harmonic oscillator and expansion of universe

From: alistair (alistair_at_goforit64.fsnet.co.uk)
Date: 06/20/04 

Date: 20 Jun 2004 04:43:31 -0700

A hydrogen molecule vibrates at about 10 ^ 13 times per second.
If it is modelled by a simple harmonic oscillator the equation
w = ( k / m) ^ 1/2 applies to it., where w = frequency of oscillation,
k = force constant and m = mass.

For hydrogen, m = 10^ - 27 kg, so using the value of w listed above,
we get k = w^2 x m = 10^26 x 10 ^ -27 = 10^ -1

Now, the cosmological constant has a value of about 10^ - 27 kg / m^3
If I assume that this mass density, in a vacuum at 2.7 K, results
from one electronically neutral hydrogen atom per cubic metre,and that
hydrogen atoms one metre apart vibrate together( and are held together
by their gravitational attraction for one another), then the force
constant k becomes 10 ^ -42 x 10^ -1 x 10 ^ -20 = 10^ - 63 ( the
value of 10^ - 42 is the relative strength of the Newtonian force of
gravity for the attraction between an electron and a proton in a
normal hydrogen molecule - compared to the electric force between an
electron and a proton at the same distance in a normal hydrogen
molecule ( it is the attractive electric force between an electron and
proton that holds the normal hydrogen molecule together. The value of
10^ - 20 comes from the fact that gravity and electricity obey the
inverse square law and usually hydrogen atoms would be 10^ - 10 metres
apart at 2.7 K and not 1 metre).

Using w = ( k / m) ^ 1/2 we get w = ( 10^ -63 / 10 ^ -27) ^ 1/2 = 10 ^
-18 seconds.

If this reflects the oscillation of the universe as a whole,then the
universe vibrates about once every 10 ^ 18 seconds.So it will not
expand for much longer in cosmological terms.

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