Although we don’t know whether parallel universes exist, we know something else about them with certainty: many people instinctively dislike them, and whenever a physicist writes a book about them, the Web erupts with claims that they are unscientific nonsense.

My new book “Our Mathematical Universe” proved to be no exception. “Is this still science?” the biologist Mark Buchanan wondered on the pages of New Scientist, “Or has inflationary cosmology veered towards something akin to religion?” The physicist Peter Woit dismissed it as “grandiose nonsense”.

If you’re a multiverse skeptic, you should know that there are many potential weaknesses in the case for parallel universes, and I hope you’ll find my cataloging of these weaknesses below useful. To identify these weaknesses in the pro-multiverse arguments, we first need to review what the arguments are. Many physicists have explored various types of parallel universes in recent books, including Sean Carroll, David Deutsch, Brian Greene, Michio Kaku, Martin Rees, Leonard Susskind and Alexander Vilenkin. Interestingly, not a single one of these books (my own included) makes any outright claims that parallel universes exist. Instead, all their arguments involve what logicians know as “modus ponens”: that if X implies Y and X is true, then Y must also be true. Specifically, they argue that if some scientific theory X has enough experimental support for us to take it seriously, then we must take seriously also all its predictions Y, even if these predictions are themselves untestable (involving parallel universes, for example).

As a warm-up example, let’s consider Einstein’s theory of General Relativity. It’s widely considered a scientific theory worthy of taking seriously, because it has made countless correct predictions - from the gravitational bending of light to the time dilation measured by our GPS phones. This means that we must also take seriously its prediction for what happens inside black holes, even though this is something we can never observe and report on in Scientific American. If someone doesn’t like these black hole predictions, they can’t simply opt out of them and dismiss them as unscientific: instead, they need to come up with a different mathematical theory that matches every single successful prediction that general relativity has made - yet doesn’t give the disagreeable black hole predictions. This has proven a remarkably difficult task, eluding many brilliant scientists for about a century. In other words, for a theory to be testable (and hence scientific), we don’t have to be able to test all its predictions, merely one of its predictions.

So are there parallel universes, or is the universe we observe (the spherical region of space from which light has had time to reach us during the 13.8 billion years since our Big Bang) all that exists? We don’t know. The interesting claim that these books collectively make is that various theories imply that various types of parallel universes exist (see table), so that by modus ponens, if we take any of these theories seriously, we’re forced to take seriously also some parallel universes. Conversely, if we can experimentally rule out any of these theories based on their other predictions, we’ve destroyed the evidence for the corresponding parallel universes.

For example, Alan Guth, Andrei Linde and Alexander Vilenkin have argued that the cosmological theory of inflation generically predicts the Level I multiverse: a single space so large that it contains many universe-sized regions. Inflation may or may not turn out to be correct, but the recent confirmation of many of its predictions by cosmic microwave background experiments etc. have caused it to emerge as the most popular scientific theory for what happened early on, and ongoing experiments may provide additional tests. A second argument is that if we add to inflation the separate assumption that the correct theory of quantum gravity (say string theory, loop quantum gravity or some competitor) has more than one homogeneous solution (just as the equations for water have three solutions corresponding to ice, steam and gas), then this implies the Level II multiverse: a single space containing universe-sized regions with each kind of space. A third argument, first made by Hugh Everett III, is that the bare-bones theory of quantum mechanics free from so-called wave-function collapse implies a third type of multiverse. A fourth argument, made in my book, is that if there’s an external reality completely independent of us humans, then there’s a fourth type of multiverse realizing all mathematically possible universes.

The most persistent and acrimonious debates often occur when the debating parties misunderstand each other, so it’s important that people on both sides of the multiverse debate be as explicit as they can about what they’re claiming. The fact that parallel universes aren’t a theory, but predictions of certain theories, means that there are three (and only three) logically possible lines of attack on parallel universes, corresponding to three types of claims:

One or more of these “X implies Y” arguments is incorrect (inflation doesn’t predict Level I, say).

One or more of the theories X predicting multiverses are incorrect (inflation, say).

Parallel universe are indeed predicted by scientific theories, but scientists shouldn’t waste their time thinking about such topics.

Since C is a matter of personal opinion, let’s focus in more detail on A and B, which are straightforward scientific claims that can hopefully one day be settled by calculation and observation. We’ll see that there’s no shortage of such scientific lines of attack. Before delving into them, however, it’s worth noting that the best way to weaken a strong case is to overstate it, so multiverse skeptics should avoid undermining their case by going beyond A, B and C with vague and unscientific claims of “fantasy,” “nonsense,” etc.

A type-A attack on Level I would show that inflation doesn’t produce a Level I multiverse. Although Guth, Linde and Vilenkin have shown that almost any inflation model produces an infinite space, the “almost” allows a line of attack: there are still some models which don’t, and even though they’ve been criticized as contrived, they remain a logical possibility. A type-B attack on Level I should weaken the case for inflation. This could happen either through theoretical progress (for example, proof that competing theories such as the ekpyrotic universe or string gas cosmology are free from the obstacles currently limiting their popularity) or through new experimental results disagreeing with generic inflation predictions (for example, detection of a small but non-zero curvature of space, or growing evidence that the claimed anomalies in the cosmic microwave background images from the Planck satellite need to be taken seriously).

A more radical and potentially devastating type-B attack is to question the assumption that space can be stretched out indefinitely. Although it’s a standard assumption in physics that physical space is continuous, with even the smallest volume containing infinitely many points, it’s an Achilles heal in the sense that we have no experimental evidence for anything truly continuous or infinite in nature. Contrariwise, we suspect that our intuitive picture of space breaks down on tiny scales. Killing the continuum could kill eternal inflation, resulting in a Level I multiverse that is merely large but not infinite, potentially eliminating the prediction that there are near-identical copies of you far out in space.

Any of the above-mentioned Level I attacks could torpedo Level II as well. A second line of attack against Level II is to challenge the other assumption upon which it rests: that the correct theory of quantum gravity has more than one homogeneous solution. If further work on quantum gravity leads to a theory with a unique solution that matches what we experimentally observe, Level II will have had the rug pulled from under it. A third line of attack is to give a compelling explanation for the observed fine-tuning of physical constants that doesn’t rely on a Level II multiverse.

Since the Level III multiverse is implied by the (collapse-free) Schrödinger equation of quantum mechanics, it can be demolished with a type-B attack: an experimental demonstration of a violation of the Schrödinger equation. For example, if the current multi-million dollar attempts to build quantum computers fail and the cause is determined to be that the Schrödinger equation is violated by some form of wavefunction collapse process, then there are no Level III parallel universes.

The Level IV multiverse is also vulnerable to a type-B attack: we can simply reject the notion that there’s an external reality completely independent of us humans, for example in the spirit of Niels Bohr’s famous dictum, “no reality without observation”. A second type-B attack option is to falsify the mathematical universe hypothesis by demonstrating that there’s some physical phenomenon that has no mathematical description.

In summary, there is no shortage of potential weaknesses in the arguments for parallel universes. Attacking all these weaknesses involves doing interesting experimental and theoretical physics research. If any of the attacks succeed, the corresponding multiverse evidence is discredited. Conversely, if all the attacks fail, then we’ll be forced to take parallel universes more seriously whether we like them or not - such are the rules of science. In this way, parallel universes are no different from any other scientific idea.