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

by Carlo Rovelli

That ...

The equation is the analogue of the Maxwell equations, but for gravity ra...

But it is not only space that curves: time does too. Einstein predicts that time on Earth passes more quickly at higher altitude, and more slowly at lower altitude.

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 that expands and shrinks, according to the vicinity of masses: Earth, like all masses, distorts spacetime, slowing down time in its vicinity.

Two twins spend their time, one at sea level and the other in the mountains. When they meet up again, the twin in the mountains is older. This is the gravitational dilation of time.

It seems like a joke, but Einstein was not kidding. With mathematics, he needed help: he had it explained to him by patient fellow students and friends, such as Marcel Grossmann. It was his intuition as a physicist that was prodigious.

The math that was necessary to formulate the theory was geometry in four dimensions, and Hilbert writes: Any youngster on the streets of Göttingen understands geometry in four dimensions better than Einstein.

And yet, it was Einstein who completed the task.

Why? Because Einstein had a unique capacity to imagine how the world might be constructed, to “see” it in his mind. The equations, for him, came afterward; they were the language with which to make concrete his visions of reality. For Einstein, the theory of general relativity is not a collection of e...

But the world we inhabit does not have only two dimensions; it has three. Four, in fact, when time is included.

In technical terms: the description of the geometry of Earth offered by Brunetto Latini in Li tresor is given in terms of intrinsic geometry (seen from the inside) rather than extrinsic (seen from the outside), and this is exactly the one that is suitable to generalize the notion of “sphere” from two dimensions to three.

The best way of describing a 3-sphere is not to try to “see it from the outside” but rather to describe what happens when moving within it.

That is to say, the idea is to describe a curved space not as “seen from the outside,” stating how it curves in an external space, but instead in terms of what may be experienced by somebody within that space, who is moving and always remaining within it.

Einstein’s spacetime is not curved in the sense that it curves “in an external space.” It is curved in the sense that its intrinsic geometry—that is to say, the web of distances between its points, which can be observed by staying within it—is not the geometry of a flat space.

It is a space where Pythagoras’s theorem is not valid, just as Pythagoras’s theorem is not valid on the surface of Earth.

There is a way of understanding the curvature of space from within it, and without looking at it from outside, th...

The angle through which the arrow has turned in the course of the loop measures the curvature.

I will return later to this method of measuring curvature by making a loop in space. These will be the “loops” that give the name to the theory of “loop quantum gravity.”

In the end, Dante does no more than mount the pieces that were already existing into a coherent architectural whole, which follows the suggestive architecture of the Baptistery, and resolves the ancient problem of the borders of the universe. In so doing, Dante anticipates by six centuries Einstein’s 3-sphere.

Our culture is foolish to keep science and poetry separated: they are two tools to open our eyes to the complexity and beauty of the world.

Dante’s 3-sphere is only an intuition within a dream. Einstein’s 3-sphere has mathematical form, and follows from the theory’s equations.

when Einstein tries to insert the idea of the 3-sphere into his equations. Here he encounters a problem. He is convinced that the universe is fixed and immutable, but his equations tell him that this is not possible. It isn’t difficult to understand why. Everything attracts, therefore the only way for a finite universe not to collapse on itself is to be expanding:

For all his bravery, Einstein the genius lacks the courage to believe his own equations.

it is literally a cosmic explosion. This is the “Big Bang.” Today we know the expansion is real. The definitive proof of the scenario foreseen by Einstein’s equations arrives in 1964, when two American radio-astronomers, Arno Penzias and Robert Wilson, discover by accident a radiation diffused throughout the universe, which turns out to be precisely what remains of the original immense heat of the early universe.

the leap made by Einstein is unparalleled: spacetime is a field; the world is made only of fields and particles; space and time are not something else, something different from the rest of nature: they are just a field among the others (figure 3.17).

The two pillars of twentieth-century physics—general relativity and quantum mechanics—could not be more different from each other.

This chapter illustrates the strange physics of this theory, relates how the theory came into being, and discusses the three aspects of reality it has unveiled: granularity, indeterminism, and relationality.

Quantum Mechanics

The size of the packets, he assumes, depends on the frequency (that is, the color) of the electromagnetic waves. For waves of frequency ν, every quantum, or every packet, has energy: E = hν This formula is the first of quantum mechanics; h is a novel constant, which today we call the “Planck constant.”

It fixes how much energy there is in each packet of energy, for radiation of frequency (color) ν. The constant h determines the scale of all quantum phenomena.

This is where 'the sausage' of consciousness is made? Is this portal between relative and ultimate?

For Max Planck, taking energy in finite-size packets was only a strange trick that happened to work for the calculation—that is, to reproduce laboratory measurements—but for utterly unclear reasons. Five years later it is Albert Einstein—him again—who comes to understand that Planck’s “packets of energy” are in fact real. This is the subject of the third of the three articles sent to the Annalen der Physik in 1905. And this is the true date of the birth of quantum theory.

What is observed is that the phenomenon only happens 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 color of light (the frequency) rather than its intensity (energy).

This explains why it is the color and not the intensity that determines whether the photoelectric effect occurs or not.

It is easy to understand things once someone has thought them through. The difficulty lies in thinking them through in the first place.

I agree

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

To comprehend how light may be simultaneously an electromagnetic wave and a swarm of photons will require the entire construction of quantum mechanics.

Hmmm maybe this is the portal between relative and ultimate truth. This exchange of electrcity for magnetism, is light electromagnetic?

But the first building block of this theory has been established: there exists a fundamental granularity in all things, including light.

Experiments had shown that 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 colored.

I have had this intuition since my early twenties, when I read the Tao of Physics by Fritzof Capra

Salt is white, pepper is black, chili is red. Why? Individual substances have specific colors. Since color is the frequency of light, light is emitted by substances at certain fixed frequencies. The set of the frequencies that characterizes a given substance is known as the “spectrum” of this substance.

Color is the speed at which Faraday’s lines vibrate, and this is determined by the vibrations of the electric charges that emit light. These charges are the electrons that move inside the atoms.

But then why does the light emitted by an atom not contain all colors, rather than just a few particular ones? Why are atomic spectra not a continuum of colors, instead of just a few separate lines? Why, in technical parlance, are they “discrete” instead of continuous? For decades, physicists seemed incapable of finding an answer.

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 now not for the energy of light but rather for the energy of the electrons in the atom.

This explains the dualaity of the positive and negative charges inherent in electromagnetic spectrum... More curious why the human form can only physically see .0035 percent of the entire spectrum. Probably why in the theory of general relativty, Einstein's equation assumed space to be a void - physically empty

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.

These hypotheses define Bohr’s “atomic model,” whose centenary was commemorated in 2013. With these assumptions (outlandish, but simple) Bohr manages to compute the spectra of all atoms, and even to accurately predict spectra not yet observed. The experimental success of this simple model is astonishing.

until a young German finds the key to unlock the door of the mystery of the quantum world. Werner Heisenberg is twenty-five years old when he writes the equations of quantum mechanics, the same age as Einstein was when he wrote his three major articles. He does so on the basis of dizzying ideas.

He emerges, sometime later, with a disconcerting theory: a fundamental description of the movement of particles, in which they are not described by their position at every moment, but only by their position at a particular instant—the instants in which they interact with something else.

This is a 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 whe...

The “quantum leaps” from one orbit to another constitute their way of being real: an electron is a combination of leap...

When nothing disturbs it, an electron does not exist in any place. Instead of writing the position and velocity of the electron, Heisenberg writes tables of numbers (technically called “matrices”). He multiplies and divides tables of numbers representing possible interactions of the electron. And, as if from the...

These are the first fundamental equations of quantum mechanics. From here on, these equations will do...