Concept Of Rest Mass of Photon

Concept Of Rest Mass of Photon

Photons are said to be massless. The logic can be demonstrated as follows:

Consider a “particle” accelerating to velocity v (a vector). As per newton’s laws this particle has “momentum” p (also a vector), such that p behaves in a simple way when the particle is accelerated, or when it’s involved in a collision. For this behaviour to hold justified,  p must be proportional to v.  The proportionality constant is called the particle’s “mass” m, so that p = mv.

In special relativity, it turns out that they are no longer proportional; in this case we relate them via the particle’s “relativistic mass” m_rel . Thus

p = m_relv.

When the particle is at rest, its relativistic mass has a minimum value called the “rest mass” (m_rest)  The rest mass is always the same for the same type of particle. For example, all protons, electrons, and neutrons have the same rest mass; As the particle is accelerated to ever higher speeds, its relativistic mass increases without limit.

It also turns out that in special relativity, we are able to define the concept of “energy” E, such that E has simple and well-defined properties just like those it has in newtonian mechanics.  When a particle has been accelerated so that it has some momentum p (the length of the vector p) and relativistic mass m_rel, then its energy E turns out to be given by

E = m_relc² ,   and also    E² = p²c² + m²_restc⁴ .           (1)

There are two cases of equation(1):

1. If the particle is at rest, then p = 0, and E = m_restc².
2. If we set the rest mass equal to zero, then E = pc.

In classical electromagnetic theory, light has energy E and momentum p, and these happen to be related by E = pc. Quantum mechanics tells that light can be viewed as a collection of “particles” i.e. photons. Even though these photons cannot be brought to rest, and so the idea of rest mass doesn’t really apply to them, we can certainly bring these “particles” of light into the fold of equation (1) by just considering them to have no rest mass.  That way, equation (1) gives the correct expression for light, E = pc. Equation (1) can then ne be applied to particles of matter and “particles” of light. Thus it can now be used as a fully general equation.

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