Why you can’t ever “know” anything exactly?

Ethan Siegel in Starts With A Bang:

Looking down at the fundamental nature of matter, down past our cells and organelles, deep into the individual molecules and inside of the atoms that make them up, at long last, you get to things like the fundamental particles that make up all the known matter in the Universe.

Things like electrons, photons, and the quarks that make up protons and neutrons, are all, as best as we can tell, fundamental particles. That means we can't break them up into anything smaller; they're not “made” of anything else.

And that's where things get weird.

Let's say I take some light — what particle physicists call photons — and I shine it through some slits. Two slits of finite width, two infinitely-thin slits, and one slit of a finite width. What type of pattern would I see?

Well, you'd see the classic patterns that come about because of two well-known and well-understood phenomena: interference and diffraction. Now it might seem weird to you, because these are properties of waves, but we can treat light like a wave without too much difficulty.

On the other hand, if we used something like electrons, you might expect a different result.

This is the result you'd get if you threw a bunch of tiny grains of sand at these two slits. Some grains go through one slit, some grains go through the other, and you wind up with two separate piles of sand on the other side.

So what happens when you send the electrons through? They make the interference pattern!

But we're clever, so what we do, to avoid the electrons from interfering with one another, is to send them through one-at-a-time. And over time, we count up what they're doing. Here are the results.

More here.