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

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

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.

Some of the strangest characteristics of quantum theory can be demonstrated by firing a photon into an interferometer

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

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.

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!

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!

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.

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.

Even at absolute zero, the lowest temperature possible, nothing has zero energy. In these conditions, particles and fields are in their lowest energy state, with an energy proportional to Planck’s constant.

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.

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.

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.

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.

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

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

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.

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.

In 1801, Thomas Young proved light was a wave, and overthrew Newton’s idea that light was a “corpuscle”.

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.

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.