The reason particles have finite positive masses while classical waves, such as electromagnetic waves, travel at the speed of light can be understood through the concepts of mass-energy equivalence and the nature of wave propagation.
In the theory of relativity, mass and energy are interrelated through Einstein's famous equation, E=mc², which states that energy (E) is equal to mass (m) multiplied by the speed of light (c) squared. This equation implies that mass and energy are different manifestations of the same underlying concept.
Particles, such as electrons, protons, and neutrons, have finite positive masses because they possess rest mass, which is a measure of the intrinsic energy associated with their existence. Rest mass is a property of particles that arises from their interaction with the Higgs field in the Standard Model of particle physics. This interaction gives rise to the particles' inertia and the resistance they offer to changes in their motion.
On the other hand, classical waves, including electromagnetic waves, do not have rest mass. They are a manifestation of energy and do not possess intrinsic mass like particles do. Electromagnetic waves consist of oscillating electric and magnetic fields that propagate through space at the speed of light. In the absence of any interaction with matter, electromagnetic waves travel at the maximum possible speed in the universe, which is the speed of light in vacuum.
The speed at which waves propagate is determined by the properties of the medium through which they travel. In the case of electromagnetic waves, their speed is primarily governed by the electric and magnetic properties of the vacuum, which are characterized by the permittivity and permeability of free space. These properties lead to the speed of light being constant and independent of the wavelength or frequency of the electromagnetic wave.
In summary, particles have finite positive masses due to their intrinsic rest mass, which arises from their interaction with the Higgs field. Classical waves, such as electromagnetic waves, travel at the speed of light because they are manifestations of energy and do not possess rest mass. The speed of light in vacuum is determined by the fundamental properties of space and is constant for all electromagnetic waves.