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THERE are two kinds of theoretical physicists: those who use the correct equation for calculating distances in space-time, and those who don’t.

Obviously, I’m being a bit tongue in cheek here, but I’m serious when I say there is a real bifurcation. The two formulations of this equation for distance – what we call the metric – are equivalent and when used correctly will give the same answers for all calculations. But each group has reasons for believing that one is more natural than the other. Particle physicists tend to use one; relativists (people trained in general relativity) tend to use the other. I’m among the group of particle physicists who use the one favoured by relativists, and this is for two reasons: it is better, and I trained as a relativist .

These differences in how scientific groups approach the same scientific question aren’t often obvious to outsiders. It was on my mind when I got a letter from a 91av reader who had seen my June column, about the problem of defining mass and explaining its presence. I wrote it very much from the perspective of particle physics, describing the Higgs-Englert-Brout mechanism, which explains how most other particles in the standard model of particle physics gain mass.

But the astute reader pointed out that I had sidestepped a whole other side to the question of mass that pre-dates the advent of the quantum field theories, a calculational framework that merges special relativity with quantum mechanics in order to describe particle physics.

I admit to being caught red-handed and showing my bias towards how particle physics approaches the question of mass, which is to use quantum field theories to try to explain where it comes from. My transition from graduate student relativist to professor of particle physics feels complete, but just as some might feel my perspective on the space-time metric is incomplete, so too is a single-sided discussion of the physical meaning of mass in physics.

So let us return to a simpler time, before the advent of quantum mechanics, to Newton’s laws, which describe some basic properties of forces. Isaac Newton’s most famous contribution to physics is likely to be his second law, F = ma, which states that any force (F) an object is experiencing is equal to its acceleration (a) multiplied by its mass (m).

A letter from a reader showed my bias towards how particle physics approaches the question of mass

Today we know there are four fundamental forces: the strong nuclear force, the weak nuclear force, the electromagnetic force and the gravitational force. Newton gave a mathematical form to the weakest one, gravity. His law of gravitation posited that massive objects were attracted to each other, and the strength of the force of that attraction was proportional to the mass of both objects.

One of the first things students in high school physics learn is that one can set the equation in Newton’s second law equal to the one in his law of gravitation, which means that we can say the force in his law of gravitation is equal to the force that appears in F = ma.

In principle, the mass of the object being described appears twice in such a description: on both sides of the equal sign, once on the law of gravitation side and once on the second law side. But this raises an interesting question: are these in fact the same mass?

The one that appears in Newton’s law of gravitation is known as the gravitational mass, while the one that appears in his second law is known as inertial mass because it describes how resistant the object is to a force that is applied to it – giving a sense of how much inertia against motion it has.

The apparent equivalence of gravitational mass to inertial mass is a remarkable and beautiful feature of the cosmos with a deep implication: mass is mass, regardless of an object’s structure. That is to say, there is no way for gravity to know what the object is made of. The mass of a halo of dark matter particles looks the same to gravity as the mass of a black hole. The structure of an object makes no difference to the law of gravitation. This principle of equivalence eventually led Albert Einstein to the revelations that would translate into his magnificent general theory of relativity.

Today, we mostly take it for granted that gravitational and inertial mass are equivalent. But physicists aren’t ones to rest on our assumptive laurels and people are still testing whether this is true, such as the . Their experiments are an example of ones where a null result is the expectation (and maybe for some, the hope). But there is always the possibility that, as the experiments become more exacting, there will be a surprise.

We take mass for granted, and tend to think of Newton’s laws as rather simple. But ultimately, they still give us a lot to think about.

Chanda’s week

What I’m reading

Legally blind Star Trek actor Bruce Horak recommended There Plant Eyes: A personal and cultural history of blindness by M. Leona Godin, and I’m looking forward to digging in.

What I’m watching

I’m just back from a Star Trek convention, so a lot of Trek to stay connected with the wonderful feeling of that space.

What I’m working on

I’m trying to keep track of all of the amazing labour actions happening – so proud to be a union member right now!

Chanda Prescod-Weinstein is an associate professor of physics and astronomy, and a core faculty member in women’s studies at the University of New Hampshire. Her research in theoretical physics focuses on cosmology, neutron stars and particles beyond the standard model

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