Particle Physics and Gothic Cathedrals

David Lindley, The End of Physics. The Myth of a Unified Theory, 1993. From Chapter 9, The New Heat Death

Particle physicists have sometimes drawn an analogy between their machines and the Gothic cathedrals of medieval Europe – both, in their own ways, monuments to a search for truth by their respective communities. The analogy may be more apt that physicists would like: Gothic cathedrals occupied generations of now nameless carpenters and masons.

Still, the Gothic cathedrals were built, and remain today. Physicists may feel that if the world is prepared to foot the bill, they are prepared to embark on efforts that they will not see finished in their lifetimes.

Prologue. The Lure of Numbers.

In 1960, the Hungarian-American physicist Eugene Wigner published an essay entitled “The unreasonable Effectiveness of Mathematics in the Natural Sciences.”

What puzzled Wigner puzzled many others, including Albert Einstein: “How can it be that mathatics,” he once asked, “being a product of human thought which is independent of experience, is so admirably appropriate to the object of reality?”

There is a temptingly simple explanation for the fact that science is mathematical in nature: it is because we give the name of science to those areas of intellectual inquiry that yield to mathematical analysis.

The puzzle becomes a tautology: mathematics is the language of science because we reserve the name “science” for anything that mathematics can handle. If it’s not mathematical to some degree at least, it isn’t really science.

Scientific history, however, tends not to record the zigzags. History is written by the winners, and failed attemnts to explain this or that phenomena are soon forgotten, though the faild theory may have provided a useful stimulus. Kepler spent years working with the observational data collected by the Danish astronomer Tycho Brahe, and trying who knows how many geometrical shapes for the planetary orbits before he hit on ellipses. But when he published his results, ellipses were all that he offered the reader. In the same way, Isaac Newton, though he presumably reached his theories of motion and gravity and his theorems on orbiral shapes by some sort of trial and error (albeit guided by general principles), wrote up his researches in the Philosophiae naturalis principia mathematica as if he had been fortunate enough to glimpse directly the divine rules that govern the universe and, thus blessed, had worked out the consequences.

Quantum mechanics was born when Max Planck, struggling to understand the relationship between the temperature of a glowing body and the color and intensity of the light it emitted, played at fitting mathematical formulas to experimentally derived results until he found one that worked.

In the same vein, Niels Bohr began to understand how the quantum idea could explain the characteristics frequencies of light emitted by hydrogen atoms because he was familiar with a simple numerical formula, stumbled accros many years before by the Swiss mathematician Johann Jakob Balmer, which expressed all the known wavelength of hydrogen light in terms of the difference between the reciprocal of the squares of whole numbers. Balmer’s formula had been the result of arithmetical quesswork, but it turned out to be of profound significance.

There are many cases, however, where an excessive devotion to the search for mathematical simplicity can mislead. For example, there is a venerable numerical formula that claims to explain the distances of the planets from the Sun by simple arithmetic.

Good and bad numerology are easiliy distingquished in retrospect.

What forms does numerology take today, and how are we to judge, whether they are good or bad?

Pythagoras and Einstein

The other way is to find mathematical laws whose beuty and simplicity have particular appeal, and then attempt to fit the world to them. The latter method, which seems rather rarefied to us nowadays, is what Pythagoras intended, millenia ago, by his idea of “the harmony of numbers”. He and his followers believed that the world ought to be based on mathematical concept – prime number, circles and spheres, right angles and parallel lines – and their method of doing science was to strain to understand the phenomena they observed around them in terms of these presupposed concerpts. It was for many centuries a central believe that the whole world, from the motion of falling bodies to the existence of God, could be ultimately be understood be pure thought alone.

At the same time, it is apperant that the greatest successes of twentieth-century physics have been theories that make use of novel and enticing mathematical structures imported from the realm of pure thought. Aesthetic judgement are taking on greater importance in theoretical physics not as the result of some conscious change in the methods of science but by default.

Some of the blame, unfortunately, for this shift back toward the old Pythagorean ideal must go to Albert Einstein. His general theory of relativity is the prime example of an idea that convinces by its mathematical structure and power, and for which experimental verification is something of an afterthought.

Chapter 1, Lord Kelvin’s Declaration.

It was Kelvin’s assertion, on the other hand, that the world could be no more that one hundred million years old, a figure he obtained by applying the newly formulated principles of energy conservation and thermodynamics to the present state of the Earth and the Sun. In this matter he opposed not only the geologists but also, later, the biologists. Charles Darwin and his followers wanted more time than Kelvin would allow for natural selection and evolution to raise the human race from its lowly beginnings, and in the first edition of the Origin of Species Darwin attempted to match Kelvin, calculation against calculation, by estimating the age of the Weald, a geological feature in southern England, from contemporary estimates of the rate of erosion. He produced a figure of three hundred millions years, which he found satisfactory to his purposes, but his method was roundly attacked by Kelvin and other physicists, and in the second edition of the book Darwin acceded to their superiority and sheepishly withdrew this number in favor of something closer to Kelvin’s.

Chapter 9, The New Heat Death

This is surely a generous way of thinking:  particle physicists have argued for the existence of all kinds of new particles in addition to the ones we know about, in order to allow supersymmetry or supergravity or superstrings to work, but proponents of the strong anthropic principle are multiplying whole universes in order to provide a home for us, and then, moreover, concealing those universes from us so that we can never see the extravances enacted for our benefit. This illustrates the basic dilemma in all this puzzling. We live in but a single universe that has been created, in which case we have to explain why that universe should have properties congential to our existence, or in one of an infinite variaty of universes, in which case the fact that we live in a congencial one becomes a tautology. The problem is that, by definition, we cannot know about universes other than our own; if we knew about them, they would part of our universe.

We are already at the point where experiments are becoming impossible for technological reasons and unthinkable for social and political reasons. An accelerator bigger that the supercollider would be a vast technical challenge, and even if physicists are willing to try it, the likelihood of society paying the bills seems faint.

The physicists must hope instead that they can complete physics in the manner the ancient Greeks imagined, by means of thought alone, by rational analysis unaided by empirical testing. The ultimate goal in physics seems to demand, paradoxically, a return to old ways.

Perhaps physicists will one day find a theory of such compelling beauty that its truth cannot be denied; truth will be beauty and beauty will be truth – because, in the absence of any means to make practical tests, what a beautiful is declared ipso facto to be the truth.

This theory of everything will be, in precise terms, a myth. A myth is a story that makes sense within its own terms, offers explanations for everything we can see around us, but can be neither tested nor disproved. A myth is an explanation that everyone agrees upon because it is convenient to agree on it, not because its truth can be demonstrated. This theory of everything, this myth, will indeed spell the end of physics. It will be the end not because physics has at last been able to explain everything in the universe, but because physics has reached the end of all the things it has to power to explain.