Well, about now, a hundred years ago today, in so far as that phrase means anything, the telegraph wires were buzzing with a story about how a new theory had changed science and the way the world worked (and why telegraph wires buzzed as well). On November 25, 1915 at the Prussian Academy of Science, Albert Einstein presented his theory of general relativity to an audience composed of people who got it immediately, those bemused by it, and those outraged at this attempt to abolish absolute space and time — this successful attempt, it should be said. Which may have been why they were outraged. Amid all the horror around today, it’s nice to stop and consider for a moment the sheer beauty of such science and human striving, the sudden understanding of the universe — which would lead eventually to the development of the weapons that might end life on Earth and make possible the satellites that track us if we try to do anything about that. Heh, but seriously …

General relativity, or the Einstein Field Equations as they’re known, was the culmination of nearly a decade’s work by Einstein, following the publication of four papers in 1905 that established special relativity, helped found quantum mechanics (by showing that light has to be regarded as a particle sometimes, not a wave), showed that mass and energy have equivalence (e=mc2) and offered a proof of the atomic structure of matter. He was 25. He had a day job. Feeling shit yet? (He had some help in the mathematics, perhaps significant help, from his wife, Mileva Maric). Special relativity is the set of equations that show how to calculate the way in which frames of time and space will differ for different parties depending on their velocity in relation to each other. Solving a small problem in 19th-century physics, it tore a hole not merely in existing science, but in the relationship between science and everyday perception. It would be superseded, or contextualised, by general relativity, but it remains the easier way to understand what a revolution this was.

The explanation of special relativity is usually given via trains, etc, which seems to be a way of making it more more difficult than it is, if anything. The simpler path to it is this: in the late 19th century it was established that the speed of light in a vacuum, c, is the same for all observers no matter what their velocity. Which is weird. So imagine. One kilometre away from you is a stationary nozzle (n), shooting water at you at 50 km/hour. A drone (d) is coming towards you at 100 km/hour, which is also shooting water at 50 km/h. So the water from the drone is coming at you at 150 km/hour (n+d). Both the stationary nozzle and the drone are shooting a beam of light (c) at you. So the speed of light from the drone should be n+c, right? Wrong. The speed of light from the drone is exactly the same as light from the fixed nozzle, and the time and space frames of you and the drone — effectively the shape and dimensions of the world — are “shifting” relative to each other as a result. If that doesn’t sound weird, go back and read it again.

Light moves through a vacuum at around 300,000 km/second, so in any human activity until recently, the principle of the constant speed of light (hence c) and the effect on relative time and space is unnoticeable. But what if a spaceship were coming towards you at half the speed of light, shooting a beam of light at you? The speed of light and the time taken to send it will be constant, but the light “should” be coming at you at faster than the speed of light. But the speed of light doesn’t change (and nothing can go faster than it), so relative to you, time on the spaceship itself is slowing down. If the light signal it was sending to you was the picture of a clock on the spaceship, it would be moving slower than your clock.

But here’s the crucial thing: this is not simply a matter of perception. The clocks are not going to equalise. The higher the velocity of an object, the slower time moves within its reference frame. When you reach the speed of light (and only light can do that), time ceases to exist. There is no time. The photons streaming into your eyes from the star you look at tonight have taken no time to travel between there and here (relative to themselves). There are no events for them, no before, during and after.

The core of special relativity is the constant speed of light, a fact that was experimentally established in the 1880s, and confirmed countless times since. It was the establishment of this that threw physics into crisis during the period, and that started the hunt for a way to give an account of reality allowing for this. Einstein didn’t work in a vacuum (haha!). The mathematician Henri Poincare almost cracked the riddle, and so did Hendrik Lorentz, whose maths techniques Einstein used to nail special relativity. Special relativity is overwhelmingly a mathematical system for predicting “spacetime” transformations for objects moving at very high and uniform velocities relative to each other.

Einstein’s advantage over other scientists was a metaphorical physical imagination. He posed the question: knowing what we know about the constant speed of light, what would you see if you were riding a particle of light? The answer, of course, is nothing. Or everything. The constant speed of light, and the fact that time and space change to “accommodate” it — that the time of an object moves slower the faster it goes, and its dimensions too (a spaceship at rest will be longer than the same ship moving at half the speed of light) — is what most people don’t get about relativity, thus seeing it as merely an expression of relative difference of appearance. By the 1970s, this could be tested. The Hafele-Keating experiment of 1971 sent atomic clocks going eastward and westward round the world on jumbo jets. When they landed, the eastward plane had lost 59 nanoseconds compared to a ground-based atomic clock (lesser gravitation speeding it up, velocity slowing it down), while the westward going plane had gained 273 nanonseconds, gaining from both effects. These were predicted by the theories; in the latter case stunningly so: the predicted dilation was 275 nanoseconds plus or minus 21.

What’s “special” about special relativity is that its equations only work for uniform rate of motion. It’s not a “special” thing out in the world. “Special” relativity is simply the easiest case to work out. And one of the least common. Most things stop and start, move at different speeds. And one of the things that moved them most was gravity. Both of these had to be factored into a wider theory that allowed for prediction of gravity-bound and irregular movement. Otherwise special relativity was Einsteinian motion in a Newtonian universe, where time and space were absolute.

Einstein’s mathematical solution was that these stop-start motions were, mathematically, a series of curves (where special relativity could only do the sums for straight lines). But what did these curves relate to? Einstein’s answer was that the curvature was in space itself. Or spacetime. Spacetime, the fabric of happening and duration, was curved by the presence of mass within it, stars and planets (and everything, though the gravity of most things is so infinitesimal as to be factored out). Newton presumed space to be flat, and that’s how it looks (an empty box, for example, looks straight in all three dimensions). How could the whole of space be curved?

One way to think through curved spacetime is to compare our presence in it to the experience of a species of two-dimensional beings living on the surface of a sphere. They have no concept of three dimensionality. As they move across the sphere they see only edges and gaps. And though the sphere loops around, to them it appears infinite in all directions — because there is no large dimensional space they can imagine the surface they live on as being in.

Something else happens on the sphere, too. Geometry works differently. The surface people, like us, apply Euclidean geometry to their situation, believe triangles to have 180 degrees of angles, etc. But of course they don’t. As the mathematician Riemann had observed before Einstein, geometry on curved surfaces obeys different rules — a triangle’s angles add to more or less than 180 degrees (because they’re stretched or compressed). Every curved surface has its own geometry, and so, too, does space and spacetime.

So in curved spacetime, we’re exactly like the creatures of the sphere surface world. We apply equations to it as if it were flat, because it looks flat, and for the most part they are accurate enough for our purposes. But really, it’s curved, and a vastly more complex set of equations are required to fully describe the real processes of the universe. The curvature of spacetime explains what gravity is — not the mysterious attraction-at-a-distance of large objects, but the process of an object following the curve in spacetime that the large object creates. Falling is like rolling down a hill, except you can’t see the hill. That yields a further insight, that gravity and acceleration are the same thing, the movement within a shaped and contoured space, controlled by the degree of curve. Matter tells space how to curve; space tells matter how to move. That “matter” includes light. Time is “curved”, too — a clock far from a source of gravity will move faster than one close to it. Thus, for bodies moving rapidly in space, we have to calculate the degree to which their time will be slowed down relative to ours (due to velocity), and speeded up (due to lesser gravity).

The crucial thing to understand is that this is not merely a conceptual framework; it arises from the mathematics of curved, irregular motion — which we calculate using Riemannian rules — and this mathematics in turn yields testable results. And with general relativity, Einstein had two big tests that would mean the rise or fall of the theory. The more famous is the behaviour of light and gravity. Big stars should create such huge gravitational curvature that the light of the stars coming to us from behind them should be shifted from a straight line, or even bifurcated so that the same star appears as two stars, one on either side of the intervening star — and the Einstein Field Equations should yield precise predictions about the degree of shift, relative to the star itself and the star behind. (the light photons, have no mass, but they have energy, and since energy is mass — e=mc2 — they are affected by gravity).

In 1919, Arthur Eddington tested this prediction using a solar eclipse to make possible some cutting-edge photography of the star system — and the resultant photographs showed exactly what general relativity predicted (and not what a Newtonian system predicted). The result was publicised worldwide, front page in every major paper of the world. Einstein acquired the fame we associate with him today.

But Eddington’s test was preceded by another and more moving confirmation of general relativity, and that was the prediction of the orbit of Mercury. Ever since Newton’s physics had been accepted and generated fantastically accurate predictions for the movement of planets, one anomaly had bugged astronomers — and all science, really. Mercury’s orbit didn’t correspond to the Newtonian calculations. Or rather the orbit of its orbit didn’t. This is known as a precession, the way in which an elliptical (oval) orbit of a planet round the sun will shift in a regular fashion. Various possibilities were suggested, including an unseen shadow planet, throwing the orbit out. Having devised the field equations, Einstein plugged the Mercury numbers into the equations — and they predicted the orbit exactly (and all the orbits predicted with sufficient accuracy by Newtonian mechanics). Mercury was so close to the Sun that the curvature of space was shaping its orbit in a way that diverged from the path that would have occurred in “flat” spacetime.

This really is the most stupendous result in the history of science (with the possible exception of Alain Aspect’s proof of Bell’s theorem in 1984, I mean, obvs), because it instantly situated the most complete system of physical prediction to date — Newtonian mechanics — as a subset of a wider system, working, to a degree, on contrary principles. At the same time, it split science utterly from “common sense” observation, that everything happens in a universal frame of reference. It said that different observers, from different points of view, might see a set of events in another frame, in differing orders, that a twin, famously, could leave Earth and by travelling and returning at sufficient velocity, come back much younger than her earthbound twin.

General relativity has long ceased to be of purist interest. The satellite the link for this piece may bounce off if someone texts it to someone else is plotted using general relativity; using Newtonian mechanics, it would desynchronise. In recent decades a number of problems with the theory have turned up, and a new unified theory of spacetime may emerge from the other side of modern physics, quantum mechanics, some versions of which essentially digitise space, rendering it not as a continuous curved entity, but as a series of discreet, very small (very small, 1.6 x 10 to the power -35m, the so-called Planck length) units, which would, if confirmed, re-render our theory of what the universe is, and provide still more accurate predictions of physical behaviour (though by that stage, there would be such little divergence from Einsteinian calculations as to be of little use, for the moment).

That is all worth retelling simply because it is marvellous. But there’s a more practical point to these things, both scientific succession — Newton to Einstein to possible quantum explanations — and the act of confirmation, with the orbit of Mercury. Theories aren’t hypotheses; theories are frameworks and sets of principles that work, allowing us to predict (and thus cause) physical behaviour of objects. Newton’s theories weren’t “true” because they gave a true “picture” of the universe; they didn’t. They were “true” because they generated reasonably accurate predictions using a framework of absolute space and time. Einstein’s theory is “truer” or “less untrue” because it proposes a framework that allows for more accurate predictions, not because it has now established the “real” picture of the world after all those false ones. Should quantum solutions prove better, curved spacetime will take its place as one of the discarded models of how the universe “really” is — but its capacity for extremely accurate predictions won’t be diminished.

Yet between Newton and Einstein’s theory there was, for Newton’s theory, an anomaly — the aforementioned orbit of Mercury. This anomaly indicated that there was a better theory beyond Newton’s, which would nevertheless situate Newton’s theory within it. The entirely incorrect thing to do would have been to reject Newton’s theory because of a single anomaly. That would have meant no steam engine, no “galvanism”, no electromagnetic effect, etc. The whole edifice of modernity was erected on the base of something that was apparently disproven by observation.

Fast forward a few hundred years, and the “chuck-out” approach to science is exactly what the climate change denialists would want us to adopt. Their argument is that even if theory 1 explains and predicts 99%+ of observed phenomena, and there is no competing theory 2, theory 1 should be thrown out, because it cannot currently explain 1% of anomalies. By that measure the practice of science, pure and applied, could not continue.

Ironic, isn’t it? Those of us arguing for minor change of existing practices based on the best science are accused of being anti-industrial, wanting to live in caves, etc. Had they been around in Newton’s day, and urged a rejection of his theory because it could not explain everything, there would have been no industrial revolution. It’s the tolerance of anomalies while using the best possible theory on offer, while also seeking to build a new theory that would situate it, that constitutes progress. Not according to the brown denialists, who would rather we abandon all existing scientific procedure, simply because it yields results friendly to Green politics.

Mind you, they’re in good company. Einstein’s special and general relativity was initially rejected by the English scientific establishment (because it was created by a German), by Franco’s phalangists (because it denied an absolute god), and by the Nazis (as “Jewish pseudo-science”). We know what spurning modern science did for the Nazi regime — partly caused them to miss out on the A-bomb. Right-wing politics will eventually be destroyed by climate change denialism (how much they will also destroy before that happens remains to be seen). For all their talk of the Enlightenment, they remain small, cramped people unable to appreciate the true character of science, amply displayed by Einstein’s work — the sheer beauty of it, and of the chance it offers us to take control of our destiny in a universe indifferent to us.

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## Leave a comment

Well, I understood it Guy. Which reminds me of an old maths joke. A pure mathematics professor was delivering a lecture and after writing a theorem on the blackboard simply said that it was “obvious”, meaning no written proof was necessary. Then, standing back, he scratched his chin and said, “no, wait a minute.” With that, he dashed out of the lecture theatre and was missing for 30 minutes. He finally returned with six pages of calculations. He then declared to the students, “Yes, it’s obvious”.

Guy,

You’ve made all the points I would have made. Anyway – there’s a new book ‘the Hunt for Vulcan… and how Albert Einstein Destroyed a Planet, Discovered Relativity, and Deciphered the Universe’ by Thomas Levenson, which is not only easy to understand but also a great read.

Vulcan had actually been seen dozens of times, before astronomers realised that they were fooling themselves, seeing something they thought should be there. So they ignored the embarrassment and went on to other topics.

Einstein had been assured by astronomers that the Universe was static, so he adjusted his equation of General Relativity to add the cosmological constant, to stop the Universe collapsing under gravity (Newton knew of the same problem – he decided the Universe was spatially infinite, so it didn’t have a ‘centre’ upon which gravity could cause it to collapse. Which doesn’t work).

All observers have favoured ideas. And there’s a temptation to look for only the evidence which supports not refutes the idea. Anomalies are useful indicating that your hypothesis is wrong or incomplete, provided they’re real anomalies, not manufactured ones as with the so-called global warming ‘pause’.

An excellent book which bears some parallels with the current debate on climate change is “The Gods Themselves” by Isaac Asimov.

Basically humanity gets hooked on free energy created by swapping matter in our universe with matter in a parallel universe with slightly different physical laws. The problem is that overdoing it will eventually cause our Sun to turn into a supernova. Persuading the powers that be that it is necessary to stop proves difficult.

The full quote that the title is taken from is “Against stupidity the gods themselves contend in vain”.

Bravo! A very neat sketch of special and general relativity.

The equations of special relativity are still widely used in physics. Most of the formulas used in calculating position from GPS signals are from special relativity, with some much smaller corrections due to the general theory.

That was an unexpected pleasure during my lunchtime reading, I’ll have to save this one.