The strange metaphor of Euglena’s tail

A single-celled organism provides an excellent metaphor for what quantum mechanics says about the world. Robert P Crease and Gino Elia explain Strange parallel Proponents of an interpretation of quantum mechanics known as “QBism” have devised a metaphor involving Euglena – a single-celled freshwater algae that has a long whip, or “flagellum”, that can sense nutrients and propel it towards the food. (Courtesy: iStock/wir0man) Quantum mechanics is so full of strange phenomena that it’s not surprising that physicists have had to dream up some vivid metaphors to explain them. Who can’t help but think of cats in boxes when contemplating superposition or balls of jumbled yarn when musing over entanglement? Like all metaphors, these use familiar experiences to help understand the unfamiliar. Metaphors come in many different types. “Love is a rose”, for instance, is a “filtrative” metaphor, in which a secondary subject (a rose) guides us how to perceive another, primary subject (love) by drawing our attention to key features. In a “creative” metaphor, however, the secondary subject eventually becomes the technically correct term for the primary subject. This has happened over and over again in quantum mechanics: entanglement, superposition and spin are all examples. A third kind is a “perceptual” metaphor, which seeks to recast our overall view of something. A good example is physician Lewis Thomas’s remark that the Earth is “most like a single cell.” But one extraordinary metaphor proposed 10 years ago by Christopher Fuchs, a physicist at the University of Massachusetts Boston, involves a type of algae known as Euglena. Fuchs decided to invoke this single-celled, biological organism to help understand not just one quantum-mechanical phenomenon but possibly the deepest mystery of all: the relationship between quantum formalism and the world around us. Subjective matters Ever since Werner Heisenberg and others developed quantum mechanics more than a century ago, physicists have been debating what it means and what it says about the world. Over the years, there have been many different points of view, or “interpretations”, of quantum mechanics, but they all fall into two main camps. One set claims that the formalism of quantum mechanics quantifies some actual, objective structure that existed even before humans and is independent of what we do. Another set of interpretations treats the formalism like a tool that lets humans make predictions about the world. In philosophical terms, the former interpretations are “ontological” and the latter “epistemological”. Fuchs and a loose conglomerate of physicists and philosophers, however, have been advocating an entirely different approach, known as QBism. It says that any measurement we make – whether determining the spin of an electron or stamping our feet on the ground – is a new creation; it’s an experience that never existed in the world before. Quantum states aren’t therefore real states of affairs in nature but subjective probabilities we assign to our interactions with the world. Subjective probabilities aren’t as strange as they sound, simply descxribing a user’s degree of belief about an individual event. Objective interpretations, in contrast, see probability distributions as physical. QBism’s conclusion that many pieces of the formalism are subjective simultaneously distances our subjective control over nature. For a one-horse race, I can predict the winner with certainty, but nevertheless, the race can still get washed out by rain. Even if I make a prediction with certainty about an event, nature can throw us a curveball and do otherwise. For Fuchs and his supporters, quantum theory is therefore an appendix to Bayesian probability theory. Originally developed by the British philosopher and statistician Thomas Bayes in the 18th century, it evaluates a user’s judgment about how likely an outcome is (such as whether a horse will win a race) rather than being about pre-existing states of affairs (such as passively recording the speed of particles in a gas). Fuchs calls his interpretation of quantum mechanics QBism as it derives from the term “Quantum Bayesianism”. Quantum mechanics, according to Fuchs, is a “user’s manual” that “anyone can pick up”, devised by experienced players to guide individual experimentalists to make wise bets on measurement outcomes. Subjective interpretations of quantum mechanics treat the formalism as something for individuals to use and apply for all kinds of physical phenomena The key point is that while quantum state assignments are subjective, the rules underlying them aren’t. They have been analysed, evaluated and corrected over time by communities of physicists. Subjective interpretations of quantum mechanics treat the formalism as something for individuals to use and apply for all kinds of physical phenomena.

Enter Euglena If you’re struggling to get your head around all of this, that’s where Euglena comes in. It’s a single-celled freshwater algae, roughly 50 microns long, that has a long whip or “flagellum” that can sense nutrients and propel the organism towards the food. The tail, which is the product of many years of evolution, helps only the organism to which it is attached. However, by studying it, we can learn not just about an individual Euglena but also the wider environment in which it moves. The metaphor of Euglena’s tail therefore does two things. First, it expresses the idea that quantum formalism is a manual – a means to get around in the world. Second, it says something about how we interact with the world. Each organism uses its inherited tail, constantly tested and improved by a community of others, to “guess” how to get around in its environment. But each time the organism does, it encounters something in the environment it never did before. Euglena’s tail can, in other words, help us to explain why quantum mechanics can be both a single-user theory and the product of extensive study. “By dissecting it,” Fuchs wrote in a 2016 arxiv preprint (1601.04360), “you can learn something about the world that all of us are immersed in.” Leprechauns on tombstones: your favourite physics metaphors revealed Read more Like all metaphors, however, Euglena has its shortcomings. Imagine standing above the Euglena and observing it through a microscope. It would be perfectly reasonable to say that “there is” an environment that the organism senses “thanks to” the whip. We might also conclude that what a Euglena encounters is objective, independent of its presence, and could be predicted by the organism, provided it had enough data and processing ability. But all this assumes we are looking down from above to adopt a point of view completely detached from Euglena and its environment; we, as researchers, are outsiders. The Euglena organism itself is different. It has no such outside standpoint and each move is creative, encountering a fresh environment. Physicists have no external standpoint from which to look down on the world Now here’s the key point of the metaphor. Quantum physicists, too, cannot become “outsiders”. They have no external standpoint from which to look down on the world. They have the quantum formalism, but it’s a guide to what we find in our fresh encounters with the world. The critical point Fuchs’s Euglena metaphor has a much broader scope than the other scientific metaphors mentioned above. It is not so much about comparing a piece of the organism to quantum mechanics, but a way of comparing an organism’s adaptation to its world to the experimentalist’s user-manual; in turn, it becomes a story about what the world is. The Euglena’s tiny whip is a way to grapple with the ontological lesson of quantum mechanics. You might, in fact, call it an “ontologizing” metaphor. Robert P Crease (click link below for full bio) is a professor in the Department of Philosophy, Stony Brook University, US, and Gino Elia is a philosopher of physics who is spending 2026–27 at the Ludwig Maximilian University of Munich, Germany, e-mail gino.elia@stonybrook.edu Want to read more? Registration is free, quick and easy Note: The verification e-mail to complete your account registration should arrive immediately. However, in some cases it takes longer. Don't forget to check your spam folder. If you haven't received the e-mail in 24 hours, please contact customerservices@ioppublishing.org. E-mail Address Register