Physics
Special Relativity: Mass, and Relativistic Mass
What is Mass?
A problematic term for many aspiring physicists. Whilst the most famous equation in the world states that energy and mass are equivalent, countless textbooks and articles also like to describe it as the ‘measure of inertia’. So, which one’s correct?
Both of them.
Here’s a good example to show you what I mean.
At the most fundamental level, mass can be described as the inertia (resistance to a change in motion) caused by the interactions between particles and their energy fields.
Sounds complex, so let’s visualise a swimming pool. A small lightweight person like me would require less force to swim through the water as I will face less resistance from the water. Somebody like Eddie Hall though would require much more force to swim through the water because of the extra resistance it’ll face. This is represented through Newton’s Second Law,
m = F/A.
As I exert less force to gain the same acceleration as Eddie, I, therefore, have less mass.
Applying this logic to particles, we can understand where sub-atomic particles such as quarks and electrons get their mass from. They’re always interacting with a field called the ‘Higgs Field’, which provides the inertia and resistance to the particles, like the water in a swimming pool, thus ‘giving’ them mass. And since everything is composed of electrons, protons and neutrons with quarks inside of them, surely we can attribute the mass of everything to the Higgs Field?
No. The mass of a nucleon is not the sum of its constituent quarks. In fact, the mass of quarks only makes up about 1% of the mass of a nucleon. How? Well, this is where we introduce everyone’s favourite equation, E = mc².
The quarks inside of these nucleons are travelling at speeds close to light, within a very very small radius, so an obscene amount of binding energy is required to counteract the kinetic energy of the quarks. This binding energy is called the strong force, and due to E = mc², it accounts for 99% of all the mass in the universe.
The immortal fame of the equation relies not only on its utter simplicity but also on its ability to unite the two entities of mass and energy together. By defining mass as the measurement of the energy of an object at rest, the interchangeability of mass and energy gives us explanations as to how stars and nuclear reactors release so much energy, along with how most of our mass is a result of the strong force.
This mass is also called ‘proper mass’, ‘rest mass’, ‘intrinsic mass’ and ‘invariant mass’. All because of Einstein and the confusion he caused with his relativistic mass.
Relativistic Mass
Relativistic mass plagues popular culture by defining itself as the idea where ‘mass increases with velocity’. This definition is then used to explain why travelling at the speed of light is impossible, not knowing that Einstein himself was against this interpretation of the concept. Instead, he preferred for it to be regarded as an ‘expression for the momentum and energy of a body in motion.’
What does this mean? Isn’t energy and momentum both strictly related to mass?
That’s true, but only in our Newtonian perception of physics. Whilst inertia, momentum and mass have a clear relationship at low speeds through the equation p = mv, this doesn’t apply in the world of special relativity. We use the Lorentz Factor (γ) to augment it into p = γmv, giving us an equation that works both in low and high velocities. I would highly recommend for you to read my article on Lorentzian Transformations if you want to get more familiar with it.
Mass never changes as a result of high velocities, rather the momentum of the object increases at an accelerating rate the nearer you go to light speeds. When expressed in Layman’s terms, the object becomes increasingly harder to stop, but this implies that it’s because of the object becoming heavier, leading to the misconception that mass increases. But no, the introduction of the Lorentz Factor into our momentum equation makes it clear how momentum increases, without a change in mass.
The effects of colloquialism and popular culture has skewed with physics so much, that it’s pretty much impossible to self-teach physics. The unfortunate truth is that most of our theories violate common sense and logic, but science communicators have to resort to using exactly that in order to teach the masses. It never goes well, and leads to many misnomers and misconceptions, especially within the fields of special relativity and quantum physics.
