Seven Brief Lessons on Physics (2 page)

Quanta

The two pillars of twentieth-century physics—general relativity, of which I spoke in the first lesson, and quantum mechanics, which I’m dealing with here—could not be more different from each other. Both theories teach us that the fine structure of nature is more subtle than it appears. But general relativity is a compact gem: conceived by a single mind, that of Albert Einstein, it’s a simple and coherent vision of gravity, space, and time. Quantum mechanics, or “quantum theory,” on the other hand, has gained unequaled experimental success and led to applications that have transformed our everyday
lives (the computer on which I write, for example), but more than a century after its birth it remains shrouded in mystery and incomprehensibility.

It’s said that quantum mechanics was born precisely in the year 1900, virtually ushering in a century of intense thought. The German physicist Max Planck calculated the electric field in equilibrium in a hot box. To do this he used a trick: he imagined that the energy of the field is distributed in “quanta,” that is, in packets or lumps of energy. The procedure led to a result that perfectly reproduced what was measured (and therefore must be in some fashion correct) but clashed with everything that was known at the time. Energy was considered to be something that varied continuously, and there was no reason to treat it as if it were made up of small building blocks. To treat energy as if it were made up of finished packages had been, for Planck, a peculiar trick of calculation, and he did not himself fully understand the reason for its effectiveness. It was to be Einstein once again who, five years later, came to understand that the “packets of energy” were real.

Einstein showed that light is made of packets: particles of light. Today we call these “photons.” He wrote, in the introduction to his article:

It seems to
me that the observations associated with blackbody radiation, fluorescence, the
production of cathode rays by ultraviolet light, and other related
phenomena connected with the emission or transformation of light are
more readily understood if one assumes that the energy of
light is discontinuously distributed in space. In accordance with the assumption
to be considered here, the energy of a light ray
spreading out from a point source is not continuously distributed
over an increasing space but consists of a finite number
of “energy quanta” which are localized at points in space,
which move without dividing, and which can only be produced and absorbed as complete units.

These simple and clear lines are the real birth certificate of quantum theory. Note the wonderful initial “It seems to me . . . ,” which recalls the “I think . . .” with which Darwin introduces in his notebooks the great idea that species evolve, or the “hesitation” spoken of by Faraday when introducing for the first time the revolutionary idea of magnetic fields. Genius hesitates.

The work of Einstein is initially treated by colleagues
as the nonsensical juvenilia of an exceptionally brilliant youth. Subsequently it will be for the same work that he is awarded the Nobel Prize. If Planck is the father of the theory, Einstein is the parent who nurtured it.

But like all offspring, the theory then went its own way, unrecognized by Einstein himself. In the second and third decades of the twentieth century it was the Dane Niels Bohr who pioneered its development. It was Bohr who understood that the energy of electrons in atoms can take on only certain values, like the energy of light, and crucially that electrons can only “jump” between one atomic orbit and another with determined energies, emitting or absorbing a photon when they jump. These are the famous “quantum leaps.” And it was in his institute in Copenhagen that the most brilliant young minds of the century gathered together to investigate and try to bring order to these baffling aspects of behavior in the atomic world, and to build from it a coherent theory. In 1925 the equations of the theory finally appeared, replacing the entire mechanics of Newton.

It’s difficult to imagine a greater achievement. At one stroke, everything makes sense, and you can calculate everything. Take one example: do you remember the
periodic table of elements, devised by Dmitri Mendeleev, which lists all the possible elementary substances of which the universe is made, from hydrogen to uranium, and which was hung on so many classroom walls? Why are precisely these elements listed there, and why does the periodic table have this particular structure, with these periods, and with the elements having these specific properties? The answer is that each element corresponds to one solution of the main equation of quantum mechanics. The whole of chemistry emerges from a single equation.

The first to write the equations of the new theory, basing them on dizzying ideas, would be a young German of genius, Werner Heisenberg.

Heisenberg imagined that electrons do not
always
exist. They only exist when someone or something watches them, or better, when they are interacting with something else. They materialize in a place, with a calculable probability, when colliding with something else. The “quantum leaps” from one orbit to another are the only means they have of being “real”: an electron is a set of jumps from one interaction to another. When nothing disturbs it, it is not in any precise place. It is not in a “place” at all.

It’s as if God had not designed reality with a line that was heavily scored but just dotted it with a faint outline.

In quantum mechanics no object has a definite position, except when colliding headlong with something else. In order to describe it in mid-flight, between one interaction and another, we use an abstract mathematical formula that has no existence in real space, only in abstract mathematical space. But there’s worse to come: these interactive leaps with which each object passes from one place to another do not occur in a predictable way but largely at random. It is not possible to predict where an electron will reappear but only to calculate the
probability
that it will pop up here or there. The question of probability goes to the heart of physics, where everything had seemed to be regulated by firm laws that were universal and irrevocable.

Does it seem absurd? It also seemed absurd to Einstein. On the one hand he proposed Heisenberg for the Nobel Prize, recognizing that he had understood something fundamental about the world, while on the other he didn’t miss any occasion to grumble that this did not make much sense.

The young lions of the Copenhagen group were dismayed: how was it possible that
Einstein
should think
this? Their spiritual father, the man who had shown the courage to think the unthinkable, now retreated and was afraid of this new leap into the unknown that he himself had triggered. The same Einstein who had shown that time is not universal and that space is curved was now saying that the world cannot be
this
strange.

Patiently, Bohr explained the new ideas to Einstein. Einstein objected. He devised mental experiments to show that the new ideas were contradictory: “Imagine a box filled with light, from which we allow a single photon to escape for an instant . . .” So begins one of his famous examples, the mental experiment of the “box of light.” In the end Bohr always managed to find an answer with which to rebut these objections. For years, their dialogue continued by way of lectures, letters, articles . . . During the course of the exchange both great men needed to backtrack, to change their thinking. Einstein had to admit that there was actually no contradiction within the new ideas. Bohr had to recognize that things were not as simple and clear as he’d initially thought. Einstein did not want to relent on what was for him the key issue: that there was an objective reality independent of whoever interacts with whatever. Bohr would not relent on the validity of the profoundly new
way in which the real was conceptualized by the new theory. Ultimately, Einstein conceded that the theory was a giant step forward in our understanding of the world, but he remained convinced that things could not be as strange as it proposed—that “behind” it there must be a further, more reasonable explanation.

A century later we are at the same point. The equations of quantum mechanics and their consequences are used daily in widely varying fields—by physicists, engineers, chemists, and biologists. They are extremely useful in all contemporary technology. Without quantum mechanics there would be no transistors. But they remain mysterious. For they do not describe what happens to a physical system but only how a physical system affects another physical system.

What does this mean? That the essential reality of a system is indescribable? Does it mean that we lack only a piece of the puzzle? Or does it mean, as it seems to me, that we must accept the idea that reality is only interaction? Our knowledge grows, in real terms. It allows us to do new things that we had previously not even imagined. But that growth has opened up new questions. New mysteries. Those who use the equations of the theory in the laboratory carry on regardless, but in articles
and conferences that have been increasingly numerous in recent years, physicists and philosophers continue to search. What is quantum theory a century after its birth? An extraordinary dive deep into the nature of reality? A blunder that works, by chance? Part of an incomplete puzzle? Or a clue to something profound regarding the structure of the world that we have not yet properly digested?

When Einstein died, his greatest rival, Bohr, found for him words of moving admiration. When a few years later Bohr in turn died, someone took a photograph of the blackboard in his study. There’s a drawing on it. A drawing of the “light-filled box” in Einstein’s thought experiment. To the very last, the desire to challenge oneself and understand more. And to the very last:
doubt.

The Architecture of the Cosmos

In the first half of the twentieth century Einstein described the workings of space and time, while Niels Bohr and his young disciples captured in equations the strange quantum nature of matter. In the second half of the century physicists built upon these foundations, applying the two new theories to widely varying domains of nature: from the macrocosmic structure of the universe to the microcosm of elementary particles. I speak of the first of these in this lesson, and of the second in the next.

This lesson is made up mostly of simple drawings.
The reason for this is that before experiments, measurements, mathematics, and rigorous deductions, science is above all about visions. Science begins with a vision. Scientific thought is fed by the capacity to “see” things differently than they have previously been seen. I want to offer here a brief, modest outline of a journey between visions.

This first image represents how the cosmos was conceptualized for millennia: Earth below, the sky above. The first great scientific revolution, accomplished by Anaximander twenty-six centuries ago when trying to figure out how it is possible that the sun, moon, and stars revolve around us, replaced the above image of the cosmos with the one here:

Now the sky is all around Earth, not just above it, and Earth is a great stone that floats suspended in space, without falling. Soon someone (perhaps Parmenides, perhaps
Pythagoras) realized that the sphere is the most reasonable shape for this flying Earth for which all directions are equal—and Aristotle devised convincing scientific arguments to confirm the spherical nature of both Earth and the heavens around it where celestial objects run their course. Here is the resultant image of the cosmos:

And this cosmos, as described by Aristotle in his book
On the Heavens
, is the image of the world that remained characteristic of Mediterranean civilizations right up until the end of the Middle Ages. It’s the image of the world that Dante and Shakespeare studied at school.

The next leap was accomplished by Copernicus, inaugurating what has come to be called the great scientific revolution. The world for Copernicus is not so very different from Aristotle’s:

But there is in fact a key difference. Taking up an idea already considered in antiquity, Copernicus understood and showed that our Earth is not at the center
of the dance of the planets but that the sun is there instead. Our planet becomes one among the others, turning at high speed upon its axis and around the sun.

The growth of our knowledge continued, and with improved instruments it was soon learned that the solar system itself is only one among a vast number of others, and that the sun is no more than a star like others. An infinitesimal speck in a vast cloud of one hundred billion stars—the Galaxy:

In the 1930s, however, precise measurements by astronomers of the nebulae—small whitish clouds between the stars—showed that the Galaxy itself is a speck of dust in a huge cloud of galaxies, which extends
as far as the eye can see using even our most powerful telescopes. The world has now become a uniform and boundless expanse.

The illustration below is not a drawing; it’s a photograph taken by the Hubble telescope in orbit, showing a deeper image of the sky than any seen previously with the most powerful of our telescopes; seen with the naked eye, it would be a minute piece of extremely black sky. Through the Hubble telescope a dusting of vastly distant dots appears. Each black dot in the image is a galaxy containing a hundred billion suns similar to ours. In the past few years it has been observed that the majority of these suns are orbited by planets. There are therefore in the universe thousands of billions of billions of billions of planets such as Earth. And in every direction in which we look, this it what appears:

But this endless uniformity, in turn, is not what it seems. As I explained in the first lesson, space is not flat but curved. We have to imagine the texture of the universe, with its splashes of galaxies, being moved by waves similar to those of the sea, sometimes so agitated as to create the gaps that are black holes. So let’s return to a drawn image, in order to represent this universe furrowed by great waves:

And finally, we now know that this immense, elastic cosmos, studded with galaxies and fifteen billion years in the making, emerged from an extremely hot and dense small cloud. To represent this vision, we no longer need to draw the universe but to draw its entire history. Here it is, diagrammatically:

The universe began as a small ball and then exploded to its present cosmic dimensions. This is our current image of the universe, on the grandest scale that we know.

Is there anything else? Was there something before? Perhaps, yes. I’ll talk about it after a couple of lessons. Do other similar universes exist, or different ones? We do not know.