Part 8 (1/2)

Figure 9.4 Possible prediction of the spectrum of background radiation, of loop quantum gravity (shown by the solid line) compared with the current experimental errors (as represented by the points). Courtesy of A. Ashtekar, I. Agullo and W. Nelson.

Traces of the great primordial heat must also be in the gravitational field itself. The gravitational field, too, that is to say, s.p.a.ce itself, must be tremulous like the surface of the sea. Therefore, a cosmic gravitational background radiation must also exist older even than the electromagnetic one, because the gravitational waves are disturbed less by matter than the electromagnetic ones and were able to travel undisturbed even when the universe was too dense to let the electromagnetic waves pa.s.s.

We have now observed gravitational waves directly, with the LIGO detector, formed by two arms of a few miles in length, at a right angle to each other, in which laser beams measure the distance between three fixed points. When a gravitational wave pa.s.ses, the s.p.a.ce lengthens and shortens imperceptibly, and the lasers reveal this minuscule variation.fn46 The gravitational waves observed were generated by an astrophysical event: colliding black holes. These are phenomena described by general relativity which do not involve quantum gravity. But a more ambitious experiment called LISA is at the stage of being evaluated and is capable of doing the same thing but on a much larger scale: by putting into orbit three satellites, not around the Earth but around the Sun, as if they were miniature planets tracking the Earth in its...o...b..t. The three satellites are connected by laser beams measuring the distance between them or, better still, the variations in the distances when a gravitational wave pa.s.ses. If LISA is launched, it should be able to see not only the gravitational waves produced by stars and black holes but also the diffuse background of primordial gravitational waves generated at a time close to the Big Bang. These waves should tell us about the quantum bounce.

In the subtle irregularities of s.p.a.ce, we should be able to find traces of events which took place 14 billion years ago, at the origin of our universe, and confirm our deductions on the nature of s.p.a.ce and time.

10. Quantum Black Holes

Black holes populate our universe in great number. They are regions in which s.p.a.ce is so curved as to collapse in on itself, and where time comes to a standstill. As mentioned, they form, for instance, when a star has burned up all of the available hydrogen and collapses.

Frequently, the collapsed star formed part of a pair of neighbouring stars and, in this case, the black hole and the surviving counterpart circle one around the other; the black hole sucks matter from the other star continuously (as in figure 10.1).

Astronomers have found many black holes with a size (that is, ma.s.s) of the order of our Sun (a bit larger, in fact). But there are also gigantic back holes. There is one of these at the centre of almost all of the galaxies, including our own.

Figure 10.1 Representation of a couple star/black hole. The star loses matter, which is partly absorbed by the black hole, partly projected by it in jets in the direction of its poles.

The black hole at the centre of our own galaxy is currently being studied in detail. It has a ma.s.s a million times greater than our Sun. Every so often, a star gets too close to this monster, is disintegrated by the gravitational distortion and swallowed by the cyclopean black hole, like a small fish swallowed by a whale. Imagine a monster the size of a million Suns, which swallows in an instant our own Sun and its miniature planets ...

There is a wonderful ongoing project to construct a network of radio antennae distributed across the Earth from pole to pole, with which astronomers will be able to achieve a resolution sufficient to 'see' the galactic black hole. 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. 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 pa.s.sed. 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 s.p.a.ces.h.i.+p, 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 have elapsed in the rest of the universe.

The really surprising thing is that the properties of these strange objects, today commonly observed, were foreseen by Einstein's theory. Now, astronomers study these objects in s.p.a.ce, but until not long ago black holes were considered a scarcely credible and bizarre consequence of an outlandish theory. I remember my university professor introducing them as solutions to Einstein's equations, to which 'real objects were unlikely ever to correspond'. This is the stupendous capacity of theoretical physics to discover things before they are observed.

The black holes we observe are well described by Einstein's theory, and quantum mechanics is not needed to understand them. But there are two mysteries of black holes that do require quantum mechanics in order to be unravelled and, for each of these, loop theory offers a possible solution. One of these could also offer an opportunity to test the theory.

The first application of quantum gravity to black holes concerns a curious fact discovered by Stephen Hawking. Early in the 1970s he theoretically deduced that black holes are 'hot'. They behave like hot bodies: they emit heat. In doing so, they lose energy and hence ma.s.s (since energy and ma.s.s are the same thing), becoming progressively smaller. They 'evaporate'. This 'evaporation of black holes' is the most important discovery made by Hawking.

Objects are hot because their microscopic const.i.tuents 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.

Figure 10.2 The surface of a black hole crossed by loops, that is to say, by links of the spin network that describe the state of the gravitational field. Each loop corresponds to a quantum area of the black hole's surface. John Baez.

What are the elementary 'atoms' that vibrate, making a black hole hot? Hawking left this problem unanswered. Loop theory provides a possible answer. The elementary atoms of a black hole that vibrate, and are thus responsible for its temperature, are the individual quanta of s.p.a.ce on its surface.

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 s.p.a.ce. These vibrate because in the world of quantum mechanics everything vibrates; nothing stays still. The impossibility of anything being entirely and continuously still in a place is at the heart of quantum mechanics. Black-hole heat is directly connected to loop quantum gravity's fluctuations of the atoms of s.p.a.ce. The precise position of the black hole's horizon is determined only in relation to these microscopic fluctuations of the gravitational field. Hence, in a certain sense, the horizon fluctuates like a hot body.

There is another way of understanding the origin of the heat of black holes. The quantum fluctuations generate a correlation between the interior and the exterior of a hole. (I will speak at length about correlations and temperature in Chapter 12). Quantum uncertainty across the horizon of the black hole generates fluctuations of the horizon's geometry. But fluctuations imply probability, and probability implies thermodynamics, and therefore temperature. Concealing from us a part of the universe, a black hole makes its quantum fluctuations detectable in the form of heat.

Figure 10.3 Stephen Hawking and Eugenio Bianchi. On the blackboard are the princ.i.p.al equations of loop quantum gravity which describe black holes.

It was a young Italian scientist, Eugenio Bianchi, today a professor in the United States, who completed an elegant calculation which shows how, starting from these ideas and from the basic equations of loop quantum gravity, it is possible to derive the formula for the heat of black holes foreseen by Hawking (figure 10.3).

The second application of loop quantum gravity to black-hole physics is more spectacular. Once collapsed, a star vanishes from external view: it is inside the black hole. But, inside the hole, what happens to it? What would you see if you let yourself fall into the hole?

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 pa.s.ses 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, basically, this is what a black hole is: a shortcut to the distant future.

Thus, quantum gravity might imply that black holes are not eternally stable objects, as cla.s.sical general relativity predicted, after all. They are, ultimately, unstable.

Seeing these black-hole explosions would be a spectacular confirmation for the theory. 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. Let's wait and see ...

11. The End of Infinity

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 s.p.a.ce. The universe cannot be smaller than the Planck scale, because nothing exists which is smaller than the Planck scale.

If we ignore quantum mechanics, we ignore the existence of this lower limit. The pathological situations predicted by general relativity, where the theory gives infinite quant.i.ties, are called singularities. Quantum gravity places a limit to infinity, and 'cures' the pathological singularities of general relativity.

The same happens at the centre of black holes: the singularity that cla.s.sic general relativity antic.i.p.ated disappears as soon as we take quantum gravity into account.

There is another case, of a different kind, in which quantum gravity places a limit to the infinite, and it regards forces such as electromagnetism. Quantum field theory, started by Dirac and completed in the 1950s by Feynman and his colleagues, describes these forces well but is full of mathematical absurdities. When we use it to compute physical processes, we often obtain results which are infinite, and mean nothing. They are called divergences. The divergences are then eliminated with calculations, using a baroque technical procedure which leads to finite final results. In practice, it works, and the numbers, in the end, come out right; they reproduce the experimental measurements. But why must the theory go via the infinite to arrive at reasonable numbers?

In the last years of his life, Dirac was very unhappy with the infinities in his theory and felt that, all things considered, his objective of truly understanding how things worked was not achieved. Dirac loved conceptual clarity, even if what was clarity to him was not always clarity to others. But infinities do not make for clarity.

But the infinities of quantum field theory follow from an a.s.sumption at the basis of the theory: the infinite divisibility of s.p.a.ce. 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: s.p.a.ce is not infinitely divisible, there are no infinite points; there are no infinite things to add up. The granular discrete structure of s.p.a.ce resolves the difficulties of the quantum theory of fields, eliminating the infinities by which it is afflicted.

This is a tremendous result: on the one hand, taking quantum mechanics into account resolves the problems generated by the infinities of Einstein's theory of gravity, that is to say, the singularities. On the other, taking gravity into account solves the problems generated by quantum field theory, that is to say, the divergences. Far from being contradictory, as they at first seemed, the two theories each offer the solution to the problems posed by the other!

Putting a limit to infinity is a recurrent theme in modern physics. Special relativity may be summarized as the discovery that there exists a maximum velocity for all physical systems. Quantum mechanics can be summarized as the discovery that there exists a maximum of information for each physical system. 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 summarized in table 11.1.

The existence of these minimum and maximum values for length, velocity and action fixes a natural system of units. Instead of measuring speed in kilometres per hour, or in metres per second, we can measure it in fractions of the speed of light. We can fix the value 1 for the velocity c and write, for example, v = , for a body which is moving at half the speed of light. In the same way, we can posit by definition and measure length in multiples of Planck's length. And we can posit h = 1 and measure actions in multiples of Planck's constant. In this way, we have a natural system of fundamental unities from which the others follow. The unity of time is the time that light takes to cover the Planck length, and so on. The natural unities are commonly used in research on quantum gravity.

The identification of these three fundamental constants places a limit to what seemed to be the infinite possibilities of nature. It suggests that what we call infinite often is nothing more than something which we have not yet counted, or understood. I think this is true in general. 'Infinite', ultimately, is the name that we give to what we do not yet know. Nature appears to be telling us that there is nothing truly infinite.

Table 11.1 Fundamental limitations discovered by theoretical physics.

Physical Quant.i.ty Fundamental constant Theory Discovery Velocity c Special relativity A maximum velocity exists Information (actions) Quantum mechanics A minimum of information exists Length Lp Quantum gravity A minimum length exists There is another infinity which disorientates our thinking: the infinite spatial extension of the cosmos. But as I ill.u.s.trated in Chapter 3, Einstein has found the way of thinking of a finite cosmos without borders. Current measurements indicate that the size of the cosmos must be larger than 100 billion light years. This is the order of magnitude of the universe we have indirect access to. It is around 10120 times greater than the Planck length, a number of times which is given by a 1 followed by 120 zeroes. Between the Planck scale and the cosmological one, then, there is the mind-blowing separation of 120 orders of magnitude. Huge. Extraordinarily huge. But finite.

In this s.p.a.ce between the size of the minute quanta of s.p.a.ce, up to quarks, protons, atoms, chemical structures, mountains, stars, galaxies (each formed by one hundred billion stars), cl.u.s.ters of galaxies, and right up until the seemingly boundless visible universe of more than 100 billion galaxies unfolds the swarming complexity of our universe; a universe we know only in a few aspects. Immense. Finite.

The cosmological scale is reflected in the value of the cosmological constant , which enters into the basic equations of our theories. The fundamental theory contains, therefore, a very large number: the ratio between the cosmological constant and the Planck length. It is this large number that opens the way to the vast complexity of the world. But what we see and understand of the universe is not an infinity to drown in. It is a wide sea, but a finite one.