Quantum mechanics' uncertainty principle

By Ryan Ng

Let’s imagine a hypothetical electron gun. A gun that shoots electrons, towards a wall. Because of quantum physics, it happens that the electron will shoot in a random direction; we cannot aim this electron gun perfectly.

We have a small detector on that wall all the way to the left. If the electron hits the detector, it will make a “click” sound. We’d like to determine what the probability is of the electron hitting the spot the detector is at. So we’ll shoot the gun many times, calculating the probability by taking the ratio between the total clicks heard and the total gunshots. We’ll move the detector slightly to the right, then repeat. The results will resemble a normal distribution centered at the middle of the wall.

Next, we’ll add another wall between the electron gun and the previous wall. This wall will have a small hole in it—so the electron must pass through the point the hole is at, then hit the wall. We’ll do the same thing, as above, finding the probability distribution. Then, we’ll move the hole on the in-between wall to a different location on the wall, and try again. We’ll get something like the following:

We see the distributions P1 and P2, for the experiments we did with hole 1 and hole 2. These make sense. Then, we hypothesize that if we had both holes open, not just one at a time, we’d get the distribution in (c), which is simply both added together. In reality, however, with both holes open, the distribution looks like the following diagram, at (c):

This doesn’t make any sense. To further investigate this, let’s put a light source right next to the wall:

We’ll do the same as before, but having both holes open and counting separately when we see an electron pass through Hole 1 and Hole 2. Watching the experiment with light, we see that the electrons don’t split apart—they do pass through either hole. But now, our total distribution looks like, on the very right:

So by adding light, we’ve lost our old erratic wave distribution entirely. When we remove the light, the old jagged distribution comes back. It turns out that the photons from the light interfere with the electron: when the photons hits the electron, the electron gets redirected. The electric field of the light acting on the electron will also influence its trajectory.

What if we dim our light source? Weaker light waves could possibly disturb the electron less. The result of this, is that sometimes, we don’t even see the electron pass by, even when we hear a click on the detector. This is because the photons are now sent less frequently; the electron would’ve passed through the hole when a photon wasn’t there.

There is one last way we could change the light source, by decreasing the light’s frequency. The momentum of a photon is inversely proportional to its frequency, in p = hf; this essentially means we’re making the photons slower. However, this now causes the electron to be blurry as it passes through either hole.

This is because the photon’s wavelength is inversely proportional to its frequency: f = 1/λ, so p = h/λ. This means we’ve increased the wavelength of the light wave. A fundamental property of light is that, when we shine light on two objects next to each other, if the distance between them is less than the light’s wavelength, they are seen as being in the same place. In terms of our experiment, we see a big fuzzy flash that prevents us from determining which hole the electron went through. We cannot see the electron and get our strange pattern at the same time.

This is known as the uncertainty principle in quantum mechanics, discovered by Werner Heisenberg. When it is applied to our experiment, it says that we cannot tell which hole the particle went through, without interfering with the electron in a way that destroys the jagged wave pattern.

Though this is extremely counterintuitive, no one has thought of a way to get around this rule. This forms the basis of quantum mechanics.