The Measurement Problem and Many Worlds
Wavefunction collapse is loosely defined as the point at which a “quantum” system becomes a “classical” one. But what does that mean?
Warning: This post may contain traces of philosophy.
Quantum mechanics tells us that the variables we conventionally think of as “definite” (such as position and momentum of an object in 3d space) don’t actually correspond to real, definite quantities when you go down to a small enough scale. This is surprising to learn at first, since it contradicts our intuition that objects have properties that persist over time, which we can measure whenever we feel like it.
Put together a source that can produce one particle at a time (e.g. a photon), a pair of slits through which the particle can go, and a detector, and you’ll find that instead of the particle going through one slit or the other, it behaves as if it went through both slits at once (creating an interference pattern over many trials).
This is the classic double-slit experiment, and it exemplifies the so-called wave-particle duality that physicists sometimes like to talk about. This experiment tells us that despite the particle-like qualities of matter and radiation (such as photons of light), our macroscopic notion of position does not apply so well to small things, which appear to take on a whole continuum, or superposition of position states simultaneously.
Ok then, so if position isn’t well-defined for our exemplary photon when it’s going through the double slit, what changes when it hits the detector? Why does the photon “land” at a seemingly definite point, if we were just told it was in multiple places at once?
This question is quintessential of the measurement problem of quantum mechanics, which asks exactly what happens when a wave-like system “collapses” into a single, macroscopic state. The measurement problem has been the topic of much debate ever since the very beginnings of quantum mechanics, and gives rise to several, mutually exclusive but individually self-consistent interpretations of what “really” happens during wavefunction collapse.
The Many Worlds Interpretation
The “many worlds” interpretation of wavefunction collapse is, in fact, that there is no wavefunction collapse. In other words, when the photon (still being in a superposition of many positions) hits the detector, the detector itself enters a superposition of having detected the photon in all possible places.
To get a better idea of what this means, picture the detector as being actually composed of many smaller detectors, each of which will send an electrical pulse whenever it detects a photon, which gets recorded and stored somewhere for later. Now we can consider the system of the photon and all the detectors as a single, interconnected whole.
What we know for certain about this system, is that we are forbidden from seeing multiple detectors activate in response to the same photon: this would contradict our prior knowledge about the system (that the photon is in a definite number state, i.e. there is exactly one photon).
What quantum mechanics does not forbid is that the system can enter a state of superposition, such that we simultaneously associate a non-zero amplitude (corresponding to probability) to every single detector having been activated. In other words, collapse hasn’t happened (yet). In fact, for this to hold true we need only assume that the detectors themselves are made of the same stuff as the photon (quantum fields).
So have we solved the measurement problem? Not quite. Because we’ve still not explained how the detector system eventually goes from being in superposition to being in just one of the possible states. In effect, we’ve just moved the problem rather than solving it. We could, in principle, move the problem even further by saying that anyone who even looks at the detector system also enters a superposition by becoming entangled with the state of the detector.
This is precisely what the many worlds interpretation asserts: we do away with the idea that the photon picks a single position at the moment of detection, with a single version of events playing out until the observer (you) observes the outcome. Instead, all possible versions of what “could” happen play out simultanously, ad infinitum.
The role of consciousness
This view is still somewhat unsatisfactory. After all, wouldn’t this imply that we (the observer) ourselves enter a superposition of possible states upon observing the outcome of some quantum experiment?
We can answer this question with another question: How would you know the difference between being in superposition, and not being in superposition? If a quantum experiment has (for instance) two outcomes
The key thing to note here is that neither of the superimposed “versions of you” can ever observe each other, and each version has just one of two possible subjective experiences. While both simultaneously “exist” in a very real way, they can never interact with each other (they are orthonormal in the quantum mechanical sense). We can then think of our conscious experience as having followed one of two equally possible trajectories through time.
In this way, the wavefunction never actually collapses, rather we just become a part of it. And that’s the crux of the many world interpretation. This still raises questions about the exact nature of consciousness, but at the very least clarifies its role in this particular interpretation of quantum mechanics.
Conclusion
With this post I aim to share my understanding of the many worlds interpretation. I’ve written it based on my own learnings and thoughts about quantum mechanics. I hope it sheds light on the measurement problem in a useful way. I intend to write more on this topic and related topics in the near future.
Take care!
Jamie