Eli5 Why can’t we “know” the speed and position of an electron simultaneously? Why can we only measure one of these properties at a time?

Question

This always confuses me and I’m not sure how it works. Please explain…

In: 252

Answer 1

(Edit to add): A lot of explanations here make it sound like the uncertainty principle is an artifact of observation: if the only tool you have to measure the position and momentum of a marble is by throwing other marbles at it, then clearly you can’t measure both at the same time.

This is a wonderful intuitive explanation, **and it is wrong.**

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So the best explanation I have ever seen for this came from [a video by 3Blue1Brown](https://www.3blue1brown.com/lessons/uncertainty-principle)—and while it’s not really geared towards 5-year-olds (the “ELI5” thing), the video presentation does walk you through the relationship between waves and the Heisenberg Uncertainty Principle (which you’re alluding to) makes the entire thing incredibly easy to understand.

Essentially the idea is this, and I’m condensing from a spectacularly well done video here—is that there is a relationship between knowing the frequency of a sound and the duration of that sound. A solid tone that lasts for a second, for example: you can determine the frequency of that sound with a high degree of certainty. But if that sound is a brief chirp, it becomes harder to know the frequency of the sound: if the chirp is less than 1/100th of a second, it can be quite impossible to determine if the sound was an C or a D on a piano.

Now electrons being waves (hand-waves at the association here), if frequency is like momentum, and time is like position, the more certain you are of the position (that is, the shorter the time), the less certain you can be of momentum (that is, frequency). If you can be certain of the position of an electron, it’s like the brief chirp that lasts less than 1/100th of a second—and it’s harder to know what the momentum is, just as it’s hard to know if that chirp was a C or a D note.

This implies, by the way, that the relationship in the uncertainty of position and momentum of an electron is **NOT** a feature of observation: it’s not just a matter of figuring out a better way to measure electrons.

It is instead, a fundamental feature of anything constructed out of waves.

But watch the video to get a full appreciation of the argument. I promise you it will be well worth 18 minutes of your life. And to be frank, I wish I had 3Blue1Brown’s video presentations when I was in college: he makes so many different concepts out of mathematics incredibly clear.