or why Vera Rubin and Albert Bosma deserve a Nobel Prize
Natural Law: a concise statement describing some aspect of Nature.
In the sciences, we teach about Natural Law all the time. We take them for granted. But we rarely stop and think what we mean by the term.
Usually Natural Laws are items of textbook knowledge. A shorthand all in a particular field known and agree to. This also brings with it an air of ancient authority, which has a flip side. The implicit operating assumption is that there are no Natural Laws left to be discovered, which implies that it is dodgy to even discuss such a thing.
The definition offered above is adopted, in paraphrase, from a report of the National Academy which I can no longer track down. Links come and go. The one I have in mind focussed on biological evolution. To me, as a physical scientist, it seems a rather soft definition. One would like it to be quantitative, no?
Lets consider a known example: Kepler’s Laws of planetary motion. Everyone who teaches introductory astronomy teaches these, and in most cases refers to them as Laws of Nature without a further thought. Which is to say, virtually everyone agrees that Kepler’s Laws are valid examples of Natural Law in a physical science. Indeed, this sells them rather short given their importance in the Scientific Revolution.
Kepler’s Three Laws of Planetary Motion:
- Planetary orbits are elliptical in shape with the sun at one focus.
- A line connecting a planet with the sun sweeps out equal areas in equal times.
- P2 = a3
In the third law, P is the sidereal period of a planet’s orbit measured in years, and a is the semi-major axis of the ellipse measured in Astronomical Units. This is a natural system of units for an observer living on Earth. One does not need to know the precise dimensions of the solar system: the earth-sun separation provides the ruler.
To me, the third law is the most profound, leading as it does to Newton’s Universal Law of Gravity. At the time, however, the first law was the most profound. The philosophical prejudice/theoretical presumption (still embedded in the work of Copernicus) was that the heavens should be perfect. The circle was a perfect shape, ergo the motions of the heavenly bodies should be circular. Note the should be. We often get in trouble when we tell Nature how things Should Be.
By abandoning purely circular motion, Kepler was repudiating thousands of years of astronomical thought, tradition, and presumption. To imagine heavenly bodies following elliptical orbits that are almost but not quite circular must have seemed to sully the heavens themselves. In retrospect, we would say the opposite. The circle is merely a special case of a more general set of possibilities. From the aesthetics of modern physics, this is more beautiful than insisting that everything be perfectly round.
It is interesting what Kepler himself said about Tycho Brahe’s observations of the position of Mars that led him to his First Law. Mars was simply not in the right place for a circular orbit. It was close, which is why the accuracy of Tycho’s work was required to notice it. Even then, it was such a small effect that it must have been tempting to ignore.
If I had believed that we could ignore these eight minutes [of arc], I would have patched up my hypothesis accordingly. But, since it is not permissible to ignore, those eight minutes pointed the road to a complete reformation in astronomy.
This sort of thing happens all the time in astronomy, right up to and including the present day. Which are the important observations? What details can be ignored? Which are misleading and should be ignored? The latter can and does happen, and it is an important part of professional training to learn to judge which is which. (I mention this because this skill is palpably fading in the era of limited access to telescopes but easy access to archival data, accelerated by the influx of carpetbaggers who lack appropriate training entirely.)
Previous to Tycho’s work, the available data were reputedly not accurate enough to confidently distinguish positions to 8 arcminutes. But Tycho’s data were good to about ±1 arcminute. Hence it was “not permissible to ignore” – a remarkable standard of intellectual honesty that many modern theorists do not meet.
I also wonder about counting the Laws, which is a psychological issue. We like things in threes. The first Law could count as two: (i) the shape of the orbit, and (ii) the location of the sun with respect to that orbit. Obviously those are linked, so it seems fair to phrase it as 3 Laws instead of 4. But when I pose this as a problem on an exam, it is worth 4 points: students must know both (i) and (ii), and often leave out (ii).
The second Law sounds odd to modern ears. This is Kepler trying to come to grips with the conservation of angular momentum – a Conservation Law that wasn’t yet formally appreciated. Nowadays one might write J = VR = constant and be done with it.
The way the first two laws are phrased is qualitative. They satisfy the definition given at the outset. But this phrasing conceals a quantitative basis. One can write the equation for an ellipse, and must for any practical application of the first law. One could write the second law dA/dt = constant or rephrase it in terms of angular momentum. So these do meet the higher standard expected in physical science of being quantitative.
The third law is straight-up quantitative. Even the written version is just a long-winded way of saying the equation. So Kepler’s Laws are not just a qualitative description inherited in an awkward form from ancient times. They do in fact quantify an important aspect of Nature.
What about modern examples? Are there Laws of Nature still to be discovered?
I have worked on rotation curves for over two decades now. For most of that time, it never occurred to me to ask this question. But I did have the experience of asking for telescope time to pursue how far out rotation curves remained flat. This was, I thought, an exciting topic, especially for low surface brightness galaxies, which seemed to extend much further out into their dark matter halos than bright spirals. Perhaps we’d see evidence for the edge of the halo, which must presumably come sometime.
TACs (Telescope Allocation Committees) did not share my enthusiasm. Already by the mid-90s it was so well established that rotation curves were flat that it was deemed pointless to pursue further. We had never seen any credible hint of a downturn in V(R), no matter how far out we chased it, so why look still harder? As one reviewer put it, “Is this project just going to produce another boring rotation curve?”
Implicit in this statement is that we had established a new law of nature:
The rotation curves of disk galaxies become approximately flat at large radii, a condition that persists indefinitely.
This is quantitative: V(R) ≈ constant for R → ∞. Two caveats: (1) I do mean approximately – the slope dV/dR of the outer parts of rotation curves is not exactly zero point zero zero zero. (2) We of course do not trace rotation curves to infinity, which is why I say indefinitely. (Does anyone know a mathematical symbol for that?)
Note that it is not adequate to simply say that the rotation curves of galaxies are non-Keplerian (V ∼ 1/√R). They really do stay pretty nearly flat for a very long ways. In SPARC we see that the outer rotation velocity remains constant to within 5% in almost all cases.
Never mind whether we interpret flat rotation curves to mean that there is dark matter or modified gravity or whatever other hypothesis we care to imagine. It had become conventional to refer to the asymptotic rotation velocity as V∞ well before I entered the field. So, as a matter of practice, we have already agreed that this is a natural law. We just haven’t paused to recognize it as such – largely because we no longer think in those terms.
Flat rotation curves have many parents. Mort Roberts was one of the first to point them out. People weren’t ready to hear it – or at least, to appreciate their importance. Vera Rubin was also early, and importantly, persistent. Flat rotation curves are widely known in large part to her efforts. Also important to the establishment of flat rotation curves was the radio work of Albert Bosma. He showed that flatness persisted indefinitely, which was essential to overcoming objections to optical-only data not clearly showing a discrepancy (see the comments of Kalnajs at IAU 100 (1983) and how they were received.)
And that, my friends, is why Vera Rubin and Albert Bosma deserve a Nobel prize. It isn’t that they “just” discovered dark matter. They identified a new Law of Nature.