Why you can’t ever “know” anything exactly

“What we observe is not nature itself, but nature exposed to our method of questioning.” –Werner Heisenberg

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?

Image credit: Benjamin Crowell.

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.

Unbelievably, each individual electron appears to interfere with itself!

So you go back and ask which slit each electron went through, like a good scientist would. So when you re-run the experiment, only this time you turn on a light to measure which slit the electron goes through, what do you find?

When you measure the electron, you destroy the interference pattern, and you force it to go through one slit or the other! It no longer interferes with itself, it no longer acts like a wave, and you just get the same pattern that you get for particles of sand.

The way you were likely taught this — if you were taught this at all — is that measuring the electron “collapses its wavefunction.” And this is right… kind of.

Here’s an — as far as we know — accurate depiction of what a helium atom looks like.

Now you might want to know where this electron is at any given instant. So you can shoot a photon at it. And the higher energy (i.e., shorter-wavelength) your photon is, the more accurately you can measure the electron’s position. But you can never know it exactly. Why not?

Image credit: UCSD.

Heisenberg’s uncertainty principle! Not only can you never know something like “position” exactly, but the more accurately you measure its position, the less accurately you’re allowed to know its momentum!

The same thing happens for energy and time. This is so spectacular that — because E = mc2 — particles that live for very, very small amounts of time have an inherent uncertainty in their mass! (If you ever hear a physicist talk about the “width” of a particle like the W or Z boson, or the top quark, this mass-uncertainty is what they’re referring to.)

Is there a good, classical analogy for this? Sure there is; imagine a water balloon.

Imagine trying to measure exactly where the water balloon is in one direction. Well, you can’t quite do it with just a ruler; a water balloon has a finite thickness to it. So what can you do? Well, you can squeeze it in one direction, and make it smaller.

But when you do this, it stretches in the other directions. The volume has to be conserved, or all the dimensions multiplied together cannot be less than a certain number.

That’s what quantum mechanics is like. So you might wonder, with this in mind, what happens if you go back to your two-slit experiment, and only measure which slit the particles travel through a little bit?

Image credit: S. Kocsis et al.

Well, this experiment was just done (and other writeups are here and here), and what they can do is measure the average trajectory of the particles, but without destroying the interference pattern! In other words, if you look with low enough precision at whatever you’re looking at, you allow the balloon to be “large enough,” in some sense, in the direction that’s important to the experiment.

But as far as nature goes? You never know either position, momentum, energy, or time exactly. The best you can do is to measure it well-enough to take away some of its options. The first double slit experiment was performed in 1799, and with new discoveries and measurements like this, we’re likely to keep on playing with this setup for centuries to come.