Higgs at last
On March 15, 2013, researchers at the European Organization for Nuclear Research (CERN) finally confirmed that the new particle discovered last summer is indeed the Higgs boson, a particle predicted purely by mathematical reasoning back in 1964.
Initial measurements announced in July 2012 confirmed that it was a boson, and that its mass was about 126 GeV. Both of these findings strongly suggested that it was the longsought Higgs particle, which is thought to endow particles with mass among other things. Bosons belong to one of two basic particle classes; the others are known as fermions. Both were named by Paul Dirac—whom Niels Bohr called the “strangest man”—after Bose and Fermi respectively.
The final confirmation of the Higgs boson came when evidence was found that the new particle decays into W bosons. One lingering detail, according to Raymond Volkas of the University of Melbourne in Australia, is that while the discovered particle is “a Higgs boson,” it is not entirely confirmed that this is “the Higgs boson,” namely the particle that gives mass to fermions as well as bosons.
Confirming this requires a large number of decays, and CERN’s Large Hadron Collider might never be able to generate the requisite energy level.
As to why the Higg’s boson matters there are many reasons.
What does it mean?
The Higgs boson was hypothesized in 1964, when British physicist Peter Higgs and several colleagues (François Englert, Robert Brout, Tom Kibble, Carl R. Hagen and Gerald Guralnik) showed by purely mathematical derivations that if there exists a universal background field of a certain type, then particles that convey forces would behave as if they have mass. Subsequently, Texas physicist Steven Weinberg (who shared the 1979 Nobel prize with Abdus Salam and Sheldon Glashow) showed that this same idea could be applied to all fundamental particles, including protons, neutrons and electrons.
That conjectured particle is the Higgs boson, and its discovery by scientists at the Large Hadron Collider has been described as a “remarkable celebration of the human mind’s capacity to uncover nature’s secrets.” Or as Lawrence Krauss of Arizona State University explained,
Hidden in what seems like empty space … are the very elements that allow for our existence. By demonstrating that, last week’s discovery will change our view of ourselves and our place in the universe. Surely that is the hallmark of great music, great literature, great art … and great science.
Itay Yavin of McMaster University in Hamilton Canada added
By collaborating, we can unlock one of deepest mysteries in nature and discover a particle that was predicted on paper some 50 or so years ago. … It’s really a remarkable testimony about everything that is good about the human spirit, to collaborate and to think deeply about the universe.
Why is mathematics so effective?
Underlying the discovery of the Higgs boson is one of the truly great mysteries of modern science: Why in Eugene Wigner’s terms is mathematics so unreasonably effective in physics? Or, as we might also ask, is mathematics the root of reality?
One can easily point to a long string of successes for mathematics. Beginning in the 1600s, Newton’s laws of motion and gravity, expressed in their true form as differential equations, succeed in explaining virtually every physical phenomena studied in science for the next 300 years.
In the late 1800s, Maxwell showed mathematically that light was an electromagnetic wave. When he then calculated the speed of this wave, he obtained a value very close to the speed of light (299,792 km/sec or 186,282 mi/sec) that had been measured in careful experiments at the time. These calculations in turn laid the foundation for Einstein’s special theory of relativity in 1905. Another of 1905 Einstein’s papers, on the photoelectric effect, laid the foundations for quantum mechanics.
In 1917, Einstein published an even more ambitious theory, the general theory of relativity, which implied that the spacetime continuum was curved in the presence of a massive object. Subsequent measurements of starlight bending around the sun dramatically confirmed these counterintuitive predictions. In the following decades, physicists applied this theory to predict such exotic phenomena as black holes, as well as an initial singularity now known as the big bang.
Other physicists, extrapolating from the growing mathematical framework of quantum mechanics, predicted particles, and nature obediently produced these particles in experiments. Dirac predicted the positron on purely mathematical grounds long before it was discovered experimentally.
Beginning in 1948, physicists Ralph Alpher and Robert Herman deduced that the universe must be bathed in an afterglow of the big bang, redshifted to roughly five degrees K (i.e., 5 degrees above absolute zero). Then in 1965, Arno Penzias and Robert Wilson at Bell Laboratories, using a telecommunications antenna, observed exactly such a signal (albeit at roughly 3.5 K), now known as the cosmic microwave background. More precise measurements of this radiation in the 1990s further confirmed the big bang theory, verified the geometric flatness of the universe and pointed to inflation as source of the first perturbations.
The list goes on and on. Thus, perhaps it is not surprising that the Higgs boson made its predicted appearance at the Large Hadron Collider party, with exactly the properties earlier projected for it. Indeed, there is a deep fear in the physics community that the Higgs boson will prove to be so “ordinary” that no new physics will be glimpsed in the LHC. Is the Higgs the end of the line?
A theory of everything?
In the wake of these successes, many physicists and mathematicians have been searching for a “theory of everything,” namely a complete and concise mathematical framework that would completely explain all of physical reality. Yet the dream remains frustratingly elusive.
The best we have today is the standard model, based on quantum mechanics, which describes the microscopic world with breathtaking accuracy, combined with general relativity, which governs the largescale structure of space and time. But there is a snake in the Eden of the standard model, namely the fact that quantum mechanics and general relativity are fundamentally incompatible from a mathematical viewpoint.
At the present time, string theory constitutes the best candidate for a “theory of everything.” String theory invokes additional dimensions (11 dimensions in the most popular current version), combined with various symmetries, to describe different fundamental particles and their forces. One very promising feature of string theory is that it permits a straightforward union of quantum mechanics with relativity.
But there are serious problems with string theory, not the least of which is the fact that none of the theory’s predictions so far are testable with reasonable technology. This has led some to question the entire string theory research enterprise.
Another rather discouraging development is that the theory appears to predict a huge ensemble of potential universes, numbering, by one reckoning, more than 10^{500}, utterly crushing the hope by string theory pioneers that ultimately the theory would describe just one universe — ours. What is the value of a theory that can be “massaged” to be anything desired?
Is the philosophy of physics in need of a deep rethink?
Other paradoxes loom. For example, according to currently understood physical laws, the zeropoint mass density of the universe should have a value of 10^{93} grams per cc. Instead, the actual mass density of the universe is roughly 10^{28} grams per cc, a discrepancy that has been termed the worst prediction in the history of physics. A closely related conundrum is the cosmological constant paradox. According to theoretical calculations, the positive and negative contributions to this constant must cancel out to 120digit accuracy, yet still be nonzero!
Some string theorists have suggested an imaginative solution to such paradoxes: The ensemble of 10^{500} universes actually does exist, and we just happen to live in one whose parameters are extraordinarily welltuned to permit the existence of intelligent life. In other words, we observe an exceedingly special universe, because if it weren’t so special, we would not be here to talk about it.
But other scientists are extremely wary of this type of anthropic reasoning, viewing it as the last and desperate attempt to save a fundamentally flawed theory.
So will string theory, with its impressive albeit arcane mathematical structure, ultimately prevail? Or will it finally be crushed by some nagging experimental fact for which it has no defence? Only time will tell.
Some things are clear. As Gino Segre describes in Faust in Copenhagen, the great successes of 20th century physics were coupled to philosophical ideas. The birth of relativity and quantum theory were very much a part of the intellectual ferment of the first three decades. Einstein, Born and others were greatly influenced by the positivist ideas of Vienna circle, as was Kurt Gödel. Gödel and Einstein’s friendship is told in Palle Yourgrau’s A world without time. The book, while questionable philosophically, is compelling in its account of the period.
For many of the great theoretical physicists of the last century, mathematical notions were fundamental. Concepts of elegance or beauty, simplicity or parsimony, symmetry or parity were both inspirational and fruitful. As Paul Dirac put it:
It seems to be one of the fundamental features of nature that fundamental physical laws are described in terms of a mathematical theory of great beauty and power, needing quite a high standard of mathematics for one to understand it.
and
Just by studying mathematics we can hope to make a guess at the kind of mathematics that will come into the physics of the future.
But why should it be that these precepts necessarily apply to the physical universe? John Satchel wrote in his 2007 review of Yourgrau’s book:
The real question is: What is the physical significance of such models? Every physical theory that we know has two properties:
1) There are physical phenomena that fall outside its scope, i.e., that cannot be modeled by the theory (it is not a “theory of everything”).
2) There are “unphysical” models of the theory, which do not correspond to any physical phenomena. The class of all models must be restricted by some additional criteria, such as boundary conditions, not inherent in the theory, in order to fit some limited range of physical phenomena.
The smaller the number of phenomena in class 1), and smaller the number of models in class 2), the more we value a theory. But there is no reason to believe that general relativity is an exception to this rule. To use the existence of a class of models with closed timelike world lines as an argument against the concept of time, without a shred of evidence that such models apply to any physical phenomena, is an example of that fetishism of mathematics, to which some Platonists are so prone.
Summary
The predictions of current particle physics have been spectacularly validated by the discovery of the muchhyped God particle, as the Higgs boson is sometimes called. But it is worth remembering how well the classical Ptolemaic epicycles could predict astronomical positions.
Solving the many unresolved problems of physics may need a greater detachment from mathematics (philosophically if not technically). Additionally, there is no scientific reason to justify the belief that all the big problems have solutions, let alone ones we humans can find.
[A version of this article appeared in the Conversation.]
Postscript (March 23 2013) The strange combination of idealism and Platonism (see the already mentioned review of A world with out time ) that pervades some current philosophers’ and physicists’ discussions of the nature of reality is far from new. James Boswell (1740 – 1795) wrote
After we came out of the church, we stood talking for some time together of Bishop Berkeley’s ingenious sophistry to prove the nonexistence of matter, and that every thing in the universe is merely ideal. I observed, that though we are satisfied his doctrine is not true, it is impossible to refute it. I never shall forget the alacrity with which Johnson answered, striking his foot with mighty force against a large stone, till he rebounded from it, ‘I refute it THUS.’
(The Project Gutenberg EBook of Life of Johnson, by James Boswell [page 90, EBook #1564])
An idealist accounting does nothing to help describe the actual human experience of reality or of qualia. As Erwin Schrödinger (18871961), the famous physicist, put it in What is life? : the physical aspects of the living cell:

The sensation of color cannot be accounted for by the physicist’s objective picture of lightwaves. Could the physiologist account for it, if he had fuller knowledge than he has of the processes in the retina and the nervous processes set up by them in the optical nerve bundles and in the brain? I do not think so.^{ }
Not much has changed.
[Added 26 Mar 2013: The potential impact of the Higgs discovery is further discussed in this Scientific American article.]