8. Dragging of inertial frames

Written for George Ttoouli's creative non-fiction seminar, week 9. Context: we were challenged to take a topic from a science textbook or periodical, and write a piece on it in the style of popular science writing.

The first thing to do is to picture a bath-mat. Imagine time, the fabric of your life, stretching out into infinity (itself a difficult image to master), and space, your concrete surroundings, extending as if caught in a rapidly zooming-out camera-eyepiece. Take the co-ordinates of these two, plotted together, and you get… a bath-mat.

Bear with me here. This, after all, was Einstein’s view of the nature of reality. Everything that exists in time and space exists on this bath-mat, making in it greater or lesser indents according to their mass. These curvatures in the fabric of space-time were how Einstein pictured gravity – one can imagine Earth, on this infinite suspended bath-mat, as a golf-ball, and perhaps Jupiter as a water-filled Zorb, weighing down one spot so much that it causes everything around it, from the breadcrumbs of asteroids to the peas and sweetcorn of Io and Ganymede, to roll toward it. If we follow this logic, then the nature of time itself changes in tandem with the shape of space: under the crushing force exerted by, say, Jupiter, time will, from moment to moment, be stretched and warped; if we could have watched Europa’s fragmented form rolling languidly in towards Jupiter’s orbit, we would have seen its progress slow further and further. And if, indeed, we could stand on Callisto’s hyperborean desolation of a surface, and look out, we would see the rest of the Solar System whizzing around us like an overcharged children’s mobile, and Earth’s population going grey before our telescope-aided eye.

All this fascinated me when I was younger – poring over encyclopaedias with crumbling spines, absorbing what my parents called “useless facts”, marvelling over illustrations and comparing the rendering of dinosaurs between books – a longer neck on the brontosaurus here, shorter arms on the tyrannosaurus rex there. I must have been relatively old – 12 or 13, perhaps, aged from my vantage point then – when I began to be curious about what Einstein had actually said. It eludes me now where I first read about the theories of general and special relativity; perhaps it’s appropriate that one time can’t access another’s knowledge. But I know what struck me was the sadness inherent in the ‘twins experiment’: a thought experiment in which, with one twin travelling on a space-ship (I imagined it as one of the smaller shuttles from Star Trek, the latest series of which I would watch with my parents) close to the speed of light, and the other left on Earth, the former, for whom time would slow to the most infinitesimally creeping of flows, would return and confront, with unchanged countenance, a brother on the brink of death. Terrified as I was by the constant, lurking thought of death, and of life’s brittle shortness, it was both depressing and liberating – the idea of remaining young appealed to my sense of childhood desperation. I’m not quite so keen on it now.

This was, perhaps comfortingly, just a thought experiment; nothing – as my younger self might have feared – was actually done in the way of concrete testing – although, ominously, second-long time disparities have been found between the previously-synchronised watches of those carried in ultra-sonic aircraft and those left on the ground. But there is something, indeed, in this that affects us everyday. If we assume that time is experienced relatively according to the distribution of Einsteinian mass-energy (keep in mind that energy is related to mass by the figure of the speed of light squared) or our own acceleration, then it is apparent we have our own ‘frames’ of time-experience, local to us. But what, then, about objects undergoing no acceleration at all? Look at any object in the room which is not moving, or, on hearing a likely noise, look outside your window, and see if you can spot a bird or an aircraft moving at a constant speed. Both these things are in a state of ‘inertia’, and you won’t be surprised to learn that they have their own local ‘inertial frames’, systems in which they exist in an inertial state.

Einsteinian physics, of course, can’t just leave things be at that. According to the model of classical physics as formulated by Isaac Newton, all inertial frames exist in relation to ‘absolute space’; you can picture the universe, in this version, as an enormous fish-tank, in which objects sit still, or move at a constant speed, in relation only to the unchanging glass walls. In Einsten’s conception, there are no fish-tank sides, the quality of water, altering in viscosity, changes from place to place, and this character is dependent on the nature of the objects themselves. Once time’s relativity is grasped, it isn’t that difficult to understand.

However, there is a certain implication of this theory which needed to be tested practically. Imagine two satellites, travelling in fixed orbits at identical heights, at a constant speed, around the Earth. Their conditions, theoretically, are the same, so their inertial frames will be identical – a small refuge of stability in Einstein’s flux. Unfortunately not, though. Imagine these two satellites launched and fixed with clocks, travelling in opposite directions with regards to Earth’s spin. When they arrive back in the same place, the clock of the satellite travelling against the axial twirl, will be considerably behind the other – for it, less time has actually passed. The centrifugal force of Earth’s strange circling has carved changes in time and space, has dragged the satellite’s inertial frame. This is, incidentally, known as the Lense-Thirring Effect, which I rather enjoy for its suggestion of boffins with exotic names, spectacles perched on the ends of their noses.

In 1969, during the Apollo 11 mission, the astronauts visited the Sea of Tranquility, a region of the Moon with one of the best views of Earth. They left behind an array of retro-reflectors, like a single, mirrored eye, a tiny trace of home, winking at those still trapped on the other planet. From Earth, laser-beams – no longer simply the preserve of clichéd Bond villains – were fired repeatedly at this oasis of glass, and, once returned, used to measure not merely the exact distance between the Earth and the Moon, but the degree to which the frame of the Moon’s inertial orbit is itself dragged, subject to the Lense-Thirring Effect, by the spin of the enormous gyroscope of Earth. The same principle has been observed in binary pulsar systems – those stellar conglomerations, unlike our own, with two stars that send out regular light or radio pulses; calculating their distance from us by the inertial travel of light, we can see how that changes from star to star, altered by the effect of their rotation on each other, and measure the frame-dragging involved. Our own lives are warped by these same forces, and, in doing so, connect us with the circling of the stars.