Farewell to Reality

by Jim Baggott

  Newton’s bucket revisited: Gravity Probe B

  Einstein pulled our understanding of space and time inside out. He had dismissed the notion of absolute space and time in his special theory of relativity. But the notion of an absolute spacetime persisted, as did the question posed by Newton’s bucket, which suggested that absolute motion is possible.

  When Einstein delivered the last of a series of four lectures on general relativity at the Prussian Academy of Sciences on 25 November 1915, he believed he had finally settled the matter. In the paper he wrote summarizing the theory, he claimed that its general relativistic principle ‘takes away from space and time the last remnant of physical objectivity’.19 In other words, he declared the defeat of the absolute and the triumph of the relative.

  So, if the motion of the water in Newton’s bucket is not absolute, to what, then, is it relative? We have established that it cannot be relative to the bucket itself. So it must be relative to the rest of the universe. And this means that if the bucket and the water in it were perfectly still, and we could somehow spin the entire universe around it, we would expect that the surface of the water would become concave. How can this be?

  The answer is simply stunning. We could expect that the stationary water would be affected by the universe spinning around it because all the mass-energy in the universe collectively drags spacetime around with it as it spins. This was an effect first deduced from general relativity by Austrian physicists Josef Lense and Hans Thirring, known variously as frame-dragging or the Lense—Thirring effect. Frame-dragging means that there is no measurement we can make that would tell us if it is the water that is rotating in a stationary universe or the universe that is rotating around a stationary bucket of water. The motion of the water is relative.

  So, is frame-dragging a real phenomenon? The answer is yes. On 24 April 2004, an exquisitely delicate instrument called Gravity Probe B was launched into polar orbit, 642 kilometres above the earth’s surface. The satellite housed four gyroscopes, each with a 38-millimetre-diameter spherical rotor of fused quartz coated with superconducting niobium, cooled to -2710C. SQUIDs were used to monitor continually the orientations of the gyroscopes as the satellite orbited the earth. To eliminate unwanted torque on the gyroscopes, the satellite was rotated once every 78 seconds and thrusters kept it pointing towards the star IM Pegasi in the constellation of Pegasus.

  Two effects were being measured. The fact that the earth curves the spacetime in its vicinity, and this causes the rotation axis of the gyroscopes to tilt (or precess) by a predicted 6,606 milliarc seconds per year (about 1.8 thousandths of a degree per year) in the plane of the satellite’s orbit (that is, in a north-south direction). This precession is called geodetic drift, a phenomenon first identified by Dutch physicist Willem de Sitter in 1916.

  The second effect is frame-dragging. As the earth rotates on its axis, it drags spacetime around with it in the plane perpendicular to the plane of the satellite orbit (in a west-east direction). This gives rise to a second precession of the gyroscopes, predicted to be 39.2 milliarc seconds per year.

  The idea of an experimental test of general relativity based on satellite-borne gyroscopes had first been conceived in 1959. Over forty years elapsed from initial conception to launch, at a cost of $750 million. Data collection began in August 2004 and concluded about a year later. The project suffered a major disappointment when it was discovered that the gyroscopes were experiencing a substantial and unexpected wobble. Small patches of electrostatic charge on the rotors interacted with electrostatic charge on the inside of their housing, caused unexpected torque. These effects could be accounted for using an elaborate mathematical model, but at the cost of increased uncertainty in the final experimental results.

  Consequently, analysis of the data took a further five years. The results were announced at a press conference on 4 May 2011. The geodetic drift, measured as a north—south drift in the orbital plane of the satellite, was reported to be 6,602±18 milliarc seconds per year. The west—east drift caused by frame-dragging was reported to be 37.2±7.2 milliarc seconds per year. The high (19 per cent) uncertainty in this last result was caused by the need to model the unexpected wobble.

  Despite the uncertainty, this is still a very powerful experimental vindication of general relativity.

  Einstein had argued that spacetime is relative. It owes its existence to matter and energy. Take all the matter and energy out of the universe and there would be no empty container. There would be nothing at all.

  Interestingly, the debate did not end in 1916. There are further arguments to suggest that Einstein may have misinterpreted his own equations of general relativity. Today, many contemporary physicists and philosophers argue that Einstein was mistaken: spacetime may exist absolutely. It nevertheless behaves relatively, as the phenomenon of frame-dragging demonstrates. The debate is likely to run and run.

  * Readers interested in exploring the nature of this synthesis should consult Michael Morgan’s The Spate Between Our Ears: How the Brairt Represents Visual Space, published by Weidenfeld $ Nicolson in 2003.

  * It’ll have to be your garden. I live in a fourth-floor apartment.

  * The speed of light in a vacuum is about 299.792 million metres per second, or 186,282 miles per second.

  * Kinetic energy is energy associated with the motions of objects.

  * No pun intended.

  * The perihelia of other planets are also susceptible to precession caused by the curvature of spacetime, but the contributions are much less pronounced.

  5

  The (Mostly) Missing Universe

  The Universe According to the

  Standard Model of Big Bang Cosmology

  We admittedly had to introduce an extension to the field equations that is not

  justified by our actual knowledge of gravitation.

  Albert Einstein1

  One of the most remarkable aspects of contemporary theoretical physics is its relatively new-found capacity to address questions that might be considered the preserve of high priests. Human beings possess a deep-rooted desire to understand their place in the universe. We have an innate need to fathom the seemingly unfathomable. Typically, what we are unable to fathom using observation, experiment and simple logic, the high priests attempt to explain through invention and the spinning of elaborate religious mythologies.

  Today, the two principal building blocks that underpin our contemporary understanding of the physical world — relativity and quantum theory — are combined to tell the truly fascinating story of the origin and evolution of our universe. It is a story that is certainly no less remarkable than the creation myths of religious doctrine, and all the more remarkable because it happens to be ‘true’, at least for now, in the sense of the Veracity Principle.

  Most readers will be already familiar with aspects of this modern creation story.

  We now know that, insofar as the word ‘began’ is deemed appropriate, the universe began some 13.7 billion years ago in a ‘big bang’, a primeval quantum fluctuation of some kind that led to the creation of space, time and energy. What we now recognize as the four fundamental forces of nature disentangled themselves from the first, primeval force, in a series of what we might think of as phase transitions, much as steam condenses to water which freezes to ice.

  Gravity was the first to be spun off, followed by the strong nuclear force, whose splitting triggered a short burst of exponential expansion of spacetime called inflation. Quantum fluctuations from this beginning of all things became imprinted by inflation on the large-scale structure of the universe we see today: a telltale thumbprint left at a cosmic crime scene. A subsequent phase transition separated the weak nuclear force from electromagnetism.

  About 380,000 years after the big bang, primordial electrons latched themselves on to primordial atomic nuclei in a process called ‘recombination’. The first neutral hydrogen and helium atoms were formed, releasing a flood of hot electromagnetic radiation to fill al
l of space.

  The universe continued to evolve and expand, a fact belied by the simple observation that the night sky is largely dark.2 The hot radiation released during recombination cooled as the universe expanded, and appears today in the form of microwaves with an average temperature of around -270.5°C, or 2.7 kelvin, almost three degrees above absolute zero. It is a cold remnant, an ‘afterglow’ of a tumultuous time in the history of the universe.

  This cosmic microwave background (CMB) radiation was first detected in 1964. A succession of satellite surveys has mapped the CMB in exquisite detail, and provides much of the observational evidence on which theories of the origin and evolution of the universe are constructed. The quantum fluctuations that rippled through spacetime as the universe ballooned in size were the seeds for the subsequent formation of gas, clouds, stars, galaxies and clusters of galaxies. So, the pattern of points of light that we see in a night sky is a reflection of those quantum ripples from the dawn of time.

  Despite this astonishing progress, the universe remains an almost complete mystery. But it remains a mystery for all the right reasons. More evidence from observational astronomy led physicists to conclude that there must exist an extraordinary form of matter presently unknown to the standard model of particle physics. We know next to nothing about this form of matter. Whatever it is, it cannot be affected by the electromagnetic force, since then it would become visible to us (in the form of radiation). It cannot be affected by the strong nuclear force, otherwise we would be able to observe its effects on visible matter. We know it exerts gravitational effects, and may also be susceptible to the weak force. It is utterly mysterious, and truly deserving of the name ‘dark matter’.

  There’s more. Observational astronomy also suggests that the expansion of the universe is (rather counter intuitively) accelerating. Present theoretical structures can accommodate an accelerating expansion by assuming that the universe is filled with an invisible energy field, which has inevitably become known as ‘dark energy’.

  Dark matter and dark energy are no mere quirks. These are not mildly curious phenomena at the edges of our understanding waiting, like undotted i’s and uncrossed t’s, for the tidy pen strokes of explanation. When placed in a theoretical structure called the standard model of big bang cosmology, the most recent data from observational astronomy indicate that the density of dark matter represents about 22 per cent of all the mass-energy in the universe. The density of dark energy accounts for a further 73 per cent.

  Visible physical matter and radiation — everything we can see in the universe and everything we are — accounts for just 5 per cent of everything there must be.

  The universe is mostly missing.

  Einstein’s biggest blunder

  The development of the ΛCDM (lambda: cold dark matter) model of the universe, also known as the standard model of big bang cosmology, is a triumph of modern physics. It will come as no surprise to learn that this is a development whose origins can be traced back to Einstein.

  General relativity is all about the large-scale motions of planets, stars and galaxies and the structure of the universe within a four-dimensional spacetime. It deals with the universe in all its vastness.

  At first, the task of applying general relativity to develop a theory of the entire universe (in other words, a cosmology) seems impossibly difficult. It’s hard enough to keep track of the subtle interplay between gravitational forces and planetary motions within our own solar system. How then could it ever be possible to apply the theory to all the stars and galaxies in the observable universe?

  The simple answer is: by making a few auxiliary assumptions. Although we can clearly see that the patterns of stars and galaxies are quite different in different parts of the night sky, we can nevertheless draw some simplifying conclusions about the ‘coarse-grained’ structure of the universe.

  For one thing, there are no large patches of night sky that are completely devoid of starlight. The universe looks more or less the same in all directions, in the sense that we see roughly the same numbers of stars and galaxies, with roughly the same brightness. Secondly, the stars and galaxies that we see are not vastly different from one another in composition. There are certainly differences in the sizes of stars, galaxies and clusters of galaxies, and this leads to differences in their physical behaviour, but they are all made of the same kind of ‘stuff, mostly’ hydrogen and helium.

  So, we can assume that the universe is roughly uniform in all directions and uniform in composition. We must also further assume something called the cosmological principle, which states that stargazers on earth occupy no special or privileged position in the universe.* What we see from our vantage point on earth (or earth orbit) accurately reflects the way the universe appears from any or all such vantage points. What we see is a ‘fair sample’ of the universe as a whole.

  With these assumptions in place, in 1917 Einstein applied the general theory of relativity to the entire universe. But he immediately hit a major problem. He expected that the universe that should emerge from his calculations would be consistent with prevailing scientific prejudice — a universe that is stable, static and eternal. What he got instead was a universe that is unstable and dynamic.

  Gravity is the weakest of nature’s forces, but it is cumulative and inexorable and acts only in one ‘direction’ — it attracts but does not repel. Einstein realized that the mutual gravitational attraction between all the masses in the universe would inevitably result in a universe that collapses in on itself. This was a disastrous result, quite inconsistent not only with prevailing scientific opinion but also arguably with simple observation. Several centuries of astronomy had yielded no evidence that all the stars in the universe were rushing towards each other in a catastrophic collapse.

  This was a problem that was neither new nor a particular feature of general relativity. When applied to the universe as a whole, Newton’s gravity also predicts a collapsing universe. Newton had resolved the problem by suggesting that God acts to keep the stars apart: ‘… and lest the systems of the fixed stars should, by their gravity, fall on each other mutually, he hath placed those systems at immense distances one from another’.3 Einstein felt he needed something a little more scientific than this.

  His solution was to modify arbitrarily the equations of general relativity as applied to the universe by introducing a ‘cosmological constant’, usually given the symbol Λ (lambda). This is the ‘extension to the field equations’ referred to in the title quotation.

  In essence, the cosmological constant imbues space itself with a kind of anti-gravitational force, a negative pressure which increases in strength over longer distances. By carefully selecting the value of this constant, Einstein found that he could counterbalance the gravitational attraction that tended to pull everything together with a space that tended to push everything apart. The result was equilibrium, a static universe.

  It was a relatively neat solution. Introducing the cosmological constant didn’t alter the way general relativity works over shorter distances, so the successful predictions of the perihelion of Mercury and the bending of starlight were preserved. But it was, nevertheless, a rather unsatisfactory ‘fudge’, one that was ‘not justified by our actual knowledge of gravitation’. There was no evidence for the cosmological constant, other than the general observation that the universe seems to be stable, and static.

  Einstein found it all rather ugly and would come to regret his decision, as he later revealed to Ukrainian-born theoretical physicist George Gamow: ‘When I was discussing cosmological problems with Einstein he remarked that the introduction of the cosmological term was the biggest blunder he ever made in his life.’4

  The expanding universe

  Einstein had taken great pains to ensure that the solutions to the gravitational field equations of general relativity yielded a universe that conformed to physical experience. But, of course, equations are just equations — the fact that they can be applied to physical proble
ms doesn’t necessarily mean that the only solutions are physically realistic or sensible ones.

  In 1922, Russian physicist and mathematician Alexander Friedmann offered three models based on solutions of Einstein’s field equations. These were essentially descriptions of three different kinds of ‘imaginary’ universe.

  In the first, the density of mass-energy is high (lots of stars in a given volume of space) and spacetime is expanding, although the rate of expansion is modest. Such a universe is said to be ‘closed’: it would expand for a while before slowing, grinding to a halt and then turning in on itself and collapsing. In the second, the density of mass-energy is low (fewer stars) and the effects of gravity are insufficient to overcome expansion. Such a universe is said to be ‘open’, and would expand for ever.

  In the third model, the density of mass-energy and the rate of expansion are finely balanced, such that gravity can never quite overcome the expansion. Such a universe is said to be ‘flat’. The rate of expansion slows but it never stops. And a slow rate of expansion would give the appearance of a static universe.

  Each of these different universes is characterized by the value of a density parameter, given the symbol Ω (omega), the ratio of the density of mass-energy to the critical value required for a flat universe. A closed universe has Ω greater than 1, an open universe has Ω less than 1 and a flat universe has Ω equals 1.

  Friedmann’s model universes were very different to Einstein’s. They were dynamic, not static. Einstein initially rejected Friedmann’s solutions as wrong, and was quickly obliged to retract when he realized that, mathematically speaking, the solutions were perfectly acceptable: