A forgotten member of the Quantum Club: Grete Hermann

One of those endless lockdown days, I was studying for my History of Physics exam, working through fragments of the Einstein-Bohr debates on the epistemology of quantum mechanics. It was during one of those study sessions that I first came across the name Grete Hermann—a name buried at the bottom of the page, but a contribution that, as I’d soon learn, far exceeded the confines of a mere footnote.

Grete Hermann was one of those anachronistic figures, whose ideas seemed out of step with her time, yet ahead of it in hindsight. In the early 20th century, women in science were rare, and their contributions even rarer to be acknowledged. Hermann was the only female student of nothing less than Emmy Noether, who herself was the only female professor at the University of Göttingen. At the time, Göttingen was more than just a university—it had become the playground for the brightest minds of quantum mechanics. Heisenberg, Born, and Hilbert were filling its corridors, where the new theory of quantum mechanics was taking shape.

After completing her PhD in mathematics under Noether’s guidance, Hermann took an unexpected turn and pursued philosophy. Noether, surprised by this shift, could only say, “Da studiert sie vier Jahre lang Mathematik, und auf einmal entdeckt sie ihr philosophisches Herz!”

Discoveries are distilled through the continuous efforts of looming over the shoulders of giants, sedimenting in the cathedrals of knowledge. One and a half centuries before Heisenberg’s magic paper, Immanuel Kant glimpsed that what we know about how the universe works is not a reflection of absolute truth but of our attempt to comprehend it. We are doomed particles of the totality, yearning to see the whole. As we look through our instruments and our theories, we do not see the universe, but just ourselves.

In order to measure something, change must happen. The moment we observe a particle, it is transformed by the very act of measurement. But this leads us to a paradox dating back to the Ancient Greece¹): the precise moment of change. How can a particle remain perfectly identical to itself in space and time—the same particle we are measuring—and yet, at the same time, be different enough to have changed? The blur of the instant of change, the logical prerequisite for stitching together any two moments in space-time, inheres in the very reality being observed. Ultimately, the laws of physics do not describe how things behave, but rather our observations of how things behave.

Kant had understood this long before quantum mechanics emerged. He realised that our experience of the world is always shaped by the way our minds work. We naturally think of things as existing in space and unfolding in time, but these aren’t properties of the world itself—they’re the ways in which we perceive it. In other words, we don’t have direct access to reality as it truly is. Instead, what we’re really seeing is how the world appears to us through the structures of space and time. Heisenberg came to the same realisation.

Physics was going through an existential crisis at the beginning of the 20th century. It was behaving in a way physicists could no longer recognise. Once defined by its deterministic nature, it was now full of uncertainties, caught in an entangled state and questioning its own identity. Heisenberg was the first to embrace this new version of physics, offering a rigorous framework known as matrix mechanics without judging it against classical expectations. Schrödinger, still conservative about this new identity, sought to reconcile the long-standing traditions of classical physics with the emerging mechanics of discontinuity by reframing them in a more familiar approach using waves.

Although they seemed to be saying very different things, both formulations were now giving the right answers—if one could ignore the existential consequences. The mathematical approaches of Heisenberg’s matrix mechanics and Schrödinger’s wave mechanics both seemed to work, yet they painted very different pictures of reality. Physicists trying to reconcile both views encountered the borderline between quantum and classical physics, giving rise to a plethora of interpretations of quantum mechanics.

Within this landscape, one cannot but wonder how we can obtain objective knowledge. This question becomes more evident in quantum mechanics than in any other area. How can we claim to know anything objectively when the very act of measurement changes what we observe?

At Göttingen, John von Neumann was aiming to contribute to the axiomatisation of physics, a project initially proposed by David Hilbert. Realising the deep mathematical structure underlying quantum mechanics, he chose to focus on formalising the theory. In Mathematical Foundations of Quantum Mechanics, von Neumann laid out a rigorous framework that unified the both approaches under a single mathematical structure.

Grete Hermann, heiress of Kant’s school of thought, was willing to tackle this task.

Complementary Material

Here is an insightful video about Grete Hermann’s contributions to quantum mechanics: