What are the most important constants of nature? Of course physicists debate about which of the constants are the important ones, because physicists debate EVERYTHING. Some lists have 19 numbers, some have more. Some try to build categories of numbers, like really really fundamental constants, less fundamental but still important constants, and…others. Some say that the only REAL constants are the ones that don’t have any units, the ones that are just bare numbers, like the fine structure constant. Others…well, others disagree.
But in general, and this is my very own Paul Sutter classification scheme, there are a few GROUPINGS of numbers that seem to be important. Some of them have units, some don’t. some of them may be considered “derived” (in the sense that you can maybe combine other constants to form them), but honestly the precise number and categorization scheme is just numerology to me. Losing the forest for the trees. The constants represent GAPS in our knowledge; they are the places in our very complicated, very sophisticated models that we must fill in from raw measurement, and we cannot derive or explain, and that to me is the essence of a truly fundamental constant. And so, I have fit all the constants into the following four categories:
• Strengths of the forces: newton’s G, FSC, and many other numbers to describe the weak and strong nuclear forces (these take a lot)
• Rest masses of the fundamental particles (just how heavy is an electron, or a neutrino, or a gluon, etc.)
• Properties of the quantum: Planck’s constant (describes scale at which quantum takes over), Higgs field, phase for the QCD vacuum, strength of dark energy / cosmological constant
• And then there is the last category, which I call “structure of the universe”: there are some familiar friends here, like the speed of light. I’m also going to add in here some numbers that you don’t often see in tables of fundamental physical constants: the number of forces (4), the number of particle generations (3), things like pi, the number 4 (dimensions of the universe) and -1 (the relation between time and space)
But like I said, that’s just my own personal categorization scheme. You can make up your own classification if you want, more power to you.
However you divide it up, whatever categorization scheme you use, these numbers share things in common, besides being important, and fundamental. The real thing that fundamental constants share, whether there are 20 or them or 40 of them, is that they are UNEXPLAINED. They cannot be derived from some deeper theory. They have no origin, no…purpose. The electron weighs this much because…because the electron doesn’t weigh anything else. the electromagnetic force is this strong because…it has no other strength. The universe has 4 dimensions because….it has 4 dimensions.
This opens up some really big questions. Questions like: are they REALLY constant, as if they never change? And dang it, where DO these numbers come from?
We’re really interested in the first question because it can help answer the second one. If some of these numbers change, either in time or throughout space, then that tells us that they’re not really REALLY fundamental. Imagine if we found that, I don’t know, the mass of the electron can change with time. that would tell us that what we call the mass of that particle, what APPEARs to be constant and fundamental, is nothing but. Instead it’s just a reflection of our IGNORANCE of deeper physics. it’s like the earth’s gravity or the bounciness of a basketball. It’s telling us that we haven’t reached the bottom level, the ground floor, in our search for understanding in the universe.
And let’s go with this fantasy a bit longer. Imagine we DO find that one of these constants changes with time, or is different in different parts of the universe. We would have a...hook. a pathway. A route to uncovering what that new physics is. imagine if we figured out newton’s laws before newton’s gravity. And at first we would have the acceleration of the earth, and we don’t know where it comes from…and then we find that it changes with elevation or in different parts of the globe…we could USE that information to uncover a deeper reality, that of universal gravitation.
Anyway, are the constants of nature really constant, through all of space and time? Sigh…well, it seems that way. Of course we can’t say for sure 100% totally case closed, because there are always limits and uncertainties and error bars to what we can measure. But every test we’ve ever concocted always comes to the same conclusion.
Measuring the constants in the first place is one thing, involving some of most high-powered and clever experiments. But seeing if they change? Hoo-boy. That takes…volume. Absolute volumes of data. streams of data. rivers, oceans of information. At this point we’re looking for parts-per-BILLION shifts in these constants. And there are two approaches to getting the volumes of data that you need:
Get hyper-precise on measuring something that changes often (like atomic energy transitions) Get away with less precision but let the universe do the work for you (like studying something from the extremely early universe (quasars, CMB), seeing if it’s changed at all in 13-and-change billion years)In either case, what helps us investigate changes in the constants are the very models that we incorporate those constants into. all we have to do is relax the assumption that the constants are…constant. Like, okay, we’ve got newton’s gravitational constant over here in our calculations of gravity. Well what if it’s not constant. What if it goes up or down with time? We can use our models to see what the follow-on effects may be. Or we can assume that the speed of light changes, or that the fine structure constant isn’t so constant, we can fold that new reality into our theories of physics and predict how, say, the cosmic microwave background should appear, or how many light elements should be in the universe.
If the gravity of the earth changed while I was in the act of tossing the ball to you, then its final trajectory, the outputs of the models, will be different. And I can compare what I actually get in real life to version a (constants are constant) to version b (constants aren’t so constant) and see what matches up.
And every time we perform one of these tests, whether it’s something hyper-precise nearby or something big and large far away, we keep getting the same answer: the constants sure do act like constants. The speed of light, the strength of gravity, the fine structure constant, the electron mass. They’re all…constant, and we’re talking we see no variations to one part in a billion per year here which is….yep, pretty dang constant.
Again, I need to make this point loud and clear: variations in the constants are not ruled out – in fact, we can NEVER rule them out, we can only crank down our precision. We will never, ever be able to PROVE that the constants are constant. We can only say they are with higher degrees of confidence.
And so, for now, we have to ACT like the constants are constant and…grapple with that.