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.

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.

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.

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.

These elementary particles hold together the quarks that lie at the heart of matter.

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.

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

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

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

Quantum states, which represent the state of affairs of a quantum system, change by a different set of rules than classical states.

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

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.

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!

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

Many researchers working in quantum theory believe that information is the most fundamental building block of reality.

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.

Quantum tricks allow a particle to be transported from one location to another without passing through the intervening space – or that’s how it appears. The reality is that the process is more like faxing, where the information held by one particle is written onto a distant particle.

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

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!

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.

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.

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 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.

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.