by Marcus Chown
‘Think binary,’ said the novelist John Updike. ‘When matter meets antimatter, both vanish, into pure energy. But both existed; I mean, there was a condition we’ll call “existence”. Think of one and minus one. Together they add up to zero, nothing, nada, niente, right? Picture them together, then picture them separating – peeling apart … Now you have something, you have two somethings, where once you had nothing.’
The Dirac equation, as Updike emphasised, unveiled a world of matter and antimatter created out of absolutely nothing. There was a certain pleasing symmetry in the fact that the equation that did this had itself been conjured out of nothing by Dirac. Today it is universally admired by physicists. ‘Of all the equations of physics, perhaps the most “magical” is the Dirac equation,’ says American physicist and Nobel Prize winner Frank Wilczek. ‘It is the most freely invented, the least conditioned by experiment, the one with the strangest and most startling consequences.’22
Dirac is considered pre-eminent among the magicians of science. His equation is inscribed on a square tablet commemorating the physicist on the floor of London’s Westminster Abbey.
It is not just the beauty of the equation that is universally admired, but the sheer intellectual bravery of Dirac in formulating it. ‘He made a breakthrough, a new method of doing physics,’ said Richard Feynman, another Nobel Prize-winning physicist. ‘He had the courage to simply guess at the form of an equation, the equation we now call the Dirac equation, and to try to interpret it afterwards.’23 Feynman, a man also widely recognised as a magician of physics, was unable to go where Dirac went. ‘I think equation guessing might be the best method to proceed to obtain the laws for the part of physics which is presently unknown,’ he said. But he confessed that it was not his forte. ‘When I was much younger, I tried this equation guessing, and I have seen many students try this, but it is very easy to go off in wildly incorrect and impossible directions.’
As Dirac himself said, ‘I think it’s a peculiarity of myself that I like to play about with equations, just looking for beautiful mathematical relations which maybe don’t have any physical meaning at all. Sometimes they do.’24 Dirac characterised his technique as ‘simply a search for pretty mathematics. It may turn out later that the work does have an application. Then one has had good luck.’25
In the search for ‘pretty mathematics’, Dirac was like an artist, a poet or a novelist, tapping into his unconscious. ‘If you are receptive and humble, mathematics will lead you by the hand,’ he said. ‘Again and again, when I have been at a loss how to proceed, I have just had to wait until I have felt the mathematics lead me by the hand. It has led me along an unexpected path, a path where new vistas open up, a path leading to new territory, where one can set up a base of operations, from which one can survey the surroundings and plan future progress.’26
Dirac was struck by the fact that mathematics so perfectly describes nature. ‘It seems to be one of the fundamental features of nature that fundamental physical laws are described in terms of a mathematical theory of great beauty and power, needing quite a high standard of mathematics for one to understand it,’ he said. ‘You may wonder: Why is nature constructed along these lines? One can only answer that our present knowledge seems to show that nature is so constructed. We simply have to accept it.’ Dirac went on to speculate: ‘One could perhaps describe the situation by saying that God is a mathematician of a very high order, and He used very advanced mathematics in constructing the universe.’27
Dirac never quite gave up on the hole theory, and continued to believe in it until at least the 1970s. It did not bother him in the least that it had been comprehensively trashed by his peers. ‘That’s not a theory,’ scoffed Bohr. The truth was that, although the hole theory made little sense to most people, it gave the same results as a modern theory of the electron and so was a great insight. In the words of Dutch Nobel Prize winner Gerard’t Hooft, it was ‘Genius!’28
As it happens, the hole theory is unnecessary and cannot explain the existence of the antiparticles of subatomic particles known as ‘bosons’, which unlike electrons are able to crowd into any energy state in unlimited numbers. Antimatter, it turns out, is a generic consequence of combining quantum theory and relativity.
In the modern picture of antimatter, the ‘fields’ which permeate all of space are the primary things. The most familiar one is the electromagnetic field, which can create or destroy indivisible chunks, or ‘quanta’, of the field, better known as ‘photons’ of light (think of light being created by a torch or destroyed by being absorbed by a black cat). Another field is the ‘electron field’, which, just as the electromagnetic field can create and destroy quanta of the electromagnetic field, can create and destroy quanta of the electron field: electrons and positrons.
Positrons are not as rare as you may think and are naturally emitted by unstable atomic nuclei. Whereas neutron-rich nuclei can achieve stability by turning a neutron into a proton with the emission of an electron, proton-rich nuclei can achieve the same end by turning a proton into a neutron with the emission of a positron. The ejected positrons do not get far before they meet an electron and are annihilated in a puff of high-energy photons, which is why nobody had spotted them before 1932.
Positron-emitting nuclei, however, have proved enormously important in medical imaging. In positron-emission tomography, or PET scanning, a substance containing positron-emitting nuclei is injected into the body. When positrons meet electrons, they create pairs of oppositely directed photons, which can be detected. Since they point back to the location of each annihilation, they can be used by a computer to create a three-dimensional image of the body.
The discovery of the antiproton had to await the advent of a particle accelerator with sufficient energy to create a particle about two thousand times heavier than a positron. It was finally achieved by the ‘Bevatron’ proton accelerator at the University of California at Berkeley in 1955. A year later came the discovery of the antineutron. And since then, antiparticles of essentially all nature’s fundamental subatomic particles have been discovered.
Creating an antiatom, which consists of a positron orbiting an antiproton rather than an electron circling a proton, is a formidable experimental challenge because both antiparticles, once created, must be slowed down hugely before they can combine. But in 1995, physicists at CERN, the European laboratory for particle physics near Geneva, used the Low Energy Antiproton Ring (LEAR) to slow down rather than accelerate antiprotons. By so doing, they managed to bring positrons and antiprotons together, creating nine antiatoms of hydrogen, which each survived for just forty nanoseconds.
Antimatter has the potential to make the perfect rocket fuel because, when antimatter encounters matter, 100 per cent of its mass-energy is converted into other forms. Pound for pound, it therefore packs the biggest punch of any fuel – one hundred times more than a nuclear fuel of equivalent mass. An antimatter rocket therefore need carry only a minimal quantity of fuel; fuel mass is a serious problem for a rocket since it must be boosted along with the rocket itself.
Despite the fact that antimatter powered the Starship Enterprise on its five-year mission to boldly go where no man has gone before, the creation of a real-life antimatter-fuelled spacecraft is fraught with problems. First, the antimatter needs to be stored in such a way that it does not touch the matter of a rocket, which would risk a catastrophic explosion. This might conceivably be achieved by confining the antimatter in a ‘magnetic bottle’. Secondly, matter–antimatter annihilation always results in the creation of high-energy photons which, rather than flying out the back of the rocket, which is required to push it forwards, would fly away in all directions.
But the biggest problem in creating an antimatter rocket is accumulating enough antimatter in the first place. So far, we have managed to create only a minuscule quantity of antimatter, and this has taken an enormous effort. If it were possible to make enough antimatter to drive a space probe to Alpha Centauri, our nearest star,
a lot more energy would be required to create it in the first place than would be released in its annihilation with matter.
Whether or not antimatter could ever be used for powering an interstellar spacecraft is a minor question. The question of why we live in a matter universe is a deep mystery because all known processes of particle creation, such as pair production, produce equal amounts of matter and antimatter. Dirac said in his Nobel Lecture in Stockholm on 12 December 1933, ‘If we accept the view of complete symmetry between positive and negative electric charge so far as concerns the fundamental laws of Nature, we must regard it rather as an accident that the Earth (and presumably the whole solar system), contains a preponderance of negative electrons and positive protons. It is quite possible that for some of the stars it is the other way about, these stars being built up mainly of positrons and negative protons. In fact, there may be half the stars of each kind. The two kinds of stars would both show exactly the same spectra, and there would be no way of distinguishing them by present astronomical methods.’
As Dirac pointed out, antimatter stars would radiate photons just like stars made of normal matter, but he was wrong to say that if our universe contained domains of antimatter intermixed with matter, it would be impossible to tell. Wherever a region of antimatter came up against one of matter, there would be copious annihilation, and astronomers have observed none of the gamma rays expected from this process.
By rights, there should be no universe of either matter or antimatter, only empty space filled with their annihilation products: photons. A clue to why we find ourselves in a universe made entirely of matter comes from the fact that there are about ten billion photons for every particle of matter in the universe. The implication is that, in the Big Bang, there were ten billion and one particles of matter for every ten billion particles of antimatter. After an orgy of annihilation, all antimatter particles were destroyed, leaving one matter particle for every ten billion photons. The key question is: What was the origin of this matter–antimatter asymmetry? Either the fundamental laws of physics are skewed to favour the creation of matter over antimatter or the destruction of antimatter over matter. Exactly how and why they are skewed remains one of the biggest mysteries in modern cosmology.
Notes
1 The Physicist’s Conception of Nature: Symposium on the Development of the Physicist’s Conception of Nature in the Twentieth Century, edited by Jagdish Mehra (Springer, 1973, p. 271).
2 ‘Paul Dirac: The Purest Soul in Physics’ by Michael Berry (Physics World, 1 February 1998: https://physicsworld.com/a/paul-dirac-the-purest-soul-in-physics/).
3 Robert Andrews Millikan was a controversial scientist, and many accusations have been made against him since his death in 1953: that he was a misogynist, an anti-Semite and that he committed scientific fraud by discarding data that did not fit his hypothesis in the famous oil-drop experiment, in which he measured the charge on the electron. On the first two charges, Millikan was probably a man of his time, with the views to match. And the latter charge may not hold up (‘In Defense of Robert Andrews Millikan’ by David Goodstein (Engineering and Science, vol. 63 (4), p. 30; http://calteches.library.caltech.edu/4014/1/Millikan.pdf)). However, one thing Millikan is guilty of is taking full credit for measuring the charge on the electron. The experiment was carried out with a graduate student, Harvey Fletcher. Two things were discovered: the charge on the electron; and that an oil drop, suspended in mid-air by an electric force field balancing gravity, was buffeted by air molecules – an effect known as ‘Brownian motion’. In order to use a scientific paper as a doctoral thesis, Fletcher needed to be the sole author. Millikan assigned Fletcher the Brownian result and himself the electric charge result, knowing that the latter was the most important. He was right, and while he achieved fame when he won the Nobel Prize, Fletcher was forgotten.
4 ‘Seth Neddermeyer (1907–88)’ interviewed by John Greenberg (California Institute of Technology Archives, 7 May 1984: http://oralhistories.library.caltech.edu/199/1/neddermeyer_oho.pdf).
5 ‘Carl Anderson (1905–91)’ interviewed by Harriett Lyle (California Institute of Technology Archives, 9 January–8 February 1979: http://oralhistories.library.caltech.edu/89/1/oh_anderson_c.pdf).
6 ‘Recollections of 1932–33’ (Engineering and Science, vol. 46 (2), p. 15: http://calteches.library.caltech.edu/3353/1/Recollections.pdf).
7 Nowadays, we know that cosmic rays are high-energy atomic nuclei – mostly hydrogen nuclei – from space. The lower energy particles come from the Sun, and high-energy particles – some of which have energies tens of millions of times higher than anything achievable at accelerators such as the Large Hadron Collider – come from deep space. One extragalactic source, identified in 2018, is the supermassive-black-hole-powered ‘blazar’ galaxy TXS 0506+056 (‘Neutrino Emission from the Direction of the Blazar TXS 0506+056 Prior to the IceCube-170922A Alert’ by the IceCube Collaboration (23 July 2018: https://arxiv.org/pdf/1807.08794.pdf)).
8 ‘Possible Existence of a Neutron’ by James Chadwick (Nature, vol. 129, 27 February 1932, p. 312).
9 It Must Be Beautiful: The Great Equations of Modern Science, edited by Graham Farmelo (Granta Books, London, 2002).
10 The Strangest Man: The Hidden Life of Paul Dirac, Quantum Genius by Graham Farmelo (Faber & Faber, London, 2010).
11 Ibid.
12 An equivalent description of the quantum world, known as ‘matrix mechanics’, was devised by Werner Heisenberg, Max Born and Pascual Jordan, also in 1925.
13 Antimatter by Frank Close (Oxford University Press, Oxford, 2007).
14 The effect was first revealed in 1896 by the Dutch physicist Pieter Zeeman. Electrons in atoms are permitted by the laws of quantum theory to occupy only a discrete set of orbits, each with its own energy. When an electron makes a transition from one energy level to another, it either emits or absorbs a photon of energy equal to the difference in the two levels. However, Zeeman discovered that if a substance such as sodium is placed in a strong magnetic field, the energy of its characteristic photons is no longer well defined. The ‘spectral lines’ they produce in a ‘spectroscope’, rather than being sharp, are blurred. Later, more powerful instruments revealed that the lines are split into two, or more. This was a deep puzzle. As Wolfgang Pauli recorded, ‘A colleague who met me strolling rather aimlessly in the beautiful streets of Copenhagen said to me in a friendly manner, “You look very unhappy”, whereupon I answered fiercely, “How can one look happy when he is thinking about the anomalous Zeeman effect?”’ The splitting of spectral lines, however, was exactly what would be expected if the electron is a tiny magnet that can be aligned in the direction of the magnetic field or against it, the two possibilities having a slightly different energy.
15 Or it may have been early December.
16 ‘The Quantum Theory of the Electron’ by P. A. M. Dirac (Proceedings of the Royal Society A, vol. 177, issue 778, 1 February 1928: http://rspa.royalsocietypublishing.org/content/royprsa/117/778/610.full.pdf).
17 ‘Quantised Singularities in the Electromagnetic Field’ by P. A. M. Dirac (Proceedings of the Royal Society A, vol. 133, issue 821, 1 September 1931).
18 ‘Lectures on Quantum Mechanics’, Princeton University, October 1931.
19 ‘The Standard Model’ by Sheldon Glashow (Inference, 2018: http://inferencereview.com/article/the-standard-model).
20 Life on the Mississippi by Mark Twain (1883).
21 Actually, the tracks of positrons had been seen but not recognised as early as 6 May 1929. In Leningrad, Russian physicist Dimitry Skobeltzyn had been using a cloud chamber to investigate high-energy ‘gamma rays’, but they not only ejected electrons from atoms in the gas of his chamber but from the chamber walls. To get rid of the latter, which interfered with his measurements, he had the idea of using a magnetic field to sweep them away; it was then that he saw the inexplicable tracks of electrons curving the wrong way.
22 It Must Be Beautiful, edited by Graham Farmelo (Granta Bo
oks, London, 2002).
23 ‘The Reason for Antiparticles’ by Richard Feynman (Dirac Memorial Lecture, University of Cambridge, 1986).
24 Interview with Paul Dirac by Thomas Kuhn at Dirac’s home, Cambridge, 7 May 1963.
25 ‘Pretty Mathematics’ by P. A. M. Dirac (International Journal of Theoretical Physics, vol. 21, issue 8–9, August 1982, p. 603).
26 The Strangest Man: The Hidden Life of Paul Dirac, Mystic of the Atom by Graham Farmelo (Faber & Faber, London, 2009, p. 435).
27 ‘The Evolution of the Physicist’s Picture of Nature’ by Paul Dirac (Scientific American, vol. 208, May 1963, p. 45).
28 From a conversation between Gerard’t Hooft and Dirac biographer Graham Farmelo, told to me by Farmelo.
* Arthur Compton was an American physicist who won the 1927 Nobel Prize in Physics for demonstrating that high-energy light bounces off electrons exactly as if it were made of tiny bullets. It was proof of Einstein’s 1905 claim that light travels through space as a stream of particles, or ‘photons’.
† Actually, this is not quite true. Although special relativity predicts that someone moving relative to you should appear to shrink in the direction of their motion, this is not what you would see because of another effect at play. Light from more distant parts of the person takes longer to reach you than from closer parts, which causes them to appear to rotate. So if their face is pointing towards you, you will see some of the back of their head. This peculiar effect is known as ‘relativistic aberration’ or ‘relativistic beaming’.
