__Why many worlds?__

Quantum mechanics is often presented as being “our most successful theory ever”. Despite 100 years of stringent experimental tests it has never been proved wrong. It has been confirmed to an accuracy of 1 part in 10^{12} and has even now been tested in space-based experiments. It underlies much of modern technology, including pretty much the whole information and computing industry. And it has predictive power in an extreme range of scenarios, from the smallest constituents of our universe to a fraction of a second after the Big Bang. For these reasons, it seems reasonable to assume that quantum mechanics is correct, and does not need to be modified, at least not yet.

We can then ask the question: If quantum mechanics is correct, then what does it tell us about the universe? But before answering this, we should probe whether this is a reasonable question in the first place. There is another option: quantum mechanics could just be a tool that is extremely powerful for predicting the outcomes to experiments, and we could say that it’s equations don’t directly tell us about the world itself. To explore this option, we can ask what it would mean for other scientific endeavours. Is the theory of dinosaurs only useful as a tool for predicting what kind of fossils we will dig up in the future, or does it tell about tell us about real creatures that existed in our past? When DNA was first discovered, was the theory of its double-helix structure only useful as an explanation of why a certain x-ray diffraction pattern was observed, or does it tell us about a real molecule that exists in ourselves? And are our theories of stars and galaxies only relevant to explain why we detect certain patterns of light in our observatories, or do they tell us about fantastic objects beyond our solar system? Of course in all these cases we assume that our theories tell us about real objects that exist independent of us. In that case, it seems reasonable to assume that quantum mechanics is telling us about the universe in which we live, about its structure and behaviour and our place in it.

What, then, does quantum mechanics tell us about the structure of the universe? To answer this I will refer to the Schrödinger’s cat thought experiment, which I introduced in more detail in two previous posts (here and here). Briefly, a cat is placed in a sealed box containing a radioactive atom and a vial of cyanide. If the atom decays, the cyanide will be released, killing the cat. It is straightforward in quantum experiments to put the atom into a strange state known as a *superposition state*, in which it has both decayed, and not decayed, at the same time. Now comes the bizarre prediction of quantum mechanics: if the atom is in a superposition, then the cat will also end up in a superposition of being dead and alive.

It is reasonable to wonder whether the cat can really be dead and alive simultaneously. One option here is to assume that the prediction must be incorrect, and therefore that quantum mechanics is incorrect and must be modified in some way. But, as we have seen above, modifying quantum mechanics should not be taken lightly. Before taking such a drastic step, we should first explore whether the situation can be explained without having to modify quantum mechanics. Yet another option is to say that the equations in quantum mechanics aren’t telling us about the actual state of the cat, and are only a tool that tells us what would happen if we observe the cat. But again, it is a drastic departure from how we normally view science, and should only be used if we can’t make sense of the situation otherwise. I discussed these alternative options __here__ and __here__.

But despite being wildly counterintuitive (I will return to this later), what is the problem with saying that the cat is dead and alive simultaneously? The problem comes because we know that when we open the box we will either see a dead cat or an alive cat. If the cat was truly dead *and* alive, shouldn’t we expect to see a weird fuzzy cat when we open the box? The answer is no. Remember we are attempting to use unmodified quantum mechanics directly, so we should use it now to get us out of this riddle. What, then, does quantum mechanics predict we will see? The answer is even more obscure than before: quantum mechanics does not predict that you will see a fuzzy cat, but rather it predicts that *you* will enter a superposition of seeing the alive cat and seeing the dead cat. Again there seems to be an immediate intuitive objection to this. *Surely I cannot be in a superposition – surely I would notice this and be able to tell in some way that I am in this obscure state.*

Again we can use quantum mechanics to resolve this, but it turns out that it takes a significant amount of work and effort to do this. Nonetheless, the now well-established theory of *decoherence*, which I explain in a __previous post__ and in __this article__, provides the answer. To cut a long story short, decoherence shows that the two parts of the superposition cannot interact or interfere with one another, and for all practical purposes (FAPP) they can never know of the other’s existence. We therefore interpret this superposition state as follows: FAPP there are two versions of you, one who has seen a dead cat, and the other who has seen an alive cat. These two versions cannot interact with each other, and will never be able to know of the other’s existence. When you open the box we say that the universe “branches”. From your perspective you either see the cat dead or alive. But there will be another version of you somewhere out there, on another branch of the universe, who sees the other outcome.

Another reasonable objection here could be to question whether it makes sense to interpret both parts of the superposition as being real. But with some straightforward calculations it can be shown that it is perfectly reasonable to do this: the physics is completely the same whether there is just one version of you or two. It can be shown that both parts of the superposition obey the laws of physics as usual, and essentially live in what appear to be normal universes.

Initially there was just one cat. But after the radioactive decay and cyanide release the universe branched into two “sub-universes”, one containing the dead cat and one containing the alive cat. These sub-universes are called *branches*, but they are also popularly termed “worlds”, hence the theory being called many worlds theory. They are even called parallel universes, in which case the totality of universes is the “multiverse”. But this terminology can be misleading, because there is really only one world, and one universe, which contains a superposition state of a dead and alive cat. Proponents of this theory prefer to call it “Everettian quantum mechanics”, named after the great Hugh Everett, who first realised that quantum mechanics could be interpreted in this way.

The superposition then spreads out in the following way: Before opening the box there was only one version of you. But on opening the box you join the branches of the superposition state. On one branch the cat is dead and you are observing the dead cat, whereas on the other branch the cat is alive and you are observing it as such. If you then talk to your friend they will also join the branches. On one branch they might see you as relieved that the cat was alive, whereas in the other branch they are consolidating you or berating you for your unethical choice of experiment. As you and your friend interact with more people, and more objects, the branching spreads. In fact, it often only takes a tiny amount of information to be distributed for branching to happen. A single photon that has interacted with you can fly out of the window hitting a nearby building, at which point the building also splits and joins the two branches. This process carries on – as information spreads more and more things join the branches.

I am unsure whether it is known the exact manner by which the branching spreads, and at what rate etc, but the basic theory is now pretty advanced in predicting that, despite the obscure superposition state that quantum mechanics predicts we live in, the normal classical reality emerges and we are completely oblivious to the other branches (e.g. see __quantum Darwinism__). I should also briefly mention that this branching process happens almost continuously all around us. The fundamental constituents of our bodies – the electrons, quarks, and photons – are constantly splitting into superpositions, and often these superpositions lead to branching in a similar way as in the Schrödinger’s cat thought experiment. For example, in chaotic systems or systems at a critical point small changes in the microscopic initial conditions can lead to vastly different macroscopic final states. Then, if the initial conditions are in a superposition, which they often will be, a branched macroscopic world will emerge from this.

I will now address some of the common criticisms against many worlds theory. I invite comments to this blog of more criticisms, and I will try to address these in a future blog. I will try to keep things un-technical, but near the end things might get a little technical in order to give more complete explanations.

__Common criticisms__

*“Many worlds is far too radical.”*

On the contrary, the basic formalism of many worlds theory can be seen as our most *conservative* option! As explained above, the other options are to assume that quantum mechanics is incorrect, and therefore modify it in some way. Or to assume that the equations in quantum mechanics do not tell us about reality. As I argued above, the first option is radical in the sense that it disregards our most successful theory ever, and tries to change it. Whereas the second option goes against pretty much all of our scientific thinking to date. Many worlds theory, on the other hand, takes quantum mechanics seriously, at face value, and we have seen above that such a theory can indeed explain the apparent paradoxes presented in the Schrödinger’s cat thought experiment. The only catch is that the picture of reality predicted by such a theory is completely counterintuitive…

*“Many worlds is unintuitive and ridiculous.”*

Should intuition be used to rule out theories? It used to be counterintuitive that the world was round, or that the Earth orbits the sun, or that we evolved from monkeys. But our intuition seems to have been refined to encompass these. It is still counterintuitive that all objects around us are largely empty space, or that our bodies are filled with billions of microbes that are essential for our survival, or that our planet is flying through space at millions of mph. The last point bears a resemblance to the explanation of Schrödinger’s cat above: wouldn’t we expect to feel the wind rushing past us if we were flying through space? At first sight maybe yes, but after more careful analysis scientists have made perfect sense of this conundrum.

For me, the examples just given make it very clear that our intuition should not be used to rule out theories. Sure, if our theories predict contradictory things, such as 1+1=1, then we should seriously question our assumptions and calculations. But the picture of reality that many worlds predict is self-consistent and fits perfectly with our observations.

*“Many worlds theory unnecessarily invents the existence of almost infinite numbers of worlds.”*

Many worlds theory doesn’t *invent* the existence of other “worlds”. We don’t take the Schrödinger’s cat paradox and say “we can solve this paradox if we *invent* multiple parallel worlds”. Rather, we take the reasonable assumptions that quantum mechanics is correct and that we can take it literally, and from this we *predict* the existence of multiple worlds.

*“Surely the universe isn’t that big.”*

What we thought of as our “universe” used to be much smaller. Ancient Europeans used to believe that the whole world was just Europe, and other cultures thought in similar ways. Then eventually people discovered that the world was actually round and was far bigger than just one continent. Then we discovered that the sun was not just a part of our sky, but rather we were part of a huge solar system. Nowadays, it is assumed that the universe is humongous, maybe infinite, and contains billions of stars. At each stage our picture of the world grew exponentially. Sure, the jump that many worlds theory makes is unimaginably bigger than these other jumps, but it still fits with the pattern that the universe is actually much bigger than we would otherwise expect.

*“Many worlds is untestable.”*

As discussed above one of the main alternatives to many worlds theory is that we must modify quantum mechanics. This has the obvious perk that it can be tested. Attempts are already being made to see whether gravity collapses the quantum state (thus leaving Schrödinger’s cat either dead or alive, not both). In short, a large mass must be put into a superposition, and it must be sufficiently isolated from the environment so that decoherence doesn’t already lead to the appearance of collapse. Then, because the mass is large, gravity-collapse theories would predict that the mass will spontaneously collapse. Observing this spontaneous collapse would provide strong evidence for this theory.

In many worlds theory, we cannot ever interact with or interfere with other branches of the universe. In this sense, we cannot directly test the existence of these other “worlds”. However, there seems to be double standards in favour of collapsed theories, because if the experiments to test collapsed theories came out negative, then this would rule them out and provide strong evidence that quantum mechanics is correct as it stands. If this pattern continued eventually leading to experiments putting massive objects, or conscious objects, or highly complicated objects such as quantum computers into superposition states, then this would also provide strong evidence that quantum mechanics is correct as it stands. On the other hand, and most importantly, if these experiments proved collapse theories to be correct, then this would directly disprove many worlds theory. *Many worlds theory is therefore falsifiable.*

One other main alternative to many worlds theory, which was introduced above, is to say that quantum mechanics is just a tool for predicting outcomes to experiments, and it’s equations don’t tell us about reality. This is an alternative philosophy of quantum mechanics, or an alternative interpretation, and in this sense there is no experimental way to distinguish between them. However, in my opinion, if we are eventually able to put massive and maybe even conscious objects into a superposition state, and if repeated experiments prove that decoherence does indeed mean that different branches in many worlds theory cannot ever interact with each other, then these facts would make many worlds theory much more acceptable and plausible. My prediction is that eventually many worlds theory will be the textbook way to interpret quantum mechanics!

__Some more-technical objections__

The following two issues seem to have been, for a long time, two of the most important technical objections to many worlds theory. However, these seem to have now been solved (at least according to many worlds practitioners!). I won’t go into details, but I’ll try and briefly summarise the objections and their resolutions. However, so that this post doesn’t go on too long I will use a bit of technical jargon at times and assume some more detailed knowledge of quantum mechanics.

*Probability in many worlds*

Again imagine Schrödinger’s cat just before you open the box. This experiment can be set up so that the amplitudes of the two parts of the superposition (dead and alive cat) are equal. In the usual way quantum mechanics is presented, we say that there would be a 50% chance of seeing the dead cat when the box is opened, and a 50% chance of seeing the alive cat. But in many worlds *both* outcomes happen. In fact, the Schrödinger equation is deterministic, so many-worlds quantum mechanics is an entirely deterministic theory! So how does the probability come in? In many worlds we say that *the probability that “you” end up in the branch *with the dead cat is 50%, and similarly for the alive cat. I put “you” in quote marks because there are two versions of you. Just from your perspective you only see one outcome. So in that sense if you see the alive cat, then you will consider this version of you to be the real you! This would be the same for any quantum experiment: the probabilities don’t tell us the probabilities of the different outcomes happening, but rather they tell us the probability that you will end up in a branch with a given outcome.

When the different branches have equal probabilities then the basic idea of probability is somewhat intuitive: initially there was one version of you, but in the end there are two versions of you. Both versions are equally real. Therefore, it makes sense that there will be a 50% chance that the version of you that you experience is the one that sees the alive cat, and so on. However, if the two parts of the superposition have unequal weightings, say 80% alive and 20% dead, then this is no longer intuitive. These probabilities would mean that you have an 80% chance of ending up in the branch with the alive cat. But there are still two versions of you, and they are both real. How can one have a bigger “weight” than the other one? Is one more real than the other?

To resolve this problem, many worlds practitioners (who seemingly largely work at Oxford University!) have provided rigorous proofs to demonstrate that probability does actually make sense in many worlds. They do this in two ways. Firstly, using decision theory, it can be shown that a rational agent should make decisions based on these weightings. For example, if the weightings are 80% and 20%, then a rational agent would be willing to bet £1 at 1/4 odds that they will end up in the 20% branch. Secondly, it can be shown that, if you repeat an experiment many times, in the limit the number of times a certain outcome happens will fit with these weightings. In this sense, you do have an 80% chance of ending up in the branch with an 80% weighting. I acknowledge that this explanation might still feel unsatisfactory, but the maths works!

In addition, many-worlds practitioners will argue that when properly scrutinised, we are far from fully understanding probability anyway (I won’t go through the arguments here, but e.g. watch this). They then argue that certain unanswered questions in classical probability theory *can* be answered in many worlds theory. In particular, the Born rule can be derived from some simple assumptions (rather than being merely postulated, as it is usually). I’m sure that many readers will be unsatisfied with this brief answer, but the details are beyond the scope of this blog post! Interested readers are referred to David Wallace’s book “The emergent multiverse”.

*The preferred basis problem*

Historically a serious technical objection to the many worlds theory was the so-called preferred basis problem. I will only give a brief introduction here – I give a much more detailed (and more clear) explanation in __this article__. In quantum mechanics, there are different *bases* in which we can represent quantum states. A qubit has two states, which here I will call **one** and **zero**. However, we can write these states in a different basis to get **plus** = **one** + **zero**, and **minus** = **one** – **zero**. The two different bases are equally valid, and equally real, and in the lab it is just as easy to prepare the state **one** as it is to prepare the state **plus**. Does this same principle hold in the macroscopic world? The answer is no: we only ever see a **dead** cat or an **alive** cat. Mathematically it would be equally valid to write these states in the basis **plus** = **dead** + **alive**, and **minus** = **dead** – **alive**. But there is a big difference between these different bases. We know from the Schrödinger’s cat thought experiment that the **plus** state exhibits branching in many worlds theory. But the **dead** state does not – the **dead **state does not branch into a **plus **branch and a **minus **branch, as we might expect from the maths. We say that the **dead**, **alive **basis is the “preferred basis”. But *why *is it preferred, and what mechanism makes one basis preferred over and other?

The theory of decoherence now provides rigorous and comprehensive answers to these questions. In short, we can’t just treat the cat as an isolated system, but rather we have to factor in the interaction between the cat and the photons and particles in the box. Once this interaction has been accounted for, it can then be shown that there is one particular basis that remain stable and does not exhibit branching – this is known as the preferred basis. It can then be shown (though not directly) that the preferred basis for the cat is indeed the** dead**, **alive **basis. If the cat is prepared in a superposition of these basis states then branching will quickly occur. Whereas if the cat was, for example, alive, then branching would not occur. The same goes for us when we open the box: if the radioactive atom and cyanide were removed from the box, meaning that the cat would always be alive, then we would simply open the box and see the alive cat. No branching would happen. But if the cat is in a superposition then when we open the box branching occurs.

*Conclusion*

I hope that, at the very least, I have convinced you that many worlds theory is a reasonable and rigorous theory for how we should understand our quantum universe. By taking quantum theory seriously, and literally, we can overcome the paradoxes such as Schrödinger’s cat, and provide a self-consistent picture of our universe. At worst this picture is unintuitive, but at best it paints a fantastically interesting and endlessly fascinating picture of our universe. If you are still not happy with many worlds theory, rest assured that somewhere in the multiverse there is a version of you that is!

Acknowledgements: My general interest and knowledge about many worlds theory comes from David Wallace’s comprehensive book “The emergent multiverse” and Max Tegmark’s popular book “Our mathematical universe”. Specifically for this post, much inspiration and information came from David Wallace’s YouTube talks: https://www.youtube.com/watch?v=2OoRdyn2M9A&t=21s and https://www.youtube.com/watch?v=8turL6Xnf9U&t=2s . I’ve been told that David Deutsch’s books are also excellent!

Fantastic. One of my favorite topics. I wrote a novel about it. Thanks for writing such an elaborate, yet simple to grasp, piece.

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Thanks! What’s you novel called?

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Existential Tableau. You should be able to find it by clicking on my avatar, name.

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Excellent discussion. I would greatly appreciate your thoughts on entanglement and Bells Theorem using the Many Worlds Interpretation.

Thank you

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Thanks Bill. I haven’t thought about this in a while but this is my understanding: We start with two particles in an entangled state, |00>+|11>, and one particle is sent to Alice and one to Bob. Say Alice makes a measurement first. Then Alice splits into a superposition of measuring 0 and measuring 1. As Alice (almost instantaneously) interacts with her surrounding environment, this quickly create a universe-branch, and hence a pair of parallel universes, one in which Alice measured 0 and one in which Alice measured 1. Say the state of Alice (and her surroundings) measuring 0 is A0, and similarly for 1, then after Alice’s measurement results in the state |A0>|00> + |A1>|11>.

Next Bob makes a measurement. In a similar way, Bob will become entangled with the particles, and also with Alice and her surroundings, giving the state |A0>|00>|B0> + |A1>|11>|B1>. But Bob’s and Alice’s environments increasing interact with a larger volume of space, e.g. by photons flying around hitting things, then quite quickly the border between the two environments will meet. But at this point nothing magical happens because Bob and Alice are entangled already because they were entangled with the particle, so the branch in which Alice measures 0 is the same as the branch in which Bob measures 0.

In short, there is no non-locality, because everything travels only at the speed of light. And there is realism, because we can assume that the particles have a specific state (I think). So as far as I know in many worlds there is no problem at all with Bell’s Theorem, and we can have both locality and realism for free!

To do this analysis properly we have to imagine Alice and Bob measuring in difference bases, which basically results in a branch into more (probably 4) universes. But it still works nicely and retains locality and realism as far as I know.

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