The dark room
Imagine being in the middle of a large, dark room, with just a tennis ball in your hand and the knowledge that somewhere in that room is a chair. The only way to find the chair, let’s call it’s position ‘x’, is to throw the ball and see how long it takes to bounce back. The closer the chair the sooner the ball will return, the further away, the longer. So now you know the position of the chair as the ball hit it. The problem: in hitting the chair the ball has knocked it away, and you have no idea of its position now. Even if you know how hard you threw the ball and in what direction, you don’t know the direction or momentum of the chair before it was struck. Let’s call the momentum of the chair ‘p’.
This is Heisenberg’s uncertainty principle, and it says that it is impossible to know at the same time, both the position, x, and momentum, p, of a subatomic particle. This idea was groundbreaking; it shook physics, and keeps shaking.
In the equation above, the uncertainties in position, ∆x, and momentum, ∆p, are multiplied. Their product must be more than the constant ħ/2, (an incredibly small number 5.27285863 × 10-35 m2kg/s, that’s 5 with 35 zeros in front). In our large scale lives we never need think about it, the uncertainties of measurements never multiply to become less. In making a cake, a few grams too much sugar or a cake tin a few millimeters too big don’t matter, but on a subatomic scale uncertainties of this size are millions of times bigger than the particles being measured. The subatomic scales are minute, and the smaller our measurements the smaller our uncertainties. It is at this point that the ‘>’ limits us: if you are very certain about the position, or momentum of a subatomic particle, in order to stay above the ħ/2 limit, somewhere your uncertainty must increase. The more you know the particles position the less you can know about the particles momentum, and vice versa.
Stop making sense
It stops making sense, once you get to sizes much smaller than atoms, to see particles as solid spheres with definite positions in space and time. Quantum mechanics says that close up particles behave more like waves, whose qualities cannot be separated. When unobserved they behave incredibly strangely. Experimental results show that:
-Particles can be in two places at the same time, (a superposition), whilst also at that moment, being everywhere and nowhere.
-Particles can be ‘entangled’: however far away from each other they are, they can know instantaneously information about the other. I.e. information must travel faster than light.
-Everything is probable. Particles are not pinned down, they exist in probability clouds. So it is more likely that when you leave home in the morning, it will be where you left it on your return; not because it is impossible for buildings to disappear, quite the contrary, but because the probability of all particles that make up your house going elsewhere at exactly the same time is almost so improbable it is impossible.
-At the very moment of observation, by humans or even machines, particles change their behaviour. This means that all the strange implications of quantum mechanics above; probability clouds, entanglement, superpositions: stop happening the moment we look.
The origin of uncertainty
In 1900 Max Planck said light was a particle and a wave. In trying to understand this apparent contradiction, he peeled the lid off a secret world that looks nothing like our own. This moment marks the classical-quantum divide, and physicists have been trying to combine the two ever since.
Classical physics described our physical reality. Objects were individual cogs that unless touched by matter or force were at rest, taking up space and moving through time in the machine like universe. The world was deterministic and predictable. Quantum physics then blurred the lines between ‘stuff’; cup and table, dog and lead, planet and star. It said that every thing is made up of quanta: the smallest building blocks of the world are not blocks at all, but are fuzzy entities that only exist in terms of their likelihood of being in a certain place at a particular time.
In the history of science, people have had ludicrous ideas and been wrong a great deal. We have also understood and proved a huge amount. Heisenberg’s uncertainty principle marks the first time that the answer was uncertainty.
Imagine a square circle. Not only can it not exist in your mind, but nor can it anywhere in the universe. Given the very simple qualities of a circle, and the slightly more complicated rules of a square, their definitions depend upon them being nothing like each other. They are a physical and mathematical contradiction.
This is the best way to understand what the uncertainty principle is. It will not go away with better technology or harder maths, it isn’t a misunderstanding or something we may solve in the future. Here, maths is telling us that there are secrets woven deep into the fabric of what makes us. Much like the square circle is a complete impossibility, so is the chance that we may be able to completely understand the universe.
Synopsis: The world is full of secrets, literally. Not only are there things we do not know about the universe, but the more we try to find out, the more the universe conceals its true self from us. The act of observation changes the fundamental structure of the subatomic, and maths tells us we can never know what it was when we weren’t looking. -‘it’s as if some thing is trying to pull the wool over our eyes’, A. Einstein
Bio: Rosa studied Physics with Astrophysics at Leeds University and currently works in a Gallery in South London, curating and managing artists’ shows as well as tutoring science and maths. She is interested in how the mathematics of physics relates to our everyday reality, how can abstract equations tell us about ourselves and reality as we live in it? You can see more of her work at http://www.fromylem.com