Heisenberg’s Uncertainty Principle has been eulogized as one of the leading theories of quantum physics. It has also evolved to become something that has been popularly adapted into various media streams to address philosophical topics, such as nihilism and absurdism. However, the principle in itself is too clouded in obscurity for most of us mere mortals to grapple with.
And that is, of course, unsurprising. Quantum physics is a perplexing rabbit hole that is best left to the professionals, thank you very much. Despite this, I will make a meager attempt at trying to simplify this concept to the best of my understanding, with as little math being involved as possible.
Heisenberg Uncertainty Principle: The Equation
Well, let’s first try and grasp the math behind the Principle. What it basically refers to is the fundamental incoherence of quantum particles. In a single statement, Heisenberg’s Uncertainty Principle points out that both the position and momentum of a particle cannot be known at the same time. The more certain you are of one, the more uncertain you are of the other. When you multiply the uncertainties of position (x) and momentum (p) (uncertainty is represented in the equation by the Greek letter Delta), you get a number that is greater than or equal to half of a constant ‘h-bar’. This is called Planck’s constant (usually represented as h/2π). This constant is extremely important in quantum physics, as it is an absolute way to measure the granularity of the world in the smallest of scales. The value of this crucial constant is x joule seconds.
Because most objects visible to us are much larger than this constant, quantum uncertainty is not witnessed by us. For the visible world, Newtonian physics seem to suffice, but the smaller the particle gets, the more uncertainly it objectively behaves.
As we approached the early years of the 20th century, a new stream of science took the academic world by storm. This revolution of thought was the unfathomable, colorful, mystical world of quantum physics. Scientists argued that energy was not received in a continuous stream, but in separate packets, known as ‘quanta’. These quanta can be visualized as the occasional spikes in a heartbeat monitor.
Therefore, a small particle like a photon or a free-moving electron functions like a ‘wave packet’, in which it has wave-like properties, such as wavelength, as well as particle-like properties, such as position and size. Let me focus a little more on the wavelength part. As you know, waves can be measured by their wavelengths. The lighter the object, the larger its wavelength will be and vice versa. The wavelength of a person is only one-millionth of a centimeter – far too short to be measured. Basically, this is why things bigger than Planck’s constant don’t act as waves.
Quantum particles, however, are much tinier and more slippery than your average Newtonian object. Their wavelengths are as prominent as their particle properties, which is called the wave/particle duality of quantum objects.
Momentum / Position
To determine the position of a particle, you would have to look at a wave packet, but the particle’s position can never be truly pinned down, as quantum particles can exist in multiple states at the same time (Superposition, much better described by Schrodinger, states that quantum particles can be both waves and particles at the same time, whereby they can occupy several positions, but if you measure them, they can be in only one of the states and positions). However, you can narrow down your measurement regarding the particle’s position if you simply make your field of measurement, i.e. the wave packet, smaller.
Didn’t get it? Imagine that you have a slippery guppy fish in a swimming pool. It swims everywhere and you can’t determine its exact position. However, you can make the pool smaller, so that the guppy’s position can be studied more accurately.
On the other hand, we have momentum.
Momentum, if you remember your school lessons well enough, is the mass of a particle multiplied by its velocity (M=mv). The velocity of the particle (its speed and direction) is entirely determined by the wavelength of that particle. Therefore, the momentum of a wave depends on its wavelength.
However, a wave packet, like a photon or an electron, is made of many waves with different wavelengths. So how do we find out the momentum of a single particle? The obvious way would be to derive the average of these different waves. To increase the precision of this average, it becomes necessary to take more waves into consideration. To do so, the area of measurement, i.e. the wave packet, would have to increase.
Basically, to precisely measure the position you would have to make the wave packet smaller. If you want to measure the momentum, you would have to make the wave packet larger. You obviously can’t do both. That is why you can never really know both the position and momentum of a particle.
So, there you have it! That’s basically what it says! Of course, this is me simplifying a highly mystifying natural law, but it’s a good start for your brain to begin processing quantum physics. In fact, there is an experiment that actually captures particles adhering to the Uncertainty Principle! Youtuber Veritasium showcases the slit experiment to explain the Principle in a more visual way. Enjoy!