All the stable elements must remain truly "stable" over time: otherwise, mankind would never have looked out on the light of the stars. In order that a universe can bring forth observers, then, it must guarantee the conditions that are necessary for the stability of matter - conditions which must also still prevail today. Even physicists, however, were far from spotting that this presented anything in the way of a problem. It is taken too much for granted as part of our everyday existence that we are surrounded by more or less stable matter - rocks, water, air, refrigerators, nuclear power stations - for us to suppose this conceals a scientific poser. Anything so simple and obvious, one would think, must have a simple and obvious physical explanation. The opposite is the case. "Some features of the physical world are so commonplace that they hardly seem to deserve comment. One of these is that ordinary matter, either in the form of atoms or in bulk, is held together with [electrical] Coulomb forces and yet is stable," as Elliot H. Lieb, one of the physicists to have been intensively concerned with the problem, wrote in 1976. By then, however, this irksome gap in our understanding of the cosmos had already been bridged, not least by Lieb himself. The stability of matter, "this truly remarkable phenomenon" (Lieb), follows from the theory of quantum mechanics developed in the 1920s, which finally offered a comprehensive scheme for atoms built of nuclei
containing protons and neutrons and atomic shells consisting of electrons. But for some years the problem was left in abeyance; and it was not until 1967 that two of America's leading scientists, Freeman J. Dyson and A. Lenard, finally led "a heroic frontal attack on this difficult problem," as the Viennese theoretician, Walter Thirring, described it.
The "Coulomb forces" mentioned by Lieb are none other than the force of electrical attraction that two electric charges - one positive and one negative - exert on each other. (Two positive or two negative charges repel each other.) This force diminishes by the square of the distance between the charges; to this extent, the Coulomb forces act similarly to the force of gravity between two bodies. Let us carry out a small, imaginary experiment. If we take two (opposite) charges, one in the left hand and one in the right, and let them go, they will attract each other more and more strongly the closer they approach each other: they will move towards one another until. .. until what? Until they collide? Can this really hold good if the negatively charged shell of each atom is to maintain a minimum separation from its positively charged nucleus? Even the nucleons of the nucleus itself, while they are tightly packed, can only be forced together up to a certain point. Wouldn't this situation lead to continual catastrophes, for instance, in the case of the most common atom in the universe, that of hydrogen, in which one proton and one electron circle each other? How could atoms ever exist in the expanded form we know?
Embarrassment over this "awkward matter" in theoretical physics was expressed as long ago as 1915 by the British astrophysicist J. H. Jeans. Shortly before the advent of quantum mechanics, he noted that "there would be a real difficulty in supposing that the law 1/r2 [stating that the attraction is inversely proportional to the square of the distance] held down to zero values of r [i.e. zero distance]. For the force between the two charges at zero distance would be infinite, we should have charges of opposite sign continually rushing together and, when once together, no force would be adequate to separate them. . .. Thus the matter in the universe would tend to shrink into nothing or to diminish indefinitely in size." Why, then, do atoms not collapse in on themselves? When the principles of quantum mechanics crystallized in the early 1920s - as a result of the work of Erwin Schrodinger, Wolfgang Pauli, Pascual Jordan, Neils Bohr, and others - the Austrian physicist Paul Ehrenfest was struck by the remarkable fact that every atom actually consists almost entirely - up to 99.99 percent, in fact - of empty space:
"We take a piece of metal. Or a stone. When we think about it, we are astonished that this quantity of matter should occupy so large a volume. Admittedly, the molecules are packed tightly together, and likewise the atoms within each molecule - but why are the atoms themselves so big?" This size of each atom - for instance, that of hydrogen - is explained by the "uncertainty principle." The closer the orbit of the electron is to the proton, the higher it's orbital velocity. From this can be derived a smallest possible radius for the electron's orbit: the minimum orbit available to the electron is 100,000 times as large as the diameter of the proton - which is why atoms are so surprisingly large.
If there are several protons and neutrons in the nucleus of the atom and several electrons in its shell, "peaceful coexistence" among these particles is regulated by a further law, known as the Pauli Exclusion Principle. This is actually a prohibition, stating what may not happen rather than what does: its effect is, in short, that no two particles may exist in the same state. Thus, two electrons may not occupy the same "room," but must make do with neighboring rooms. And when the ground floor is full, they must climb to the next floor. In the shell of the atom, the ground floor offers two rooms, the second floor 8, the third 18, and so on. Analogous "stories" regulate the arrangement of the particles in the nucleus. Dyson and Lenard's "heroic frontal attack" of 1967 proved that, without the Pauli principle, the force of electromagnetic attraction would mean that "not only individual atoms but matter in bulk would collapse into a condensed high-density phase. The assembly of any two macroscopic objects would release energy comparable to that of an atomic bomb."
Let us examine this Pauli principle. It was formulated by Wolfgang Pauli in 1935 and represents a firm statement regarding the most important characteristics of a particular group of particles including the electron and proton. It states that if there are several identical particles in the nucleus or the shell of an atom, then each must occupy a different state. Thus, for instance, no atom may contain two electrons which are equal in their position and their other quantum characteristics such as their spin. The group of particles affected by the Pauli principle includes - not by chance - all the particles involved in the make-up of the atom: electrons (and their anti-particles, positrons), protons and neutrons as well as all atomic nuclei consisting of an odd number of particles; to these can be added neutrinos. The quality that unites them, their "spin" - a sort of internal angular momentum - goes by odd halves (1/2, 3/2, 5/2, etc. in appropriate units). In recognition of the work of Enrico Fermi, these are known as fermions or "Fermi particles." Particles with whole-number spin (0,1,2, etc.) are not subject to the Pauli principle:
these include photons, mesons, and atomic nuclei with an even number of particles - the bosons ("Bose particles").
SPACE MUST BE THREE-DIMENSIONAL
The size of the atom, the distance between nucleus and shell, was the second essential property of matter to become comprehensible once the principles of quantum mechanics were established. In approaching the nucleus of the atom, the electrons are forced, so to speak, to take up an orbit that stays above a certain minimum level of energy. Instead of falling into the nucleus, the electron increases its orbital velocity, and this arrests its fall at a fixed minimum distance from the nucleus - a consequence of Heisenberg's uncertainty principle. It is thanks to the Pauli principle and the uncertainty principle, then, that matter has acquired the necessary size and stability!
Lenard and Dyson, in putting together their proof of the stability of matter, made use of an everyday quality of space: the fact that the physical world exists in three dimensions. We can see that this applies to the reality we know by the fact that we need just three figures to fix the location of any point - one for each of the three dimensions length, breadth, height. For a two-dimensional surface only two figures are required; and in a four-dimensional space four would be necessary. There is a close link between the three-dimensional nature of space and the fact that the force between electric charges falls off by the square of the increasing distance between them. This seems simple and logical and is in any case taken for granted as a facet of everyday life; but to prove it required a tour de force of mathematics we can only regard with awe.
Dyson and Lenard solved the problem in the sixties; and in 1975 Lieb and Thirring were able to simplify the proof considerably and improve it. Let us return to the anthropic principle and establish the main points
that are essential to the existence of the universe of an intelligent observer:
- There can be no abundance of matter with long-term stability without the Pauli principle and the uncertainty principle;
- both must be valid over cosmic periods of time;
- space must be three-dimensional.
In a different cosmos, with other spatial dimensions, matter might well be stable in a different way from that established for "our " universe. There would likely be quite different fundamental principles and natural laws in place of the uncertainty principle, the Pauli principle, and electromagnetic force. About this we can only speculate. Nor can we exclude the possibility that a cosmos in which the Pauli principle is not valid might contain quite different varieties of stable matter and thus might even have produced totally different kinds of intelligence.
Requirement of a three-dimensional world for life to exist
John Barrow writes:
“Only three-dimensional worlds appear to possess the ‘nice’ properties necessary for the transmission of high fidelity signals because of the simultaneous realization of reverberation less and distortionless propagation.” For audiophiles, these terms refer to sound quality in stereos, but they apply equally to all wave phenomena. Reverberation occurs when signals emitted at different times arrive simultaneously; signal distortion is an alteration of the form of the wave as it propagates. Astronomers take for granted the remarkable fidelity of information carried by light across the universe. Life, too, almost certainly requires high fidelity in neurological signal transmission, as Whitrow suggested. A three-dimensional universe, unlike the alternatives, allows information to flow with a minimum of fuss and bother. It seems reasonable to conjecture that altering the number of time dimensions would also enormously complicate cause-and-effect relationships and consequently make prediction much more difficult, if not impossible. Indeed, the only safe prediction in such a place might be that accurate prediction weren’t possible. 2
Framework settings 3
Our universe exists within a framework of four dimensions: three of space and one of time. But it didn’t have to be that way. In theory, universes can be created with many other dimensions. (String theory physicists believe our universe may sport seven more undetectable, tiny, curled-up dimensions.)
Princeton physicist Max Tegmark argues that it is only a universe containing the 3+1 dimensions with which we are familiar that could support life. Given the diverse possibilities, we must ask again: how did our universe arrive at this sweet spot?
1. Reinhard Breuer The Anthropic Principle Man as the Focal Point of Nature, page 50
2. THE PRIVILEGED PLANET, pg.210, Guillermo Gonzalez and Jay W. Richards