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.

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.

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.

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.

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

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

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.

This is the basic building block of matter that creates the world of chemical elements – although it is made up of more fundamental particles.

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

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

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.

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.

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.

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.

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.

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!

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.

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

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.

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

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.

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

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.