Why Does the Higgs Particle Matter?

Frank Wilczek in Big Questions Online:

The first inkling of its existence came in the 1960s. By that time physicists had devised especially beautiful equations for describing elementary particles with zero mass. Nature likes those equations, too. The photons responsible for electromagnetism, the gravitons responsible for gravity, and the color gluons responsible for the strong force are all zero mass particles. Electromagnetism, gravity, and the strong force are three of the four fundamental interactions known to physics. The other is the weak force.

A problem arose, however, for the W and Z bosons, which are responsible for the weak force. Though they have many properties in common with photons and color gluons, W and Z bosons have non-zero mass. So it appeared that one could not use the beautiful equations for zero mass particles to describe them. The situation grew desperate: The equations for particles with the properties of W and Z, when forced to accommodate non-zero mass, led to mathematical inconsistencies.

The right kind of cosmic medium could rescue the situation, however. Such a medium could slow down the motion of W and Z particles, and make them appear to have non-zero mass, even though their fundamental mass––that is, the mass they would exhibit in ideally empty space––is zero. Using that idea, theorists built a wonderfully successful account of all the phenomena of the weak interaction, fully worthy to stand beside our successful theories of the electromagnetic, strong, and gravitational interactions. Our laws of fundamental physics reached a qualitatively new level of completeness and economy.

More here.