Albert Einstein knew the truth. “As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.” However good we are at maths – or theoretical physics – our efforts to apply it to the real world are always going to mislead. So perhaps we shouldn’t be surprised that reality is not what it seems – even when, like the Italian physicist Carlo Rovelli, you’ve done the maths.

It is a lesson we could certainly learn from the history of science. Whenever we have ventured into new experimental territory, we’ve discovered that our previous “knowledge” was woefully incomplete. With the invention of the telescope, for instance, we found new structures in space; Jupiter’s moons and sunspots were just the beginning. The microscope took us the other way and showed us the fine structure of the biological world – creatures that looked uninteresting to the naked eye turned out to be intricate and delicate, with scales and hooks and other minute features. We also once thought that the atom lacked structure; today’s technology, such as the particle colliders at the Cern research centre in Geneva and Fermilab in the United States, have allowed us to prove just how wrong that idea was. At every technological turn, we have redefined the nature of reality.

Unfortunately, we don’t yet have the technology to take the next step. The present challenge to physicists seeking to discover how things really are is to investigate our environment on a scale known as the “Planck length”. Rovelli tries to convey just how small this is. Imagine, he says, a walnut magnified until it is the size of the universe. If we were to magnify the Planck length by that much, we still couldn’t see it. “Even after having been enormously magnified thus, it would still be a million times smaller than the actual walnut shell was before magnification,” he tells us.

We simply cannot probe the universe at these scales using current methods, because it would require a particle accelerator the size of a small galaxy. So – for now, at least – our search for the nature of reality is in the hands of the mathematicians and theorists. And, as Einstein would tell us, that is far from ideal.

That is also doubly true when theoretical physicists are working with two highly successful, but entirely incompatible, theories of how the universe works. The first is general relativity, developed by Einstein over 100 years ago. This describes the universe on cosmic scales, and utterly undermines our intuition. Rovelli describes Einstein’s work as providing “a phantasmagorical succession of predictions that resemble the delirious ravings of a madman but which have all turned out to be true”.

In relativity, time is a mischievous sprite: there is no such thing as a universe-wide “now”, and movement through space makes once-reliable measures such as length and time intervals stretch and squeeze like putty in Einstein’s hands. Space and time are no longer the plain stage on which our lives play out: they are curved, with a geometry that depends on the mass and energy in any particular region. Worse, this curvature determines our movements. Falling because of gravity is in fact falling because of curves in space and time. Gravity is not so much a force as a geometric state of the universe.

The other troublesome theory is quantum mechanics, which describes the subatomic world. It, too, is a century old, and it has proved just as disorienting as relativity. As Rovelli puts it, quantum mechanics “reveals to us that, the more we look at the detail of the world, the less constant it is. The world is not made up of tiny pebbles, it is a world of vibrations, a continuous fluctuation, a microscopic swarming of fleeting micro-events.”

But here is the most disturbing point. Both of these theories are right, in the sense that their predictions have been borne out in countless experiments. And both must be wrong, too. We know that because they contradict one another, and because each fails to take the other into account when trying to explain how the universe works. “The two pillars of 20th-century physics – general relativity and quantum mechanics – could not be more different from each other,” Rovelli writes. “A university student attending lectures on general relativity in the morning, and others on quantum mechanics in the afternoon, might be forgiven for concluding that his professors are fools, or that they haven’t talked to each other for at least a century.”

Physicists are aware of the embarrassment here. Hence the effort to unite relativity and quantum mechanics in a theory of “quantum gravity” that describes reality at the Planck scale. It is a daunting task that was the undoing of both Einstein and his quantum counterpart Erwin Schrödinger. The two men spent the last years of their working lives trying to solve this problem, but failed to make any headway. Today’s physicists have some new ideas and mathematical intuitions, but they may also be heading towards a dead end. Not that we’ll find out for sure any time soon. If the history of science offers us a second lesson, it is that scientific progress is unbearably slow.

In the first third of his book, Rovelli presents a fascinating dissection of the history of our search for reality. The mathematical cosmology of Ptolemy, in which the Earth stood at the centre of the universe and the other heavenly bodies revolved around it, ruled for a thousand years. It was unfairly deposed: the calculations based on Copernicus’s sun-centred model “did not work much better than those of Ptolemy; in fact, in the end, they turned out to work less well”, the author observes.

It was the telescope that pushed us forward. Johannes Kepler’s painstaking observations opened the door to the novel laws that accurately and succinctly described the planets’ orbits around the sun. “We are now in 1600,” Rovelli tells his readers, “and for the first time, humanity finds out how to do something better than what was done in Alexandria more than a thousand years earlier.”

Not that his version of history is perfect. “Experimental science begins with Galileo,” Rovelli declares – but there are any number of Renaissance and pre-Renaissance figures who would baulk at that claim. In the 12th century the Islamic scholar al-Khazini published a book full of experiments that he had used to test the theories of mechanics. The man who helped Galileo achieve his first academic position, Guidobaldo del Monte, also carried out many experiments, and possibly taught Galileo the craft.

It’s a small misjudgement. More irritating is Rovelli’s dismissal of any path towards quantum gravity but his own, a theory known as “loop quantum gravity”. He spends the last third of the book on explaining this idea, which he considers the “most promising” of all the assaults on the true nature of reality. He does not mention that he is in a minority here.

Most physicists pursuing quantum gravity give a different approach – string theory – greater chance of success, or at least of bearing useful fruit. String theory suggests that all the forces and particles in nature are the result of strings of energy vibrating in different ways. It is an unproven (and perhaps unprovable) hypothesis, but its mathematical innovations are nonetheless seeding interesting developments in many different areas of physics.

However, Rovelli is not impressed. He summarily dismisses the whole idea, characterising its objectives as “premature, given

current knowledge”. It’s a somewhat unbecoming attitude, especially when we have just spent so many pages celebrating millennia of ambitious attempts to make sense of the universe. He also strikes a jarring note when he seems to revel in the Large Hadron Collider at Cern having found no evidence for “supersymmetry”, an important scaffold for string theory.

As readers of his bestselling *Seven Brief Lessons on Physics* will know, Rovelli writes with elegance, clarity and charm. This new book, too, is a joy to read, as well as being an intellectual feast. For all its laudable ambition, however, you and I are unlikely ever to learn the truth about quantum gravity. Future generations of scientists and writers will have the privilege of writing the history of this particular subject. With theory ranging so far ahead of experimental support, neither strings nor loops, nor any of our other attempts to define quantum gravity, are likely to be correct. Reality is far more elusive than it seems.

*Michael Brooks’s books include “At the Edge of Uncertainty: 11 Discoveries Taking Science by Surprise” (Profile)*

*Reality Is Not What It Seems: the Journey to Quantum Gravity by Carlo Rovelli. Translated by Simon Carnell and Erica Segre is published by Allen Lane (255pp, £16.99)*