by Jim Baggott
Are we really supposed to take this seriously?
It is certainly true that an increasing number of theorists are sufficiently perplexed by the quantum measurement problem that they are willing to embrace many worlds, despite all its metaphysical baggage. At a scientific workshop on the interpretation of quantum theory held in August 1997, the participants conducted an informal poll. Of the 48 votes recorded, 13 (or 27 per cent) were cast in favour of the Copenhagen interpretation. The second most popular choice, attracting eight votes (17 per cent) was the many worlds interpretation. Tegmark reported:
Although the poll was highly informal and unscientific (several people voted more than once, many abstained, etc.), it nonetheless indicated a rather striking shift in opinion compared to the old days when the Copenhagen interpretation reigned supreme. Perhaps most striking of all is that the many worlds interpretation … proposed by Everett in 1957 but virtually unnoticed for about a decade, has survived 25 years of fierce criticism and occasional ridicule to become the number one challenger to the leading orthodoxy…9
Before we go any further, I think we should probably remind ourselves of precisely what it is we’re dealing with here. The many worlds interpretation singularly avoids assumptions regarding the collapse of the wavefunction and does not seek to supplement or complete quantum theory in any way. Rather, it takes the framework provided by quantum theory’s deterministic equations and insists that this is all there is.
But the consequence of this approach is that we are led inexorably to the biggest assumption of all:
The Many Worlds Assumption. The different possible outcomes of a quantum measurement or the different possible final states of a quantum transition are all assumed to be realized, but in different equally real worlds which either split from one another or exist in parallel.
The reality check
Attempts to rehabilitate the many worlds interpretation by devising versions that appear to carry less metaphysical baggage have been broadly frustrated. Despite the reasonableness of these versions and their use of less colourful language, the measurement problem remains particularly stubborn. We might at this stage be inclined to think that, after all, there’s no real alternative to the many worlds interpretation’s more extreme logic. Perhaps we should just embrace it and move on?
But before we do, it’s time for another reality check.
The first thing we should note is that the many worlds interpretation is not a single, consistent theory that carries the support of all who declare themselves ‘Everettians’. It is not even a single, consistent interpretation. It’s more correct to say that there is a loose-knit group of theorists who buy into the idea that the quantum measurement problem can be solved by invoking the many worlds assumption. But each has rather different ideas about precisely how this assumption should be made and how the practical mechanics should be handled. As Cambridge theorist Adrian Kent recently noted:
Everettian ideas have been around for 50 years, and influential for at least the past 30. Yet there has never been a consensus among theoretical physicists either that an Everettian account of quantum theory can be made precise and made to work, or that the Everettian programme has been comprehensively refuted.10
One of the single biggest challenges to the acceptance of the many worlds interpretation lies in the way it handles probability. In conventional quantum theory in which we assume wavefunction collapse, we use the modulus squares of the amplitudes of the different components in the wavefunction to determine the probabilities that these components will give specific measurement outcomes. Although we might have our suspicions about what happens to those components that ‘disappear’ when the wavefunction collapses, we know that if we continue to repeat the measurement on identically prepared systems, then all the outcomes will be realized with frequencies related to their quantum probabilities.
Let’s use an example. Suppose I form a superposition state which consists of both ‘up’ and ‘down’ (it doesn’t matter what actual properties I’m measuring). I take 0.866 times the ‘up’ wavefunction and 0.500 times the ‘down’ wavefunction and add them together. I now perform a measurement on this superposition to determine if the state is either ‘up’ or ‘down’. I cannot predict which result I will get for any specific measurement, but I can determine that the probability of getting the result ‘up’ is given by 0.8662, or 0.75 (75 per cent), and the probability of getting the result ‘down’ is 0.5002, or 0.25 (25 per cent).* This means that in 100 repeated experiments, I would expect to get ‘up’ 75 times and ‘down’ 25 times. And this is precisely what happens in practice.
How does this translate to the many worlds scenario? The many worlds assumption suggests that for each measurement, the universe splits or partitions such that each ‘up’ result in one world is matched by a ‘down’ result in a parallel world, and vice versa. If in this world we record the sequence ‘up’, ‘up’, ‘down’, ‘up’ (consistent with the 75:25 probability ratio of conventional quantum theory), then is it the case that the other we in another world record the sequence ‘down’, ‘down’, ‘up’, ‘down’? If so, then this second sequence is clearly no longer consistent with the probabilities we would calculate based on the original superposition.
Things are obviously not quite so simple.
Perhaps each repeated measurement splits or partitions the sequence among more and more worlds? But how then do we recover a sequence that is consistent with our experience in the one world we do observe? Should the probabilities instead be applied somehow to the worlds themselves? What would this mean for parallel worlds that are meant to be equally real? Should we extend the logic to include an infinite number of parallel worlds?
In The Hidden Reality, Brian Greene acknowledges the probability problem in a footnote:
So from the standpoint of observers (copies of the experimenter) the vast majority would see spin-ups and spin-downs in a ratio that does not agree with the quantum mechanical predictions … In some sense, then … (the vast majority of copies of the experimenter) need to be considered as ‘nonexistent’. The challenge lies in understanding what, if anything, that means.11
As we dig deeper into the problem, we realize that the seductive simplicity that the many worlds interpretation seemed to offer at first sight is, in fact, an illusion.
Various solutions to the problem of probability in the many worlds interpretation have been advanced, and Everett himself was convinced that he had shown in his PhD thesis how the quantum mechanical probabilities can be recovered. But it is fair to say that this is the subject of ongoing debate, even within the community of Everettians.
Eternal inflation
The multiverse interpretation that we have so far considered has been invoked as a potential solution to the quantum measurement problem. Its purpose is to free the wavefunction from the collapse assumption so that it can be applied to describe the universe that we observe. If this was as far as it went, then perhaps the multiverse of many worlds would not provoke more than an occasional research paper, a chapter or two in contemporary texts on quantum theory and the odd dry academic conference.
But there’s obviously more to it than this.
We have seen how cosmic inflation provides solutions to the horizon and flatness problems in big bang cosmology. However, inflation is more a technique than a single cut and dried theory, and it may come as no surprise to discover that there are many ways in which it can be applied. One alternative approach was developed in 1983 by Russian theorist Alexander Vilenkin, and was further elaborated in 1986 by Russian-born theorist Andrei Linde.
One of the problems with the current ACDM model of big bang cosmology is that it leaves us with quite a few unanswered (and possibly unanswerable) questions. Perhaps one of the most perturbing is the fine-tuning problem. In order to understand why the universe we inhabit has the structure and the physical laws that it has, we need to wind the clock back to the very earliest moments of its existence. But it is precisely her
e that our theories break down or run beyond their domain of applicability.
But now here’s a thought. We can try to determine the special circumstances that prevailed during the very earliest moments of the big bang, circumstances that shaped the structure and physical laws that we observe. Alternatively, we can question just how ‘special’ these circumstances actually were. Just as Copernicus argued that the earth is not the centre of the universe; just as modern astronomy argues that our planet orbits an unexceptional star in an unexceptional galaxy in a vast cosmos, could we argue that our entire universe is no more than a relatively unexceptional bit of inflated spacetime in an unimaginably vaster multiverse?
If inflation as a technique is freed from the constraint that it should apply uniquely to our universe, then all sorts of interesting things become possible. Linde discovered that it was possible to construct theories on a rather grander scale:
There is no need for quantum gravity effects, phase transitions, supercooling or even the standard assumption that the universe originally was hot. One just considers all possible kinds and values of scalar [i.e. inflaton] fields in the early universe and then checks to see if any of them leads to inflation. Those places where inflation does not occur remain small. Those domains where inflation takes place become exponentially large and dominate the total volume of the universe. Because the scalar fields can take arbitrary values in the early universe, I called this scenario chaotic inflation.12
The kind of model developed originally by Vilenkin and Linde is now more commonly referred to as eternal inflation. In this model, our universe is merely one of countless ‘bubbles’ of inflated spacetime, triggered by quantum fluctuations in a vast inflaton field (or fields) driven by competition between the decay of the field’s energy and the exponential growth of energy in pockets of inflation. In certain models the competition is unequal, and the bubbles proliferate like a virus, or like the bubbles in a bottle of champagne when the cork is extracted.
The bubbles form a multiverse much like holes in an ever-inflating piece of Swiss cheese. This is, of course, an imperfect analogy, as it is the holes or bubbles themselves (rather than the cheese) that account for much of the spacetime volume. Such an ‘inflationary multiverse’ could be essentially eternal, with no beginning or end.
In the inflationary multiverse, anything is possible. The essential randomness of the quantum fluctuations that trigger bubbles of inflation imply a continuum of universes with different physical laws (different cosmological constants, for example).
Let’s reserve judgement on this idea for now, and simply note that we’re dealing here with another assumption.
The Inflationary Multiverse Assumption. Certain inflationary cosmological models describe a multiverse consisting of bubbles of inflating spacetime triggered by quantum fluctuations in a vast inflaton field. Our universe may be a relatively unexceptional bubble in this multiverse.
We need to be clear that the multiverse of the many worlds interpretation and the multiverse of eternal inflation are necessarily different. They originate from within different theoretical structures and have been proposed for very different reasons. But, as the saying goes: in for a penny, in for a pound. If we’re going so far as to invoke the idea of a multiverse, why not simplify things by assuming that the bubble universes demanded by eternal inflation are, in fact, the many worlds demanded by quantum theory?
In May 2011, American theorists Raphael Bousso and Leonard Susskind posted a paper on the arXiv pre-print archive in which they state:
In both the many-worlds interpretation of quantum mechanics and the multiverse of eternal inflation the world is viewed as an unbounded collection of parallel universes. A view that has been expressed in the past by both of us is that there is no need to add an additional layer of parallelism to the multiverse in order to interpret quantum mechanics. To put it succinctly, the many-worlds and the multiverse are the same thing.13
Breathtaking.
But we’re still not quite there. Joining the many worlds interpretation to the inflationary multiverse cannot explain the current fascination with multiverse theories. To understand this fascination, we must return once again to superstring theory. As Alan Guth explained in 2007:
Until recently, the idea of eternal inflation was viewed by most physicists as an oddity, of interest only to a small subset of cosmologists who were afraid to deal with concepts that make real contact with observation. The role of eternal inflation in scientific thinking, however, was greatly boosted by the realization that string theory has no preferred vacuum …14
The cosmic landscape
In The Hidden Reality, Brian Greene wrote of his early experiences with Calabi—Yau shapes, the manifolds which are used to roll up and hide away the six extra spatial dimensions demanded by superstring theory:
When I started working on string theory, back in the mid-1980s, there were only a handful of known Calabi—Yau shapes, so one could imagine studying each, looking for a match to known physics. My doctoral dissertation was one of the earliest steps in this direction. A few years later, when I was a postdoctoral fellow (working for the Yau of Calabi—Yau), the number of Calabi—Yau shapes had grown to a few thousand, which presented more of a challenge to exhaustive analysis — but that’s what graduate students are for. As time passed, however, the pages of the Calabi—Yau catalog continued to multiply … they have now grown more numerous than grains of sand on a beach. Every beach.15
Greene wasn’t kidding. In 2003, theorists Shamir Kachru, Renata Kallosh, Andrei Linde and Sandip Trivedi worked out the number of different Calabi—Yau shapes that are theoretically possible. This number is determined by the number of ‘holes’ each shape can possess, up to a theoretical maximum of about five hundred. There are ten different possible configurations for each hole. This gives a maximum of 10500 different possible Calabi—Yau shapes.
The precise shape of the Calabi—Yau manifold determines the nature of the superstring vibrations that are possible. It thus determines the physical constants, the laws of physics and the spectrum of particles that will prevail. In other words, the shape determines the type of universe that will result. The figure 10500 therefore refers to the number of different possible types of universe, not the total number of possible universes. This is what Guth meant when he talked about string theory having no preferred vacuum.
I believe there was a time in the history of physics when this kind of result would have been taken as evidence that a theoretical programme had failed. We could conclude that 10500 different possible Calabi—Yau shapes with no compelling physical reason to select the one shape that uniquely describes our universe — and hence describes the laws and the particles that we actually observe — leave us with nowhere to go. Time to go back to the drawing board.
Except, of course, we now have eternal inflation and the inflationary multiverse.
Far from this vast multiplicity of possible Calabi—Yau shapes being seen as evidence for the failure of the superstring programme, it is instead used to bolster the idea that what the theory is describing is actually a multiverse. Greene again:
The idea is that when inflationary cosmology and string theory are melded, the process of eternal inflation sprinkles string theory’s 10 possible forms for the extra dimensions per bubble universe — providing a cosmological framework that realizes all possibilities. By this reasoning, we live in that bubble whose extra dimensions yield a universe, cosmological constant and all, that’s hospitable to our form of life and whose properties agree with observations.16
Each bubble in the inflationary multiverse represents a universe that may be much like the one we inhabit, or it might be subtly different, or it might be vastly different. It doesn’t take a great leap of the imagination to suggest that each bubble is characterized by the Calabi—Yau shape that governs its extra spatial dimensions.
Leonard Susskind calls it the cosmic landscape. He is at pains to explain that the landscape of possibilities afforded b
y the 10 Calabi— Yau shapes is not ‘real’. It is rather a list of all the different possible designs that universes could possess. However, he is unequivocal on the reality of the multiverse: ‘The pocket [i.e. bubble] universes that fill it are actual existing places, not hypothetical possibilities.’17
Let’s log it as another in what is proving to be a long series of interconnected assumptions.
The Landscape Assumption. The 10500 different possible ways of compactifying the six extra spatial dimensions of superstrittg tlieory represent different possible types of universe that may prevail within the inflationary multiverse.
The universe next door
The inflationary multiverse provides a mathematical metaphor for a cosmos in which countless bubbles of spacetime are constantly inflating like balloons. Any region of spacetime devoid of content but for the inflaton field is potentially unstable and susceptible to quantum fluctuations which may trigger inflation. When combined with superstring theory’s demand for extra ‘hidden’ dimensions, we conclude that the bubbles are characterized by different Calabi—Yau shapes, giving rise to universes with different physical constants, laws and particles.
Of course, we have already encountered something very similar to this. The D-branes of M-theory represent extended string-like objects that can accommodate whole universes with different physical constants, laws and particles. Indeed, the Hořava—Witten and Randall—Sundrum braneworld scenarios are examples of cosmological models involving parallel universes. In the latter, the two branes describe universes in which gravity acts very differently. In one universe it is strong. The warped spacetime of the bulk then dilutes the gravitational force so that when we experience it in our braneworld, is it considerably weakened.
It doesn’t require a great leap of imagination to propose that there may be many more than just two braneworlds ‘out there’. If the structure of each brane is governed by the Calabi—Yau shape that hides its extra dimensions, then M-theory would suggest that the multiverse is actually one of parallel braneworlds.