This is the International Year of the Quantum, celebrating quantum science and its many applications. It also marks the centenary of Werner Heisenberg’s seminal work in modern physics.
In recent years there have been dramatic developments in quantum communications, cryptography and computing, and quantum science is key to solving pressing problems in clean energy, climate change, health and industry. The economic benefits of such applications are enormous.
The highlight of the year for physicists is “Helgoland 2025”, a workshop in June, with participation of world-leading scientists including five Nobel Prize winners. The workshop will be held on the tiny island of Heligoland, in the German Bight, where Heisenberg established the foundations of quantum mechanics 100 years ago.
Heisenberg’s “matrix mechanics” did not emerge from a vacuum. In 1900 Max Planck, in “an act of sheer desperation” to harmonise theory with observations, assumed that radiation is not continuous but is emitted and absorbed in discrete packets or quanta. The size of a quantum is indicated by a tiny number h, now known as Planck’s constant.
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Instead of treating variables such as position and momentum as quantities, Heisenberg expressed them as operators acting on functions. These operators do not commute: A before B is different to B before A, the difference being related to Planck’s constant. This noncommutativity leads on to the uncertainty principle, which means that complete knowledge of a quantum system is impossible.
New era in physics
After 10 days on Heligoland in June 1925, Heisenberg went to Göttingen and wrote up a paper that was published just three months later. This was the dawn of a new era in physics.
Quantum mechanics is profoundly counter-intuitive: matter at atomic scales has the characteristics of both particles and waves, and this wave-particle duality produces paradoxical results. If this perplexes you, take comfort in Niels Bohr’s words: “Anyone who is not shocked by quantum theory doesn’t understand it.” Even after a century, quantum science retains the capacity to mystify.
Some of the critical aspects of the new physics were adumbrated by the Irish mathematician William Rowan Hamilton. The idea of non-commuting operations is very familiar: try putting your shoes on before your socks! But the order doesn’t matter for ordinary numbers: multiplying three by seven gives the same result as multiplying seven by three. However, in 1843, Hamilton discovered a new species of numbers, called quaternions, that do not commute. This led immediately to new developments in mathematics and later proved essential for quantum physics.
[ Hamilton’s dynamics: A prescient framework for quantum mechanicsOpens in new window ]
Quaternions brought fame to Hamilton, but he is also renowned for his work on dynamics. His canonical equations and his energy function, now called the Hamiltonian, which first appeared in 1833, turned out to be perfectly suited to the needs of the new physics.
His mathematical formulation of classical mechanics is fundamental in quantum mechanics and the Hamiltonian plays a central role as an operator acting on the quantum wave function. Erwin Schrödinger, in a stroke of genius, interpreted the variables in Hamilton’s function as operators and derived the equation that underlies quantum mechanics.
Only a select group of leading physicists have been invited to the Heligoland workshop. Registration has now closed, and all accommodation has been booked up; some participants will have to camp out on the beach. Another meeting, closer to home is the Institute of Physics Spring Conference in Galway at the end of this month. The theme of the conference is quantum science and details are at https://iop.eventsair.com/isc2025/
Peter Lynch is emeritus professor at the School of Mathematics and Statistics, University College Dublin. He blogs at thatsmaths.com
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