The Uncertainty Principle

Heisenberg’s Uncertainty Principle

Today, I watched a lecture on Heisenberg’s Uncertainty Principle – one of the most famous ideas in Physics. The Principle states that: “the more precisely you know the position of a particle, the less precisely you can simultaneously know the momentum of that same particle, and vice versa.”

The idea might seem simple at first glance. But, it is also strange as it doesn’t conform to what we experience in our everyday life. You know, for example, that it is possible to both measure the speed of a car and its position at a definite time. So, why wouldn’t it be possible to do the same for particles?
It turns out that measuring the position and speed of an object is only possible because the uncertainties in position and velocity are so small that we can’t detect them. The Uncertainty Principle is not visible on the macroscopic scales of everyday experience. In other words, it is not possible to bring our experience of the world around us to the world of atomic-sized phenomena.

But, why does the Uncertainty Principle take place?

Try to imagine an electron. What do you see? I personally think of a little round ball or something similar. But, that is not even close to what an electron is. It turns out that electrons can be described as both particles and waves. It’s actually impossible to picture what they look like. This goes for all other quantic entities too. It’s known as the wave-particle duality.

The core idea in understanding why the Uncertainty Principle takes place has to do with the fact that particles exhibit wavelike behaviour. This video explains the concept very well.

In brief, when position is well defined, the wave is pulse-like and has a badly defined wavelength (which determines the momentum of the particle). On the other hand, when momentum (and thus wavelength) is well defined, the wave is spread out and thus, the particle’s position isn’t clear.

The Uncertainty Principle

This is of course a simplistic view of why the Uncertainty Principle takes place. The better explanation involves pure maths and playing with the Cauchy-Schwarz inequality.

A little video

Here is a short video that shows particles of light passing through a slit. As the slit becomes smaller, the direction of the particles becomes less known. This is shown by a wider horizontal distribution of the light. In other words, the more you decrease the uncertainty in position, the more the uncertainty in momentum increases. Watch the video to understand.


 

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