Cosmic Coincidences?

by Fred Vaughan

There seem always to be these nearly insurmountable epistemological traps and barriers to overcome. We seem always to be peering down the wrong end of telescopes, until very occasionally by some accident of fate, we run off yelling "Eureka! Eureka!" like demented hippies in the backwoods of California. Our various highly evolved linguistic and mathematical skills get applied primarily to justifying the particular inanity that happens to be in vogue — never with actually changing paradigms. There seem always to be mathematical mappings of what is known of the unknowable depths of our universe to the shallow waters of our intellectual wading preference, but the veracity of such mappings are warranted no more than formal propriety justifies aphorisms depicted in poesy.

Consider what we know of our universe with regard to its composition as a very diffuse but impure hydrogenous plasma. Yes, as surely as to a first approximation we ourselves are mere bags of salt water, the universe is a hydrogenous plasma, both being pretty damn good approximations! With only this much firmly in our grasp, we must resist urges to charge off like rabid string theorists to find the big end of some telescope, waving at cameras and grabbing microphones as they go!

How diffuse? About 10^-25 grams per cubic meter. So in sifting through a cubic meter or so of universal debris at random you might find an odd proton, an electron to neutralize the concoction, and by-product neutrinos all whizzing about at significant fractions of the speed of light. The most obvious decomposition of this plasma being that apparently on large scales everywhere in the universe it is 76 percent hydrogen nuclei and 24 percent helium nuclei (by mass such that there are about twelve hydrogen nuclei per each helium) with mere traces of other isotopes.

At high temperatures helium nuclei are formed from hydrogen nuclei by nuclear fusion. (Of course at even higher temperatures protons which comprise the nucleus of hydrogen can be created from neutrons, and positrons, with neutrinos and associated "opposites" dashing about, but let us ignore third tier observations.) All nuclear reactions are reversible with equilibrium percentages of each product determined by temperature. Those of us who still accept the conservation of energy — notice that most cosmologists do not — insist that if the 24 percent helium did indeed derive from primordially pure hydrogen plasma, then the energy released would not be totally lost. This caveat holds to the extent that the universe is a closed system, which it would seem to this author to be by definition. This radiant energy, however thermalized, must therefore still be present somewhere in the universe.

Now if you go through the calculations, and they are very straight-forward, you will find that the amount of radiation energy released per cubic centimeter is precisely the amount of energy invested in the microwave background radiation. All fashionable cosmological theories take this to be a mere coincidence. They tell us that the facts of annihilation associated with an unknowable primordial imbalance in matter and antimatter right after a miracle happened resulted in that glut of energy which today is viewed as some sort of perversely understood "fact" of the universe supposedly in reality being only 3 degrees Kelvin rather than the many orders of magnitude higher temperatures observed everywhere we look! According to these theories the energy balance coincidence is just a strange happenstance of our being here now rather than somewhere somewhat similar a billion years ago or hence! With such a perspective my confusion might have been avoided. But I don't have it!

So how "bright" should it be if this coincidental amount of radiation that we all agree is actually out there is actually out there? Well, let's think about that: On average every hundred cubic meters or so of the universe contains evidence of these reactions having taken place. From our observation point the intensity from each reaction is diminished as 1/r² where r is the distance to each occurrence. We arrive at Olbers paradox with the number of cubic meters increasing as the square of the distance, r². Thus, we get to the crux of the paradox when we combine these two effects for the entire universe. But of course modern cosmology resolves such difficulties by demanding a finite universe of radius R_o = 1/H_o where H_o is Hubble's constant. So we end up with a modest(?) intensity given by:

So a finite universe and a justifying Bang are made for each other. But if the redshift-distance relation is accepted as mere fact rather than some grandiose deduction from conjecture, to the accuracy of precise observations the relation is characterized by r = R_o ln (z+1), which theorists will tell you corresponds to an "Einstein-de Sitter Universe." Here we have distance given by the natural log of redshift, z, plus one, all divided by Hubble's constant. The effect of redshift is to reduce the frequency of radiation, thereby reducing its intensity by the factor 1/(z+1) = e^{− r/Ro}. So that in an infinite universe we would have:

Thus, identical facts can be used to justify opposite theories if you're into that.

Of course cosmology involves a mass of observations concerning a broad scope of concepts, all of which must be understood in such a way that they agree before any comprehensive theory will ever even approach some sort of validity. But, as with the preceding, there seem to be more ways of looking at each fact than initially meets the eye. Einstein's gravitation equations don't address the obvious possibilities of gravitational energy suffering the depredation by redshifting while being propagated. Why not? Nor, of course, should "Newton's iron sphere theorem" be taken as having any relevance once one realizes that the metaphor does not hold for a closed universe for which there is no inside-outside surface. Here too, therefore, observed gravitational effects of finite universes cosmologists favor can be matched or bettered by virtually identical ones involving indefinite extension.

Are these mere cosmic coincidences? I don't think so.