Albert Einstein decided quantum theory couldn’t be right because its reliance on probability means everything is a result of chance. “God doesn’t play dice with the world,” he said.

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.

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.

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.

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.

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

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.

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.

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!

Our most successful theories of cosmology suggest that our universe is one of many universes that bubble off from one another. It’s not clear whether it will ever be possible to detect these other universes.

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.

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.

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.

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.

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

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.

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.

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

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.

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 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.

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!