Does light have mass?

Charlotte Morgan from West Yorkshire (age 15-24)

**Answer**

No. But it does carry energy. So it does have a “mass equivalent” given by Einstein’s famous equation.

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Frank Langbein, on February 29, 2008 at 7:59 pm said:The answer to this really depends on what you consider light and how you think of mass. If you think of light as a photon (a small particle or a quantum of energy), then a photon definitely has no mass in the usual physical meaning.

Physicists like to think of properties that do not change, and so they talk about an invariant mass which gives a relation between the photon’s energy and its momentum (its movement). In brief, as nothing goes faster than light, all the photons energy is used for its momentum, and so its invariant mass is zero.

It becomes more interesting when you trap photons in a box. Say you put photons between two perfectly reflecting mirrors. While these photons would still have no mass on their own (moving very fast from one side to the other), the box with the photons is not moving – its momentum is zero, and the lights energy becomes part of the mass of the box. So at least in principle it should be possible to measure a very small increase of the mass of the box if you trap light like this. The trapped light contributes to the mass of the box, but on its own it has no mass.

Then there is Einstein’s famous equation which relates mass and energy – this gives you a different type of mass, which is usually called the relativistic mass. But the relativistic mass is essentially the same thing than energy (i.e. the mass is the energy divided by a constant value c*c). So physicists prefer to refer to energy in this case. But with the relativistic mass some of the classical formulas can be generalised to still work in these cases. In this sense a photon has a relativistic mass (it’s really a matter of interpretation now).

If m is the invariant and M is the relativistic mass, E the energy and P the momentum, and v the speed of the particle (e.g. the photon), and c the speed of light, then in formulas this becomes:

m = sqrt(E^2/c^4 – P^2 / c^2)

E = Mc^2

P = Mv

So for light with v = c, you’ve got m = 0, but M = E/c^2 (and E for light is hf where h is a constant and f its frequency).