Nature Abhors a Constant

Why is a neutrino lighter than an electron? Why is the strong nuclear force so much stronger than the weak nuclear force, and why are both so much stronger than gravity? For that matter, why do any particles have the masses they do, or forces have the strengths they do?

To some people, these sorts of questions are meaningless. A scientist’s job is to find out the facts, to measure what the constants are. To ask why, though…why would you want to do that?

Maybe a sense of history?

See, physics has a history of taking what look like arbitrary facts (the orbits of the planets, the rate objects fall, the pattern of chemical elements) and finding out why they are that way. And there’s no reason not to expect this trend to continue.

The point can be made even more strongly: increasingly, it is becoming clear that nature abhors a constant.

To explain this, I first have to clarify what I mean by a constant. If you were asked to think of a constant, you’d probably think of the speed of light. The thing is, the speed of light is actually not the sort of constant I have in mind. The speed of light is three hundred million meters per second…but it’s also 671 million miles per hour, or one light year per year. Choose the right units, and the speed of light is just one. To go a bit further: the speed of light is merely an artifact of how we choose our units of distance and time, so it’s not a “real” constant at all!

So what would a “real” constant look like? Well, imagine if there were two fundamental speeds: a maximum, like the speed of light and a minimum, which nothing could go slower than. You could pick units so that one of the speeds was one, or so that the other was…but they couldn’t both be one at the same time. Their ratio stays the same, no matter what units you’re using. That’s the sign of a true constant. To say it another way: a “real” constant is dimensionless.

It is these “real” constants that nature so abhors, because whenever such a “real” constant appears to exist, it is likely to be due to a scalar field.

To remind readers, a scalar field is a type of quantum field consisting of a number that can vary through space. Temperature is an iconic illustration of a scalar field: at any given point you can define temperature by a number, and that number changes as you move from place to place.

Now constants, being constant, are not known for changing from place to place. Just because we don’t see mass or charge being different in different places, though, doesn’t mean they aren’t scalar fields.

To illustrate, imagine that you live far in the past, far enough that no-one knows that air has weight. Through careful experimentation, though, you can observe air pressure: everything is pressed upon in all directions by some mysterious force. Even if you don’t have access to mountains and therefore can’t see that air pressure varies by height, maybe you have begun to guess that air pressure is related to the weight of the air. You have a possible explanation for your constant pressure, in terms of a scalar pressure field. But how do you test your idea? Well, the big difference between a scalar and a constant is that a scalar can vary. Since there’s so much air above you, it’s hard to get air pressure to vary: you have to put enough energy in to the air to make it happen. More specifically, you vibrate the air: you create sound waves! By measuring how fast the sound waves go, you can test out your proposed number for the mass of the air, and if everything lines up right, you have successfully replaced a mysterious constant with a logical explanation.

This is almost exactly what happened with the Higgs. Scientists observed that particle masses seemed to be arbitrary numbers, and proposed a scalar field to explain them. (As a matter of fact, the masses involved actually cannot just be constants; the mathematics involved doesn’t allow it. They must be scalar fields). In order to test out the theory, we built the Large Hadron Collider, and used it to cause ripples in the seemingly constant masses, just like sound waves in air. In this case, those ripples were the Higgs particle, which served as evidence for the Higgs field just as sound waves serve as evidence for the mass of air.

And this sort of method keeps going. The Higgs explains mass in many cases, but it doesn’t explain the differences between particle masses, and it may be that new fields are needed to explain those. The same thing goes for the strengths of forces. Scalar fields are the most likely explanations for inflation, and in string theory scalars control the size and shape of the extra dimensions. So if you’ve got a mysterious constant, nature likely has a scalar field waiting in the wings to explain it.

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