Danish physicist and pioneer of modern quantum mechanics Niels Bohr is famously quoted as saying: “Anyone who is not shocked by quantum theory has not understood it.”

Well, Niels, you were right. But things might be getting even more complicated.

First came the news about the W boson measurement, in which the actual measurement of the particle appears to deviate from the predictions of the Standard Model. Now, new research has found a way to connect two complex phenomena – without having to resort to quantum theory.

For nearly a century, quantum theory has been extremely successful in understanding the microscopic world of molecules, atoms and particles. But because quantum theory doesn’t merge well with gravity, many physicists believe it’s only a matter of time before quantum theory is proven to be incomplete and replaced with a new, more general theory of reality. New mathematical research shows that this won’t nullify all the tools that quantum theory has given us.

Quantum mechanics, as opposed to classical mechanics of the Isaac Newton ilk, is bizarre and unpredictable. The weirdness of this tiny world is highlighted in two phenomena: *superposition* and *entanglement*.

The superposition principle says that we can’t know the “state” of a particle (its location, speed, energy, etc.) unless a measurement is done on it. Instead, the particle exists in a “superposition” of distinct states, each with its own probability. Famously – and head-spinningly – this leads to the notion that a particle exists in two places at the same time until an observation is made, forcing the particle to “choose” its exact location.

The other concept – entanglement – is a ghostly link between an “entangled” pair of particles which remains even if entangled particles are on opposite ends of the universe. If something is done to one of the entangled particles, the same effect is seen instantaneously in the other particle regardless of the distance between them. You might see why Einstein derided entanglement as “spooky action at a distance.” But, we not only understand entanglement mathematically, it has been used in experiments including the first attempts to make quantum telecommunicators and quantum encryption.

*More on quantum entanglement: The quantum internet is already being built*

In quantum theory, entanglement is a consequence of superposition. Entanglement happens when the superpositions of two or more particles are correlated in a multi-particle system.

Research partly funded by the Foundational Questions Institute (FQXI) and published in *Physical Review Letters* examines the connection between superposition and entanglement. The authors write that the link should be independent of theory, and the fact that we have only understood the = between entanglement and superposition through the lens of quantum theory is “conceptually unsatisfying” given quantum theory is not a complete theory of the universe.

The mathematicians have now found a connection between entanglement and superposition which does not assume the correctness of quantum theory. “We were really excited to find this new connection that goes beyond quantum theory, because the connection will be valid even for more exotic theories that are yet to be discovered,” says Ludovico Lami, FQXI member and physicist at the University of Ulm, in Germany.

This is not just fancy theorising. There are practical implications. Entanglement is already used in quantum computing and encryption which is, currently seen as unhackable. But if quantum theory is proven wrong one day, does that mean cryptography based on entanglement is not as secure as we once thought?

Thankfully, the team’s research suggests that entanglement cryptography will remain secure. In particular, they showed that the quantum cryptographic Bennett-Brassard 1984 secret key distribution (BB84) protocol will always work, even if one day a theory is developed beyond quantum theory. BB84 is the first quantum cryptography protocol and it uses entanglement between two strings of bits made of quantum mechanical objects, usually single atoms, known as “qubits.” “It is somehow reassuring to know that cryptography is really a feature of all non-classical theories, and not just a quantum oddity, since many of us believe that the ultimate theory of nature will likely be non-classical,” says Lami. “Even if one day we found quantum theory to be incorrect we will still know that secret key distribution can in principle work.”