Photons: Are they really massless particles?

 Decoding Einstein’s famous mass-energy relation: Photon Edition

How can photons possess energy when they have zero mass?

Photons. Right from the beginning, since its theoretical introduction by Max Planck and Albert Einstein in the quantum theory of light, it has played a central role in overturning our primary ideas in physics. What's interesting about them is that this electromagnetic radiation composed of tiny corpuscles of energy, which we call photons, has now transformed into one of the basic constituents of a revolutionary branch of physics: quantum mechanics.

Introduction

We know that photons are the messengers involved in the electromagnetic interaction between two entities, which is why they are classified as Gauge Bosons, which are the force-carriers in the Standard Model. 

But that’s not the only thing we know about them. We know that they are chargeless particles and that they could have identical sets of quantum numbers, which means that two or more photons can be in the same position simultaneously. We also know that they are massless. In fact, they’re the only particles that have zero rest mass, which explains why they’re always in constant motion travelling at the speed of about 300 kilometres in a single second! 

The real question here is how come they possess energy while they have no mass? This question arises naturally because we know that, anything that has mass has a certain amount of energy associated with it, and that energy will be directly proportional to its mass  (E=mc^2). In Einstein’s mass-energy equation, it is important to note that the 'm' denotes the rest mass of an entity. 

Rest mass of Photons

But what do you mean by rest mass? In layman’s terms, the rest mass of an object is the mass it possesses when it is stationary (at rest). The rest mass of an object is the mass it already possesses, like an inherent property (the rest mass of the moon is 7.3510^22 kg). Everything in this universe has a rest mass, except photons. 

So to sum up, we know they have energy and they have zero mass. If we put these conclusions in Einstein's mass-energy equation,  we’d obtain the final result as E=0, as m=0. 

But this can’t be true, because according to Planck’s energy equation, we know that photons carry energy E=hf, where 'F is the frequency of radiation. So where does the problem occur?

Einstein’s energy-momentum relation

 To understand this mystery of photons, we need to understand the actual origin of Einstein’s mass-energy relation, which is the energy-momentum relation.

In this equation, we see that the energy (E) depends on the momentum (p) and mass (m) of the object (c being the constant speed of light). Moreover, it is the relativistic energy we’re talking about, which is the energy obtained by an object or a particle when it’s in motion, nearing the speed of light, and thus the reason why momentum ‘p’ is introduced in the relation.

Now, if we consider a photon’s rest mass (m) as zero, and its momentum (p) as some finite value (because it is always in motion), we’d get the final value of energy (E) of a photon as ;

 E = pc 

This relation shows us that photons possess relativistic energy, which depends on their momentum (p), rather than their mass. In simple words, a photon's energy arises from its momentum, which is associated with its motion or velocity. 

Again, if we consider a resting object’s energy, we can say that the stationary object has a non-zero rest mass because it is the intrinsic mass of the object. So in this case, unlike that of a photon, the rest mass (m) would be a finite value, whereas the momentum (p) would be zero (the object is at rest). Thus, the energy (E) associated with the object would be E = mc^2

We saw how a photon's energy is dependent on its momentum based on its zero mass. But its energy is not the only thing that has exceptions - what about the gravitational effect on a photon?

Naturally, we'd expect that it wouldn't have gravitational properties because it's massless and because it's always in motion. That's true to some extent, but also we know that light can be bent around massive objects like black holes. Here, the gravitational force of the black hole isn't causing the light to bend, whereas, it's the spacetime itself that's bent, and the light is just following that path.

Einstein's mass-energy relation was the key to understanding two major building blocks of the universe, mass and energy. And this single equation made us understand that they're interconvertible and that they're the same after all!