Reality Is Not What It Seems: The Journey to Quantum Gravity

by Carlo Rovelli

The majority of physicists who have worked on string theory, or string-related theories, expected that as soon as the new particle accelerator at CERN in Geneva began to function (the LHC or Large Hadron Collider), particles of a new kind never before observed, but anticipated by the theory, would immediately become evident: supersymmetric particles. String theory needs these particles to be consistent: that is why the string theorists eagerly expected them to be found. Loop quantum gravity, on the other hand, is well defined even without supersymmetric particles. The loop theorists were inclined to think that these particles might not exist.

What we expect to see is a small black disc surrounded by the light produced by the radiation of the matter falling in. What enters a black hole does not come out again, at least if we neglect quantum theory. The surface of a black hole is like the present: it can be crossed only in one direction. From the future, there is no return. For a black hole, the past is the outside; the future is the inside. Seen from outside, a black hole is like a sphere which can be entered but out of which nothing can come.

Bh

A rocket could stay positioned at a fixed distance from this sphere, which is called the horizon of the black hole. To do so it needs to keep its engines firing intensely, to resist the gravitational pull of the hole. The powerful gravity of the hole implies that time slows down for this rocket. If the rocket stays near enough to the horizon for one hour, and then moves away, it would then find that, outside, in the meantime, centuries have passed. The closer the rocket stays to the horizon, the slower – with respect to the outside – time runs for it. Thus, travelling to the past is difficult, but travelling to the future is easy: we need only to get close to a black hole with a spaceship, keep within its vicinity for a while, and then move away.

On the horizon itself, time stops: if we get extremely close to it and then move away after a few of our minutes, a million years might ha...

Objects are hot because their microscopic constituents move. A hot piece of iron, for example, is a piece of iron where the atoms vibrate very rapidly around their equilibrium position. Hot air is air in which molecules move faster than in cold air.

Thus, it is possible to understand the peculiar heat of black holes predicted by Hawking using loop theory: the heat is the result of the microscopic vibrations of the individual atoms of space. These vibrate because in the world of quantum mechanics everything vibrates; nothing stays still.

Cold blooded animal?

fluctuations imply probability, and probability implies thermodynamics, and therefore temperature.

At first, nothing in particular: you would cross the surface of the black hole without major injuries – then you would plummet towards the centre, at ever greater speed. And then? General relativity predicts that everything is squashed at the centre into an infinitely small point of infinite density. But this is, once again, if we ignore quantum theory.

If we take quantum gravity into account, this prediction is no longer correct – there is quantum repulsion – the same repulsion that makes the universe bounce at the Big Bang. What we expect is that, on getting closer to the centre, the falling matter is slowed down by this quantum pressure, up to a very high but finite density. Matter gets squashed, but not all the way to an infinitely small point, because there is a limit to how small things can be. Quantum gravity generates a huge pressure that makes matter bounce out, precisely as a collapsing universe can bounce out into an expanding universe.

The bounce of a collapsing star can be very fast, if watched from down there. But – remember – time passes much more slowly there than outside. Seen from the outside, the process of the bounce can take billions of years. After this time, we can see the black hole explode. In the end,...

Very old black holes, such as those formed in the early universe, could be exploding today. Some recent calculations suggest that the signals of their explosion could be in the range of radio telescopes. It has even been suggested that certain mysterious radio pulses which radio astronomers have already measured, called Fast Radio Bursts, could be, precisely, signals generated by the explosion of primordial black holes. If this was confirmed, it would be fantastic: we would have a direct sign of a quantum gravitational phenomenon.

Wow

When we take quantum gravity into account, the infinite compression of the universe into a single, infinitely small point predicted by general relativity at the Big Bang disappears. Quantum gravity is the discovery that no infinitely small point exists. There is a lower limit to the divisibility of space. The universe cannot be smaller than the Planck scale, because nothing exists which is smaller than the Planck scale.

Scale

But the infinities of quantum field theory follow from an assumption at the basis of the theory: the infinite divisibility of space. For example, to calculate the probabilities of a process, we sum up – as Feynman has taught us – all of the ways in which the process could unfold, and these are infinite, because they can happen in any one of the infinite points of a spatial continuum. This is why the result can be infinite. When quantum gravity is taken into account, these infinities also disappear. The reason is clear: space is not infinitely divisible, there are no infinite points; there are no infinite things to add up. The granular discrete structure of space resolves the difficulties of the quantum theory of fields, eliminating the infinities by which it is afflicted.

The minimum length is the Planck length LP, the maximum velocity is the speed of light c, and the total information is determined by the Planck constant h.

This is the order of magnitude of the universe we have indirect access to. It is around 1060 times greater than the Planck length, a number of times which is given by a 1 followed by 60 zeroes. Between the Planck scale and the cosmological one, then, there is the mind-blowing separation of 60 orders of magnitude. Huge. Extraordinarily huge. But finite.

The molecules of tea are extremely numerous and extremely small, and we don’t know their precise movements. Therefore, we lack information. This lack of information – or missing information – can be computed. (Boltzmann did it: he computed the number of distinct states the molecules can be in. This number depends on the temperature.) If the tea cools, a little of its energy passes into the surrounding air; therefore, the molecules of tea move more slowly and the molecules of air move more quickly.

If you compute your missing information, you discover that it has increased. If, instead, tea absorbed heat from the colder air, then the missing information would be decreased. That is, we would know more. But information cannot fall from the sky. It cannot increase by itself, because what we don’t know, we just don’t know. Therefore, the tea cannot warm up by itself in contact with cold air. It sounds a bit magical, but it works: we can predict how heat behaves just on the basis of the observation that our information cannot increase for free!

This is one of the ways of computing the heat of black holes: the quanta of area of a black hole enclosed in a surface of a certain area can be in N different possible distributions. It is like for the cup of tea, in which the molecules can move in N different possible ways. Thus we can associate a quantity of missing information, that is to say, entropy, with a black hole.

the larger the hole, the greater the amount of missing information. When information enters into a black hole, it is no longer recoverable from outside. But the information which enters the black hole carries with it the energy by which the black hole becomes larger and increases its area. Viewed from outside, the information lost in the black hole now appears as entropy associated with the area of the hole.

Where does the information that has fallen into the black hole as the black hole shrinks end up? Theoretical physicists are debating the question, and no one has a completely clear answer. All of this, I believe, indicates that in order to grasp the basic grammar of the world, we need to merge three basic ingredients, not just two: not just general relativity and quantum mechanics, but also the theory of heat, that is, statistical mechanics and thermodynamics, which we can also describe as information theory. But the thermodynamics of general relativity, that is to say, the statistical mechanics of quanta of space, is as yet only in its first infancy. Everything is still confused, and there is a very great deal which remains to be understood.

The same goes for ‘hot’ and ‘cold’: there are no ‘hot’ or ‘cold’ things at a microscopic level but, when we put together a large number of microscopic constituents and describe them in terms of averages, then the notion of ‘heat’ appears: a hot body is a body where the average speed of single constituents is raised. We are able to understand the meaning of ‘up’ or ‘hot’ in certain situations: the presence of a nearby mass, or the fact that we are dealing only with average values of many molecules, and so on.

If you think about it, all phenomena where we detect the passage of time are co-involved with temperature. The salient characteristic of time is that it moves forwards and not backwards, that is to say, there are irreversible phenomena. Mechanical phenomena – ones that don’t involve heat – are reversible.

When the stone reaches the ground, it stops, you might object: if you watch the film reversed, you see a stone leaping up from the ground by itself, and this is implausible. But when the stone reaches the ground and stops, where does its energy go? It heats the ground! At the precise moment when heat is produced, the process is irreversible: the past differs from the future. It is always heat and only heat that distinguishes the past from the future.

This is universal. A burning candle is transformed into smoke – the smoke cannot transform into a candle – and a candle produces heat. A boiling-hot cup of tea cools down and does not heat up: it diffuses heat. We live and get old: producing heat. Our old bicycle wears out with time: producing heat through friction. Think of the solar system. At first approximation, it continues to turn like an immense mechanism always equal to itself. It doesn’t produce heat and, in fact, if you watched it in reverse you wouldn’t notice anything strange about it. But looked at more closely, there are also irreversible phenomena: the Sun is using up its combustible hydrogen and will eventually exhaust it and extinguish: the Sun, too, is getting older and, in fact, produces heat. The Moon also appears to orbit the Earth unchangingly and be always equal to itself, whereas in reality it is slowly moving away. This is because it raises tides, and the tides heat the sea a little, thus exchanging energy with the Moon. Whenever you consider a phenomenon certifying the passage of time, it is through the production of heat that it does so. There is no preferred direction of time without heat.

Time and heat

We are always correlated with averages. Averages behave like averages: they disperse heat and, intrinsically, generate time.

Time is an effect of our overlooking of the physical microstates of things. Time is information we don’t have. Time is our ignorance.

Wow

Where does a wave finish? Where does it begin? Think of mountains. Where does a mountain start? Where does it end? How far does it continue beneath the Earth’s surface? These are questions without much sense, because a wave and a mountain are not objects in themselves; they are ways which we have of slicing up the world to apprehend it, to speak about it more easily. These limits are arbitrary, conventional, comfortable: they depend on us (as physical systems) more than on the waves or the mountains.