The uncertainty principle

Here’s a bad physics joke.



It’s bad because the premise of the joke (the uncertainty principle) applies to quantum particles, and does not observably affect macro-sized objects (like people).

The uncertainty principle in its most simplified form is this: the position and momentum of a particle cannot be measured at the same time. So the more accurately you try and measure its momentum (think of the speed that the particle’s travelling at), the less accurately you know where the particle actually is. Or if you know exactly where it is, you will have absolutely no idea how fast it is travelling.

This weird and unusual principle arises because every quantum particle is not just a particle, and also displays characteristics of a wave and has a wave function. This means that the “particle” is spread out over a space and doesn’t necessarily have a defined location, and its location is given as a probability of finding it between two points. This means that really we have no idea where it might be between those defined points.

One way of making its position more clear is by constructing a wave function modelling many waves. This gives a far more precise description of the position, but the introduction of multiple waves gives a huge variety in the possible momentum of the particle/wave.


The limit to what we can measure is modelled by this equation:

Δp*Δ≥ h/4π

What it means is that the error in measuring the momentum (Δp = mass * velocity of particle) multiplied by the error in measuring the position (Δx), cannot be less than Planck’s constant divided by 4π (Planck’s constant is another term that frequently comes up in quantum mechanics).


Previously to Heisenberg, people had assumed that the exact position and momentum of an object could be measured at any time. This was a very reasonable conclusion, because the uncertainty principle does not apply to large and visible objects, only to the absolute tiniest of tiny. The reason for this is clear: the momentum of the object is dependent on its mass, so the error in momentum is always far higher than the theoretical limit. But on a subatomic scale, with an electron weighing only 9.1 * 10^-31 kg, the uncertainty of measurement becomes very relevant.




Further reading:


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