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

By measuring the position you disturb the wave function so that it has a sharp peak where you found it, and wiggles around zero everywhere else, since it can now be expressed as a sum of a wide range of wavelengths (via CFT) which are all nonzero at the peak. So its second derivative is highest at the measured position. In the Schrodinger equation that second derivative corresponds to “kinetic energy”(kinda sorta) which means the electron is going to high-tail it out of there and since its function is built by a wide range of wavelengths you can’t accurately determine how fast it’s going.

If you do it the other way you get a nice sine wave composed of one wavelength (or at least a n narrow range), so there are peaks all over the place destroying your knowledge of its position.