# Relativistic mass

**Classical Mechanics**Level 3

Our next step towards the Higgs mechanism is to understand a bit more about mass in special relativity. In both special relativity and Newtonian mechanics, the mass of an object plays a particular role - it determines how the total energy of a particle relates to its momentum. In special relativity the energy of a particle is a function of the momentum and the mass, just like in Newtonian mechanics. The function \(E(p,m)\) is called the *dispersion relation* of the particle. What differs between Newtonian mechanics and special relativity is the form of the dispersion relation. Furthermore, since the velocity of particle can always be written as a function of the momentum and energy of the particle, the dispersion relation controls the velocity function \(v(p,m)\).

In one dimension (for simplicity) we have:

*Newtonian mechanics*:

\(E=\frac{p^2}{2m}, v=\frac{p}{m}\)

*Relativistic mechanics*:

\(E=\sqrt{p^2 c^2 + m^2 c^4}, v=\frac{p}{E}\).

According to these relationships, which of the following statements is incorrect?