Google “multiverse paradigm” and you get more than a thousand hits.

According to Wikipedia a paradigm “describes distinct concepts or thought patterns”. Unfortunately, the multiverse is pretty much the opposite: There’s no distinct concept, but instead a variety of loosely related properties of existing theories that are being construed to have a common theme which, we are then told, is sign of an impending paradigm shift.

I’m starting to take offense in this forward defense. If the spread of multiversal “thought patterns” is sold as a paradigm shift, everybody opposed to the multiverse is discarded as being stuck in yesterday. It’s only the enlightened who are ahead of their time and understand the significance. I really don’t think there’s any paradigm here and certainly nothing is shifting. To see why, it’s helpful to distinguish two different classes of multiverses that are presently being discussed, usually thrown together.

**1. The Multiverse of Disappointed Hopes**
Science works by constructing models for real world systems. These models can then be used to understand what happens in the real world, and to make predictions. A theory is a map from a model to the real world. The model should not be confused with the theory itself. The theory is what tells you how to identify properties of the model with the real world. The model is the actual stand-in for the real world system.

Einstein’s General Relativity for example is a theory: it’s a prescription for how to deal with space-time and particles moving in it. A model is the space-time of a star or an approximately homogeneous matter distribution. It’s the

* theory* of General Relativity, but the ΛCDM

*model*. Likewise, there’s quantum field

* theory*, and the standard

*model*. Needless to say, not everybody uses this terminology all the time, but that’s how I want to use it.

Models and theories are not only used in physics and don’t necessarily have to be mathematical. Psychologists have models for human behavior that they apply to patients – the ‘real world’. A drawing is a model, in this case the “theory” that connects it to the real world comes for free with your visual cortex. A story is a model, the “theory” is your knowledge of the language that relates letters to real world objects or actions. And so on. The merit of mathematical models is that they have a very strict quality control, which is self-consistency.

And then there are toy models.

Toy models are models that do not have real world counterparts. It’s drawings of creatures that don’t exit or stories of people that have never lived. They’re playgrounds of creativity that can teach us lessons about the theory, which is why studying toy models is a very common and often fruitful exercise. There’s an infinite amount of such toy models. You could say there’s a whole multiverse of them, all these toy models that don’t map to any part of the universe we know. Asking whether what they describe is real is like asking if Harry Potter really exists because a story has been written about him. The difference between fantasy novels and physicist’s toy models is the size of the interested audience, but in spirit they’re the same exercises in creativity.

So, sure there are models that don’t describe the real world, in physics as well as in painting. That’s because mathematical consistency alone does not imply a model describes what we observe, much like using English does not imply you talk about real people. Additional requirements are needed besides consistency to construct a useful model, and these requirements are always agreement with observations, though this isn’t always explicitly phrased this way. When we assume Lorentz-invariance or renormalizability or absence of ghosts, these are physical requirements ultimately based on our experience.

This means a multiverse that you can get rid of by adding the requirement that the model needs to describe observation is neither new, nor surprising, nor something to worry about. It just means that mathematical consistency of whatever theory it is you’re dealing with is not sufficient to make a particular prediction. The string theory landscape is a multiverse of this type. The only reason people talk about this now is that many of them had been hoping string theory would make some requirements that one needs in the standard model unnecessary. Alas, these hopes were disappointed, though the last word might not be spoken yet.

Does it make sense to instead talk about probability distributions over the models you get when you refuse to use existing ties to observations, here specifically the values of certain parameters? No. Because that’s cherry picking the observations you want to neglect.

In the construction of the model there always enter many other observations that are being neglected if one considers such probability distributions, such as the number of (large) dimensions, Lorentz-invariance, or the existence of space-time to begin with – these are not requirements of mathematical consistency, these are physical requirements based on observations. If you wanted to be serious with asking for the probability of particular models, you should sample over all models, in the end over all that is mathematically consistent. You’d be left with Tegmark’s mathematical multiverse. And in that mathematical universe you’d have replaced the question “Which model describes the real world?” with “Where are we in the mathematical universe?” You don’t gain anything.

Once you have seen the power of mathematical models to describe natural systems, it is natural to ask if there is a mathematical model that describes “everything” we see. I believe there is. But people who search for a “theory of everything” today mean more than that. They want in particular a theory that delivers the parameters in the standard model. But even if that would be achieved, we would still have to use other axioms that are ultimately based on observations. So while it is worthwhile to try to find a simpler model that reduces the number of axioms, including values of parameters, we can never avoid using input from observation. If we do, we’ll end up with a multiverse which just tells us that mathematical consistency isn’t sufficient.

So if you have a multiverse that can be eliminated by the requirement that the model is consistent with observation, this isn’t a paradigm shift, it’s just disappointed hopes.

**2. The multiverse package deal**
But there’s a different type of multiverse, one that you cannot get rid of by requiring match to observation. It’s the case in which a theory applied to a model that describes a real world system necessarily maps into a space that is larger than what we observe. Eternal inflation and the many worlds interpretation of quantum mechanics are of this type. Or, more mundanely, there is nothing in ΛCDM that predicts the universe just ends beyond the distance that we can (presently) observe, so you have a multiverse beyond our observations.

This opens a can of interpretational worms because we can now endlessly discuss whether the not observable images of the map are real or not. Personally, I find this a rather fruitless debate about the meaning of the world ‘real’. To me a model is a tool to describe the real world and if it does that, and if it’s an improvement over other models, I don’t care if there are mathematical elements in the model that don’t correspond to real world observables. Mathematics is full of structures that for all we know don’t correspond to anything we observe anyway. I don’t see a reason why we must be able to observe them all.

But, no, I don’t think you should just shut up and calculate. Because we might be mistaken in thinking that what the theory predicts beyond our observable universe is indeed unobservable. Maybe we just haven’t asked the right questions and there are ways to observe it after all.

So it’s an interesting feature that theories can display, but it’s certainly not a new concept. There’s been a century of discussion about the presence of mathematical objects in quantum mechanics that for all we presently know are fundamentally non-observable. So if that’s a paradigm shift it’s one that has already happened long ago.

**3. Wilzcek’s Multiversality**
Frank Wilzcek recently had a paper on the arxiv titled “Multiversality”. The first half of the article is a nicely written general introduction, the second half is about axion cosmology and then the paper ends quite abruptly. The most interesting part of the paper are three positive answers to the question

“Are there aspects of observable reality, i.e. the universe, that can be explained by multiversality, but not otherwise?”

It is fruitful to look at the answers to gauge the depth of the existing arguments in favor of the multiverse:

“Yes – one is the apparent indeterminism of quantum mechanics, despite its deterministic equations.”

Wilczek claims here the apparent indeterminism of quantum mechanics can be explained by the many worlds interpretation but not otherwise. That’s an objectionable claim, in particular because the qualifier didn’t include anything about locality.

“Yes – the outrageously small, but non-zero, value of the dark energy density.”

Here he is claiming that there is no other way to explain the measured value of the dark energy density than anthropic reasoning and that anthropic reasoning necessarily implies a multiverse. There are many people who would object on the former and the latter is manifestly wrong. You don’t need a multiverse to do anthropic reasoning, see my post

Misconceptions about the anthropic principle.

“Yes – the opaque and scattered values of many standard model parameters that are not subject to the discipline of selection.”

An interesting answer because it is phrased to suggest that the values of the standard model parameters are scattered to begin with. Even if they were however that wouldn’t force us to believe that any possible distribution of values actually exists in a more meaningful sense than Harry Potter exists.

Taken together, these answers tell you aptly just how weak the case for a multiverse really is.

**Summary** We should distinguish between multiverses that you can eliminate by adding axioms to the theory that tie the model to the real world, and those that you can’t eliminate this way. The string theory landscape is of the former type, you “just” have to find the right vacuum, and good luck with finding that. Eternal inflation and the many worlds interpretation are of the latter type. In this case you get more than you asked for. One can interpret this type of multiverse as a calculation device which might have its uses. It might also turn out that these multiverses aren’t unobservable after all, so these ideas certainly merit some investigation. In any case however, there’s no paradigm shifting here.