“The Book of Nature is written in the language of Mathematics”, Galileo famously said. The language of mathematics is clean, precise and absolute, with no regard for the concept of uncertainty. But Uncertainty, this frowned‐upon offspring of Mother Earth and Father Science, of theory and practice, which we’d rather throw to the wolves on a cold winter’s night, is central to all science. In physics, uncertainty is particularly special, because physics has always been concerned with the hunt for certainty – the hunt for the capital Truths of nature.
Physics is about breaking nature down to smaller and smaller pieces, and fully understanding these pieces and their interactions from the smallest elementary particles to the biggest galaxies. Where the humanities could be viewed as doing a literary analysis on the Book of Nature, where the science of religion tries to understand why so many people are caught up with the Author of the book, and where metaphysics wonders why the Book of Nature exists at all – physics delves deep down, brings out its looking glass and scrutinizes the Book’s grammar and syntax. Why are the letters in this specific order? What are the letters really made of? What happens if we read the book backwards?
Through countless carefully devised experiments, the physicists tries to quantify the rules of the universe. These laws should be described purely using the language of mathematics, with the desired parameter on the left side of the equal sign and something beautiful and solvable on the right. When this happens, as it often does in theory, uncertainty is completely eliminated. Uncertainty is simply not a part of the equation. These analytic solutions to the riddles of nature provides valuable insight into how nature works. By looking under the hood we open the “black box”; we understand why we accelerate when we step on the accelerator, seeing that this is a process involving a complicated series of steps involving valves, spark plugs and gears, and we can explain each step along the way using these magical equal signs. By studying the equations and realizing, say, that if you throw a ball it always moves in a parabolic arc, we can mathematically deduce countless other pages in the Book of Nature – countless other truths, all just as mathematically exact as the parabolic arc of the ball.
In practice, the Truth is not nearly as pure. If you step out of the comfortable walls of Theory and instead play ball with Mother Earth, you’ll discover that the ball doesn’t move as you initially predicted. Complicating aspects like air resistance get in the way, and even though you can go back to the drawing board and incorporate these spoilsports into your equation, you’ll find that suddenly, the equation is not unambiguously solvable using the noble tools of mathematics. The original Truth is still just as true, in itself – but on its own, it’s not as useful anymore when theory meets practice. The system you are describing has moved from depending on each part by itself, to depend also on the interaction between the parts – like how air resistance depends on the speed of the ball you throw, and the speed of the ball is of course influenced by the air resistance. And now, this more complicated system is non‐linear and can only be approximated, never to be solved exactly.
Slouching erratically on the sidelines, Uncertainty smiles slyly. He knows nothing can be measured exactly – even with perfect methods and equipment, we will never be able to create a perfect model of the state of the universe right now, and therefore we cannot predict precisely how the universe will look in the future. The reason for this fundamental uncertainty is the dark secret of quantum mechanics: Deep down, at the very core of Nature, you can never know exactly where a particle is and exactly how it is moving. The best you can hope for is a bit of both, resulting in a fundamental wall of uncertainty no matter how you approach it. This principle is not something we have measured – it’s derived purely theoretically, and is a capital Truth in both theory and practice as long as quantum mechanics exists.
In its hunt for the Truths of nature, physics have ironically uncovered the Eternally Unknowable; the Forever Uncertain.
Cover image by user Dhatfield on Wikimedia Commons.