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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.

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.

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.

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

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

Some of the strangest characteristics of quantum theory can be demonstrated by firing a photon into an interferometer: the device’s output is a pattern that can only be explained by the photon passing simultaneously through two widely-separated slits.

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.

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.

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

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.

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.

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.

The atoms of a radioactive substance break apart, emitting particles. It is impossible to predict when the next particle will be emitted as it happens at random. All we can do is give the probability that any particular atom will have decayed by a given time.

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

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.

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 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.

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

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!

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.

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.

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