by Andrew Boothroyd

What makes a good PhD thesis?

One hundred years ago, Louis-Victor de Broglie completed a 70-page doctoral thesis in which he proposed that electrons, and by extension all matter, have an associated wave. Within a year or two, de Broglie’s conjecture was to become one of the central ideas of quantum theory, and in 1929 the Swedish Academy of Sciences conferred on him the Nobel Prize for Physics ‘for his discovery of the wave nature of electrons’.

De Broglie did not have a conventional background for a physicist. He was from an aristocratic French family, and later in life became the 7th duc de Broglie. By all accounts he was a bookish child. He immersed himself first in literary studies, and took a degree in history in 1910. He then changed direction and studied for a degree in science, which he completed in 1913.

Although remarkable, the ideas set out by de Broglie in his thesis had a solid foundation in the work of earlier greats of science. Simply put, the argument goes like this: according to Planck, light is a wave but also comes in discrete quanta of energy, and according to Einstein, particles are localised packets of energy; ergo, particles are waves.

Very soon after de Broglie’s work, Schrödinger developed a quantum wave equation from which one can obtain a mathematical description of a matter wave, and around the same time Heisenberg, Born and Jordan developed an equivalent but more general formulation of what is now known as the quantum theory.

Quantum theory is one of the most successful theories of all time. It provides a collection of mathematical recipes to calculate the observable properties and behaviour of matter very precisely. Its predictions have been tested against experiment, and in some controlled cases the agreement is better than one part in 100 million.

And yet, for the last century, scientists have been puzzling over the meaning of de Broglie’s so-called wave–particle duality. The solutions of Schrödinger’s quantum wave equation provide exquisite descriptions of real-world systems, but don’t tell us what is behind the mathematics at a fundamental level. Is there a more satisfactory physical picture hidden behind the quantum theory, or is the mathematics of quantum theory the last word? How can Schrödinger’s cat be at the same time dead and alive until we observe her, at which point the act of measurement determines her state of being? Philosophers continue to debate these and other issues.

Meanwhile, we are currently experiencing what is often termed a second quantum revolution, in which the principles of quantum theory, developed a century ago by de Broglie and others, are being applied to make quantum technologies, such as quantum secure communications, quantum computers and quantum sensors. Through these advances, quantum theory has the potential to revolutionise the way we communicate and process information, and may lead to breakthroughs in medicine and energy production of utmost importance to humanity.

So, you want to know what makes a good PhD thesis? Ask a simple but profound question, be creative and see where it takes you.

Louis de Broglie died on March 19, 1987, at the age of 94.