A Higgs, the Higgs … is math at the root of reality? 

By Jonathan Borwein, University of Newcastle and David H. Bailey, The Conversation | March 30, 2013

Last Updated: April 10, 2013 11:25 am

Recently, researchers at the European Organization for Nuclear Research (CERN) finally announced the new particle discovered last summer is indeed a Higgs boson, a particle predicted purely by mathematical reasoning back in 1964. 

The final confirmation of the Higgs boson came when evidence was found that the new particle decays (transforms in a spontaneous process) 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. 

Praise be

The requisite matter-inducing particle was first hypothesised in 1964, when British physicist Peter Higgs and several colleagues showed, by purely mathematical methods, the following: if there were a universal background field of a certain type, particles that convey forces would behave as if they have mass. 

That conjectured particle is now called the Higgs boson, and its recent discovery by scientists at the LHC has been universally praised. 

As Lawrence Krauss of Arizona State University put it last year, shortly after the CERN discovery:

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. 

Be reasonable …

Underlying the discovery of the Higgs boson is one of the truly great mysteries of modern science: why, in the physicist Eugene Wigner’s terms, is mathematics so unreasonably effective in physics? 

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 following 300 years. 

In 1917, Einstein published an even more ambitious theory, the general theory of relativity, which implied the space-time continuum was curved in the presence of a massive object. 

Subsequent measurements of starlight bending around the sun dramatically confirmed these counter-intuitive 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. 

Such examples barely scratch the surface – and the list goes on and on. 

So perhaps it’s not surprising the Higgs boson made its predicted appearance at the LHC 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. 

Where are we now? 

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 the English theoretical physicist 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. 

In many ways, such thoughts still hold true.  The predictions of current particle physics have been spectacularly validated by the discovery of the much-hyped Higgs boson. 

But 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. 

The predictions of current particle physics have been spectacularly validated by the discovery of the God particle, as the Higgs boson is, unfortunately, sometimes called. 

But it’s worth remembering how well classical Ptolemaic epicycles could predict astronomical positions despite being based on false (but highly-tuned) Roman science.