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

by Carlo Rovelli

This is the weave of the world. This is reality. Everything else is nothing but a by-product, random and accidental, of this movement and this combining of atoms. The infinite variety of the substances of which the world is made derives solely from this combining of atoms.

Think of taking a piece of string, cutting it in half, and then again in half, and again, ad infinitum. At the end, you will obtain an infinite number of small pieces of string; the sum of these, however, will be finite, because they can only add up to the length of the original piece of string. Hence, an infinite number of strings can make a finite string; an infinite number of increasingly short times may make a finite time, and the hero, even if he will have to cover an infinite number of distances, ever smaller, will take a finite time to do so, and will end up catching the tortoise.

the extension of the string must be formed by a finite number of finite objects with finite size. The string cannot be cut as many times as we want; matter is not continuous, it is made of individual ‘atoms’ of a finite size.

If the air’s molecules were infinitely small and infinitely numerous, the effect of the collisions from right and from left would balance and thus cancel out at each instant, and the granule would not move. But the finite size of the molecules – the fact that these are present in finite rather than infinite number – causes there to be fluctuations (this is the key word): that is to say, the collisions never balance out exactly; they only balance out on average.

Wow

Each substance has a ‘natural place’, that is to say, a proper altitude to which it always returns: earth at the bottom, water a little way above it, air a little higher still, and fire even higher. When you pick up a stone and let it fall, the stone moves downwards because it wants to return to its natural level. Air bubbles in water, fire in the air; and children’s balloons move upwards, seeking their natural place.

Wow

Michael Faraday is an impoverished Londoner without formal education, who works first in a bookbindery, then in a laboratory, where he excels, gains his master’s confidence and grows into the most brilliant experimenter of nineteenth-century physics and its greatest visionary. Without knowing mathematics, he writes one of the best books of physics ever written, virtually devoid of equations.

Wow

What is it, then, a field? Faraday sees it as formed by bundles of very thin lines (infinitely thin), which fill space; an invisible, gigantic cobweb filling everything around us. He calls these lines ‘lines of force’ because, in some way, these lines ‘carry the force’: they transmit the electric and the magnetic forces from one body to another, as if they were cables pulling and pushing

An object with an electric charge (a rubbed glass rod, for instance) distorts the electric and magnetic fields (the lines) around itself, and in turn these fields produce a force on each charged object immersed in them. Thus, two distant charged objects do not attract or repel each other directly but only via the medium interposed between them.

Maxwell’s equations. They describe the behaviour of the electric and the magnetic fields: the mathematical version of the ‘Faraday lines’.

Maxwell realizes that his equations predict that Faraday’s lines can tremble and undulate, just like the waves of the sea. He computes the speed at which the undulations of Faraday’s lines move and the result turns out to be … the same as for light! Why? Maxwell understands: because light is nothing other than this rapid trembling of Faraday’s lines!

We see the world around us in colour. What is colour? Put simply, it is the frequency (the speed of oscillation) of the electromagnetic wave that light is. If the wave vibrates more rapidly, the light is bluer. If it vibrates a little more slowly, the light is redder. Colour, as we perceive it, is the psychophysical reaction of the nerve signal generated by the receptors of our eyes, which distinguish electromagnetic waves of different frequencies.

blows. It isn’t true that we ‘do not see’ Faraday lines. We only see vibrating Faraday lines. ‘To see’ is to perceive light, and light is the movement of Faraday lines. Nothing leaps from one location in space to another without something transporting it. If we see a child playing on the beach, it is only because between them and ourselves there is this lake of vibrating lines which transport their image to us. Is the world not marvellous?

It wasn’t much of a profession for a physics graduate, but it gave Albert time to think, and to work independently. And he did think and work. After all, this is what he had done since his early youth: he would read Euclid’s Elements and Kant’s Critique of Pure Reason instead of attending to what he was being taught at school. You don’t get to new places by following established tracks.

This is why it is impossible to hold a smooth conversation between here and Mars. Say I am on Mars and you are here. I ask you a question and you reply as soon as you’ve heard what I said; your reply reaches me a quarter of an hour after I posed the question. This quarter of an hour is time that is neither past nor future to the moment in which you’ve replied to me.

relativity

The figure describes that which in physics is called spacetime: the set of all past and future events, but also those that are ‘neither-past-nor-future’; these do not form a single instant: they have themselves a duration.

Einstein realizes that energy and mass are two facets of the same entity, just as the electric and magnetic fields are two facets of the same field, and as space and time are two facets of the one thing: spacetime. This implies that mass, by itself, is not conserved; and energy – as it was conceived at the time – is not independently conserved either. One may be transformed into the other: only one single law of conservation exists, not two. What is conserved is the sum of mass and energy, not each separately. Processes must exist that transform energy into mass, or mass into energy. A rapid calculation teaches Einstein how much energy is obtained by transforming one gram of mass. The result is the celebrated formula E = mc².

Since the speed of light c is a very large number, and c² an even greater number, the energy obtained from transforming one gram of mass is enormous; it is the energy of millions of bombs exploding at the same time – enough energy to illuminate a city and power the industries of a country for months or, conversely, capable of destroying in a second hundreds of thousands of human beings, in a city such as Hiroshima.

Newton himself, as we have seen, had suspected that in the idea of a force acting between distant bodies that do not touch there was something missing; and that in order for the Earth to attract the Moon something that could transmit this force had to be there between the two. Two hundred years later, Faraday had found the solution – not for the force of gravity, but for the electric and magnetic forces: the field. Electric and magnetic fields ‘carry around’ the electric and magnetic force.

To us, the idea of space seems natural, but it is our familiarity with Newtonian physics that makes it so. If you think about it, empty space is not part of our experience. From Aristotle to Descartes, that is to say, for two millennia, the Democritean idea of space as a peculiar entity, distinct from things, had never been seen as reasonable. For Aristotle, as for Descartes, things have extension: extension is a property of things; extension does not exist without something being extended. I can take away the water from a glass, but air will fill it. Have you ever seen a really empty glass?

If between two things there is nothing, Aristotle reasoned, then there is nothing. How can there be at the same time something (space) and nothing?

And it’s here that Einstein’s extraordinary stroke of genius occurs, one of the greatest flights in the history of human thinking: what if the gravitational field turned out actually to be Newton’s mysterious space? What if Newton’s space was nothing more than the gravitational field? This extremely simple, beautiful, brilliant idea is the theory of general relativity.

The world is not made up of space + particles + electromagnetic field + gravitational field. The world is made up of particles + fields, and nothing else; there is no need to add space as an extra ingredient. Newton’s space is the gravitational field.

With a great deal of effort, seeking help from friends better versed in mathematics than himself, Einstein learns Riemann’s maths – and writes an equation where R is proportional to the energy of matter. In words: spacetime curves more where there is matter. That is it. The equation is the analogue of the Maxwell equations, but for gravity rather than electricity.

Einstein predicts that time on Earth passes more quickly at higher altitude, and more slowly at lower altitude. This is measured, and also proves to be the case. Today we have extremely precise clocks, in many laboratories, and it is possible to measure this strange effect even for a difference in altitude of just a few centimetres. Place a watch on the floor and another on a table: the one on the floor registers less passing of time than the one on the table. Why? Because time is not universal and fixed, it is something which expands and shrinks, according to the vicinity of masses: the Earth, like all masses, distorts spacetime, slowing time down in its vicinity. Only slightly – but two twins who have lived respectively at sea-level and in the mountains will find that, when they meet up again, one will have aged more than the other

Wow. Time passes quicker at high altitude

Stars burn as long as they have available hydrogen – their fuel – then die out. The remaining material is no longer supported by the pressure of the heat and collapses under its own weight. When this happens to a large enough star, the weight is so strong that matter is squashed down to an enormous degree and space curves so intensely as to plunge down into an actual hole. A black hole.

And all this is the result only of an elementary intuition – that spacetime and the gravitational field are one and the same thing

a ‘loop’, as it is termed – and the arrow does not point in the same direction as when you started out (figure 3.14).

Wow. Loop

therefore the only way for a finite universe not to collapse on itself is for it to be expanding: just as the only way to prevent a football from falling to the ground is to kick it upwards. It either goes up, or falls down – it can’t stay still, suspended in the air.

Expanding universe

weak electric current when struck by light. That is to say, they emit electrons when light shines on them.

That this happens is not strange, because light carries energy (it warms us, for example), and its energy makes the electrons ‘jump out’ of their atoms; it gives them a push. But something is strange: it seems reasonable to expect that if the energy of light is scarce – namely, if the light is dim – the phenomenon would not take place; and that it would take place when the energy is sufficient – namely, when the light is bright. But it isn’t like this: what is observed is that the phenomenon happens only if the frequency of light is high and does not happen if the frequency is low. That is to say, it happens or doesn’t happen depending on the colour of light (the frequency) rather than its intensity (energy). There is no way of making sense of this with standard physics.

Einstein uses Planck’s idea of the packets of energy, with a size that depends upon frequency, and realizes that if these packets are real, the phenomenon can be explained. It isn’t difficult to understand why. Imagine that the light arrives in the form of grains of energy. An electron will be swept out of its atom if the individual grain hitting it has a great deal of energy. What matters is the energy of each grain, not the number of grains.

what determines whether your car will be dented is not the total quantity of hail that falls but the size of the individual hailstones.

water and stone

Today we call these packets of energy ‘photons’, from the Greek word for light: ϕώς. Photons are the grains of light, its ‘quanta’.

Note the wonderful initial ‘It seems to me …’, which recalls the hesitations of Faraday, or those of Newton; or the uncertainty of Darwin in the first pages of On the Origin of Species. True genius is aware of the momentousness of the steps it is taking, and is always hesitant …

There is a clear relation between Einstein’s work on Brownian motion (discussed in Chapter 1) and his work on the quanta of light, both completed in 1905.

That's 100 years ago and people somehow still cannot explain things easily and logically like they are describing enigma in the dark until I read this book :)

To comprehend how light may be simultaneously an electromagnetic wave and a swarm of photons will require the entire construction of quantum mechanics. But the first building block of this theory has been established: there exists a fundamental granularity in all things, including light.

an atom is like a small solar system: the mass is concentrated in a heavy central nucleus, around which light electrons revolve, more or less like the planets around the Sun. This picture, however, did not account for a simple fact: matter is coloured.

The set of the frequencies that characterizes a given substance is known as the ‘spectrum’ of this substance. A spectrum is a collection of fine lines of different hues, in which the light emitted by a given substance is decomposed (for instance, by a prism).

Colour is the speed at which Faraday’s lines vibrate, and this is determined by the vibrations of the electric charges which emit light. These charges are the electrons that move inside the atoms. Therefore, studying spectra, we can understand how electrons move around nuclei. The other way around, we could predict the spectrum of each atom by computing the frequencies of the electrons circling their nucleus.

But then why does the light emitted by an atom not contain all colours, rather than just a few particular ones? Why are atomic spectra not a continuum of colours, instead of just a few separate lines? Why, in technical parlance, are they ‘discrete’ instead of continuous?

Bohr finds a tentative solution, by way of a strange hypothesis. He realizes that everything could be explained if the energy of electrons in atoms could only assume certain ‘quantized’ values – certain specific values, just as was hypothesized by Planck and by Einstein for the energy of the quanta of light.

Once again, the key is a granularity, but not now for the energy of light but rather for the energy of the electrons in the atom. It begins to become clear that granularity is something widespread in nature.

Granularity

Bohr makes the hypothesis that electrons can exist only at certain ‘special’ distances from the nucleus, that is, only on certain particular orbits, the scale of which is determined by Planck’s constant h. And that electrons can ‘leap’ between one orbit with the permitted energy to another. These are the famous ‘quantum leaps’. The frequency at which the electron moves on these orbits determines the frequency of the emitted light and, since only certain orbits are allowed, it follows that only certain frequencies are emitted.

Frequency is when electron jumps from one to another in certain orbit

What if the electron could be something that manifests itself only when it interacts, when it collides with something else; and that between one interaction and another it had no precise position? What if always having a precise position is something which is acquired only if one is substantial enough – large and heavy like the man that passed by a little while ago, like a ghost in the dark, and then disappeared into the night …?

Electron

a fundamental description of the movement of particles, in which they are described not by their position at every moment but only by their position at particular instants: the instants in which they interact with something else. This is the second cornerstone of quantum mechanics, its hardest key: the relational aspect of things. Electrons don’t always exist. They exist when they interact. They materialize in a place when they collide with something else. The quantum leaps from one orbit to another constitute their way of being real: an electron is a combination of leaps from one interaction to another. When nothing disturbs it, an electron does not exist in any place.

Electron exists when it interacts

Its position and velocity, its angular momentum and its electrical potential, and so on, acquire reality only when it collides – ‘interacts’– with another object. It is not just its position which is undefined, as Heisenberg had recognized: no variable of the object is defined between one interaction and the next. The relational aspect of the theory becomes universal.

Relational. Interesting

Quantum mechanics brings probability to the heart of the evolution of things. This indeterminacy is the third cornerstone of quantum mechanics: the discovery that chance operates at the atomic level.

The first is to calculate which values a physical variable may assume. This is called ‘calculation of the spectrum of a variable’; it captures the granular nature of things. When an object (atom, electromagnetic field, molecule, pendulum, stone, star, and so on) interacts with something else, the values computed are those which its variables can assume in the interaction (relationism).

First

The second thing that Dirac’s quantum mechanics allows us to do is to compute the probability that this or that value of a variable appears at the next interaction. This is called ‘calculation of an amplitude of transition’.

Second

Probability expresses the third feature of the theory: indeterminacy – the fact that it does not give unique predictions, only probabilistic ones.

Third