There are infinite versions of you living out every potentiality in a vast multiverse of parallel worlds
Or, so says the Many-Worlds Interpretation of quantum physics. The modern idea of the Many-Worlds Interpretation of quantum physics has been in the news recently, mostly due to a new popular book on the topic, Something Deeply Hidden by Sean Carroll. These ideas can be traced back to a 1957 Ph.D. thesis by Hugh Everett III entitled On the Foundations of Quantum Mechanics. However, it was mostly ignored until 1970 when Bryce DeWitt resurrected it in an article Quantum Mechanics and Reality appearing in Physics Today. Since then, a growing number of physicists have subscribed to these ideas, many referring to themselves as Everettians.
Most popularizations of the Many-Worlds Interpretation focus on the metaphors of a universe which “branches” into “parallel” worlds. This leads to all sorts of confusion. Not only can you waste your money on a Universe Splitter app (which definitely doesn’t split anything), but physicists even argue amongst themselves at the level of these metaphors. Let’s call this kind of stuff Metaphorical Many-Worlds and not discuss it further. Is there a better way to think about the Many-Worlds Interpretation than this? Yes — and the first thing we are going to do is stop calling it that. Everett’s core idea was the universal wave function. So what is that?
A wave function is a mathematical variable (like “x” from algebra class, but more complicated) that is used to calculate what will be observed in experiments. It is usually written with the Greek letter ψ. Another name for it is quantum state. State means exactly that — all the information needed to predict what will happen, summarized in the most succinct way possible.
It’s not hard to imagine that states can change, and the point of physics is to predict how. But here’s the rub. There are two rules in quantum mechanics for how states change, and when to apply them is arbitrary and at the discretion of the user of the theory. This bothers all physicists to some extent but bothered Everett the most.
The two different ways quantum states can change in plain language are:
Process 1: ψ changes discontinuously when a measurement occurs.
Process 2: ψ changes continuously according to the Schrodinger equation otherwise.
Everett’s executive summary is this: you can do away with Process 1 by considering the quantum state of the entire universe — the universal wave function. This wave function evolves according to Schrodinger’s equation always and forever.
This is where all Everettians start. Carroll calls it “Austere Quantum Mechanics” for its beauty and simplicity. One state, one equation — all’s right with the world. There’s also just one problem — it doesn’t fit at all with our experience of reality. We don’t experience the world as quantum things — being in superposition and entangled and whatnot — we experience a definite classical world. We really do experience Process 1. That’s why it’s there, after all.
It is at this point where most discussions go off the rails. There is Austere Quantum Mechanics and there is Metaphorical Many-Worlds. No one but Everett talks about Austere Quantum Mechanics beyond this point. As promised, I won’t repeat anything more about Metaphorical Many-Worlds — you can find that in any popular science article on the topic. So, how should you think about Austere Quantum Mechanics without falling prey to the allure of Metaphorical Many-Worlds? Everett used a clever argument to illustrate his point, but we need to understand what superposition is to follow it.
Superposition is easily illustrated by waves. In the image below, the red wave is obtained by adding all the blue waves together. The red wave is a superposition of blue waves. There are several ways to think about this. First, if all you have is blue waves, then you can make the red wave by making all the blues ways at the same time. On the other hand, perhaps there really are no blue waves — maybe there is only the red wave. Well, you are always free to think about the red wave as if it were made of blue waves.
Now imagine each blue wave is a wave function that contains all possible states of the universe including the memory states of observers and the correlations they have with other perceived events. For example, the first blue wave could be, a coin was flipped and landed heads and an observer’s memory state records the same. The second blue wave could be the opposite. In classical physics, adding together states of the universe has no meaning. But, in quantum physics, the superposition of the two wave functions is also a valid state of the universe. This is roughly how Everett presented things. He imagined all the possibilities and assigned a wave function to each. Then he added them all up to arrive at the wave function of the universe.
Everett’s was the bottom-up approach. It’s liable to cause confusion because it usually starts with one observer and one event. This is too personal and what usually leads to confusion such as the idea that the observer could “split” the universe into two wave functions then and there. Let’s avoid that by considering the top-down approach. Indeed, those Everettians that claim the Many-Worlds Interpretation is the most parsimonious one should prefer this approach.
Consider the often unstated assumption that comes before Process 1 and Process 2.
In modern textbooks on quantum mechanics, this is usually called the first axiom. Let’s call it Process 0. That is,
Process 0: ψ is a complete description of a system.
Now, take the system to be the entire universe. So, it has a wave function. And that’s it — we’re done. How’s that for austerity! Process 1 is already not needed if you follow Everett. But also Process 2 is not needed because ψ contains within it the entire history of possible states.
In this view, we start and end with the red wave. That’s all there is. It can be considered a superposition of all non-interacting possibilities, and hence contains observers that perceive events happening. And if there is a universal wave function, and if it is the one true objective reality, then you are more fictitious than not — a beautiful, if not wholly imaginary blimp in an arbitrary decomposition of a static, infinitely austere mathematical reality.
A more poetic analogy might have been to decompose the red wave as many blue waves which include melodies and symphonies. Superimposing all your favorite songs would sound like horrible noise, but that noise would contain music within it. All sounds contain a Beethoven symphony. The question is, is that a useful way to think about it?
For me, the answer is no. The universal wave function serves the purpose of god. It is a simple fiction that is at once easy to comprehend but contains as much complexity as needed when the mood strikes. That is not parsimonious — it is irrelevant. If you disagree, the complaints department is in a parallel universe.