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?

The minimum energy of a massive particle is less in Newtonian mechanics than in special relativity. Massless particles are ill-defined in Newtonian physics. A particle with zero mass can be at rest. The mass is unchangeable in both Newtonian and special relativstic physics.

1 solution

Tyson Randall
Aug 15, 2014

If a particle had zero mass, it would 1) not be described by Newtonian Mechanics because mass, $m$ is in the denominator for both $E$ and $v$ , and 2) in Relativisitic mechanics, it would give $E=\sqrt { { p }^{ 2 }{ c }^{ 2 } }$ . The velocity is only defined if momentum is nonzero. If momentum is not equal to zero, then $v=c$ .

Relativistic mass

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