Intro to the Quantum Measurement Problem

See the previous page: The double slit experiment

Intro to Quantum Weirdness

As previously explained, 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.

The end. Questions? Corrections?
After this post, I think I will take a short break from quantum mechanics.