Dr Quantum - Double Slit Experiment

The double slit experiment is one of the most famous physics experiments of all time. Sub-atomic particles have dual properties.

Here's the set up. We point a laser at a plate. The plate has two slits in it. The light goes through the slits and hits a screen in the back. This results is what's known as an interference pattern. It looks like this:

When I first saw this, I thought, why are there so many bars? Shouldn't there only be two bars, one for each slit? To understand why the interference pattern appears, we have to understand two properties of waves.

Two Properties of Waves

The first important wave property is diffraction. Diffraction allows waves to move around obstacles. When you shout out, "Dinner time!" the whole family can hear you regardless of whether you have a direct line of sight to them. This is because sound can travel around corners, through doorways, and into people's ears. Whenever a wave goes through a doorway or a slit, the wave spreads out in all directions on the other side.

In a way, diffraction is the opposite of what we expect from particles. When we shoot a particle through a slit, we expect it to follow a very narrow path on the other side. The smaller the slit, the narrower the path will be. But when we shoot a wave through a slit, it will spread out in all directions on the other side. The smaller the slit, the more it will spread out. So when we shoot light through a slit, it's not going to just make a single spot on the screen, but will go in all directions.

The second important property of light is interference. If two identical waves go through each other, then their intersection will look like the sum of the two waves. Recall that all waves are fluctuations in something. A typical wave quickly alternates between a fluctuation up and a fluctuation down. That's why, in the above drawing, we represent the wave with alternating black and white lines. The black lines represent upward fluctuations and the white lines represent downward fluctuations.

If two intersecting waves both happen to be fluctuating up, then the sum will be a fluctuation up with twice the amplitude. This is called constructive interference. If one is fluctuating up while the other is fluctuating downwards, they will cancel each other out. This is called destructive interference.

Return to the Double Slit Experiment

Now that we have an idea of how waves behave, we can now predict the results of the double slit experiment. Some of the light will go through slit 1, and some through slit 2. After going through the slit the light will spread out in all directions. The light that went through slit 1 will interfere with the light that went through slit 2.

How can we tell from the diagram where the light will interfere constructively and destructively? Well, the light interferes constructively whenever both waves fluctuate up in the same place and time. The light interferes destructively when the waves are fluctuating in opposite directions at the same time. To make this clearer, I've shown the locations of constructive (red lines) and destructive interference (blue lines) in the picture below.

The result? We only see the spots where the light interferes constructively, and not destructively. Therefore, we will see alternating light and dark bars - the interference pattern.

The Particle Properties Emerge

The fact that we see an interference pattern is proof that light is a wave, right? But what about the proof that light is a particle? It had been shown by Einstein that light comes in little separate packets, called photons. What happens if we send one photon through the double slit? According to our previous analysis, the interference pattern requires that the wave go through both slits at the same time and interfere. But if we just have one photon, it can only go through one slit. After all, it can only hit one spot on the screen behind the slits.

But when this experiment is performed the interference pattern does appear. Each photon, of course, hits only one random spot on the screen. But if we shoot, one by one, a whole bunch of photons, then the sum of their landing points forms an interference pattern. That is, a photon is much more likely to land in a spot where there is constructive interference. The only way this can happen is if the photon is traveling through both slits at once and interfering with itself!

The conclusion is that light shares properties with particles and waves. Which of the two is it? Neither, of course.

The Measurement Problem

So when we shoot a photon through a double slit, it creates an interference pattern. This interference pattern is only possible if some wave-like behavior is occurring, and if the wave goes through both slits simultaneously. And yet, when we watch where the photon hits the screen behind the double slits, the photon will always land in exactly one spot. Thus a photon has some properties of a wave, and some properties of a particle. I should also add that the exact same experiment works works with any kind of particles, not just photons. All "particles" have both particle-like and wave-like properties.

You may have wondered why this experiment must provide such indirect evidence. If we only need to show that the photon goes through both slits at once, couldn't we just put a measuring device on both slits? Yes, we can. But when we do so, we find that the photon goes through exactly one slit every time. Furthermore, the interference pattern on the wall disappears! It seems that when we try to gather more observations, the results change!

This is why Quantum mechanics is said to be counterintuitive. It defies common sense. Most everything we previously knew no longer applies. So on and so forth. Every time Quantum Mechanics is explained to popular audiences, I hear the same shtick over and over about how Quantum Mechanics is so weird. Personally, I get kind of annoyed that it's repeated to no end. So instead, I'd like to emphasize that while Quantum Mechanics is weird, not everything is up for grabs. It doesn't quite jive with intuition, but it does follow rules that can be studied and understood.

The Copenhagen Interpretation

To explain the basic gist of these rules, I will first consider what is called the Copenhagen Interpretation. According to this interpretation, particles can be described by their wavefunctions. Wavefunctions behave like waves. They propagate around walls, and can go through multiple slits simultaneously. They can diffract and interfere with themselves.

Unlike normal waves, we cannot observe wavefunctions directly. If we try to observe a wavefunction, something called "wavefunction collapse" occurs. When a wavefunction collapses, it suddenly becomes like a particle. It appears in exactly one location. If the wavefunction was originally spread out over a large area, the particle will appear randomly somewhere within this area. The probability that it will appear at any given location is based on the magnitude of the wavefunction at that location.

Let's apply the Copenhagen interpretation to the double slit experiment. First, we shoot a photon through the slits. At first, the photon is a wavefunction, and thus can go through both slits at once. The wavefunction diffracts, and interferes with itself, creating an interference pattern. But then the photon suddenly hits the screen, and collapses its wavefunction in a random location. Because of the wavefunction's original interference pattern, the photon is more likely to appear in some places than others. If we repeat the experiment many times, we can get a good idea of how the original wavefunction was shaped. And that's how we show that there was indeed an interference pattern.

If we put detectors on the slits, then these detectors will collapse the photon's wave function. The photon will become particle-like as it goes through exactly one of the slits. On the other side of the slits, the photon will spread out its wavefunction again, but since it has gone through only one slit, there is no opportunity for an interference pattern to form. If we repeat the experiment many times, we would find no interference pattern.

Observations and Observers

According to the Copenhagen interpretation, wavefunction collapse occurs when a particle is observed. But what constitutes an observation, and who is observing it? In popular imagination, the observer must be a conscious human. But that's not necessarily true. If we performed the double slit experiment with detectors on the slits, no interference pattern appears. This remains true whether we actually look at the data from the detectors. So do the detectors themselves count as observers? Further complicating matters are the experiments of quantum erasure. I will not cover the details, but it's possible to set up detectors such that the information from the detectors is erased after it has been measured. If the information is erased carefully enough, the interference pattern reappears. So sometimes a detector counts as an observer, and sometimes it doesn't?

At this point, I should clear up a common misconception about wavefunction collapse. Some people confuse wavefunction collapse with observer effect. Observer effect occurs because in order to observe the particle, we must knock it with another particle. Because we're hitting the particle, we change it when we measure it. This is not the same as wavefunction collapse. There are actually other ways to observe a particle without knocking it with another particle. Wavefunction collapse can occur whether you physically touch the particle or not. I should also add that the observer in no way "decides" where the particle will appear. Wavefunction collapse is entirely random, and does not depend on the state of mind of the observer.

Back to the detectors. It turns out that it does not matter whether we consider the detectors to be observers or not. Further research has developed a mechanism called "quantum decoherence". In a complicated system, wavefunctions become "decoherent," and no recognizable interference patterns can occur. Any such system will act like an observer and appear to be able to collapse wavefunctions. This is the idea behind the Many Worlds interpretation, an alternative to the Copenhagen interpretation. According to this interpretation, wavefunctions never actually collapse, but only appear to collapse through the mechanism of decoherence. The Many Worlds interpretation implies that our universe's wavefunction is equal to the sum of many non-interacting parallel worlds. In other words, all quantum possibilities are realities in a parallel universe. That may seem like a lot to swallow, but the advantage of the Many Worlds interpretation is that there are no awkward distinctions between observers and non-observers.

There are also other, less popular interpretations to quantum mechanics. Some interpretations say that the wavefunction is not real, but is a representation of what we know about a particle. I understand the philosophical appeal of such interpretations, but in practice they require other nonintuitive rules, and generally just make things harder. Note that the scientific results of every interpretation must agree with the Copenhagen and Many Worlds interpretations, otherwise we would quickly disprove one interpretation or the other.