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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.

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.

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.

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.

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.

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.

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

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

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.

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.

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.

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.

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.

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 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.

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 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.

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.

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.

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!