The theory of stellar energy generation in the Reciprocal System is stated qualitatively in various works by Mr. Larson, such as Quasars and Pulsars. For the benefit of new readers of Reciprocity, I quote Mr. Larson in full:
To sum up, when the destructive thermat limit is reached, the following word equation holds true:
Let EI be the ionization energy, ET be the thermal energy, and EM be the oppositely directed magnetic rotational energy. Then in symbols,
Each of the terms in the equation will now be discussed.
Equivalent energy of one unit of magnetic time displacement
Before we can find the energy equivalent of one unit of magnetic time displacement, we must find the mass equivalent. According to deductions previously made from the postulates of the Reciprocal System the electric equivalent of a magnetic displacement n is 2n²; this does not refer to the total from zero to nit is the equivalent of the nth term alone. Each electrical unit is equal to two atomic mass units, and each atomic mass unit is equivalent to 931.48 MeV. For n equal to 3 and 4, the following table results:
Thus, the third magnetic time displacement is equivatent to 33533.28 MeV, and the fourth unit to 59614.72 MeV.
At the present stage of development of the Reciprocal System we do not have a theoretical equation giving the energy needed to completely ionize at atombut then neither does quantum mechanics. An empirical equation will have to do for now.
Reference three has the most comprehensive table of ionization values available, giving the complete ionization energy for the first twenty elements. From the values, I have derived the following empirical equation:
where Z is the atomic number. Of course, other equations are possible.4 Extrapolating any empirical equation to high values of Z is risky, but this will have to do. For thorium, at no. 90, eq. 2 gives
Let k be Boltzmanns constant in MeV/°K and T be the temperature of an atom in °K Then the standard equation for the thermal energy (based on the ideal gas taw) is
Calculation of critical temperature and velocity
From eq. lb,
For thorium, EM is 59614.72 MeV and EI is .413 MeV, so
This is fantastically high from our view as spectators on the earth, but in terms of natural units, the temperature is only 127.44.
With k in J/°K, equation 3 can be solved for the velocity at the critical temperature.
For thorium, this amounts to
This is 84% of the speed of light:
and the critical velocity is
This is 91% of the speed of light! No wonder atoms are accelerated to velocities above the speed of light during a supernova explosion:
Most likely the motion of the atoms in the core of a star is circular. The greater the temperature, the higher the velocitythus as theoretically expected O and B type stars have much greater rotational velocities than G and K type stars.
Rate of energy generation
Since both the unit of magnetic time displacement and the opposing space displacement revert to linear motion, the total energy radiated per critical atom is
for n = 4.
The rate of energy generation depends on the number of atoms at the critical temperature, NCRIT. This in turn depends on the total mass of the star M, the average mass per critical atom, m, and on the fraction FCRIT of the mass M that is critical. Thus
Let PST be the total power output of a star. Then assuming no accretion whatever, the litetime of a star can be calculated as follows:
For the sun,
Taking thorium as representative of the critical elements,
Assuming various values of FCRIT we can calculate the lifetime of a star with no accretion. The following table results.
According to the Reciprocal System, net accretion does occur over the life of a star, but there may be periods where there is a net loss. Since such a period may last as long as a billion years, I believe we are on good ground assuming that FCRIT is equal to .0001. At present we have no way of deducing theoretically the fraction of the mass of a star that is critical. Certainly, observation is no help; observation can only indicate the composition of the stellar atmosphere, not that of the central core.
Rate of accretion
The sun appears to be one-third along its way on the Herzsprung-Russell diagram. Since the sun has been estimated to be in existence for about 5 billion years, we can roughly assume that the average lifetime of a star is 15 billion years. According to the theory, a star slowly increases in temperature until the critical temperature of the iron group of elements is reached, at which point the life of the star is terminated in a supernova1 explosion. From the equations presented in this paper, the critical temperature of iron is 3,091,400,000 oK above that of uranium. Thus the rate of change of temperature with time can be roughly expressed as follows:
(Even if L were only 7.5x109 years, the increase in T per year would be less than .5 °K).
Thus stars are for most of their lives very stable energy generators. From this we can conclude that the rate of accretion is just slightly greater than the rate of mass lost through burning. For calculating the rate of accretion we can assume that for the short term they are identical.
Let RACC be the rate of accretion in kg/sec. Then
Using previous values of PST, ERAD, mCRIT and FCRIT equal to .0001,
This amounts to .000000096% of the mass of the star per year. It would take over 3108 years for the accretion to amount to the mass of the earth:
Clearly we cannot observe this small rate of accretion. Observation cannot tell us whether the mass of the sun is remaining constant or slowly increasing, as we believe, or whether the mass of the sun is slowly decreasing, as present theory suggests.
The current theory of stellar energy generation has been criticized elsewhere, and a summary of that criticism is presented in reference five. The basic differences between the new theory and the current one are as follows:
Thus, though observation (other than neutrino counts) cannot at present decide in favor of one theory over the other, Occams Razer can: the new theory wins hands down.
Authors Note: This paper is not meant to be the last word on subject of stellar energy. Rather it is meant only to be the second word. Constructive criticism would be welcome.