A physicist’s task is to constantly create equations that keep up with our observations of physical phenomena.
Researching a cosmic mystery like dark matter has its downsides. On the one hand, it’s exciting to be on the road to what might be a profound scientific discovery. On the other hand, it’s hard to convince people it’s worth studying something that’s invisible, untouchable, and apparently made of something entirely unknown.
While the vast majority of physicists find the evidence for dark matter’s existence convincing, some continue to examine alternatives, and the views in the press and the public are significantly more divided. The most common response I get when I talk about dark matter is: “isn’t this just something physicists made up to make the math work out?”
The answer to that might surprise you: yes! In fact, everything in physics is made up to make the math work out.
When I first got into science, what excited me was the prospect of learning some ultimate truth about the Universe. Stephen Hawking once described cosmology as an endeavour to “know the mind of God”.
But while that characterisation is inspiring, in practice, physics isn’t built around ultimate truth, but rather the constant production and refinement of mathematical approximations. It’s not just because we’ll never have perfect precision in our observations. It’s that, fundamentally, the entire point of physics is to create a model universe in math – a set of equations that remain true when we plug in numbers from observations of physical phenomena.
For example, Newton’s second law of motion, which says that force equals mass times acceleration, is a mathematical model that tells us that if we measure the force exerted on an object, in appropriate units, we should get the same number as the product of the object’s mass and the acceleration it experiences when subject to that force.
In Einstein’s version of gravity, general relativity, the equations get far more complicated, but the goal of the exercise is the same. There’s always a level of abstraction built into the effort because what allows us to make predictions or design new technologies is a set of equations that can be written down and calculated, not a philosophical discussion on the nature of reality.
This level of abstraction is especially apparent in particle physics, because the existence or non-existence of a single particle on a subatomic scale is a rather fuzzy notion. The equations describing the motion of an electron through space don’t actually include a particle at all, but rather an abstract mathematical object called a wavefunction that can spread out and interfere with itself.
Is it ever true, then, to say that an electron is ‘real’ when it’s in motion? If we believe that electrons are real things, have we just made up the wavefunction to make the math work out? Absolutely – that was, in fact, the whole point. We couldn’t get the equations to work if the electron was a solid, isolated particle, so we made up something that wasn’t, and then the numbers started making sense.
It may be that in the future, we find some solution that we prefer to a wavefunction and we abandon that concept altogether. But if we do, it will be because the math stopped working out: we’ll have some experimental or observational result that doesn’t add up when we put the data into our current equations. Then, if we’re doing our jobs right, we’ll find a new set of equations that better describe the electron’s behaviour, and we’ll give those equations names and conceptual analogies and textbooks will be written saying “this is what’s really happening.”
A scientist’s notion of what’s really happening is always driven by the math. Before it was accepted that the Earth orbits the Sun, astronomers used epicycles – little orbital loops – to describe planetary motions in an Earth-centred system. This construction is often used, a little unfairly, as a prime example of “making up something to make the math work” going wrong.
While it’s true that we abandoned epicycles in the 17th century, it was the math that made us do it. Newton’s equations of universal gravitation and Einstein’s general relativity are not made of stronger stuff than the old equations of epicyclic motion – all these frameworks are just symbols on a page – but they fit the observations better and make predictions easier, so we use them as the basis of our abstract model universe.
Dark matter, dark energy, cosmic inflation, black hole singularities, and all the other hypothetical denizens of our current cosmology might seem less real than falling apples or electricity or fluid flow because we don’t experience them in our everyday life, but from a physicist’s perspective, they’re all equally good fodder for mathematical abstraction.
While the way we observe something determines what kind of data points we can use, in the end, everything we do is to make the math work out. We certainly hope that all this calculating brings us a better description of reality, but the mind of God is best left to the philosophers; we don’t have an equation for that.
Read more about physics:
- It may be one of the basic building blocks of all matter, but there’s still a lot we have to learn about the proton
- Clingy atoms and catastrophic iron: The strange science underpinning nuclear fusion
- Evil doppelgängers, alternate timelines and infinite possibilities: the physics of the multiverse explained