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

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.

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.

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.

The rules of the quantum world mean that we can process information much faster than is possible using the computers we use now. This column from Quanta Magazine ​delves into the fundamental physics behind quantum computing.

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.

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.

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

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.

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

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.

The arrow of time is “irreversible”—time goes forward. On microscopic quantum scales, this seems less certain. A recent experiment shows that the forward pointing of the arrow of time remains a fundamental rule for quantum measurements.

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

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.

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

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.

The feature of a quantum system whereby it exists in several separate quantum states at the same time.

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.

Niels Bohr, one of the founding fathers of quantum physics, said there is no such thing as objective reality. All we can talk about, he said, is the results of measurements we make.

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.

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.

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 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.