f = E/h (h = 6,6*10^-34 Js)
and a photon cannot contain more than all the energy of the universe
E = m*c^2
which has a mass of about m = 5*10^55 g. This yields the complete
energy E = 5*10^69 J. So the unsurpassable minimal length is 4*10^-95
m.
Does the infinitely large exist in reality?
Modern cosmology teaches us that the universe has a beginning and
is finite. But even if we do not trust in this wisdom, we know that
theory of relativity is as correct as human knowledge can be.
According to relativity theory, the accessible part of the universe is
a sphere of
50*10^9 LY radius containing a volume of 10^80 m^3. (This sphere is
growing with time but will remain finite forever.) "Warp" propulsion,
"worm hole" traffic, and other science fiction (and scientific
fiction) does not work without time reversal. Therefore it will remain
impossible to leave (and to know more than) this finite sphere. Modern
quantum mechanics has taught us that entities which are non-measurable
in principle, do not exist. Therefore, also an upper bound (which is
certainly not the supremum) of 10^365 for the number of elementary
spatial cells in the universe can be calculated from the minimal
length estimated above.
[W. Mückenheim: "The infinite in sciences and arts", Proc. 2nd Intern.
Symp. of Mathematics and its Connections to the Arts and Sciences
(MACAS 2), B. Sriraman, C. Michelsen, A. Beckmann, V. Freiman (eds.),
Centre for Science and Mathematics Education, University of Southern
Denmark, Odense 2008, p. 265 - 272]
http://arxiv.org/abs/0709.4102
Compare: Every set can be well-ordered!
Does enlightenment never touch matheology?
Is that degree of energy saving necessary???
Regards, WM
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