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This is one of the universal constants of nature, and relates the energy of a single quantum of radiation to its frequency. It is central to quantum theory and appears in many important formulae, including the Schrödinger Equation.

One quantum bit of information is known as a qubit (pronounced Q-bit). The ability of quantum particles to exist in many different states at once means a single quantum object can represent multiple qubits at once, opening up the possibility of extremely fast information processing.

The arrow of time is “irreversible”—time goes forward. This doesn’t seem to follow the laws of physics which work the same going forward or backward in time. Some physicists argue that there is a more fundamental quantum source for the arrow of time.

Our best theory of gravity no longer belongs to Isaac Newton. It’s Einstein’s General Theory of Relativity. There’s just one problem: it is incompatible with quantum theory. The effort to tie the two together provides the greatest challenge to physics in the 21st century.

One school of thought says that the strangeness of quantum theory can be put down to a lack of information; if we could find the “hidden variables” the mysteries would all go away.

Since the predictions of quantum theory have been right in every experiment ever done, many researchers think it is the best guide we have to the nature of reality. Unfortunately, that still leaves room for plenty of ideas about what reality really is!

Quantum theory’s uncertainty principle says that since not even empty space can have zero energy, the universe is fizzing with particle-antiparticle pairs that pop in and out of existence. These “virtual” particles are the source of Hawking radiation.

In 1964, John Bell came up with a way of testing whether quantum theory was a true reflection of reality. In 1982, the results came in – and the world has never been the same since!

This is the basic building block of matter that creates the world of chemical elements – although it is made up of more fundamental particles.

People have been hiding information in messages for millennia, but the quantum world provides a whole new way to do it.

Unless it is carefully isolated, a quantum system will “leak” information into its surroundings. This can destroy delicate states such as superposition and entanglement.

Unpredictability lies at the heart of quantum mechanics. It bothered Einstein, but it also bothers the Dalai Lama.

It is possible to describe an atom, an electron, or a photon as either a wave or a particle. In reality, they are both: a wave and a particle.

In 1975, Stephen Hawking showed that the principles of quantum mechanics would mean that a black hole emits a slow stream of particles and would eventually evaporate.

This is the central equation of quantum theory, and describes how any quantum system will behave, and how its observable qualities are likely to manifest in an experiment.

The rules of the quantum world mean that we can process information much faster than is possible using the computers we use now.

When two quantum particles are entangled, it can also be said they are “nonlocal”: their physical proximity does not affect the way their quantum states are linked.

A hypothetical experiment in which a cat kept in a closed box can be alive and dead at the same time – as long as nobody lifts the lid to take a look.

Quantum physics is the study of nature at the very small. Mathematics is one language used to formalise or describe quantum phenomena.

Ideas at the heart of quantum theory, to do with randomness and the character of the molecules that make up the physical matter of our brains, lead some researchers to suggest humans can’t have free will.

This happens when quantum objects “borrow” energy in order to bypass an obstacle such as a gap in an electrical circuit. It is possible thanks to the uncertainty principle, and enables quantum particles to do things other particles can’t.

These are particles that carry a quantum property called strangeness. Some fundamental particles have the property known as charm!

Quantum objects can exist in two or more states at once: an electron in superposition, for example, can simultaneously move clockwise and anticlockwise around a ring-shaped conductor.

The most precise clocks we have are atomic clocks which are powered by quantum mechanics. Besides keeping time, they can also let your smartphone know where you are.