1. The Evolution of Atoms

1.1 The Prime Mover

"In the interval between dissolution and creation, Vishnou-Cesha rested in his own substance, luminous with dormant energy, among the seeds of all the lives to come." This is almost all that can be said about the time when there was no time, about the Universe when there was no Universe. The Indian poet’s vision can for the time being not be improved upon. In an altogether different language, two other poets said: E = hυ, meaning therewith that the energy (E) carried by any oscillation is a constant multiple (h) of its frequency (υ), and E=mc2, which identifies energy (E) with mass (m), c being the speed of light (299,792 km/second).

Max Planck and Albert Einstein who discovered these two fundamental equations were physicists who mastered fully the principal tool of their trade, mathematics, which allows logical tricks and short cuts, both essential to practice their profession. Throughout this chapter, I will use mathematical short cuts to manage the numbers under discussion. For example, what means E = mc2? It stands for: the capability possessed by a gram of matter of doing work equates 299,792 times 299,792 ergs. The erg is the energy expended when a force of one dyne acts through a distance of one centimeter. The dyne is the force necessary to give an acceleration of one centimeter per second, per second, to one gram of mass. What Einstein thus said is that the energy (E) hidden in a gram of mass has the capacity to accelerate that gram of mass about 90,000,000,000 centimeters per second, per second, upon a distance of a centimeter. These 90,000,000,000 centimeters per second may be short cut to 9.1010 centimeters, or 900,000,000 meters, i.e. 9 x 108 meters, or 900,000 kilometers. The size of these numbers is awkward and it must have been difficult, even for Einstein, to realize what it means for a gram of matter to possess the capability to accelerate a gram of matter 900 thousand kilometers per second, per second, on a distance of a centimeter. The expression E=mc2 is obviously simpler. It is also elegant and constructive, in that a formula composed of only three symbols links in an unexpected way matter (m) and light (c) with energy (E) and favors further developments.

"In the beginning was the Word", i.e. ENERGY. Energy is the lord and giver of Life. This is a reality that transcends our mathematical descriptions. The purest form of energy, as Einstein explained, is the gravitational energy (G) of mass that is the predominant form of energy in the Universe. The precise strength of this force is still not known accurately. Physicists have been able to build clocks that slip by only a second every million years but the accurate measurement of G is still a challenge. Recent determinations of G differ by nearly 40 times their individual error estimates2.

The two next forms of energy that come into consideration are the energies of rotation and of orbital motion. These three energies of a higher form can be degraded into energies of a lower form (light, heat, nuclear reactions, chemical reactions, microwaves, etc.) whose main characteristic is that they cannot be totally converted back into energies of a higher form. Up till 1998, it was believed that these three forces were the only ones and that the Universe evolves by gravitational contraction. This view is now amended by the observation that the speed of the expansion of the Universe does not slow down with time but, on the contrary, has considerably accelerated in the course of time, which is not explainable by the amount of matter that is supposed to compose the Universe. To account for this acceleration, a large-scale repulsive force, called lambda, is postulated. Stephen Hawking (A brief History of Time) reports that Einstein toyed since 1917 with the idea of a cosmological constant, which he finally -and erroneously- rejected as being foolish. This lambda cosmological constant represents about 70% of the Universe’s energy, and only 30% is matter.

The greatest challenge now3 is to understand and describe what most of the Universe is made of and how it is structured.

Quarks are elementary particles of matter. Quarks are the fundamental particles that make up most of the ordinary matter in the universe. Elementary carriers of force (photon, electron) mediate the interactions among these matter particles. The photon mediates the electromagnetic force and the electron is the carrier of electricity. Two enigmas exist in the present mathematical model that attempts to explain the composition of the universe. The first is the size of the elementary particles, which the mathematicians consider to be zero, a point; for a mathematician, quarks and neutrinos are particles devoid of a radius. To a physicist who deals with the real world, and also to anybody endowed with common sense, this is an enigma. How can a particle as the electron, with a mass and a determined electric charge, have no size? The concept of particles without a radius is untenable because, as the distance between two particles whose diameter is zero but whose opposite electrical charges attract each other, gets progressively closer to zero, the electromagnetic and gravitational forces become infinitely large, which is absurd. The second problem is the integration of gravity into a unified field theory that would link gravity with the other forces. Gravity, unlike the other forces, is proportional in strength to the mass of an object. But mass, according to Einstein’s formula, is simply another form of energy. There is an inconsistency here because, the closer two subatomic objects without a radius get, the stronger the forces and the greater the fluctuations in energy they may undergo, which implies that their masses can sporadically become huge, which leads to an increase in the average strength of the forces, etc. The only way out is to abandon the idea that matter is composed of points and admit that it is a continuum of strings endowed with a non-zero radius.

The struggle between these two opposing views has gone on for millennia. The Greeks initially were of the opinion that all matter is made up of four continuous substances, namely earth, water, air and fire. This was replaced by the atomic theory of Lucrecius, and so on back and forth during centuries, down to our own time: the discovery of the quarks forces again a pointillist model. At this moment in history, the absurdity of an explanation of the universe based on points is such that continuous strings are replacing points again. The use of these exceedingly short strings (10-35 meters) by physicists and mathematicians would allow the elaboration of a unified field theory satisfactory to the mind. However, their use raises a new problem. Most of us can handle a world made of three dimensions, in which we move. The fourth dimension, time, is elusive to some cultures, which cannot adequately cope with the consequences their acts generate in a not too distant future. A unifying theory based on strings requires 5 additional dimensions, which makes it incomprehensible to the immense majority of the human race.

References

2. For the time being G = 6.6873 x 10-11 m3. kg-1. sec-2; Schwarz J et al.: A free-fall Determination of the Newtonian Constant of gravity: Science 1998; 282: 2230-2234

3. Glanz J: Cosmic Motion Revealed. Science 1998; 282: 2156-2157

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