the world's mirror image

Michele DiEgo

Nothingness, Being and Appearance: concepts to which the human mind naturally tends towards and which at first sight may seem obvious for the vehemence with which they manifest themselves in the world’s reality, but which on the contrary touch the most sensitive ganglia of our intellect. From Parmenides’ Being, to the Nietzschean appearance of Being from nothingness, passing through Pascal’s studies on vacuum, man has always had to deal with his inability to completely grasp these concepts. Today modern physics adds new elements of reflection, challenging everything we intuitively thought we knew.

It is in 1926 when Paul Dirac, a taciturn student in love with the aesthetics of mathematics, earner his PhD at Cambridge University. During the last ten years he had seen the world of physics changing radically. Einstein revised the way of interpreting the universe, showing how speed transforms space-time’s tissue and that mass is nothing more than a form of energy (the famous E=mc²). Furthermore, from the minds of Planck, Bohr, De Broglie, Pauli, Schrödinger and Heisenberg quantum mechanics was born. A revolutionary theory, even more counterintuitive than Einstein’s one, which establishes particularly the wave-like behaviour of particles.

Nothingness, absolute vacuum, the perfect absence of matter and energy, in quantum mechanics acquires new properties.

Faced with all this heritage, two years after his PhD, young Dirac derives an equation able to conjugate relativity and quantum mechanics, describing an electron (treated as a wave) at a speed close to that of light (for which the theory of relativity is necessary). The equation, however, illustrates something strange: its solutions do not only describe positive energy particles but also negative energy particles.

In principle, in physics, it is not so rare for an equation to demonstrate both a physical, real and acceptable solution; and at the same time an unreal, absurd one which therefore is discarded. To understand this intuitively, we can observe an elementary example: a stationary person starts walking with an acceleration (a) of 1m/s²; how much time (t) does it take to walk through a space (s) of 2 meters?

The equation of motion is:
s = ½ a·t²
if we replace the numbers, we have
2 = ½ · 1 · t²
t = ± 2.
It is clear that the solution that indicates that in -2 seconds the person has travelled a space of 2 meters makes no physical sense and therefore must be discarded.
But Dirac belonged to a group of physicists that believed in the beauty of an equation as proof of its truthfulness and that sometimes mathematics tries to show us a world beyond our mental limits. And he was right. His equation, indeed, predicts the existence of antimatter.

Antimatter: a reality formed by particles identical to those we know, but with specular characteristics of opposite signs. The possibility of a world formed by anti-mountains and anti-oceans, in turn formed by anti-molecules and anti-atoms, in which positively charged antielectrons orbit around negatively charged antinuclei. Our world mirrored with perfect symmetry. Everything works with the same laws we already know: an external observer would not notice anything strange, but in the depths of the anti-world every fundamental constituent is reversed.

It is Carl Anderson, who four years after the publication of Dirac’s equation, experimentally observed the antielectron ̶ known from that moment on as positron (a positive electron). Anderson was studying cosmic rays, i.e. the storm of particles coming from space that engulfs Earth in every moment (and every other celestial body). His instrument of experiment was the cloud chamber: a particular vessel full of vapour surrounded by a magnetic field. If an electrically charged particle passes through the cloud chamber, it leaves a distinct trace in it ̶ like a fingerprint from which its characteristics can be traced. Anderson notes traces identical to those left by an electron, but which curve in the opposite direction. The explanation leaves no ambiguity: it is a positively charged anti-electron. The particle predicted in Dirac’s equation exists.

In 1955, it was the proton’s turn to have its anti-matter counterpart. The antiproton produced by physicists Emilio Segrè and Owen Chamberlain, inside the most powerful particle accelerator at that time ̶ the Bevatron ̶ where protons are accelerated and then collide against a metal target. During the collision, the very high energy that the accelerated protons possess is converted into matter according to Einstein’s law (E=mc²) already mentioned. This matter is formed by negatively charged protons: antiprotons. A few years later, again at the Bevatron, Oreste Piccioni and his group also discovered the antineutron.

Antielectron, antiproton, antineutron: the anti-world we imagined no longer seems so unreal. The basic building blocks of the periodic anti-table are now complete. And, from that moment on, in the particle accelerators, ever heavier antinuclei are produced: anti-deuterium (one antiproton and one antineutron), anti-tritium (one antiproton and two antineutrons), anti-helium 3 (two antiprotons and one antineutron). In 1997, at CERN, anti-hydrogen was generated, the first complete anti-atom: an antielectron orbiting around an antiproton. More recently, in 2011, again at CERN, scientists managed to keep three hundred anti-hydrogen atoms alive for the record time of one thousand seconds.

But, if we have said that nothing would prohibit a world of antimatter, why aren’t the anti-hydrogen atoms stable? What is it that makes it difficult to “keep” an anti-atom “alive”? Again, Dirac’s brilliant mind had a staggering prediction in his equations. When an anti-particle touches the corresponding particle, the two of them annihilate each other, releasing energy in the form of electromagnetic radiation. They disappear into thin air, literally in a flash.

That’s why we don’t see the anti-worlds composed of anti-mountains and anti-oceans. They could theoretically exist somewhere in the universe. Nothing prevents or affects their functioning, mirroring that of our world. However, on Earth it is clear that every particle of antimatter that comes from space or that we produce in our laboratories soon ends up being annihilated, inevitably encountering the matter with which we are surrounded. We too are crossed by antimatter; we do not realize it because the matter that makes up our body is so predominant compared to antimatter which engulfs us that the annihilation of matter/antimatter remains completely negligible.

To “keep” antimatter “alive” in our world we must therefore isolate it and keep it away from matter. To do this, physicists use cylindrical vacuum “traps” at the centre of which the antimatter is concentrated by means of electromagnetic fields. Thanks to these electromagnetic “walls”, antimatter does not touch the edges of the trap and thus remains suspended in the vacuum, protected from annihilation against matter. It is also clear that, in a world of antimatter, it would be our matter that would be in the minority. Therefore, in order to survive, it would need the same expedients that we use here against antimatter. In practice, in a world of antimatter, matter would be considered anti-antimatter.

Furthermore: if it’s true that matter and antimatter particles eliminate each other and become nothing, the opposite is also true. Nothingness, absolute vacuum, the perfect absence of matter and energy, in quantum mechanics acquires new properties.

One of the formulations of Heisenberg’s principle of indeterminacy links energy to time, through the relation
∆E · ∆t ≥ ħ / 4π
which indicates that the margin of error of a system’s energy is just as great as it is small; is the time interval in which it is measured. It therefore follows that it is possible to violate one of the fundamental laws of nature – the law of energy conservation – provided that this is done for a very short time: the greater the violation, the faster it occurs. Therefore, quantum mechanics admits the appearance of energy from nothing on infinitesimally short time scales. This energy can be used to make a particle/anti-particle pair appear from vacuum.

The absolute vaccum, therefore, has been transformed into a perpetual bubbling of quantum fluctuations in which particles and antiparticles are continuously produced from Nothingness, even if on infinitesimal time scales. Although this might seem an abstract artifice, in reality the quantum fluctuations of the vacuum have been experimentally verified. The most formidable experiment is probably that of Hendrik Casimir: two plates placed in a vacuumparallel to each other, a few microns apart, experience an attraction between them because of the pressure of quantum fluctuations in the vacuum surrounding them. The pressure of the vacuum outside the two plates, being higher than that of the vacuum between the two plates, pushes them towards each other.

Moreover, the appearance and annihilation of the particle/antiparticle pairs has also to do with the creation of the universe. The Big Bang theory predicts that originally, in the newly formed universe, matter and antimatter existed only as particle/antiparticle pairs. Each new particle was born coupled to its anti-particle and later disappeared into nothingness, disintegrating with it, in an incessant and tumultuous primordial stirring. If things had continued in this way, today there would be an equal amount of matter and antimatter, whose net balance would be zero. Yet all our observations of the universe show an abundant predominance of matter over antimatter, thus allowing the formation of the galaxies we know. Evidently, a break in symmetry between matter and antimatter occurred at a certain moment, allowing a tiny portion of matter to survive at the expense of antimatter (about one particle per billion). We are part of that tiny portion. But the cause of the asymmetry that allowed us to be here still remains a mystery.