How Antimatter Saves Lives

by Nicholas Mee on February 27, 2022

There is a YouTube video to accompany this blog article on The Cosmic Mystery Tour channel. (Please don’t forget to click the subscribe button. Subscribing is free.)


Everyone has heard of antimatter – it has long played a role in science fiction – you can imagine Dr McCoy in Star Trek probing his patients with antimatter beams, perhaps. Well, you might be surprised to know that antimatter is already routinely used in this way – possibly even in your local hospital. First, I will say a little about what antimatter is and how it was discovered.

Paul Dirac was an English theoretical physicist, famous for his absolutely logical approach to the world. He was renowned for never making an utterance unless it was strictly necessary. In 1928 Dirac took the first steps towards uniting the two great theories of the early twentieth century—relativity and quantum mechanics. He devised a wave equation that would describe the behaviour of electrons even when travelling at close to the speed of light. This equation is known as the Dirac equation.

The great theoretical physicist Paul Dirac. (There seems to be an uncharacteristic mistake on the blackboard.)

Dirac soon realised his equation had a very curious feature. It only seemed to work consistently if the electron had a mirror image counterpart, a particle with the same mass as an electron, but opposite electric charge. So, whereas the electron has a negative electric charge, this mirror particle would have a positive electric charge. At the time the only known fundamental particles were the electron, the proton and the photon—the fundamental constituent of light—so the prediction of a new particle was a really big deal.

Cosmic Rays

The first track of a positron published by Carl Anderson in 1932.

The puzzle was resolved just four years later in 1932. Carl Anderson was studying the tracks left by particles produced in collisions between high-energy cosmic rays arriving from deep space and atoms in the Earth’s atmosphere. Anderson spotted particles that looked similar to electrons, but in the magnetic field of his cloud chamber they spiralled in the opposite direction, so they had to be positively charged. We know these particles as positrons, which is short for positive electrons. The positron is the antiparticle of the electron.

Dirac’s prediction of the positron from the quirks of his equation is one of the most amazing insights in the history of theoretical physics, and his reasoning applies equally well to other matter particles. For each such particle there is a corresponding antiparticle whose existence is now well established. We have antiprotons, antineutrons, antiquarks, antimuons, antineutrinos and so on. When a particle meets its antiparticle they mutually annihilate.

It is believed that in the early universe almost equal quantities of matter and antimatter formed. Particles soon met up with their counterparts and disappeared in a blast of radiation, leaving behind the small surplus of matter particles from which the visible universe is composed. The reason for this small excess of matter over antimatter is still not fully understood. But without it we would not be here.

What Has Antimatter Ever Done for Us?

This is all rather abstruse, the everyday food for theoretical physicists musing on the meaning of it all. But, as Monty Python might have said, what has antimatter ever done for us?

Artist’s conception of an interstellar rocket with an antimatter propulsion system. Credit: NASA/MSFC.

Well, if we ever want to visit the stars antimatter propulsion may be the only feasible way of getting there, and the possibility of such propulsion systems has been considered by NASA. A space vehicle whose thrust was generated through the mutual annihilation of protons and antiprotons might achieve 40% of the speed of light. There are, however, a few challenges that remain to be overcome. The biggest being the supply of antiprotons. Antiparticles such as antiprotons are routinely created in particle physics laboratories such as CERN and Fermilab. But so far the total production may be measured in nanograms, which would be about enough to boil a kettle. Nonetheless, this hasn’t stopped the space artists from dreaming.

Back in the Real World

Back in the real world there is a very important technology that makes good use of antimatter. If you have ever had a brain scan you may well have benefited from it. It is known as PET (Positron Emission Tomography) and the way it works is quite remarkable.

PET scanning utilises a radioactive nucleus that undergoes positive beta decay, a process in which a proton transforms into a neutron with the emission of a positron and a neutrino. The neutrino disappears without a trace, but the positron proves to be very useful. The most suitable nucleus for this purpose is fluorine-18. It is composed of nine protons and nine neutrons, and converts into a stable oxygen-18 nucleus composed of eight protons and ten neutrons when it undergoes beta decay.

The positron emitted by a decaying fluorine-18 nucleus meets an electron almost immediately and they mutually annihilate to produce two gamma ray photons. This is electromagnetic radiation, just like visible light, but with much greater energy. Whereas the energy of a photon of blue light is about 3 eV (electron Volts), the gamma rays produced by electron-positron annihilation carry 511 keV, over 100,000 times as much. 

A patient having a PET scan.

Before a PET scan fluorine-18 must be delivered to the target area of the patient’s body. This is usually achieved by injecting a solution of an appropriate fluorine-18 containing compound. The patient then lies within a scanner that detects the gamma rays emitted by electron-positron annihilations. It is like having an X-ray, but with the gamma rays arising from within the body.

The most widely used delivery compound has the fancy name fluorodeoxyglucose (FDG), which simply means that one of the oxygen atoms in a glucose molecule is replaced with a fluorine atom, and for a PET scan this fluorine atom must be the radioactive fluorine-18 rather than the stable fluorine-19. FDG is chemically similar to ordinary glucose so it is transported around the body to organs that require large amounts of energy such as the brain and kidneys, but also to rapidly multiplying cancerous cells. The FDG is not easily metabolized by the body, so it remains within those cells requiring glucose until the fluorine-18 decays, at which point the fluorine atom is converted into an oxygen atom and the FDG becomes normal glucose. In the mean time the gamma rays produced following the decay of fluorine-18 reveal the sites within the body where glucose is being consumed.

The half-life of fluorine-18 is 110 minutes, so during every 110 minute period half the remaining nuclei will decay. Within a day or two the patient will be free of fluorine-18, which is great as we don’t want people walking around emitting too many gamma rays. But this means that fluorine-18 must be made on site using a cyclotron or other particle accelerator. It is a rather surprising fact that almost all the particle accelerators in the world are now found in hospitals.

Whole-body PET scan using FDG labelled with fluorine-18. The brain and kidneys can be seen, and radioactive urine from the breakdown of FDG is visible in the bladder. The scan shows a large tumour mass in the liver. Credit: Jens Maus.

About an hour after being injected with the FDG solution, the patient lies within a scanner for about thirty minutes. The scanner detects the pairs of gamma rays emitted in the electron-positron annihilations and gradually builds up a picture of the inside of the patient’s body. The gamma rays reveal the sites within the body where glucose is being consumed. It is like having an X-ray, but with the gamma rays arising from within the body.

PET scans are complimentary to other types of medical scan, such as CAT scans which reveal structural or anatomical information about the body and its tissues. PET scans reveal functional information. They provide information about the consumption of glucose in various parts of the body. Because cancer cells consume more glucose than normal tissue they show up as bright spots in a PET scan. So it is possible to locate very small tumours before they would show up with other types of scan. PET scans can also reveal brain abnormalities such as Alzheimer’s disease and other forms of dementia.

What about the risks? The half-life of fluorine-18 is 110 minutes, which is long enough to perform the imaging, but not too long. Within a few hours the radioactive tracer has completely disappeared from the patient’s body. The radiation dose received by the patient is equivalent to two to three years of normal background radiation or about what you would receive due to cosmic rays on 25 long-distance flights. The benefits of the scan far outweigh the low risk due this radiation dose.



Further Information

There is more about Dirac and the discovery of the positron in my book Higgs Force: Cosmic Symmetry Shattered.

There is more about antimatter propulsion system at the following link: Antimatter Propulsion

Snowflakes, Symmetry and String Theory

by Nicholas Mee on February 12, 2022

There is a YouTube video to accompany this blog article on The Cosmic Mystery Tour channel. (Please don’t forget to click the subscribe button. Subscribing is free.)


This video is about the great German astronomer Johannes Kepler who was a pivotal figure in the birth of science. Kepler is regarded as the father of modern astronomy. He was a devout and profoundly spiritual man who had a lifelong drive to understand the structure of Creation. Kepler believed that geometry and symmetry are built into the fundamental architecture of the universe. Many of his ideas are as relevant today as they were 400 years ago. Kepler’s intuition that the universe has a geometrical blueprint has proved to be very fruitful and remains at the heart of physics even today.

Science was in its infancy in Kepler’s time and Kepler’s books are a mixture of deep and valuable insights mingled with ideas that today seem fanciful and very strange indeed. But in many ways Kepler was the ideal scientist. He never hid his mistakes and modestly discussed all the blind alleys he explored before reaching his final conclusions.

Kepler is most famous for his laws of planetary motion. He deduced that the orbit of each planet around the Sun is shaped like an ellipse, and he found rules for how fast the planets travel around their orbits. These advances in astronomy laid the foundation for the Scientific Revolution that came to fruition with the work of Isaac Newton. Kepler also wrote the first modern treatise on the science of optics and was the first to understand how the lens of the eye focuses an image on the retina.

In 1611 Kepler was invited to the New Year celebrations of his friend Johannes Mathaeus Wacker von Wackenfels, privy councillor to Rudolf II, the Holy Roman Emperor. Kepler later recalled, while musing over a suitable New Year’s gift for his friend,

‘by happy chance water vapour was condensed by the cold into snow and specks of down fell here and there on my coat, all with six corners and feathered rays. Here was something smaller than any drop yet with a pattern. It was the ideal New Year’s gift, the very thing for a mathematician to give since it comes down from heaven and looks like a star.’

Unable to preserve a delicate and beautiful snow crystal as a present, Kepler decided to write a little booklet about the snowflake and its symmetry in honour of his friend. This booklet is called De Niva Sexangular – The Six-cornered Snowflake.

The Six-Cornered Snowflake

Kepler realised that although the exact shape of each snow crystal is different they all display the same hexagonal symmetry, and it was the origin of this symmetry that intrigued him. In the booklet he looked for clues in the geometrical structure of other familiar symmetrical objects such as rock crystals, the seed cases of pomegranates and bees’ honeycombs. Kepler concluded that the symmetrical shape of snowflakes and other crystals is due to the regular arrangement of the atoms from which they are formed. This was almost 300 years before scientists had even established the existence of atoms. But Kepler’s remarkable insight has proved to be fundamentally correct.

Kepler went on to consider the most compact way to pack collections of equal-sized spheres. In particular, he asked what is the maximum number of such spheres that will fit around a central sphere? Mathematicians refer to this number as the kissing number. It is easy to answer the equivalent question in two dimensions. With seven coins of the same denomination, we can see that six will fit exactly around the seventh, so the maximum kissing number is 6. Coins or circles can be arranged in this way to cover the entire plane. This is the densest possible packing of circles in a plane.

A space-filling honeycomb of octahedra and cuboctahedra.

Kepler believed that the spheres in the densest packings in three-dimensional space have a kissing number of 12. Such packings include those traditionally used by grocers to stack apples and bombardiers to stack cannonballs. This is also how atoms are packed together in many metals and other crystalline solids. So it is rather surprising that a definitive mathematical proof that these packings are indeed the densest did not arrive until 1998 when American mathematician Thomas Hales proved Kepler’s conjecture, as it is known.

Kepler attempted to understand the structure of the universe in terms of elegant mathematics and regular geometrical figures. Kepler’s belief in divine symmetry has proved to be a valuable insight into the laws of the universe. Everywhere that physicists have looked they see symmetry in the structure of physics, from Einstein’s theories of relativity to the standard model which is our best theory of particle physics and the structure of matter. But, whereas the symmetry of a snowflake is obvious to the eye, often these deeper symmetries can only be expressed in terms of abstract higher-dimensional geometries.

And this brings us back to Kepler’s sphere-packing problem. In 2016 the Ukrainian mathematician Maryna Viazovska proved that the E8 lattice gives the densest packing of spheres in 8-dimensional space. Life in eight dimensions can be quite cosy – this packing gives the spheres a kissing number of 240. Viazovska’s proof was then extended to show that the Leech lattice gives the densest possible packing in 24-dimensional space, where the spheres have a kissing number of 196,560.

Although you might not have heard of E8, it turns up in string theory, which is the only serious candidate that we have for an ultimate theory of physics. String theorists speculate that the symmetry group E8 might provide the ultimate description of the fundamental particles and the forces that act on them.

A string wrapped around a torus.

String theory is a theory in which each type of fundamental particle is a different sort of vibration of one fundamental entity – the string – so when the string vibrates in one way we might see it as an electron or if it vibrates in another way we might see it as a quark or a photon. A curious feature of string theory is that it only works in 10-dimensional spacetime. To describe the physics of the real universe string theorists assume that six of the nine spatial dimensions are curled up so tightly we are not aware of them. Even so, these extra dimensions might determine the properties of the particles and forces we see in particle accelerator experiments. According to string theorists the six extra dimensions form a shape known as a Calabi-Yau manifold. This animation is a three-dimensional projection of one of these shapes known as a quintic hypersurface.

Projection of a six-dimensional Calabi-Yau manifold known as a quintic hypersurface.

String theory remains an intriguing but unproven approach to physics so this is all highly speculative. As yet there is no experimental evidence to connect string theory to the structure of the real universe so no one knows whether it is in the same class as some of the brilliant insights of Johannes Kepler or whether it will eventually be dismissed just like some of his other curious and wacky ideas.

The Twilight Zone

January 18, 2022

Often black holes are portrayed as the most mysterious objects in the universe. Black holes are certainly bizarre and astonishing. Even Einstein thought that such outlandish objects could not really exist. But I am going to argue that rather than being totally mysterious, black holes are actually the most well-understood objects in the universe.

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How Fractals Were Invented Amidst the Horror of War!

January 11, 2022

It is rather surprising that the idea of fractals can be traced back to the musings of a seriously injured soldier amidst the horrors of the First World War. That soldier was Gaston Julia who was born in French Algeria in 1893. In his teens he won a scholarship to study in Paris, but within months of completing his maths degree war broke out and he was conscripted into the French army the following day. Early in 1915 Julia suffered a terrible wound during a German attack.

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How Big is a Black Hole?

January 10, 2022

A sufficiently massive star may collapse under its own gravity at the end of its life until it becomes so dense that nothing can escape its gravitational attraction. It has become a black hole. This is the ultimate collapsed body. The black hole does not have a solid surface. It is simply a spherical region of space from which nothing can escape – not even a ray of light – hence the name. The sphere that defines the boundary of the black hole is known as the event horizon of the black hole.

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The World’s First Nuclear Reactor

November 22, 2020

The investigations by the French authorities in 1972 led to a uranium mine in the Central African country of Gabon, then a French overseas territory. The reason for the missing uranium-235 turned out to be quite incredible. Fermi’s Chicago nuclear reactor had been foreshadowed 1.7 billion years earlier by a natural nuclear reactor in a uranium deposit at Oklo near Franceville. Detailed analysis of the unusual nuclear isotopes found in the deposit has enabled physicists to construct a picture of what happened there long long ago.

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Twenty Thousand Leagues Under the Seas

November 21, 2020

Walt Disney played his part in selling Rickover’s revolutionary submarine to the American public. In 1954 Disney released its steampunk blockbuster 20,000 Leagues Under the Sea based on the Jules Verne masterpiece. It was the most expensive Hollywood film up to that date and starred James Mason as the dark anti-hero Captain Nemo. Although the film is set in the nineteenth century, it suggests that Nautilus is powered by a new and mysterious source of energy discovered by Nemo. The nature of this energy would be all too obvious to the cinema-goers of the 1950s who were very familiar with the nuclear ambitions of the United States.

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The Age of Rock

October 31, 2020

Rutherford suggested that the amount of helium trapped within a rock would reveal how much uranium has decayed since the rock formed. And by comparing the amount that has decayed to the amount that remains the age of the rock could be determined. For instance, if half the uranium has decayed then the rock’s age equals the half-life of uranium, which can be measured in the laboratory. 

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Pregnant Camels Often Sit Down Carefully

October 30, 2020

After several months of arduous work Holmes could assign an age to the rock—370 million years. This is considered to be the first accurate radiometric dating. (It agrees with modern results for the Devonian, according to which this period lasted from 419-359 million years ago.) Not bad for an undergraduate project! Holmes was just twenty years old and would graduate later that year. His project must rank as one of the most remarkable ever completed by an undergraduate.

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Rutherford’s Protons and Prout’s Protyles

October 12, 2020

Aston’s Whole Number Rule resurrected Prout’s hypothesis of a century earlier. But now the picture was looking decidedly clearer. In 1917 Rutherford had discovered one of the constituents of the atomic nucleus, a positively charged particle identical to the nucleus of a hydrogen atom. In 1920, and partly as a tribute to Prout, he named this particle the proton, taking the stem from Prout’s fundamental unit—the protyle. Rutherford speculated that the nucleus might have a second electrically neutral constituent with a similar mass to the proton. He named it the neutron.

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