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Friday 1 April 2022

It's Just Basic Science!

Samuel Langhorn Clemens
In 1915, Albert Einstein predicted the existence of gravitational waves.

Makes for a nice, easily remembered story, doesn't it? Just the sort of thing we might glom onto and treat as the last word. It's one we're hearing a lot in recent times, especially since they were detected at LIGO a few years ago and in light of some of what we've learned since. Of course, the real story is - as indicated by the fact I even raise it - slightly more complicated.

There's this thing we do, we humans, probably yet another consequence of our propensities for pattern-seeking and storytelling, but it's a bit slippery to pin it down precisely, because it all begins with lies. Funny word, that. It's one of those words with an awful lot of attendant baggage meaning you may already be bristling for what's coming. Park that thought, and let's talk about learning.

The first things we learn in school about gravity are basically Newton. Depending on the curricular requirements for science, which are an enormous variable, that might be all you ever learn about gravity. What they don't teach you at this point is, well, Newton was wrong. Specifically, his model made measurably incorrect predictions concerning observable quantities. As anybody who ever saw Feynman's most famous lecture knows, if it disagrees with experiment, it's wrong. That's pretty unequivocal. So why do we still teach it?

Well, several reasons, not least of which is the reason it stood so long, even in the face of these observations, some of which were known in and shortly after his own time. It's useful. Indeed, we thought it was the last word, because it described everything in our experience except a few tiny anomalies, for which explanations were being sought. The primary anomaly was the precession of Mercury's perihelion, which Newton's predictions fell short of by 43 seconds of arc per century*. Various proposals were put forward, including a planet - Vulcan - tugging on Mercury unseen. More importantly, though, it's pretty simple. The equations are fairly rudimentary and, in fact, for most purposes, they can even be simplified by discounting the smaller of the two masses involved in a given interaction. It provides a solid point of reference and a foundation upon which better, more accurate and more general ideas can be readily constructed without serious roadblocks to intuition. You can do back-of-the-earlobe calculations with it and it gets you a decent ballpark, with only a few notable exceptions that can be accounted for.

For pretty much everything else, it works. It covers the vast majority of observations. There's a problem, though, and it's one of ontology. You can think of ontology as the set of assumptions that you bring to your enquiry. It might be your favourite flavour of quantum theory, or your personal notion of god, but it can be something as trivial and unseen as what follows. 

A major feature in Newton's ontology was the assumption that space was absolute, immutable and the same for everybody everywhere; If you and I agree on a length scale and conduct measurements of different things in different situations, including when we're moving, he expects that we will always agree on our measurements. He assumed exactly the same of time; that it ticked forward at a fixed rate which was exactly the same for a person on Earth as for an unseen observer in the Kalium galaxy. These were fixed quantities in Newton's scheme, and it had consequences, not least of which is that gravity propagates instantaneously

In 1887, one critical experiment opened a crack, though it wasn't at all obvious, because that ontology was pretty universal. The Michelson-Morley experiment, a new kind of experiment that would eventually culminate in LIGO's detection of gravitational waves, was designed to detect the luminiferous aether, a postulated medium in which light waves travel. Light had been shown to travel in waves by Thomas Young almost a century earlier, overturning another of Newton's theories in the process - sort of. The idea was very simple. If light is travelling through a medium, and we're travelling through that medium, we should be able to detect a difference in the measured speed of light in different directions. It's gone down as the most famous null result in the history of modern physics.

James Clerk Maxwell, who extended and formalised Faraday's work, had included a term for the speed of light in his field equations for electromagnetism, but as a fixed quantity, with no terms to account for the motion of either the light-source or the observer. This, Einstein tells us, is what motivated him to think about space and time in a different way. The result was a paper in 1905 entitled On the Electrodynamics of Moving Bodies, and it shattered Newton's view. This, in fact, is where the prediction of gravitational waves comes from. It isn't an explicit prediction, but this paper imposed a speed limit for propagation of information. Any distributed physical process that propagates at a finite speed must propagate in waves, and that includes gravity. Indeed, in a sense, it is the condition that gravity must propagate in waves, that set the clock ticking, and motivated a new theory of gravity. It's considerably more accurate to say that gravitational waves predicted the General Theory of Relativity. In the event, though, the 1915 paper gave us the mechanism - the curvature of spacetime - that made the predicted waves testable, along with the metric for making the predictions quantitative. The explicit prediction of gravitational waves didn't come until 1917, as the detailed consequences of General Relativity began to be understood more completely.

What Einstein had actually done was to take a couple of things that everybody had always assumed to be independent, fixed quantities and shown that they were, in fact, interdependent variables. Still we teach Newton in schools. And it's useful. NASA still do most of their calculations using Newtonian gravity, because it's a heck of a lot easier, and it works in the vast majority of cases in our experience. The difference in precision can be related when I tell you that the error is twenty metres over a distance of  5 billion kilometres as shown by the Cassini-Huygens mission. There are cases, though, outliers in our everyday experience that rely on Einstein's update, though we might not always be aware of them. Our GPS system, for example,  has time correction built in to account for both Special and General Relativistic effects, without which it would drift by about 10 kilometres a day (for exactly the same reason as the Mercury discrepancy), which would be catastrophic for the global communications network. The outliers are important, and are where effects are most pronounced.

Science is hard. Actually, it isn't hard, but it's highly non-trivial, which is to say it isn't easy, and requires work and commitment, not just to reveal it, but to learn it. The methods we use to teach science are highly effective, up to a point, and that point is the point at which you stop studying science. It's easy to come away with some absolute notions about science, and it's incredibly difficult to overcome the biases such notions represent. Those most obvious to us, like time and space being absolute, for example, are the most difficult to work around, because they're part of our ontology. They're so deeply embedded we don't even recognise them as assumptions; we treat them as brute facts and don't give them a thought. That's why new models that require changes in ontology always bring with them far-reaching revolutions in the way we think about things.

The history of science is one of learning that we were wrong about things. In fact, there's a sense in which it's a history even of learning that our terms are wrong, or defined in such a way as to exclude important things. In thermodynamics, for example, we started with only open and closed systems, based on whether energy can cross the boundary of the system. As our understanding increased, we learned that there are certain types of system that, while not fully open, are not entirely cut off from outside energy in some form, so we had to modify our nomenclature and definitions to accommodate them. We ended up with open, closed and isolated systems, with closed systems being subdivided based on the kind of energy that could cross the boundary. Just as with Newton, what we thought was strictly fixed turned out to be composed of variables.

In classical mechanics, we specify a system by two parameters, position and momentum. In quantum mechanics, our definition of 'system' fails completely, because it isn't possible to specify both. Once again, what we thought of as fixed turns out to be composed of interdependent (conjugate) variables. We find that even the best-formulated definitions let us down completely when we experience circumstances our intuitions are ill-equipped to deal with.

Worse, an enormous amount of our teaching of science is rooted in natural language (words, rather than mathematics), and that brings a whole lot of problems, not least of which is the need to avoid ambiguity. As a result, we talk about how scientific usage is much more rigid and fixed, which in turn leads to the notion that the concepts themselves are rigid and fixed, when in fact the usage in science isn't nearly as rigid and fixed as we might think. Certainly, changes in usage have to have some justification, and there are very strong linguistic conventions in science, but it's no more rigid about words than it is about anything, as long as it's justified. 

I've interacted with many scientists over the last couple of decades, and number some of them among my personal friends. Most of them, but especially the physicists, have some analogue of an exposition of the difference between the study of science at one level and at another. When you get to college they say 'forget everything you think you know; we're gonna tell you how it really is'. And then a repetition of this process when you advance through each level of better and more accurate and general understanding. There's a fantastic lecture series I go back and rewatch on occasion on Quantum Mechanics from MIT that's a perfect microcosm of this principle; three passes through the material, once very basic and specific (almost Newtonian, if it weren't for the definition of 'system'), then more advanced and slightly more general, and then fully general. And that's very much how science is taught. What this should be telling us is that, in some sense, 'just basic science' may not be sufficient to account for reality.

Take sex. 

Among the most deeply embedded notions in our collective ontology are our notions of sex and gender. There's good motivation for this, stemming from our deep evolutionary past. It's a story as old as the birds and the bees. We think of them as strictly binary, because that reflects our intuitions and our notions of what these terms mean. What may surprise many is that 'sex' is not particularly well defined in biology. It's used as a term of art in some fields, and there are reasonably well-defined conceptions applied there, but that's not the whole story, not least because they don't always agree. If you speak to somebody whose research is centred entirely on reproduction they'll employ a definition based on gametes, in which case they'll think of sex as strictly binary. It's a feature of the ontology of that field. If you speak to somebody in a different field, they may have a different definition based on, say, expression of the SRY gene or chromosome count. It's important to note these definitions can disagree with each other in a single individual, which of necessity denotes a third sex (at least). If you speak to an endocrinologist, you'll get a different definition again, this time on a spectrum, because it's based on differential production of hormones, mainly oestrogen and testosterone, which play a role in regulation of all the other characteristics determining sex, regardless of specific definition. It becomes even more complicated when you discover that the terms for sex can be applied at almost every level of granularity with slightly different consequences in terms of defining sex. That is, the same terms can be applied to both organism and organ with differing consequences even in the same individual, and the same is true at cellular level and even at a chemical level. Yes, a female can have male parts and vice versa and, more importantly, all points in between and beyond. All robust, all with their own independent determinations. 

There is no single 'scientific definition of sex'. To the degree a robust definition can be extrapolated from these fields it's that sex is bimodally distributed on a spectrum. This is the relativistic update to the Newtonian ontology, and it isn't being imposed because of ideology, because science is extremely resistant to ideology, and even more resistant to frivolous updating. This update is being imposed by the data, and by observations telling us some of the core assumptions in our ontology are simply not up to the task. What this tells us is that the term 'biological sex' is meaningless in science.

It's hard, but the lessons from history are clear. We thought Newton was the last word on gravity. Einstein showed that his assumptions of absoluteness were wrong. We thought Newton was the last word on light, and then that Young was. Einstein showed that the assumption of a dichotomy between wave and particle was wrong (it's neither). Einstein himself had an ontology which told him the universe was static in scale, le Maitre's analysis of Einstein's equations said it couldn't be, so Einstein inserted a term to fix his equations so that they matched his ontology. Observations led him to conclude this his greatest blunder. Our ontology tells us something can't be in two places at once. Observation tells us that's wrong. Our ontology tells us you can't tunnel through walls without touching them. Observation tells us we're wrong. Our ontology tells us sex is binary. Observation tells us we're wrong.

Every time in the history of science somebody has defended something as absolute, they turned out to be wrong. Science has learned the hard way to be as ontology-free as possible. Assumptions must be checked and re-checked, and then checked again by others, and continually checked. When observations tell us our assumptions are incorrect, we discard them. Indeed, we even have a rule in science a statement must be made in such a way as to make it possible to devise an experiment that can show it to be incorrect. This known as the 'demarcation problem', and the solution is Popper's, and goes by the name 'falsifiability'. If there's no way in principle for some potential observation to disprove the statement, it isn't possible to test it, thus it isn't a scientific statement.

Ultimately, the notion that the definition of sex, or gender, is 'just basic science' is entirely the problem here. basic science isn't cutting it, especially when we can go again to Feynman for an even more basic principle of science:

If it disagrees with experiment, it's wrong. That's just basic science!

Further reading:
I'm Alright, Jack (or Jill)! - More on sex and gender.
The Certainty of Uncertainty - a potted history of our ideas about light from Empedocles to Einstein and beyond.
The Idiot's Guide to Special Relativity - Why space and time are interdependent variables.
Deduction, Induction, Abduction and Fallacy - How logic is employed in science.
*1 second of arc is 1/3600th of a degree. 43 seconds of arc difference is minuscule. The perihelion is the closest point in the orbit and precession is the effect of this point rotating around the sun. We observe Mercury's perihelion precessing at 5600 seconds of arc per century, while Newton's equations predict 5557 seconds per century.

† If gravity propagated instantaneously, there would be a couple of differences. I like the example of the sun suddenly winking out of existence, because it's extreme enough to show the difference nicely. In Newton's world, were the sun to suddenly vanish, Earth and all the planets would go careening off into space immediately, like a ball on a piece of string that's been let go. In the world we live in, the warping of spacetime would flatten out in a series of concentric ripples, much as you'd see on a pond when you drop a stone (it would actually be more radial, like a pinwheel, because of the overall angular momentum of the solar system, etc., but softly, softly). We wouldn't feel the first effects until about eight minutes later, when the gravitational wavefront hit us.

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