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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.

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.

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 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.

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

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

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 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.

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 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.

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.

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

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

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.

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.

The rules of the quantum world mean that we can process information much faster than is possible using the computers we use now.

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

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

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 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.

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.

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.

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

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.