This is a post about constancy and inconstancy, one of my favorite topics. And about how alcohol can make you smarter.
There are many quantities that we call “constants of nature”. Of course, anything we call a “constant” is merely something that, empirically, appears to be constant, to the extent we can measure it. Everything we know comes from observation and experiment, and our knowledge is always limited by how good our measurements are.
We have pretty good evidence that a number of basic physical quantities are pretty much constant. A lot of evidence comes from the constancy of the colors of light waves (i.e. the frequencies of waves of electromagnetic radiation) that are emitted by different types of atoms, which appear to be very much the same from day to day and year to year and even across billions of years (neat trick! will describe that another time), and from here to the next country and on to the moon and to the sun and across our galaxy to distant galaxies. For example, if the electron mass changed very much over time and place, or if the strength of the electromagnetic force varied, then atoms, and the precise colors they emit, would also change. Since we haven’t ever detected such an effect, it makes sense to think of the electron mass and the electromagnetic force’s strength as constants of nature.
But they’re not necessarily exactly constant. One can always imagine they vary slowly enough across time or place that we wouldn’t have noticed it yet, with our current experimental technology. So it makes sense to look at very distant places and measure whatever we can to seek signs that maybe, just maybe, some of the constants actually vary after all.
[I wrote a paper in 2001 with Paul Langacker and Gino Segre about this subject (Calmet and Fritzsch had a similar one). This followed the observational claims of this paper (now thought false) suggesting the strength of electromagnetism varies across the universe and/or with time. A lot of what follows in this post is based on what I learned writing that old paper.]
Suppose they did vary? Well, the discovery of any variation whatsoever, in any quantity, would be a bombshell, and it would open up a door to an entirely new area of scientific research. Once one quantity were known to vary, it would be much more plausible that others vary too. For instance, if the electron mass varies, why not the W particle’s mass, which affects the strength of the weak nuclear force, and thereby radioactivity rates and the properties of supernovas? If the electromagnetic force strength varies, why not that of the strong nuclear force? There would be interest in understanding whether the variation is over space, over time, or both. Is it continuous and slow, or does it occur in jumps? One can imagine dozens of new experiments that would be proposed to study these questions — and the answers might reveal relations among the laws and “constants” of nature that we are currently completely unaware of, as well as giving us new insights into the history of the universe.
So it would be a very big deal. [Though I should note it would also be puzzling: even small variations in these constants would naively lead to large variations in the "dark energy" (i.e. cosmological "constant") of the universe, which would potentially make the universe very inhomogeneous. However, we don't understand dark energy, so this expectation might be too naive.] Since there’s no story about it on the front page of the New York Times, you can already guess that no variation’s been found. But a nice new measurement’s been done.
The New Measurement
The punchline: the nice new measurement of one especially interesting quantity — the ratio of the mass of the electron to the mass of the proton — shows no sign of variation, to much better precision than was possible ever before, and looking halfway across the universe.
Specifically, a group from Amsterdam and Bonn, consisting of Julija Bagdonaite, Paul Jansen, Christian Henkel, Hendrick L. Bethlem, Karl M. Menten, and Wim Ubachs, has written a paper whose abstract claims: “we set a limit on a possible cosmological variation of the proton-to-electron mass ratio μ by comparing transitions in methanol observed in the early universe with those measured in the laboratory. Based on radio-astronomical observations of PKS1830-211, we deduced a constraint of ∆μ/μ = (0.0 ± 1.0) × 10−7 at redshift z = 0.89, corresponding to a look-back time of 7 billion years.”
In other words, since the universe is 13.7 billion years old, they are looking at galaxies that are so far away that it has taken half the universe’s age for the light from those galaxies to make it to Earth… which means they are halfway across the visible universe, by some measure. And they are looking at electromagnetic radiation (in radio wavelengths) emitted by the molecule known as methanol, which isn’t a type of alcohol you would want to drink, but you might want to burn. They’re comparing what’s emitted by methanol in galaxies far, far away with what methanol emits on earth, and they can’t find any difference, to one part in 10 million.
This result is actually much more interesting and powerful than it sounds, because the ratio of the electron mass to the proton mass is sensitive to several important quantities in nature. So the measurement gives evidence against variation in numerous interesting constants of nature. Let me now explain why this is true, by explaining briefly where the electron mass and the proton mass come from. They have remarkably different origins.
The Electron Mass
Within the Standard Model of particle physics (the simplest equations for the known particles and forces that are consistent with current data — and for the purposes of this post I’ll assume the Standard Model is accurate and appropriate) the electron mass is the product of two quantities:
- the non-zero value of the Higgs field, whose presence gives mass to all the known elementary particles (but not the proton, which isn’t elementary! see below.)
- the strength of the interaction between the electron and the Higgs field, called the “electron Yukawa coupling”. (This interaction is quite weak, which is why the electron is one of the lightest known elementary particles.)
So the electron mass is pretty simple; it depends mainly on just two quantities.
The Proton Mass
The proton mass is quite a bit more subtle! There are several important ingredients, and they don’t enter in a simple way.
First, you may have heard that a proton is made of two up quarks and a down quark; you can find this statement everywhere. But this is a white lie; a proton is vastly more complicated than this. Indeed, the up and down quarks are much lighter than a proton is: the up and down quark masses are only 0.004 and 0.008 GeV/c² (with big uncertainties, because they’re really hard to measure) whereas the proton has a mass of 0.938 GeV/c²! If the white lie were true, then the proton’s mass would be given roughly by adding the down quark’s mass to twice the up quark’s mass. But it’s not. In fact, if the up and down quark’s masses were both doubled, there would barely be any effect on the proton’s mass at all! And here we’ll only be considering variations far below one part in a million.
So what does give the proton its mass?
The mass of the proton is set by a curious and crucial feature of the strong nuclear force. If you pull two electrically charged objects apart, the electric force between them will become weaker and weaker, falling as one over the distance squared. However, the strong nuclear force is different, as shown in Figure 1. if you take a quark and an antiquark that are extremely microscopically close together, the strong nuclear force between them will first become weaker, but then, at about a distance of a tenth of a millionth of a millionth of a centimeter (a centimeter is a bit more than 1/3 of an inch), the force will stop decreasing. Well, that special distance is called the “confinement scale” (let’s call it “R”), and at larger distances the “confinement force” holds the quark and antiquark together in a constant and firm grip from which they cannot (directly) escape.
Now how do we figure out the proton mass from this? Roughly speaking, trapping quarks and antiquarks and gluons in a little sphere with radius about equal to the confinement scale assures, by the uncertainty principle of Heisenberg, that the amount of energy in that little box will be related to Planck’s constant h divided by R and by the speed of light c. You see, Heisenberg tells us that you can’t know the position and the momentum of a particle at the same time; so if you squeeze down the position of a particle into a sphere of radius R (Figure 2), the particle will, on average, be speeding around with a momentum proportional to 1/R. So if the proton were to become smaller, its mass would increase. [That's a little counter-intuitive, but that's how things work in our quantum world! To make quantum things smaller requires effort and energy; that energy contributes to the mass of the object, since E = mc² (for an object that is stationary.)] Some little details ensue, but basically the proton mass is proportional to 1/R; roughly it equals h/(2πcR), times a number which has to be calculated on a computer and turns out to be about 5.
So now the question is: since the proton mass is determined by R, what determines R? Well, that’s quite interesting. R turns out to be affected by several more fundamental quantities. For instance, if you ask: how strong is the strong nuclear force at a distance scale where quantum gravity is important — the sort of question that theoretical physicists might ask when trying to make a complete theory of the world — the answer is that R depends exponentially on the answer! Just a 1% change in the strength of the strong nuclear force at very short distance can lead to a 10% change in R!
That’s not all. The confinement scale R is also affected somewhat by the masses of the top quark, bottom quark and charm quark, because of subtle effects of their fields (specifically, by effects often called “virtual particles”) on the way that the strong nuclear force changes with distance. Like the electron mass, the mass of each quark is related to the quark’s Yukawa coupling (i.e., how strongly it interacts with the Higgs field) times the non-zero value of the Higgs field.
Putting this altogether, the proton mass is sensitive to
- The strength of the strong nuclear force at short distances (to which it is very sensitive indeed)
- The non-zero value of the Higgs field
- The Yukawa couplings of the charm quark, bottom quark and top quark.
- And possibly the masses of other particles with strong nuclear forces that we haven’t yet discovered.
Quite a list!
In short, the electron mass divided by the proton mass is a quantity determined by a plethora of interesting and more fundamental quantities in nature. The fact that there is no observable variation, at one part in 10 million across half the universe, in the ratio of the electron mass to the proton mass suggests that there is no variation, more or less at that level, in the short-distance strength of the strong nuclear force, the non-zero value of the Higgs field, and the Yukawa couplings of the electron, the charm quark, the bottom quark, and the top quark. Note: although both the electron mass and the proton mass depend on the value of the Higgs field, their dependence is different, and does not cancel in the ratio of the masses.
Of course, it is possible that several of these quantities are varying, and just by chance all the variation cancels out of the electron mass to proton mass ratio. But there’s no reason theoretically to expect that to happen; simple equations you might write down for how variations might occur don’t lead to a big cancellation. So there’s a caveat, but it is a small one.
Too bad! A discovery of variation would have changed particle physics, astrophysics, and cosmology forever. Experts will keep looking for variations in other quantities, and improving the precision of their measurements. But a powerful new result of this type still provides important information, knowledge that scientists will include in their future efforts to understand what underlies our strange, and strangely constant, universe.