In his derivations, Dr. Forward shows that when we use equations of quantum mechanics to determine the average energy  of the vibrations of atoms, we get the following answer:

E = n (T) + hf/2

In a one-dimensional harmonic oscillator, the energy levels are quantized. The formula for energy state is as follows:

 

E_n = (n +1/2) h/2 p *w
E_n =n* h/2 p* w+ ½* h/2p w
w= 2 p f
E_n = n h/2 p* 2 p f + 1/2 * h/2 p* 2 p f
E_n = nhf + 1/2hf

 

 Here, n is the quantum number (photon number) and f is the frequency of the photon emitted by exited atom. In this formula, if the temperature equals zero, the particles (electrons) vibrate at energy corresponding to the n = 0 state. Then, at T = 0, n =0 because the atom is not excited (cannot emit any photon); therefore, the value of energy in this case is:

 

E_n =0 + hf/2=hf/2

 

This is the lowest value of energy. Thus, even at zero temperature (or zero kinetic energy), quantum mechanics predicts that atoms will have a residual energy (if we let n go to zero there remains the hf/2). Physicists have been grappling with this for years, because there appears to be an infinite amount of energy available if f is allowed to increase without limit. Ever since Casimir predicted it and various other scientists verified it, this simple equation is really all that underlies the theory of zero-point fields and zero-point fluctuation. The zero-point field hypotheses suggest that there is an infinite amount of energy in zero point. Since zero-point energy (ZPE) was first introduced, many unexplained phenomena have been solved. New Scientist magazine, in the article “Why Atoms Don’t Collapse,” gives an impressive endorsement of the importance of ZPE: “There is a dynamic equilibrium in which the zero-point energy stabilizes the electron in a set ground-state orbit. It seems that the very stability of matter itself appears to depend on an underlying sea of electromagnetic zero-point energy.”¹⁸

Both theory and experimentation have shown that there is non-thermal radiation in the vacuum and that it persists even if the temperature could be lowered to absolute zero. Therefore, it was simply called zero-point radiation. Further proof is evident, as Dr. Forward points out in his statement: “When physicists cooled helium to within micro degrees of absolute zero it still remained a liquid! Only ZPE can account for the source of energy which is keeping helium from freezing.”¹⁹

 

Bernard Haisch . from the California Institute for Physics and Astrophysics, readdresses the issue as follows:

 

It is shown that the electron can be seen as continually radiating away its energy as predicted by classical theory, but simultaneously absorbing a compensating amount of energy from the ever-present sea of zero-point energy in which the atom is immersed, and an assumed equilibrium between these two processes, leads to the correct values for the parameters known to define the ground-state orbit. Thus, the ground-state orbit is determined by a dynamic equilibrium in which the collapse of the state is prevented by the presence of the zero-point energy.

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18.) “Why Atoms Don't Collapse,” New Scientist (July 9, 1987), p. 26.
19.) Ibid