To better understand the Higgs field and how it works its magic, we need to make a detour into the history of physics and look at the similarities and differences between particles and waves. In ordinary life (what we call the ‘classical’ world) a particle is a localized object that is usually of small size, has a fairly well defined boundary, and a mass. A grain of rice and a speck of dust are particles. A wave, on the other hand, is the name we give to the pattern of vibrations traveling through some medium (think of the waves in water or sound waves traveling through air) that is extended, has no sharp edges, and does not have mass.
This distinction between particles and waves seemed pretty clear-cut for centuries. Any entity had to be either a particle or a wave because the properties of the two categories were quite distinct. However, there was one troublesome phenomenon that kept escaping from the category to which it was assigned, and that was light.
Isaac Newton (1642-1727) did a systematic investigation of light and declared that its properties were consistent with thinking of it as being composed of a stream of particles and this view persisted for over a century, dominating over the alternative wave theory proposed by Christiaan Huygens (1629-1695).
But during the late eighteenth and early nineteenth centuries, further investigations seemed to indicate that light also had wave-like properties and Thomas Young (1773-1829) and Augustin-Jean Fresnel (1788-1827) showed that light exhibited the phenomenon of interference (where light from two sources overlapped to sometimes create a large effect and sometimes no effect at all) and also that of diffraction (the ability to bend around edges). Both these properties had previously never been observed with particles but only with phenomena (like sound and water) that had been established to be waves. Thus light was also deemed to be a wave.
This immediately raised a new problem. Waves had always been thought to be disturbances in an underlying medium. What medium was being disturbed by light waves? This was especially problematic since light was reaching us from distant stars so this medium had to extend everywhere, even over what we had thought was the vacuum of deep space. This led to the suggestion that there was an elastic medium (which was given the name of ‘luminiferous ether’ or simply ether) that permeated all space even though we had not been aware of it up until that point. The sole function of the ether seemed to be to enable the propagation of light waves.
That state of affairs lasted about a century. Beginning with the twentieth century, all manner of problems with the wave-particle distinction started to emerge, not the least of which was that, despite determined efforts by some of the best experimentalists (including the famous Michelson-Morley experiment done at my own institution of Case Western Reserve University), no corroborating evidence could be found for the existence of this ether. It was Albert Einstein (1879-1955) who resolved this issue when he proposed his theory of relativity that made the ether redundant and soon it was dispensed with. But this resurrected the old problem of how light waves propagated and it was suggested that light waves, unlike all other waves, did not need a medium at all but were a disturbance of space itself.
Then further investigations and analyses by Max Planck (1858-1947) on black body radiation and Einstein on the photoelectric effect started revealing that light had particle-like properties, seemingly bring us back to the ideas of Newton. This was clearly a problem since light continued to show interference and diffraction effects, the defining characteristics of waves. It was suggested that light waves consisted of a stream of particles that on a large scale appeared like a wave but that it was when you looked at it on a small scale that its particle properties became apparent. The particle associated with light was called the photon.
So thanks to light, the wall of separation between particles and waves was being chipped away from the wave side.
That was not all. Louis de Broglie (1892-1987) suggested that those things that had been thought to be incontrovertibly particles (like electrons) also had wave-like properties, a prediction that was confirmed in 1927. But since electrons still had a mass, a defining characteristic of a particle, this meant that the wall of separation was also being undermined from the particle side.
It was a puzzle and the search was on to explain this strange behavior where things were neither purely particles nor waves but perhaps both or even neither.
Major progress in the search for a coherent unifying theory was achieved by Erwin Schrodinger (1887-1961) who in 1926 wrote down an equation called the Schrodinger equation that was a wave equation for particles with mass. This hybrid equation turned out to be extremely successful for calculating properties of some things like the size and energy levels of the hydrogen atom.
The Schrodinger equation was clearly something that straddled the wave-particle divide, thus eliminating the wall of separation. But although it was successful as a computational device, for some time it was not clear what the wave function that emerged as the solution to the equation meant. There was considerable debate over this, with a rough consensus eventually emerging that while particles remained particles (i.e., objects that had definite boundaries that were confined to a small region of space), the wave function represented information about the probability (technically the probability amplitude) that the particle would be found in a region of space. So a region of space with a large wave function for a particle meant that the particle was more likely to be found there than in a region of space with a smaller wave function. This wave function could extend over a large area (like waves do) and was the cause of the interference and diffraction effects that particles exhibited.
This interpretation of the Schrodinger equation became the standard one for about half a century since it seemed to be able to reconcile the troubling idea that entities seemed to exhibit both wave and particle properties, what we refer to as wave-particle duality.
But like all scientific theories, it solved some problems while creating new ones and it was the effort to resolve those that led to further advances.
Next: Fields as a unifying concept.