1996 © G. Imbalzano {TO} Moncalieri © 1998

• Classical & Modern physics ~~~ [MS LineDraw FONT]
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<=ATTI del XXV Congresso A.I.F. Bellaria 1996=>
Responsabili del Congresso: L. Brasini (Modena) e L. De Santis (L'Aquila)
"LA FISICA NELLA SCUOLA" Anno XXXI n.1 Supplemento (gennaio-marzo 1998):
: = Estremi della Rivista = :
REG. Tribunale di Modena, con atto n.540 del 29-1-1973

~ SUMMARY {some font face="symbol"} ~

The elementary Planck's probability P = exp(-E/kT) so that
do = S{n>0} exp(-n.E/kT)= 1/(exp(E/kT) - 1) --> 1/(eL-1), with L(P=max)~4.9651, involves the infinitesimal variation -dP/P=d(E/kT) where, if a "chemical potential" Gp exists: E-->G-Gp. Besides, for the Wien-Planck's law, dimensionally
P = P(hf/kT) = P(E/kT) --> P=P(G/kT-Gp/kT). It's possible to describe this distribution for a given "stationary" temperature
To=constant, that is one can regard the indipendent variations
P=P(E/kTo) or P=P(Eo/kT), respectively:
(1) dP/P = -(dG/kTo - dGp/kTo) ;
(2) dP/P = GodT/kT2 - GpodT/kT2 .
In (1) at the generic -G=-hf (bosons pressure) one usually add a Gp=Gp(r) which depends on the position r. From the law Gp = hfp => hc/lp naturally can be reached the minimum attractive potential
dGp = hc.dlp/lp2, Coulomb like. Besides
lp=lpo(1-Gp/kTo) or (lp-lpo)kTo+lpoGp=0 considering
Gp=kTo-kT (To>T, lp
< lpo) that is lpkT=lpokTo in the bounds of the well known proportion law
po/To=constant. On the other hand, the analogous limit condition
hfo/To=constant supplies
Gpo/Go=a (near to the equilibrium one can write Gp=aG). Therefore -dGp= hc.dlp/lp2=
-hc.d(1/lp)= -hc.d(1/(lpo(1-Gp/kTo))= -d(hfpo/(1-Gp/kTo)). Then the minimal variation do due to the "chemical potential" Gp generally implies
do --> d= 1/(exp[(G-Gp/(1-aG))/kT] -1)= 1/(exp[(G-aG/(1-aG/kT))/kT] -1)= 1/(exp[L(1-a/(1-aL)] - 1). Following Enrico Fermi, I equalize the interaction probability d to the ratio of the perturbative energy Gp to
G= Gp / ao :
ao = Gp/G = q2/(2ehc), so ao = 1/(exp[L-aoL/(1-aoL)] - 1). Solving the trascendent equation respectively to ao with the theoretical value of L (P max) one obtains in short ao ~ 1/137.037 < 1/137.036 ~ a (Er ~ 6. 10 -6). If one take into further (quantum-relativistic) corrections the
ao value may be improved, until it coincides almost with a.

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Nota STATISTICA.
Certo, č probabile che ciň che noi vediamo sia solamente il frutto di ciň che speravamo di vedere, ma č altrettanto possibile che ciň che speravamo di osservare sia proprio quel che vedete!
Infatti, la probabilitŕ che in un Universo di 15 miliardi di anni (almeno) nel primo miliardesimo di secondo si producano siffatte immagini č di 2*10-27. Se questo lo vedo solo io, non ne parliamo piů! Ma, se siamo anche solo in tre a vederlo, allora la PROBABILITŔ č di 10-80 (circa).

In conclusione: se dovessimo ritenere "illusorie" queste stesse immagini, allora dovremmo ritenere assurda l'esistenza ANCHE di un SOLO ATOMO nell'INTERO UNIVERSO!

. . .
STATISTICS Note.
Sure, it is probable, that we see is only the fruit of whom we hoped to see, but is equally possible that we hoped to observe just those that you see!
In fact, the probability that in a Universe of 15 billions of years (at least) in the "first 10-9 of second" produces such images is of 2*10-27. If this I to it see alone, of it we do not speak more! But, if we are also single in three to see it, then the PROBABILITY is of 10-80 (approximately).

In conclusion: if we had to think "illusory" these same images, then we would have to think absurd the existence ALSO of a SINGLE ATOM in the ENTIRE UNIVERSE!
. . .