The Multiverse Conundrum

Tim Wilkinson on the physics & philosophy of parallel universes.

In his 1895 essay Is Life Worth Living? the American philosopher William James wrote, “Truly, all we know of good and duty proceeds from nature… [which] is all plasticity and indifference – a moral multiverse, as one might call it” and a new word was born. A century later, and James’s neologism has been commandeered by physicists and pressed into service in a somewhat different context. These days ‘multiverse’ refers to the literal existence of multiple universes. But is such a thing even possible?

Aristotle thought the existence of multiple worlds, let alone universes, would be an absurdity; but by medieval times, philosopher-theologians including al-Ghazali in the East and John Duns Scotus in the West were already questioning whether God had created the best of all possible worlds – and thus acknowledging that He could have created others. In 1277 the Bishop of Paris, Étienne Tempier, issued a series of famous condemnations of all sorts of theological and philosophical propositions, and saw fit to explicitly denounce Aristotle’s view of there being only one possible world, which he thought to be at odds with God’s omnipotence.

By the seventeenth century the stage was set for Gottfried Wilhelm Leibniz: philosopher, key figure in the Scientific Revolution, and polymath of such remarkable achievements that Gottlob Frege described him as being “virtually in a class of his own.” To Leibniz’s way of thinking there were infinitely many possible worlds, each with different physics, subject to the overarching principle that all the laws of nature should together not imply a contradiction. Like most philosophers, Leibniz thought that even an omnipotent God would not be able to actualise contradictions. A ‘possible system of physical laws’ would then be one criterion by which God had chosen the actual world. Because of His innate goodness, God would also have seen fit to make the best possible world.

Leibniz’s metaphysics thus required the possibility of other universes, but he didn’t think more than one of them exists. Could there really be more than one? An increasing number of theoretical physicists seem to think so, and popular science magazines regularly publish articles describing the relationship between the multiverse and the so-called ‘fine-tuning problem’.

The Inestimable Unlikeliness of Being

Life is extremely precarious. For example, if protons were just a fraction of a percent heavier they would decay into other particles. Without protons there would be no atoms with which to make living things. InJust Six Numbers (2000), Martin Rees, who is currently Astronomer Royal and Master of Trinity College, Cambridge, describes half a dozen such cosmic flukes and points out that “If any one of [the fine-tuned constants] were to be ‘untuned’, there would be no stars and no life.” Most physicists agree: the harmonious results of the universe’s precise physical constants seems a bit too convenient to be overlooked as sheer accident, but what are we to make of the apparent coincidences?

One possibility is that cosmic fine-tuning is the result of actual design. Certainly if, like Leibniz, we take the existence of God as a given, then we would expect the universe to be fine-tuned for life. But whether the logic works in reverse, from apparent design to expect there to be a God, is somewhat doubtful, because arguments from design (‘teleological arguments’) have an unfortunate habit of collapsing in the face of advancing knowledge.

Teleological arguments can be traced back to antiquity, but the most famous example is the Reverend William Paley’s ‘watchmaker’ analogy of 1802. Paley argued that like watches, plants and animals give the appearance of having been designed, and since you wouldn’t expect to find a watch without a watchmaker, plants and animals must similarly have a designer as well. Unfortunately for Paley, the prevailing view among biologists and philosophers is that the watchmaker argument was demolished by Charles Darwin. Nevertheless, design remains a (remote) possibility as the true explanation of cosmic fine-tuning.

If actual design is not a particularly promising explanation of the universe’s suitability for life, then what is going on? Current thinking among many physicists is that the multiverse solves the problem of fine tuning via a so-called ‘anthropic selection effect’, which is one of several types of reasoning that are sometimes bundled together under the label ‘anthropic principle’. Anthropic selection is best illustrated by applying an uncontentious version to the Earth.

There are an incredible number of unlikely coincidences which together make life on Earth possible; for example, we are exactly the right distance from our parent star to allow the existence of liquid water. How did our big blue marble come to be so exquisitely fine-tuned for life? Well, there are so many planets in the universe that even if the overwhelming majority are uninhabitable there will still be billions that couldsupport life. Since only habitable planets can evolve and sustain sentient beings capable of asking such questions, it is no surprise whatsoever that we happen to find ourselves on one of them. The apparent coincidence is completely dissolved.

As a way of explaining local conditions on Earth, this argument is compelling, but can it be scaled up? According to Rees’s paper ‘Cosmology and the Multiverse’ (2007), “If our universe is selected from a multiverse, its seemingly designed or fine-tuned features would not be surprising.” This seems sound enough so far. The logical difficulties only surface if we try to turn it around: this universe is fine-tunedtherefore it must be one of many. Such reasoning does provide some support for the multiverse; after all, we might have guessed the existence of other planets based on the properties of the Earth, so why not universes?

Unfortunately, such support is extremely weak in isolation, as ought to be clear from an example. Suppose you had a coin which only ever landed heads up. In the absence of other data or better arguments, the most reasonable explanation would be that the coin was not fair. Perhaps if you knew more about the coin you would discover that it has heads on both sides. What goes for coins also goes for universes: there may be as yet undiscovered principles in play which increase the probability of this universe having the fortuitous properties we observe. When Albert Einstein asked, “Did God have any choice when he created the universe?” he was wondering whether physical constants such as the mass of the proton are not mere coincidences, but arise naturally from some as-yet-undiscovered physical laws which cover most possible worlds. If we could uncover such laws, we might even find that a universe like this one was almost inevitable. Although the multiverse idea is gaining in popularity, the search for this deeper theory has some high profile supporters. In The Emperor’s New Mind (1989), Sir Roger Penrose, one of the world’s most distinguished living physicists, expressed the view that anthropic reasoning is “somewhat dubious” and “tends to be invoked by theorists whenever they do not have a good enough theory to explain the observed facts.” An explanation of fine-tuning in terms of a deeper theory is beyond our current level of understanding, but for all we know it might take a million years to find. So unless someone can establish that no such theory is possible, it does seem a little early to give up. But even if a theory explaining why fundamental physical constants must be what they are could be found, it would still not satisfy our instinctive desire to explain the universe from first principles. Why? Because we would still not know why we live in this possible world and not another. These days, theories of fundamental physics invariably have at their heart complex mathematical structures which physicists align into a correspondence with observations in such a way that the mathematics describes the relevant properties of the physical world. But what about the infinitely many other equally respectable mathematical structures that the cosmos has chosen to ignore? Why doesn’t the universe dance to those tunes instead? Leibniz thought that even God is not free to create just any universe: but he did invoke the Almighty to explain why only one possible world was realised (the best one). To answer the question, ‘why this world?’ without resorting to the supernatural, would require additional reasoning to rule out all the possible models nature doesn’t use. Unfortunately, such reasoning is almost certainly not available – for example, as far as we can tell there is no logical prohibition on a universe completely devoid of matter and forces. This is where the deeper theory project finally runs aground. Perhaps reasons why other possible universes can be dismissed will one day be found – we can certainly live in hope – but we might also begin to sympathise with the growing number of physicists who regard the multiverse as being a better explanation of fine-tuning than some unknowable deep theory. To make the multiverse plausible, however, we need something more convincing than anthropic reasoning.

Reasons From Physics

A better argument for the multiverse is that the idea of it arises naturally from many of the mathematical models currently being deployed in theoretical physics. Eternal inflation, string theory and even Hugh Everett III’s ‘many worlds’ interpretation of good old-fashioned quantum mechanics, all suggest a vast number of universes, and conditions have to be bolted onto each of the theories to get the number of universes down to one. Without conditions the theories are much neater, but this theoretical simplicity comes at the cost of multiple universes. The various theories also suggest that the multiverse could come in different forms: the extra universes might be separated by tremendous distances, be embedded in different spatial dimensions, or might be separated only by time. Fortunately we needn’t worry too much about that, because in terms of looking for a solution to the fine-tuning problem, all multiverses are more or less equivalent – with one exception, as we shall see.

If our best current theories of physics predict multiple universes, how much support does that lend to their actual existence? Well, there are some impressive precedents for theories correctly predicting things not previously observed. Positrons, which are similar to electrons except with the opposite electrical charge, were predicted by the mathematics of Paul Dirac before their discovery was confirmed, but these days real positrons are routinely used in medical scanners. The case for the multiverse is further bolstered by the fact that there is not just a single theory predicting it. Quite the reverse; in fact, it seems to be proving almost impossible to devise any theory that tallies with our observations of the subatomic world and yetdoesn’t predict a multiverse, or at least which isn’t simpler with the multiverse than without. This should not be considered conclusive, but it is a significantly better reason than the anthropic reasoning outlined earlier.

However, there are several further philosophical hurdles, such as: what evidence could we ever collect which would rule out the multiverse? Many philosophers regard susceptibility to falsification as being a desirable feature of scientific theories generally – a view developed and promoted by Karl Popper, one of the giants of twentieth century philosophy. Although the philosophy of science has moved on since Popper, it is still good policy to be wary of unfalsifiable statements because, as every conspiracy theorist knows, it is always best to make your crackpot notions immune from being disproved by evidence. That way you will never need to back down in the face of inconvenient facts. So unfalsifiability is like a ‘beware’ sign.

Whether the multiverse is falsifiable is a matter of heated and sometimes acrimonious debate among physicists. An infamous online spat between Lee Smolin, researcher at the Perimeter Institute for Theoretical Physics and one of the inventors of loop quantum gravity, who claimed that the multiverse is unfalsifiable, and Leonard Susskind, Professor of Physics at Stanford and one of the founders of string theory, who claimed the opposite, was only brought to a halt when both men agreed to post one final letter on the topic and call a truce. However, writing in the Times Higher Educational Supplement two years later, Susskind resorted to an ad hominem attack on Smolin, rather than on his argument: “Smolin is a mid-level theoretical physicist, but his popular book-writing activities and the related promotional hustling have given him a platform high above that merited by his physics accomplishments.” Come on now boys, play nicely with your theoretical models, or you’ll have to put them back in the cupboard.

In a way, Smolin and Susskind were both correct. Any scientifically-interesting multiverse theory will be able to make predictions, including some about our universe, which can be tested. If the theory passes these tests, our confidence in the theory and hence in the multiverse it predicts increases; if it fails, it’s thereby falsified. So far, so good – multiverse theories are falsifiable.

The problem comes if our interest is not in specific theories with predictions, but in the general question of whether other universes of any kind exist. If a multiverse exists, one of its component universes must be exactly like ours, because here we are. It follows that any evidence we can ever collect in our universe will always be consistent with some sort of multiverse. We can rule out multiverses that don’t allow a universe like ours – but no-one’s interested in those – and although we could in principle falsify specific multiverse theories such as the one implied by string theory, doing so wouldn’t settle the broader issue because another theory predicting a multiverse will be along in a minute.

Direct evidence for the multiverse is effectively out of the question, because anything we can actually measure or observe is necessarily part of this universe, not another one. Indirect evidence might be possible though. For example, one of the first physicists to argue for a multiverse was Andrei Linde, a distinguished Russian physicist now at Stanford. Linde’s multiverse is an adaptation of the inflation which is widely held to have rapidly boosted the size of the universe shortly after the Big Bang. Linde argues that inflation could spawn new, disconnected regions of space, each with different properties, and that over time this process could give rise to all the different universes predicted by string theory. Researchers have recently noticed that the cosmic microwave background radiation – the echo left over from the Big Bang – contains traces of what might be ‘bruises’ caused by collisions between Linde’s other universes and our own. These observations are certainly interesting, but extremely indirect evidence such as this is very difficult to interpret without making lots of assumptions, and only becomes convincing when we have good reason for ruling out alternative interpretations of it.

Despite the difficulties, there seems to be no shortage of well-respected physicists prepared to speak about the multiverse almost as if it is an established fact. The cosmologist Bernard Carr is quoted as saying, “If you don’t want God, you’d better have a multiverse.” But surely this is going too far. There is at least one other option; namely the possibility that the universe couldn’t have turned out another way. There are also more radical alternatives. Perhaps the universe is simply not susceptible to the sort of explanation we’re accustomed to looking for. As for fine-tuning, if the multiverse is meant to explain cosmic coincidences, there is more trouble ahead. For just as there is no limit on the number of possible worlds, so there is no apparent limit on the number of possible multiverses. Some multiverses will harbour a universe like ours; but many – perhaps the majority – will not. So even if we employ the multiverse hypothesis to solve the fine-tuning problem, we will still have to explain why our multiverse is configured to produce at least one life-supporting universe rather than none, and why this particular multiverse exists, rather than another.

These sound suspiciously similar to the problems we encountered when looking for a deeper theory. The multiverse seems to have brought us no closer to an explanation of the universe from first principles. Instead, it’s just given us more universes to worry about. But there is one multiverse which might do the explanatory trick, and it can also be traced back to Leibniz’s possible worlds.

All Real Worlds

The key figure in the final part of the story is David Lewis (1941-2001), one of the most important philosophers of the twentieth century. In On the Plurality of Worlds (1986) Lewis set out his modal realism– the notion that all possible worlds are actually-existing disconnected universes.

Lewis’s reasons for advocating modal realism were somewhat different from those currently being advanced by physicists, but when he said ‘all possible worlds’, he meant all of them. The physicists’ multiverse is usually presented in terms of some mind-bogglingly large but finite number of universes; for example, the number of universes consistent with a promising branch of string theory known as M-theory is 10500 (1 followed by 500 zeros) – a number so colossal that the number of atoms in our universe (10100) wouldn’t even dent it. Lewis, on the other hand, thought there was no limit on the number of universes.

The problem-solving power of the infinite multiverse has not been lost on physicists. In ‘Is “The theory of everything” merely the ultimate ensemble theory?’ (Annals of Physics, Vol 270, 1998), Max Tegmark, Professor of Physics at MIT, suggested that “all structures that exist mathematically exist also physically.” Conceptually, the Lewis/Tegmark infinite multiverse idea is extremely appealing. If it’s wrong, and most possible worlds don’t exist, what causes the symmetry between potential existence and actual existence to break down for some possible worlds but not for others?

The infinite multiverse would certainly eliminate the need to explain why we have one particular reality, but do physicists seriously suggest that we solve the fine-tuning problem by summoning infinitely many universes, none of which can be observed directly? Haven’t they heard of Occam’s Razor [‘Don’t multiply entities beyond necessity’]? Indeed; but intuition can easily lead us astray in the search for the simplest solution. The set of all solutions to the equations of [insert your favourite theory of advanced physics] is simpler than any individual solution, because the former can be described using less information than the latter.

Tegmark notes that this logic can be extended. Consider for example the infinity of real numbers. Some numbers, such as π, can be generated comparatively easily as the output of simple algorithms, but in most cases there is no obvious way to specify a real number other than to list all its digits. Taking into account the digits after the decimal point, for most real numbers that is an infinite amount of information. On the other hand, the whole set can be specified with just a handful of axioms. Similarly, specifying the infinite multiverse is simpler than specifying any particular multiverse, or universe, and requires no free parameters whatsoever. An infinite multiverse also completely does away with the fine-tuning problem. Any sentient being thinking about the problem could only be doing so from the comfort of one of the inhabitable universes, and that is all there is to be said on the matter.

Further support for the actual existence of all ‘mathematically possible worlds’ can be inferred from what Nobel Physics Laureate Eugene Wigner had to say about the unreasonable effectiveness of mathematics: “The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve.” As Tegmark points out though, the almost spooky power of mathematics to describe the world would hardly be a surprise if there was a direct correspondence between mathematical structures and actually existing universes.

Infinite Possibilities

Can it really be true that, as T.H. White wrote in The Once and Future King, “Everything not forbidden is compulsory” – that everything that is possible must exist somewhere? It would certainly solve a few problems, and despite the initial shock of all those universes, an infinite multiverse is in some sense the last word in symmetry and simplicity. But have we done enough to establish that any sort of multiverse is out there?

Unfortunately, the exceedingly indirect nature of the evidence probably means the multiverse will remain at the furthest border of speculative science for some time to come. As for the fine-tuning problem, the Lewis/Tegmark infinite multiverse idea seems to solve it, but anything more specific such as string theory just deflects the problems up to the next level of speculation. All things considered, it is probably best to follow the wise counsel of Steven Weinberg. This Nobel Physics Laureate acknowledges that the multiverse is a useful and intriguing idea with some good theoretical support, but on reading that Andrei Linde was willing to bet his life on its existence and that Martin Rees was willing to bet the life of his dog, Weinberg wrote, “I have just enough confidence about the multiverse to bet the lives of both Andrei Linde and Martin Rees’s dog.”

© Dr Tim Wilkinson 2012

In this Universe, Tim Wilkinson has a PhD in pure maths from the University of Newcastle-Upon-Tyne, and lives with his wife and three children in the North East of England.

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