The results derived below are based on currently accepted data, and relationships. These are the following:
The conclusions, arrived at here, based on these facts, are at variance with accepted beliefs about the origin, the size, and the age of the universe; as well as the abundance of type 1A supernovae. Here is what is known and being conjectured about the type 1A supernovae:
The June l998 issue of PHYSICS TODAY contains an article by Bertram Schwarzschild, "Very Distant Supernovae Suggest that the Cosmic Expansion is Speeding Up". The diagram on page 17 showing a slight convex relation between apparent magnitude and red shift suggests on current lines of thought that a mysterious "ethereal agency" is actually accelerating the expansion of the universe.
The article is concerned with the question of the linearity of the relationship between the apparent magnitude and z, a measure of the red shift. Note that z is a measure of the red shift derived from the shift of the originating wavelength, say w(o), to the red shifted wavelength, w(r), through the formula
Figure 1. Apparent magnitude vs. z (Physics Today, June l998 p.17) Current interpretations are not concerned with the pronounced clustering of the data between the values of z = 0.4 and 0.9 . The linearity is hard to establish on the basis of the observed data, but the clustering points to a very different conclusion.
That the clustering is not due to observational selection or difficulty is made clear by the fact that the region below z = 0.4 is more readily accessible, and certainly not excluded from consideration. Supernovae in this region are "closer to home" and therefore brighter. If anything we should expect more data points here than in the region above z = 0.4. A matching of two photographs made a few weeks apart, by subtraction, can reveal a potentially bright supernovae much more readily than a more faint image corresponding to a high value of z.
These supernovae probably formed in the course of the first billion years, and most likely, as will be argued, in the first ten million or so years. Their masses ranged upward from about 1.4 solar masses. Consequently their lifetime, in terms of nuclear fuel, range downwards from about 3 billion years, to about 3/4 billion years for a star with twice the mass of the sun. After the burn, there would be a short period of unstable burning before the star explodes.
The value z = 0.4 represents a distance of about 3 billion light years - a time of 3 billion years. The lifetime before burning of the smallest ones, and the travel time of the light, before it reaches us, add up to about 6 billion years. Not the 12 or 13 billion currently believed.
It has been suggested that it requires about 5000 atoms per cubic centimeter to encourage star formation. At an age of about one million years there would be about one million atoms per cubic centimeter, and by the time the expansion of the universe has reached a diameter of ten million light years, there are still about 1000 atoms per cubic centimeter. Within these ranges there is ample opportunity for the growth of stars larger than 1.4 solar masses.
By the time the universe reached a 0.1 billion light year diameter the density would be about 10^-24 gm/cm^3, or about one atom per cubic centimeter - not enough for rapid star formation.
More specifically, at a diameter of say four million light years, there would be about 3.3 x 10^19 cubic light years as the volume of the universe. This allows for better than one hundred to ten thousand cubic light years for each of the potential 10^15 to 10^17 stars.
Each such star, if it is the size of our sun requires less than about ten percent of the matter from one cubic light year of space (assuming about fifteen thousand baryons per cubic centimeter at that point in time). If matter implodes at one percent of the velocity of light, each such star requires less than one hundred years to form! It is unlikely that more than a very small proportion of stars, probably less than ten billion, that is 10^10, would reach a mass greater than ten times that of the sun because of the potential competition for matter, as well as the longer formation times. Those that did reach this size would explode quickly, because of their large mass, at a time when the universe had an age of less than one hundred million years.
These explosions, in turn, would create dense clouds which would encourage a second, smaller, generation of stars to form early in the life of the universe. In any case this is a sequence of birth and death of generations of stars which, after some time, reduces the average and maximum size of the surviving stars.
Today, the stars with mass about 1.4 solar masses (that is the smallest ones which survived the longest), will be detectable as supernovae, but there is no reason to believe that all type 1A supernovae always necessarily had this mass (as was suggested by the white dwarf/double star theory of Schatzman in l963.)
[We should also note that the stars, whatever their solar mass to begin with, also end with about the same mass after nuclear burning - unless some cataclysmic event such as a supernova explosion occurs. The mass required to produce energy due to hydrogen conversion to helium is less than one percent of the total hydrogen mass, and for helium conversion the process requires even less mass. This means that the total loss of mass in the universe due to nuclear processes, over all time, will not reduce the initial mass by even .01 percent. ]
We can also guess that the process of exploding goes on for at least three billion years, due to the difference in the mass of the stars, and that what we now experience, belatedly, represents a moment somewhere near the end of the process (and the only reason we experience any of it is because of the long delay in the light reaching us).
All the more massive stars exploded earlier and would have been seen a few billion years ago. All this, again, leads to an estimate of the initial number of potential supernovae in the range of 10 to 100 trillion! The total number of stars formed, most of which were smaller than 1.4 solar masses, is undoubtedly even larger by perhaps two orders of magnitude.
Assuming that only 1% of the initial quantity of hydrogen and helium was used up in star formation, we are led to an estimate of the mass of the universe at between 10^50 to 10^53 grams – consistent with current estimates. Furthermore, if the number of stars formed, which give rise to supernovae, is over 10^14 or 10^15, we aren't talking about isolated condensations of clouds, but a phenomenon that involves the entire universe - which again leads us to infer an origin for these stars as a point in time near the very beginning of this universe.
Pursuing this train of thought further, we can calculate back to the size of the sphere required for all matter to have the same average density as the sun. This turns out to be a diameter of about one half to one light year. So a star with that diameter, bursting as a supernova, may be what we now call "the beginning of time" "the big bang" or more deeply suggestive "creation" - and in that case, matter existed prior to the 'beginning of time' and never did achieve the velocity of light but was probably ejected with perhaps 90 percent of that velocity, so that star formation could begin, after a cooling off period, near the beginning of the first Billenium.
This argument leads us in the direction of re-creation, rather than creation out of nothing. It is also tempting to speculate that some of these early stars were primarily, or in their innermost core, composed of helium. Helium atoms would attract each other 16 times more forcefully than hydrogen atoms. Even if helium is only 10 to 20% of the mass at the beginning of time, there might easily have evolved a small denser sphere of helium near the beginning of time, in which the initial star formation was initiated which resulted in type 1A stars. This would explain the absence of hydrogen lines in these stars.