You might be aware that the United Nations has designated 2025 as the International Year of Quantum Science and Technology. This is essentially a celebration of the hundredth anniversary of a trip to a remote German island in the North Sea by a physicist who reputedly wanted to escape the misery of hay fever to concentrate on his mathematical formulation of the new physics of quantum mechanics. That physicist was Werner Heisenberg and, whilst he may indeed have primarily sought sanctuary on Helgoland from pollen-ridden Göttingen, there is a feeling abroad that it probably didn't do any harm for him to escape what in modern parlance might be described as the echo chamber of his immediate academic environment.

Around the beginning of the 20th century, the physics community seemed fairly happy with the assumption that electromagnetic radiation was wave-like and particles were particles! The quantum revolution really emerged from the realisation, firstly, that electromagnetic waves could act like particles and, latterly, that particles could act like waves. This particularly thorny issue led to the first discovery around the so-called ultraviolet catastrophe, whereby the archaic Rayleigh-Jeans law incorrectly predicted that the intensity per wavelength interval of blackbody radiation would tend to infinity towards shorter wavelengths.

It was Max Planck who, in 1900, in what he described to a friend as “an act of desperation”, postulated that oscillators producing blackbody radiation could only absorb or release discrete packets of energy, proportional to the frequency of the standing waves formed in a notional radiating cavity. Planck's law shows that spectral emittance is suppressed at the shortest wavelengths, in comparison to the corresponding radiation predicted by the classical model. The aforementioned constant of proportionality eventually came to be named after Planck himself, and the rest, you might say, is history!  

Planck's quanta of energy would, in time, become synonymous with radiation absorbed and released by the electrons inhabiting the discrete orbits in Niels Bohr's model of the atom and, ultimately, Einstein - with not inconsiderable irony, as the person who with regard to the probabilistic nature of quantum mechanics, would insist that “God doesn't play dice” - demonstrated that these discrete packets were in effect photons; radiation behaving as particles, leading to his explanation of the photoelectric effect and subsequent Nobel Prize!

In his 1924 PhD thesis, French physicist and aristocrat Louis de Broglie put forward the idea that if waves of electromagnetic radiation could behave as particles, then particles might behave like waves. His remarkable proposition could be illustrated experimentally by the diffraction of electrons scattered by some suitable crystalline material, producing an interference pattern. This elegantly explained the quantum behaviour of electrons in an atom, which themselves could now be understood as “waves in a box” (like a guitar string, fixed at each end), only allowing certain discrete energy levels as a result of being limited to an integer number of half-wavelengths.

With the formulation of Erwin Schrödinger's famous equation following on from the remarkable insights of de Broglie, physicists could determine the “wave functions” of electrons, the squared magnitudes of which gave their probability densities - the likelihood of finding an electron at a particular location. This was the particular conclusion of Max Born, which neatly ties in with Heisenberg's uncertainty principle, whereby there is an inherent indeterminacy to certain combinations of states of particles. Most famously, according to the principle, one can never know with absolute certainty both the position and momentum of a particle. This is often interpreted as simply a limitation of the accuracy of our measurements, but it is more than this; the uncertainty principle determines the smallest possible size of an atom that may exist without the pertinent natural law being violated. At the risk of a somewhat tenuous metaphor, one's ability to exactly predict the trajectory and subsequent destination of a golf ball is limited at least as much by the golfer's inherent power to accuracy ratio as by the precision of the measuring equipment! Furthermore, the energy-time version of the uncertainty principle predicts the existence of a quantum “foam” of virtual particles filling the vacuum of space - a phenomenon which could, for example, explain the so-called Casimir effect.

It is important to realise that quantum mechanics is more than some quasi-esoteric mathematical discipline without bearing on matters of everyday existentialism. Solutions to Schrödinger's equation, for example, gave rise to an understanding of the possibility of quantum tunneling whereby particles can overcome potential barriers without the requisite kinetic energy. More profoundly, temperatures at the core of our own Sun would be insufficient for nuclear fusion to occur without the ability of protons to tunnel through the Coulomb barrier.

The story of quantum mechanics would continue with Paul Dirac's attempt to combine quantum theory with special relativity, leading to his prediction and the eventual discovery of antimatter. Indeed, alongside its incompatible if equally beguiling cousin - general relativity - quantum mechanics has never been a hotter topic, playing an exponentially growing role in the new technologies that increasingly dominate the everyday lives of millions of people. For instance, entangled pairs of particles (in superpositions of states), whereby the measurement of a particular state of one of the pair instantly determines the corresponding state of it's partner, regardless of the distance between them - what Einstein described as “spooky” action at a distance - are already being used to speed up quantum computers through the simultaneous manipulation of multiple qubits.

The implications of quantum mechanics may seem less philosophically shocking to the current generation of physics students than to its early pioneers. However, despite quantum theory’s accurate predictions and explanations of so many phenomena - from wave-particle duality to the arrangement of the periodic table and from tunnelling to entanglement - with every answer it provides, this mysterious branch of modern physics seems to reveal a host of even deeper questions. To quote character Penny in an episode of the hit TV series, Big Bang Theory, “The cat's alive!".