This ‘zero-worlds’ theory might just be crazy enough to be true

Reading | Physics

Hans Busstra | 2021-07-18

His own quantum theory made Werner Heisenberg ponder deeply on the nature of reality: “I think modern physics has definitely decided in favor of Plato. Physical objects are forms, ideas which can be expressed unambiguously only in mathematical language.”

Just like all of us mortals, physicists are somehow stuck in Plato’s cave, never being able to see the actual flames outside the cave that cast shadows on the walls inside. At the end of the day physics cannot answer metaphysical questions for us about what matter is, or if it exists independent of our observation. When I first realized this, I found it deeply unsettling, but thought to myself: at least physics can give us the laws of nature that govern the shadows in the cave, the laws governing what we call matter.

But it only took me a surface reading of modern physics to realize that things are a bit more complicated still. For instance, there is a pretty good chance that a modern physicist sitting beside you in Plato’s cave could say something like: ‘let go of the idea of one outside of the cave, there is an infinitely large amount of different ‘outsides’ that exist simultaneously, you only get to see one of them.’ Or, put differently: ‘let go of the idea that there are deterministic laws governing the flames and shadows, there are only probabilities.’ But recently I sat down with a physicist that even takes things a step further, and says: ‘what if there is no outside of the cave at all?’

Markus Müller PhD, who is Group Leader at the Institute for Quantum Optics and Quantum Information in Vienna, Austria and visiting fellow at the prestigious Perimeter Institute for Theoretical Physics in Canada, came up with a probability theory that can make accurate mathematical predictions about the world we see without the notion that an outside world actually exists. With a smile on his face Müller calls it a “zero-worlds” theory.

Müller’s ideas, based on his work in quantum information theory, are hard to grasp because they are about as counter intuitive as it gets. But to solve some of the fundamental questions of modern physics, they might be a hint to the right direction. To quote Niels Bohr, maybe Müller’s ideas are “crazy enough to be true.”

 

What is in essence the difference between information theory and quantum information theory?

The main difference is, I would say, that in standard information theory you can always reduce everything to a lack of knowledge. For any given question, you can always assume that the answer is already out there in the world. You just don’t know it. This turns out to be wrong in quantum theory: it just doesn’t work to assume that the answers to all questions are already out there before you ask, unless we give up other important principles of physics like locality. There’s a kind of missing information that’s not due to missing knowledge, but due to the fact that the world hasn’t decided yet. I hesitate putting it so simplified, and would rather go into the mathematics to explain this rigorously, but let me give a practical example of quantum information theory. If information isn’t ‘out’ yet, then you can use it to do cryptography and have a secret key that nobody can spy on, because you can’t spy on a key that’s not yet there. You can only spy on information that’s already out there in the world. Put differently: if the world hasn’t ‘decided’ yet whether an electron spins left or right, and then you measure it and find an answer, then nobody else can know the answer unless you tell them. This is a colorful way to explain the mathematics of parts of quantum cryptography or the quantum generation of random numbers—though I know how counterintuitive this sounds to someone unfamiliar with quantum information theory.

 

It is absolutely counter-intuitive and confuses everything about what we normally understand when we talk about ‘information.’ Is it correct that in quantum theory we can only speak of probabilities, instead of ‘solid’ information about the world?

On a microscopic level quantum theory only gives you probabilities for an outcome, it doesn’t tell you which outcome you will see. So if you send a photon to a half-silvered mirror, it can either be reflected or pass through, but you don’t know which of the two you will get. But if you send two million photons in a row, you can be pretty sure that you will roughly get one million passes and one million reflections. In a similar way things average out in our macroscopic world: for large objects and many particles, most predictions become essentially deterministic.

 

What fascinates me, is that in this probabilistic world everything is theoretically possible, for instance many copies of myself could be out there in the universe. What bothers you is not so much the weirdness of these ideas, but the fact that current physics cannot give us accurate probabilities about the weirdness, right?

Well, according to some models the universe is so extremely large that we should expect very unlikely things to happen, and that they should happen a large number of times. Now the idea of copies of yourself, that you’re referring to, is called the Boltzmann brain problem. Imagine a brain popping up somewhere in the universe with exactly all the memories that you’re holding of your life on earth. According to some cosmological models, it is much more likely in the universe for such a ‘Boltzmann brain’ to spontaneously emerge, than it is for our human brains to have evolved on earth. But if this is true, doesn’t this mean that we should believe that we are Boltzmann brains—and believe that in the next few moments, we will disappear as quickly as we have popped up? Cosmologists ponder about these questions, because they think it allows them to distinguish “good” from “bad” cosmological models—those with or without Boltzmann brains. But if you try to answer questions like this, you automatically run into fundamental other questions, like how big is the multiverse? Why do the laws of nature have the form that they have? Could they be different somewhere else in the universe? And: where exactly are we in this universe?

 

OK, so if I understand correctly: if we for instance want to calculate the probability that we’re a Boltzmann brain, we need to know these variables, some of which we cannot in principle know…

Yes, according to some models of our universe, there has been in the beginning after the Big Bang a phase of rapid growth. The universe was expanding very rapidly and it’s become extremely large. We only see a small portion of it until we reach the event horizon, the place from where light cannot reach us to tell us what’s out there. And in different universes different laws of physics could apply. So there are simply too many unknowns.

 

Now you came up with a rather remarkable ‘work around’ and suggest a bold thought-experiment: what if we let go for a moment of the whole idea that we are located in a physical universe, could that help us to be a bit more precise on the probabilities of, for instance, the idea of Boltzmann brains?

Instead of making all sorts of metaphysical assumptions about what is out there in the universe, I want to begin with something that’s kind of unquestionable, namely that I’m an observer and I see something. Now you could talk about consciousness and subjective experience but for me as a physicist it’s actually more technical. I would just say I have a bunch of locally available data and I want to make a guess what the data will be next. Usually, we assume that the external world determines your next data: you look up and see a bright spot in the sky because there is the Sun out there, and the laws of physics determine what the Sun looks like. So to predict, we model the world, say where we are in that world, and apply the known laws of physics. But the Boltzmann brain problem shows that this doesn’t always work—you could be a brain floating out there that has a memory of the sun, without a real sun out there.

Thus, I’m proposing something different: assume that what’s next is determined directly by the data that you hold and nothing else; no external world, no physical laws in the usual sense. Instead, a single claim: what you see next is determined by a probability law called “algorithmic probability.” It’s something that computer scientists have discovered independently. It gives computers a way to predict what happens next without knowing the laws of physics; it’s a kind of “gold standard” for machine learning. It turns out that this probability law is in principle in agreement with physics: it predicts that what you see looks very much as if there was an external world around you—without having assumed that there is actually such a world in the first place.

 

It sounds like a radical quantum approach to the macroscopic world, putting the observer or the measurement at the centre. But how exactly does algorithmic probability allow us to infer a complete external world only from ‘data’ that we see directly?

An understandable way of explaining it is to take a look at Conway’s Game of Life. This is a simulated world on your computer built up of lots of squares that can be black or white on a large canvas. These squares, called cellular automata, are governed by a couple of simple rules like: if a white square is surrounded by three other white squares it turns black. Now you start the Game with a simple initial state and then let it run and the most interesting structures evolve. It actually is a great metaphor of evolution to see how complexity emerges from very simple rules. And say this is our universe, this super large canvas with cellular automata giving us data. We are ‘trapped’ in only a very small part of the canvas and we don’t know the rules that govern the patterns we see. So what if we don’t ask what is the explanation for the patterns we see, but simply: what pattern will I see next? The way it’s mathematically formulated is to scan through all possible computations for a particular pattern and figure out what the simplest computation is, and with a high probability that will be the computation to predict what you see next.

A cellular automaton with very simple local rules (only slightly less simple than the Game of Life), seemingly giving rise to a complex world of large, interacting triangular patterns. No triangles or global interactions actually exist in the rules.

 

Still this sounds just as abstract as it sounds commonsensical: to predict what we see next around us, we look at what we’ve seen before—the basics of induction. What exactly is the value of this approach?

My approach allows us to address questions that are impossible to answer within our usual picture of physics: How should we think of cosmology‘s “Boltzmann brain problem” explained above? Why is there a world with laws of physics in the first place? How should we think about the puzzles of quantum mechanics? If we simulate a human being on a computer, will it “wake up” in the simulation?

Currently, many of these questions are studied by ad-hoc philosophical contemplation, but my approach gives concrete mathematical answers. For example, it allows you to calculate the probability that you will next disappear like a Boltzmann brain. Or, in the simulation example, if tells you the probability that you will next observe the simulated computer world around you as opposed to the ordinary one. In contrast to philosophy, we can check whether this probability law is consistent with empirical science: it’s a single law that is supposed to apply to crazy thought experiments and to ordinary physics experiments alike. This makes it in principle testable, in contrast to ad-hoc philosophical or religious approaches.

 

How does your theory relate to an idealist worldview?

It is a kind of a similar view: my approach claims that some notion of “mind” is fundamental, not the “world.” But there is an important difference: my notion of “mind” is mathematical and information-theoretic. It is not directly related to consciousness or the quality of experience. This is a big difference to many philosophical versions of idealism.

Traditional versions of idealism have always faced a difficulty: how do you account for the outside world? If there is fundamentally only mind, isn’t it a miracle that things look as if there was an external world that evolves according to stringent laws? Where does it come from? How do you explain that there are things that seem to be external to you? The good news here is that you get this for free in my model, you can prove mathematically that things look for us pretty much as if we were embedded in a physical world. There is a fun way to describe what I’m doing. In quantum theory, a popular view is the “many-worlds interpretation”: everything that can possibly happen does actually happen, in a large number of parallel worlds. I agree that there is not “one world”, but I’m proposing the other possibility: a ‘zero-worlds’ theory.

 

One thing that I like personally, but that also puzzles me about idealism, and also about your theory, is that there seems to be the suggestion that ‘mind’ or ‘the observer’ has some sort of agency, that it can really influence the world which it observes, that we somehow cause or mentally construct this ‘zero-world’ you’re talking about. What is your reflection here?

This is a very common misunderstanding, so let me make this very clear: my approach does not at all make any such claims. The ‘zero-world’ is not mentally constructed, and it cannot be modified merely by wishful thinking or one’s personal attitude. In my approach, a notion of “mind” is fundamental, in the sense that a probability law acts on it directly, without mediation by any “external world.” But see: not the mind is in control, but the mathematical probability law.