the massless-particle limit

We are used to thinking that everything with energy must weigh something. Light breaks that intuition. A beam of light carries energy and even pushes on what it hits, yet light's particles — photons — have no mass at all. The massless-particle limit is what the relativistic equations say about such objects, and it is wonderfully simple: anything with zero rest mass must travel at exactly the speed of light, no faster and no slower, in every frame.

Start from the full energy-momentum relation, E^2 = (pc)^2 + (mc^2)^2, and set the mass m to zero. The rest-energy term vanishes and you are left with E = pc: a massless particle's energy is just its momentum times c. There is no rest frame to sit still in — a photon is never at rest — and its energy can be anything from tiny (radio waves) to enormous (gamma rays) depending only on its momentum. The Lorentz factor for such a particle is formally infinite, which is the mathematical sign that it lives permanently at the speed limit.

Massless particles are not exotic; they run the show. The photon, carrier of electromagnetism, is massless, and so is the gluon that binds quarks. Whether the neutrino has a tiny mass was an open question for decades — neutrino oscillations later showed it does, though its mass is so small it is often treated as nearly massless. A common confusion is to think mass is required to carry momentum; relativity says no. Momentum and energy are what a massless particle has in abundance; mass is exactly the thing it lacks.