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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.

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.

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.

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.

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

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.

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.

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 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 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.

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

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

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 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.

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.

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.

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.

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

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

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

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.

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!

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.