Cosmic Inflation

The Austrian polymath Ernst Mach exhorted his fellow physicists in the early 1880s to recognise that all was not well with their discipline. Two hundred years earlier, Isaac Newton had bequeathed to them a remarkable system of laws which made it possible for them to describe – and predict – the motion of everything from an apple falling from a tree near Woolsthorpe to the orbit of the Moon around the Earth. When Mach was still a child, it had been concluded on the strength of Newton’s laws that there must be an as yet unseen planet in the solar system, its presence deduced from subtle wobbles in the orbit of Uranus. In 1846, the discovery of Neptune was celebrated across Europe as one more victory for Newtonian physics.

But Mach wasn’t satisfied. Portraits show a brooding man peering through narrow spectacles and sporting the kind of beard that had become common among intellectuals of the late Habsburg era. He had done well-respected research in optics, and his studies of projectiles that move faster than the speed of sound – the resulting shock wave producing a characteristic ‘sonic boom’ – gave us the nomenclature of ‘Mach numbers’ (Mach 1, the speed of sound, was exceeded by test pilots in 1947; Mach 2, twice the speed of sound, in 1953). He also studied physiology and the psychology of perception. He could have had a professorship in surgery, but instead took chairs in mathematics and experimental physics. His final academic appointment was in the history and philosophy of science, a position he earned as a result of his persistent, withering critiques of Newton. He was as impressed as anyone with the practical applications of Newton’s laws. What troubled him was the array of assumptions that undergirded the enterprise. ‘The present volume is not a treatise on the application of the principles of mechanics,’ he wrote in the opening pages of The Science of Mechanics (1883). ‘Its aim is to clear up ideas, expose the real significance of the matter, and get rid of metaphysical obscurities.’ That last charge – ‘metaphysical obscurities’ – was meant to wound.

Mach was offended principally by Newton’s notions of absolute space and time. Over and over in The Science of Mechanics, he chides Newton for losing his way, cowering ‘under the influence of medieval philosophy’, growing ‘unfaithful to his resolve to investigate only actual facts’. For how could any reliable information ever be gleaned about such abstractions as ‘absolute space’? All we are in a position to investigate, he insisted, are relations between observable objects, such as the relative motion of real bodies. Yet Newton had built his entire system on an imagined platform of infinite, unbending, everlasting space and time, bolstered only by hand-waving about ‘the Sensorium of God’.

Mach countered that a proper science must be built on objects of ‘positive experience’: those which, at least in principle, could make some impact on an investigator’s senses. If some purported scientific object could not possibly affect the touch, taste, smell, hearing or sight of a diligent researcher, then better to cast it aside. Scientists shouldn’t allow such vacuous, metaphysical baggage to get in the way of progress. Accordingly, Mach refused to believe that atoms were real, despite the accumulation of indirect evidence, right up until he died in 1916.

We don’t hear much about the Sensorium of God in debates among today’s leading physicists and cosmologists, but there’s plenty that Mach would think just as silly. Physics journals these days are filled with speculation about an infinite plurality of universes, each governed by its own set of physical laws, all bubbling away in some larger multiverse. More metaphysical obscurities, Mach would grumble. But the speculation isn’t idle. Over the past 15 years, new ideas and new data have brought the notion of the multiverse roaring back to physicists’ attention.*

One of the catalysts was the surprising discovery in the late 1990s that our observable universe isn’t just expanding, but that its rate of expansion is increasing. The acceleration seems to be driven by a mysterious quasi-substance known as ‘dark energy’, which fills every nook and cranny of the universe. Physicists had previously thought that if they could find some large void in space – some region in which there was no matter whizzing about, no stars or planets distending the fabric of space-time – then such a void would have no energy at all. The existence of ‘dark energy’ suggests, on the contrary, that even such a vast emptiness carries some small amount of energy all its own. It is as if every time you stepped off the bathroom scales, the needle failed to settle all the way back to zero. When plugged into Einstein’s equations of general relativity, which quantify how space-time responds to the distribution of matter and energy, such residual energy behaves like a repulsive force. Space literally stretches itself out, faster and faster over time. The effects of that accelerated expansion can be measured, but the cause remains unknown. Physicists’ first thought was that dark energy arose as some quantum mechanical effect, perhaps related to the unavoidable jiggling of matter as governed by Heisenberg’s uncertainty principle. But when they tried to calculate the amount of dark energy one should therefore expect to find in our universe, their calculations foundered. The numbers were off by factors of the order 10¹²⁰: a 1 followed by 120 zeros. That’s a whopping accounting error.

Whatever its origin, dark energy and the speeded-up stretching of space today resemble a process known as ‘cosmic inflation’ that many physicists believe occurred very early in the history of our universe. According to this, in just a cosmic blink, a mere billion-billion-billion-billionth of a second after the Big Bang, our observable universe stretched from the size of a single atom to the size of a galaxy. Our universe has continued to expand, albeit at a more stately pace, ever since. The theory has been tremendously successful in predicting many features of our observable universe, from its basic geometry, to the distribution of matter in superclusters of galaxies, to the most subtle wrinkles in space-time captured in the ‘cosmic microwave background radiation’, a remnant glow from the Big Bang. Quantitative predictions from inflation match the latest astronomical measurements to within a fraction of 1 per cent.

Yet most models of inflation also suggest a surprising corollary: once inflation begins, it never ends. At any given location in space, you might expect the rip-roaring acceleration to cease as the curious quantum state that drives inflation decays. Yet the rate at which space doubles in size during inflation is faster than the rate at which the quantum driving-force decays at any particular location. During the time it took for our own little patch of space to decay out of the inflating state, nearby regions would have ballooned exponentially larger, and so on, ad infinitum. If these inflationary models are taken at face value, then an infinite volume of space should exist beyond what we can detect.

Dark energy and inflation suggest that space can stretch exponentially quickly: the vast cosmic neighbourhood that we can see might be a preposterously small sample of everything that’s out there. What’s more, according to some theoretical physicists, whatever lies beyond our range of detection might bear little resemblance to the mundane patch of space-time we call home. They draw their inspiration from string theory, an esoteric effort to align the two great pillars of modern physics: relativity and quantum theory. Until recently physicists were content to think of matter as tiny, shrunken billiard balls: electrons and quarks were assumed to be mere pin-pricks with no shape or extension at all. String theorists propose that matter consists not of point-like objects, but of strings: tiny, stretched-out filaments that can vibrate at particular frequencies like plucked guitar strings. The size of the strings must be immeasurably small, about a hundred billion billion times smaller than the nucleus of a hydrogen atom. Yet by taking strings rather than particles to be the basic ingredients of matter, string theorists have demonstrated that the equations of relativity governing space-time, on the one hand, and those governing quantum mechanical forces between bits of matter, on the other, might be limiting cases of a single set of overarching laws. The contrivance only works if string theorists impose all manner of strict symmetries on their equations: for every string-like wiggle in their theory (a vibration that would manifest as one type of particle) there must be a specific type of waggle (corresponding to a companion species of particle), and vice versa.

Over the past decade, both supporters and detractors of string theory have come to agree that this teetering, highly symmetric mathematical structure admits an unfathomable number of solutions. In fact, physicists now believe that the equations governing string theory admit about 10⁵⁰⁰ distinct solutions, any one of which (or none) might describe our physical universe. According to proponents of string theory, every physical constant that we know of, from the masses of elementary particles to the strengths of nuclear forces to the magnitude of dark energy, should depend on which of the 10⁵⁰⁰ distinct states was instantiated in our universe. Yet so far no one has found a way to predict which among these possibilities is most likely to occur.

Some enterprising theorists have tried to turn this massive bug into an asset. This is where the idea of the multiverse comes back into view. Combining the embarrassing richness of stringy possibilities with the idea of cosmic inflation (all in the light of the stubborn empirical fact that our own universe seems to contain some small amount of dark energy), they have suggested that every single one of the 10⁵⁰⁰ string states describes a real universe. And, given the eternally expanding, infinite volume of space suggested by inflation, they further suggest that each of these 10⁵⁰⁰ varieties of universe exists in an infinite number of copies. They’re all real, according to this viewpoint, and they’re all out there – and, most likely, they’re all completely undetectable by us. According to this line of thinking, the physical constants that we measure in our universe have the values they have not because they are required by the laws of physics, but because these are the values that produce a universe suitable for intelligent life. We wouldn’t have evolved in most of those other universes, so we wouldn’t be around to observe universes with very different characteristics.

Lee Smolin has picked up Mach’s mantle and begun to criticise the metaphysical obscurities he detects in the latest multiverse theories. Too much of today’s physics and cosmology, he argues, remains yoked to a Newtonian framework: Newton’s notions of absolute space and time might be gone, but the basic approach remains the same. In an effort to understand large and complicated systems (like the universe), physicists focus intensely on parts of it, then make tacit assumptions about the way the behaviour of the parts translates into that of the whole. This way of doing things has worked wonders since Newton, and over the past century alone, it is in essence how scientists have learned about atoms and molecules; quarks and Higgs bosons; planets, stars and galactic clusters. But Smolin argues that the game is up when it comes to tackling the universe itself.

The main problem with the Newtonian synecdoche, as Smolin sees it, is the mental leap required of us when isolating the part from the whole. It means ignoring all the many ways in which each part is embedded within the universe – all its myriad relationships and interactions with neighbouring parts. By practising this mental leap for centuries, Smolin believes, physicists have become accustomed to doing their calculations as if various cleaved-off parts could be treated as indistinguishable cogs within a cosmic machine. But Smolin insists that the cogs aren’t in fact identical: each is enmeshed in a slightly different set of relationships with the rest of the universe. Hence there can be no genuine sub-units; the parts are only approximately interchangeable, not fundamentally so.

If no two parts are genuinely indistinguishable, Smolin continues, then no purported symmetry in nature can be exact or fundamental. This is no small move. String theorists aren’t the only ones to have placed mathematical symmetries at the heart of their schemes. Challenging the centrality of symmetry means challenging the motivation that drove particle physicists on a fifty-year search for the Higgs boson, a once hypothetical particle whose existence physicists inferred entirely because of the strict symmetries that seem to govern nuclear forces. Demoting symmetry, as Smolin suggests physicists must do, also means discarding the assumption that every electron in the universe is fundamentally indistinguishable from every other electron. Yet that core assumption serves as the basis of physicists’ calculations of very specific properties of the electron – calculations that match experimental measurements to better than one part in ten trillion.

The most important symmetry threatened by Smolin’s new framework is the one Einstein helped establish between space and time. Citing relativity, most physicists argue that space and time are mere projections of a malleable space-time, with no particular significance beyond an individual’s frame of reference. Not so, counters Smolin: time is special. For a start, we all experience time differently from the way we experience space. Time only ever seems to move in one direction, but we think nothing of jogging back and forth in space. And we only perceive a single dimension of time. There seems to be no shortcut to jump from then to now, no way to do in time what my friends and I routinely used to do in space, cutting through our neighbour’s garden to shorten the walk to school.

If physicists returned time to a special category of its own, Smolin reasons, then physical laws would no longer stand outside of time; they would change and evolve just like the matter they purport to describe. And if that were so, then physicists could avoid some of today’s outlandish cosmological quandaries. The impulse to apply seemingly timeless laws – laws honed by close study of parts of the cosmos but not the whole – would be checked. No more need to posit an infinite plurality of other worlds, all of them forever choked off from our own. By treating time as fundamentally different from space, Smolin argues, physicists can get back to the business of trying to fathom our own universe without getting tripped up by phantasms of uncountable others.

Smolin has written some technical papers that attempt to shore up a new kind of physics in which time is real, rather than a mere shadow of some underlying space-time. But the work has not yet attracted many followers. So far, his critical project – trying to ferret out hidden assumptions in today’s standard models of physics and cosmology – has advanced further than any hoped-for replacement. The legacy of such a project remains difficult to predict. I suspect that few physicists will commit an about-face on reading Time Reborn, just as few physicists dropped what they were doing when Mach’s learned volumes appeared. But then again, it was reading Mach’s Science of Mechanics, a generation after it was published, that fired the imagination of a young Albert Einstein.