mass-energy equivalence
Burning a log releases heat, and the ash plus smoke weigh a hair less than the log did — a difference so tiny no kitchen scale could catch it. That missing weight left as energy. The deep lesson of Einstein's most famous equation is that mass and energy are not two separate things but two forms of the same thing, and in particle physics this is not a curiosity at the edges — it is the central fact that lets the field exist.
Mass-energy equivalence is the statement that mass is a highly concentrated form of energy, related by E equals m c-squared, where c is the speed of light. Because c-squared is an enormous number, even a speck of mass is equivalent to a large energy. The flip side is just as important: pour enough energy into a small region and you can create mass — brand-new particles that were not there before. This is exactly what happens in a collider: two protons carrying huge kinetic energy crash, and out of that energy spring heavier particles, including ones far more massive than the protons that made them.
This two-way street is the working principle of all of high-energy physics. It is why a particle can be created from energy and why an unstable particle can decay only into products lighter than itself (the leftover mass becomes the products' kinetic energy). It is also why mass and energy share one unit. A common misconception is that E equals m c-squared is only about nuclear bombs; in fact every chemical reaction and every collision obeys it, and in particle physics the conversion of energy into new matter, and matter into energy through annihilation, is an everyday occurrence rather than a rare event.
When an electron meets its antiparticle, the positron, the two annihilate and vanish entirely, their combined mass reappearing as a flash of high-energy photons. Mass has turned completely into energy — the cleanest possible demonstration of E equals m c-squared.
Matter and energy convert into each other — routinely, in particle physics.
E equals m c-squared gives the energy of a particle at rest; a moving particle also carries kinetic energy, so its total energy is larger. The fuller statement is the energy-momentum relation, treated as its own topic.