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

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

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 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.

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.

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

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.

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

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

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

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

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 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.

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 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.

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.

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.

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

Researchers are harnessing the intricacies of quantum mechanics to develop powerful quantum sensors. These sensors could open up a wide range of applications.

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.

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.

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.

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.

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!

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 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.

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

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.

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.

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.

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.

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”.

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.

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.

As the world makes more advances in quantum science and technologies, it is time to think about how it will impact lives and how society should respond. This mini-documentary by the Quantum Daily is a good starting point to think about these ethical issues.

Is time travel really possible? This article looks at what relativity and quantum mechanics has to say.

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

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.

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 Key Distribution (QKD) is a way to create secure cryptographic keys, allowing for more secure communication.

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.

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 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.

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.

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

Some researchers think the best way to explain the strange characteristics of the quantum world is to allow that each quantum event creates a new universe.

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.

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.

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!

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

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