Are Photons Massless?

This is part of a series on common misconceptions.

Photons are the fundamental unit (quanta) of light. They have the unique property of being both particle and wave. They are often described as being "bundles of pure energy traveling at the speed of light". And one of the more interesting questions that physicists have raised is whether or not they have mass. They certainly have an energy given by $E = h\nu$, where $\nu$ is the frequency of the light and $h$ is Planck's constant. From this one might conclude that since they have energy, they must have mass given by $E = mc^2$ where $c$ is the speed of light. Alternatively, if they did have mass, then one might wonder if they therefore have infinite energy since they move at the speed of light.

So, for years, physicists have pondered the question... Do they have mass?

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 $\color{#D61F06}{\textbf{True}}$, 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 mass of $m = \frac{h \nu}{c^2}$. The consequence of the relativistic mass of photons has been verified countless times, the famous example being gravity bending photons (see below).

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However, the photon has zero invariant or rest mass. 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.

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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 a photon's path, 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.

Simulation of Gravitational Lensing by a Black Hole

$\color{#D61F06}{\textbf{No!}}$

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 defined a) inertially, as the resistance to being accelerated by force or b) 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 mass and relativistic mass.

See Also

• List of Common Misconceptions
• Einstein photon theory
• Debroglie hypothesis