Das Kalenderblatt 120611

10/06/2012 - 09:32 von WM | Report spam
MatheRealismus (1)

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/nu (c = 3*10^8 m/s)
The frequency nu is given by the energy E of the photon
nu = 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", Proceedings of
the 2nd International Symposium 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

Gruß, WM
 

Lesen sie die antworten

#1 netzweltler
10/06/2012 - 10:52 | Warnen spam
On 10 Jun., 09:32, WM wrote:
MatheRealismus (1)

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/nu   (c = 3*10^8 m/s)
The frequency nu is given by the energy E of the photon
   nu  = 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", Proceedings of
the 2nd International Symposium 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

Gruß, WM



Wie beweist man die Nicht-Existenz des Unendlichen?

Ein m.E. einleuchtendes Beispiel für die Verwendung von Omega ist die
Steigung einer senkrechten Geraden. Es làsst sich jede natürliche
(oder auch reelle) Zahl durch eine Gerade im Koordinatensystem mit
entsprechender Steigung darstellen. Omega làsst sich dann durch eine
senkrechte Gerade darstellen.

Heißt die Nicht-Existenz des Unendlichen beweisen nicht, zu beweisen,
dass es viele dieser Geraden NICHT gibt?Niemand würde z.B. die
Existenz der Geraden mit der Steigung 1 oder Steigung 10.000.000 in
Frage stellen. Wenn es nur endlich viele dieser Geraden gibt, muss man
dann nicht Geraden benennen können, die es nicht gibt?

netzweltler

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