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The mathematics of quantum theory associates each quantum object with a wavefunction that appears in the Schrödinger equation and gives the probability of finding it in any given state.

Quantum mechanics is a probabilistic theory: it does not give definite answers, but only the probability that an experiment will come up with a particular answer. This was the source of Einstein’s objection that God “does not play dice” with the universe.

We used to believe light was a wave, then we discovered it had the properties of a particle that we call a photon. Now we know it, like all elementary quantum objects, is both a wave and a particle!

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.

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

A new and growing field that explores whether many biological processes depend on uniquely quantum processes to work. Under particular scrutiny at the moment are photosynthesis, smell and the navigation of migratory birds.

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.

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

Some of the strangest characteristics of quantum theory can be demonstrated by firing a photon into an interferometer: the device’s output is a pattern that can only be explained by the photon passing simultaneously through two widely-separated slits.

This is a narrow constriction in a ring of superconductor. Current can only move around the ring because of quantum laws; the apparatus provides a neat way to investigate the properties of quantum mechanics and is a technology to build qubits for quantum computers.

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.

Some people believe this changes everything in the quantum world, even bringing things into existence.

At extremely low temperatures, quantum rules mean that atoms can come together and behave as if they are one giant super-atom.

At CERN in Geneva, Switzerland, this machine is smashing apart particles in order to discover their constituent parts and the quantum laws that govern their behaviour.

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.

The atoms of a radioactive substance break apart, emitting particles. It is impossible to predict when the next particle will be emitted as it happens at random. All we can do is give the probability that any particular atom will have decayed by a given time.

In 1923 Arthur Compton shone X-rays onto a block of graphite and found that they bounced off with their energy reduced exactly as would be expected if they were composed of particles colliding with electrons in the graphite. This was the first indication of radiation’s particle-like nature.

To many researchers, the universe behaves like a gigantic quantum computer that is busy processing all the information it contains.

One of the most famous ideas in science, this declares that it is impossible to know all the physical attributes of a quantum particle or system simultaneously.

In quantum experiments, these are the names traditionally given to the people transmitting and receiving information. In quantum cryptography, an eavesdropper called Eve tries to intercept the information.

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

When two quantum objects interact, the information they contain becomes shared. This can result in a kind of link between them, where an action performed on one will affect the outcome of an action performed on the other. This “entanglement” applies even if the two particles are half a universe apart.