## Does Light have mass?

A simple plain ‘No’ will be both, and at the same time, respectful and disrespectful to this much debated question. But, talking of mass in general sense, Light does not have mass. Of course a discussion on light can never be limited to a general sense.

Albert Einstein demonstrated through photoelectric effect that Light is composed of particles (energy packets) since it was able to knockout electrons from their orbits. But does this point to light having mass? Do Photons, particles of light, have mass?

Let’s list a few facts.

1. Light carries Energy in **packets of E = hf**, where h is the Planck’s constant & f is frequency of photonic waves.

2. E = mc^2. Here m is not object’s rest mass. It is object’s relativistic mass.

3. A travelling ray of light has no mass, indeed.

But what about a non-travelling light? And how can it be established?

## A Special Box of Light

Consider a special box. The box is such that light is trapped in the box with perfect mirrors (perfectly reflecting) so the photons are continually reflected back and forth in both directions symmetrically in the box. In such a scenario, overall momentum of photon particles with reference to the box is Zero. But, Energy certainly is not Zero.

If the box with this special arrangement is tested for the force required to move it. It is observed that a larger force is required than would have without this arrangement. One rightful implication from this result can be that the trapped light has added to the mass of this box. But, is the mass created from a travelling light to a trapped light!? Is the mass not conserved then? Or has energy been converted to mass. Well it hasn’t been converted to mass. More correctly, it is mass.

Consider the following equation

This is called as the **invariant mass** of an object. Now, a beam of light (travelling at v = c) has both momentum (p) and Energy (E). So, through simple substitution, its invariant mass reduces to 0. Since,

But what about the box? If we consider electromagnetic waves, they travel in two opposite directions forming standing waves. Similar is the case if particle nature is considered since particles are moving in opposite directions. So, the net momentum, p is zero, in box’s frame of reference. Whereas the Energy is still finite and same as that of a beam of light. So, we have a finite contribution of mass. It should be noted that rest mass of the light is still zero. It is the relativistic mass that’s adding to the box’s mass. Also, if we look closely, the invariant mass of a box of light is more than the mass of the box and the sum of the rest masses of the photons (the latter being zero). So, there is some mass associated with light. But why isn’t there with photon?

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## Rest Mass v/s Relativistic Mass

This is known as the equivalence relation between mass & energy.

Rest mass is the invariant mass of an object. So whether the object is moving or not, its rest mass remains same. So, it is convenient to say that rest mass of an object is independent of frame of reference. But, there’s one mass which changes relative to different frames. That’s the relativistic mass.

Relativistic mass of an object formed of non-moving particles is different than that formed of moving particles. Ideally speaking, relativistic mass is the measure of Energy of a particle which changes with velocity. Relativistic mass of an object is always proportional to its Energy i.e. Rest Energy + Kinetic Energy.

In the mass-energy equivalence equation, m is relativistic mass of the object in question. So, while the rest mass of a photon is zero, it does have relativistic mass. It finds significance for objects travelling at relativistic speeds. If you apply force on an object travelling at light’s speed, its Energy & momentum increase but its speed does not. Here’s another understanding of relativistic mass i.e. relativistic mass is the ratio of momentum of the body & its speed. Since, speed is a constant the added energy reflects as the relativistic mass.

A notable point here is that **relativistic mass is same as the rest mass when seen from the frame of the Center of Momentum frame**. Since from this frame, the object is necessarily at rest.

So, in principle light doesn’t have mass. But if we consider few phenomena, relativistic mass (which is both accepted and abhorred by two different sets of scientists) is the only thing which can help us sleep peacefully offering a theoretical explanation to the experience in question.

## Another interesting Case

When an object is subject to heat, its mass tends to increase. Although this increase is only slight, you solve this case for me, will you?

Also check out an interesting article on the topic Can we move faster than light here.