# Are Photons Massless?

This is part of a series on common misconceptions.

Is this true or false?

The mass of a photon is zero.

**Why some people say it's true:** Photons travel with the speed of light.

**Why some people say it's false:** Photons have momentum, thus they must have mass.

The statement is \( \color{red}{\textbf{True}}\), in a certain mathematical sense.

Explanation:Any photon of frequency \(\nu\) has energy \(E = h \nu \) and hence, in accordance with Einstein's famous mass-energy equivalence, \(E = mc^2\), the photon has a

relativistic massof \(m = \frac{h \nu}{c^2}\). The consequence of the relativistic mass of photons has been verified countless times, the famous example being gravity bending photons (see below).

However, the photon has zero

invariantorrestmass. This is an invariant of an object which is defined as follows:The rest mass (\(m_0\)) of a particle is a quantity having the dimensions of mass which is invariant in all reference frames and satisfies \[m_0^2 c^2 = \left( \frac{E}{c} \right) ^2 - \left\| \mathbf{p} \right\| ^2\]

For most other particles, it can be thought of as the mass observed from a frame of reference where the particle is at rest. Or, we could think of it as the mass not attributed to the kinetic energy, but the particle itself. If there was a way (there isn't; special relativity prohibits it) to observe a photon at rest, you would find it massless. All the relativistic mass of the photon comes from it's energy.

In particle physics when we say

mass, we usually refer to the rest mass. This is why we usually say that photons are massless. In case an author requires to refer to the relativistic mass, he should explicitly clarify it.

Query: Gravity can bend photons, thus the photons should possess mass.

Reply: The photon is affected due to its relativistic mass. When a photon passes by a massive object, then its trajectory is curvilinear. It is due to the fact that the mass bends the space around it. Due to which light follows a curve instead of going on a straight path. In fact, the photon influences the gravitational field too, which however is extremely small due to the very small relativistic mass of the photon.

\( \color{red}{\textbf{No!}}\)The relation between the relativistic mass \((m)\) and rest mass \((m_0)\) is given as follows: \[ m = \frac{m_0}{\sqrt{1-\frac{v^2}{c^2}}} \\ \implies m_0 = m {\sqrt{1-\frac{v^2}{c^2}}} \]

Plugging in \(v = c\) suggests that the rest mass of all objects travelling in the speed of light are massless.

The converse of this is true as well. It can be shown that all massless particles are travelling at \(c\)

(Effective) Mass can be defineda)inertially, as the resistance to being accelerated by force orb)gravitationally, as the ability to generate a gravitational field. In fact, it is believed that there is no way to distinguish between the two different definitions of mass. This is a starting point for general relativity.In Newtonian physics, mass could be thought of as the amount of matter in an object. However, this is not true in the context of special relativity which shows that energy contributes towards the mass of the object as well. This is why we distinguish between

rest massandrelativistic mass.

**See Also**

**Cite as:**Are Photons Massless?.

*Brilliant.org*. Retrieved from https://brilliant.org/wiki/are-photons-mass-less/