Here is a distillation of nine key ideas from my recently published book: ‘Matter – A Very Short Introduction‘ (Oxford University Press, published in 2018).

In my book, I have focussed on key concepts using hardly any equations. These include the properties of atoms, the different forms of ordinary matter, how matter is defined as mass and energy, weird quantum matter, antimatter, fundamental particles, the origin of the elements, and mysterious dark matter and dark energy.

#### 1. What is matter?

Matter is the stuff from which you and I and all the things in the world around you are made. If you had the most powerful microscope imaginable you could look inside your body and see that you are made of atoms. Inside every atom is a tiny nucleus and orbiting the nucleus is a cloud of electrons. The nucleus is made out of protons and neutrons, and by zooming in on a nuclear particle you would find that inside it there are even smaller particles, quarks. Quarks are the smallest particles that we have seen, and lie at the limit of resolution of the most powerful microscopes of matter. As far as we know, electrons and quarks are not made from anything smaller and so they are called fundamental particles.

#### 2. Atoms

Take an apple and chop it up into smaller and smaller pieces.  Eventually a point is reached where no more chopping is possible, revealing the ultimate graininess of matter, atoms. The word atom comes from the Greek word atomos, meaning indivisible. This prescient idea that the world is made of atoms was conceived of 2500 years ago by the Ancient Greek philosophers Leucippus and Democritus. Their conjecture was remarkable because atoms are too small to be seen with the unaided eye. The reality of atoms was only finally accepted in 1905 when Albert Einstein analysed the constant jiggling of tiny pollen grains suspended in water, being randomly battered by hordes of smaller unseen particles, the molecules. This jiggling about is called Brownian motion.

#### 3. Different forms of matter

When large numbers of of atoms and molecules aggregate to form a piece of matter, they assemble into the lowest energy state available. The three familiar states of matter, solid, liquid and gas, result from the competition between the attractive forces between particles, and their thermal motion which pushes them apart. Temperature has a central role in controlling when, for example, water molecules join together to form ice or disperse as a gas, steam. At very high temperatures, electrons are knocked off atoms, and a gas transforms to the so-called fourth state of matter, an electrically conducting plasma. Plasmas occur naturally in the stars, lightning, and in high energy astronomical bodies.

#### 4. Defining matter

What are the key defining properties of matter? Isaac Newton identified one as the inertial mass. This is a measure of the resistance (or inertia) that a body feels to being accelerated. An advanced view of matter emerged from  Einstein’s special theory of relativity; there,  space and time and merge into a single entity: spacetime, which is deformable, in the sense that different observers moving at high uniform speeds see lengths as being contracted and clocks running slowly. Mass and energy turn out to be the same thing, only expressed in different units. Large scale concentrations of rest mass and energy in the universe in the form of stars, galaxies, and black holes, exert gravitational influences which warp spacetime and bend light rays. Mass curves space, and the curvature of space in turn tells bodies how to move. The gravity that binds the Moon in its orbit is a result of the ‘dent’ in spacetime made by the mass of the Earth.

#### 5. Quantum particles

On human size scales, we imagine lumps of matter moving through space along sharp classically defined trajectories. This Newtonian conception is more than adequate to get a man to the Moon and back. However on microscopic atomic scales, particles reveal their quantum wave nature, enabling them to spread out in space as fuzzy entities. In the quantum world one cannot speak of particles following sharp single trajectories, but only about the probabilities of particles following various motions and paths. Quantum theory describes nature very accurately and particles behave in a mind-boggling manner. They can for example pass through classically impenetrable barriers (quantum tunnelling), and occupy many states simultaneously. Quantum tunnelling occurs in the energy producing reactions in the heart of the Sun. Without this process we would not exist. All ordinary matter is made from two basic types of particles: matter particles are fermions (for example electrons), and force-carrying particles are bosons (for example the photons of light).

#### 6. Quantum matter

While microscopic particles are governed by quantum laws, aggregates of particles can sometimes reveal large-scale quantum behaviour. In a coherent quantum fluid  billions of particles move together as a single entity, rather than moving around haphazardly as individuals. A metal contains vast numbers of free electrons which form a quantum fluid at ordinary temperatures. At very low temperatures some metals become superconductors and conduct electricity without any electrical resistance. There are also exotic atomic fluids, such as superfluid helium, in which the atoms move frictionlessly through extremely fine tubes, and appear to defy gravity by climbing out of a vessel.

#### 7. Fundamental particles

In the 1920s, quantum theory was developed to describe particles moving at near-light speeds, and the theory predicted antimatter. The first antimatter particle discovered was the positron (a positively charged electron). When a positron encounters an electron, the two particles mutually annihilate each other, producing a burst of light. All the rest mass energy is converted to radiation energy. As quantum theory developed further, all of space was viewed as being filled by a number of quantum fields. Elementary particles such as electrons or quarks emerge from an ocean of quantum wave energy, as fluctuations in the underlying fields. One of these is the Higgs field which interacts with elementary particles to confer upon them their intrinsic masses. Most of the mass of ordinary matter (this mass resides in atomic nuclei) is associated with the quark force fields operating inside the nuclear particles.

#### 8. Where do the elements come from?

The 92 naturally occurring chemical elements come from three sources. The lightest, hydrogen and helium, were made a short time after the Big Bang, 13.8 billion years ago. The middle weight elements, up to iron, were (and still are) being made inside the cores of burning stars by nuclear processes which release fusion energy. But to build elements heavier than iron, energy input is needed. This energy comes from the explosions of massive stars, supernovae; there, involving particles accelerated to extremely high energies. The remains of a supernova can contain an exotic, gravitationally collapsed object: a neutron star in which matter is squeezed so tightly that a teaspoon of would weigh as much as Mount Everest. All the  atoms in your body and in the solar system were made in the lives and deaths of stars, billions of years ago.

#### 9. Dark matter and dark energy

The planets move in roughly circular orbits in the attractive gravitational field of the Sun, in which the outward centrifugal force of a planet is balanced by the inward force of gravity. Because the Sun’s gravity gets weaker the further out a planet is, orbital speeds in the solar system decrease with distance. This motion can be used to ‘weigh’ the Sun. The same method has been used to weigh spinning galaxies, containing trillions of stars, by measuring the rotational stellar speeds. However, it turns out that the speeds  do not decrease with distance from the centre, but are constant. This indicated that the masses of galaxies are much larger than we had previously thought, and could not be accounted for by the known masses of the stars and gas.  Galaxies therefore contain extra invisible ‘missing mass’, or ‘dark matter‘, in a mysterious form, one which exerts gravity but does not emit or absorb light. Searches for dark matter, either in the form of hypothetical subatomic particle or as other larger masses, have so far drawn a blank.

Even more enigmatic is dark energy. In the 1990s, the light from exploding stars (supernovae) in distant galaxies was used to measure the expansion of the universe. This showed that the galaxies  are further away than we had thought. The space, through which the light from the supernovae had travelled, had been stretched more than expected – the expansion of the universe is accelerating.  Dark energy is the name for whatever is believed to be causing this acceleration. Whatever dark matter and dark energy are (and we don’t know), they dominate the cosmos. Normal familiar matter, as discussed above, account for only 5% of everything there is. The remaining 95% is a complete mystery!