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?


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

In: 252

I’m by far an expert but the way I see it is as follows: the act of measuring disrupts the electron because it is so small. Measure the position and you disrupt the speed like if you were to pin it down

We can easily see the position of a car by looking at it. We can pretty easily measure the speed of a car by just watching how far it goes in a certain amount of time.

But looking at things requires bouncing photons off of it. That’s fine when it’s a car. But for something as small as an electron, a single photon can easily just yeet the electron to who knows where.

Edit: This is the observer effect. Check out the other replies explaining the uncertainty principle.

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.

It’s an inherent property of things that are waves.

Technically it’s momentum and position. Speed will always be C (the speed of light).
Momentum is: how much mass you have and how fast you’re moving.

At these scales, everything is too small to have anything like a physical surface. It is instead a sort of fuzzy area of energy that vibrates.

In your mind’s eye, I want you to draw a single wave.
The height of that wave is its energy. which is also how much energy/mass it has, which is also its momentum.
The width of that wave is its position.

Now we conduct our experiment:

Since what I’m trying to look at is a few orders of magnitude smaller than light itself , I have to use something else. So we use another electron.

You can fire one of two types of electrons. Low energy and high energy.
Your low energy electron will have a long wavelength that does not go up very high. The high energy electron will have a very short wavelength but a very high peak.

If I use the low energy electron it will definitely hit the electron I’m looking for, but I won’t know exactly where. Also, when it “bounces off”, the amount of energy it has will have a slightly different amount that I can measure. So I will have a good idea of how much energy for more momentum I’ve imparted to the electron in question but I don’t know exactly where it’s at.

If I use the high energy electron, having a much shorter wavelength means I can get a very high level of precision about where that other electron is. however, since it has so much momentum or energy once I hit it the other electron now has a bunch of energy. And I can’t know how much energy was imparted to it without hitting it with *another* electron.

It makes a sort of intuitive sense if you just look at the two different wave types: wide and flat Vs short and high.

Wide and flat: A lot of positions to the left and right (position) not many positions up and down(momentum).
Short and tall: few positions to the left and right(position) a lot of positions up and down (momentum)

Sorry I rambled.

As others said, if you measure its position you mess up its speed. You can measure how much time it takes for an electron to get from place A to place B, but you can’t measure it at any one place without stopping it. If you measure it in any way, you mess it up.