In this case, we have the values \(m_e\approx9,109\cdot10^{-31}\ Kg\), about \(1836\) times lighter than the proton, \(q_e\approx−1.602\cdot10^{−19}\ \text{coulomb}\), which is the elementary electric charge, and an intrinsic angular momentum, or spin, of \(1/2\). No other particle has the same characteristics, and all observers must agree with them.
The origin of mass, charge, and spin can only be explained by the relativistic quantum field theory. Therefore, in classical mechanics, these values must be postulated. But they are the first examples of what is called dynamical invariants \label{word: dynamical invariants}. The values of \(\left(m_e,q_e,s_e\right)\) are always the same for the electron, as for any other particle, and they never change.
Another very important particle in nature is the photon, the particle of light and electromagnetic radiation. For centuries the debate about the nature of light opposed the particle and the wave points of view. Today, we understand the light fundamentally as a field, which can be made a particle when it reaches a detector. Still, it is also a wave when interacting with slits to form interference phenomena. The photon is of little use in classical mechanics since it has zero mass and zero electric charge. The photon does not have a spin value, but it has, on the other hand, a value called helicity \label{word: helicity}, which gives rise to its polarization properties.
Interaction and movement
We know movement should be part of the classical mechanical description because changes in the movement state of objects are part of our everyday lives. How can we accommodate the concept in our theory?
First, we recognize that a universe with a single particle cannot present movement states for the particle. Therefore, the movement \label{word: movement} must be a property of a system of two or more particles. If we have a universe with two particles, we must allow the particles to interact, in this case, to change their mutual states of movement. In the real world, we know by experiment that two particles with values of mass do interact by gravitation. We also know that two particles with electric charge interact by electric and magnetic fields.
A single particle that does not interact with any other particle is a free particle\label{word: free particle}. Ideally, we may have a system of two or more free particles, i.e., particles that form a mechanical system but do not interact with each other, but this would be a very uninteresting system. We may have a system with several particles that interact among themselves but do not interact with other particles or systems, in this case, we call this a closed system\label{word: closed system}, or an isolated system\label{word: isolated system}.