Universe or multiverse? The war rages on

Credit: Quanta Magazine


A growing controversy over the multiverse and the anthropic principle has exposed a major fault line in modern physics and cosmology. Some researchers see the multiverse and the anthropic principle as inevitable, others see them as an abdication of empirical science. The controversy spans quantum mechanics, inflationary Big Bang cosmology, string theory, supersymmetry and, more generally, the proper roles of experimentation and mathematical theory in modern science.

The “many worlds interpretation” of quantum mechanics

Since the 1930s, when physicists first developed the mathematics behind quantum mechanics, researchers have found that this theory appears to govern, to extraordinary precision, the world of atomic and subatomic phenomena. Inherent in the mathematics of quantum mechanics is the notion that the world is in a superposition of many possible states, and only “chooses” one when a measurement is made. While many physicists recommend a “shut up and calculate” approach, others continue to pursue a more “reasonable” framework to explain these perplexing results.

One such framework, first advanced by Hugh Everett in 1957, is known as the “many worlds interpretation” of quantum mechanics. It posits that the real world is continually bifurcating into a vast number of parallel universes, and the reason we see only one branch realized is simply that we reside in that branch. While many physicists, to this day, resist this view, others have accepted it and apply it in day-to-day work. As physicist Sean Carroll wrote in his 2019 book Something Deeply Hidden, “When it comes to understanding how to quantize the universe itself, Many-Worlds seems to be the most direct path to take.” [Carroll2019, pg. 306].

Inflationary Big Bang cosmology and pocket universes

The inflationary Big Bang theory of cosmology has its roots in some paradoxes first noted in the 1960s [Guth1997, pg. 25]:

  1. The flatness problem. In the very early universe after the Big Bang, the ratio of the actual mass density of the universe to the “critical density” must have been exceedingly close to one (to within one part in 1014). If the ratio were very slightly lower, the universe would have dispersed too rapidly for stars and galaxies to have formed, but if it were very slightly larger, the universe would have long ago recollapsed in a big crunch.

  2. The horizon problem. Different regions of space appear to be essentially indistinguishable, say in the intensity of the cosmic microwave background. But how can regions on opposite sides of the universe be in such close coordination today, since no physical force, not even light rays, could have traversed the distance between them since the Big Bang?

In the early 1980s, physicist Alan Guth hypothesized that in the first tiny fraction of a second after the Big Bang, the universe underwent an enormous “inflation,” wherein the fabric of space exploded by a factor of roughly 1030 [Guth1997, pg. 193]. The inflation hypothesis explained the two paradoxes above, and is now widely accepted in the field, although some demur. Paul Steinhart, for example, one of the early pioneers of inflationary cosmology, more recently has expressed serous doubts [Horgan2014].

In any event, one consequence of the inflationary cosmology is that the full universe created at the Big Bang is some 1023 times larger than our observable universe [Guth1997, pg. 186]. More recently, Andrei Linde of Stanford University and Alex Vilenkin of Tufts University observed that Guth’s theory leads to a “chaotic eternal inflation,” which has no beginning or end [Susskind2005, pg. 81]. Either way, what we have been calling the “universe” may be just one “pocket universe” amid an enormous ensemble of such universes.

The string theory landscape

For nearly 40 years, physicists have been exploring “string theory,” namely the notion that all physical phenomena are, at the lowest level of reality, tiny vibrating strings and membranes — roughly 10-34cm in size, or vastly smaller even than a proton. What’s more, these strings or membranes live in a 10- or 11-dimensional space, not the 3-dimensional space that we are accustomed to. Physicist Brian Greene, author of two widely read semi-popular expositions of string theory, The Elegant Universe and The Fabric of the Cosmos, emphasizes that string theory appears to neatly unify all known physical forces, including gravity, in one elegant package [Greene2003a; Greene2011].

The original dream of string theory was to deduce a unique set of physical laws and constants — namely those that govern our universe. Instead, researchers have found that the underlying mathematics suggests a vast “landscape” of possible universes, by one reckoning 10500 in number, each corresponding to a different Calabi-Yau manifold, and each governed by potentially different sets of physical laws and constants. Some researchers are deeply disappointed and perplexed by this outcome, and continue to press forward to find a unique solution. Others have accepted the landscape as an unavoidable feature of the theory, and further see it as a potential solution to some long-standing paradoxes (see below). Still others cite this outcome as evidence that the string theory framework is fundamentally flawed, and question the continuation of research in the area.

Before going further, we should note that different authors employ different terminology for various multiverse varieties and realms. Physicist Paul Davies lists five realms: the universe we can now physically observe; everything within our “horizon”; the realm created in the Big Bang but beyond our horizon; the “pocket universe” that has laws similar to our own; and the full “multiverse” [Davies2007, pg. 31-32]. Max Tegmark, in his 2014 book Our Mathematical Universe, includes his own notion of all logically consistent mathematical structures [Tegmark2014]. Brian Greene, in his 2011 book The Hidden Reality, lists seven different varieties of the multiverse, including the string theory landscape [Greene2011, pg. 309].

Apparent fine-tuning of the universe and the anthropic principle

While some researchers militantly resist the notion of a multiverse, others see lemonade in the lemons. In their view, the multiverse could resolve some nagging unexplained paradoxes, notably the fact that the universe we reside in appears to be remarkably fine-tuned for the eventual rise of intelligent life. In particular, these researchers argue that the reason that our universe is so finely tuned for the rise of intelligent life is that it is but one universe in a vast multiverse, and if ours were not so finely tuned for life, we wouldn’t be here to discuss the topic. Here are some of these finely tuned “cosmic coincidences” (see this earlier Math Scholar blog and the 2016 Lewis-Barnes book [Lewis2016] for additional details):

  1. Carbon resonance and the strong force. Although researchers can explain the creation of hydrogen, helium, lithium and beryllium in the cauldron of the first 100 seconds or so after the Big Bang, the synthesis of heavier elements, beginning with carbon, relies on a very finely tuned resonance that is just energetic enough to permit a triple-helium nuclear reaction to produce a carbon nucleus. By the way, although one can imagine living organisms based on other elements, carbon is by far is the most suitable element for the construction of complex molecules, as required for any conceivable form of living or sentient beings.
  2. The weak force and the proton-neutron balance. Had the weak force been somewhat weaker, the amount of hydrogen in the universe would be greatly decreased, starving stars of fuel for nuclear energy and leaving the universe a cold and lifeless place.
  3. Neutrons and the proton-to-electron mass ratio. The neutron’s mass is very slightly more than the combined mass of a proton, an electron and a neutrino. If neutrons were very slightly less massive, then they could not decay without energy input and the universe would be entirely protons (i.e., hydrogen), but if their mass were slightly lower, then all isolated protons would decay into neutrons, and no atoms other than hydrogen, helium, lithium and beryllium, which were synthesized in the Big Bang, could form.
  4. Anisotropy of the cosmic microwave background. In 1992, scientists discovered that there is a very slight anisotropy in the cosmic microwave background radiation, roughly one part in 100,000, which is just enough to permit the formation of stars and galaxies.
  5. The cosmological constant paradox. When one calculates, based on known principles of quantum mechanics, the “vacuum energy density” of the universe, one obtains the incredible result that empty space “weighs” 1093 grams per cubic centimeter. Since the actual average mass density of the universe is roughly 10-28 grams per cc, this figure is in error by 120 orders of magnitude. Physicists, who have fretted over this discrepancy for decades, have noted that such calculations typically involve only electromagnetism, and so perhaps when other known forces are included, all terms will cancel out to exactly zero as a consequence of some heretofore unknown principle, such as supersymmetry. But these hopes were shattered in 1998 with the discovery that the universe’s expansion is accelerating, implying that the cosmological constant must be slightly positive. This means that the positive and negative contributions to the cosmological constant somehow cancel to 120-digit accuracy, yet fail to cancel beginning at the 121-st digit. Curiously, this observation is in accord with a prediction made by Nobel Prize-winning physicist Steven Weinberg in 1987, who argued that the cosmological constant must be zero to within one part in roughly 10120, or else the universe either would have dispersed too fast for stars and galaxies to have formed, or would have recollapsed upon itself long ago [Weinberg1989].
  6. Mass of the Higgs boson. A similar coincidence has come to light recently in the wake of the 2012 discovery of the Higgs boson at the Large Hadron Collider [Overbye2012a]. Higgs was found to have a mass of 126 billion electron volts (i.e., 126 Gev). However, a calculation of interactions with other known particles yields a mass of some 1019 Gev. This means that the rest mass of the Higgs boson must be almost exactly the negative of this enormous number, so that when added to 1019 gives 126 Gev, as a result of massive and unexplained cancelation. Supersymmetry has been proposed as a solution to this paradox, but no hint of supersymmetric particles has been seen in the latest experiments at the LHC, and it is not clear that the required cancelation would occur even if the superparticles do exist. Similar difficulties afflict a number of other particle masses and forces — some are of modest size, yet others are orders of magnitude larger. These difficulties collectively are known as the “hierarchy” and “flavor” problems.
  7. The low-entropy state of the universe. The overall entropy (disorder) of the universe is, in the words of Lewis and Barnes, “freakishly lower than life requires.” After all, life requires, at most, a single galaxy of highly ordered matter to create chemistry and life on some planet.

For additional details, see this earlier Math Scholar blog and the 2016 Lewis-Barnes book [Lewis2016].

Critics of the multiverse and the anthropic principle

As mentioned above, some researchers see the multiverse as a solution to the apparent fine-tuning of the universe. According to this line of reasoning, we should not be surprised that we find ourselves in a universe that has somehow beaten the one-in-10120 odds to be life-friendly (to pick just the cosmological constant paradox as an example), because it had to happen somewhere in the multiverse, and, besides, if our universe were not life-friendly, then we would not be here to discuss it. In other words, these researchers propose that the multiverse, in particular the string theory landscape, actually exists in some sense, but acknowledge that the vast majority of these universes are utterly sterile — either very short-lived or else completely devoid of atoms or other information-rich structures, much less sentient beings like us contemplating the meaning of their existence.

But the multiverse and the usage of the anthropic principle to explain fine-tuning have sharply divided the physics-cosmology community. While some see these notions as inevitable, others reject them outright, and more broadly decry the underlying theories upon which they are based, including inflation, supersymmetry, string theory and other theories not strongly supported by rigorous empirical evidence. Among other things, these writers argue that the multiverse is a flagrant violation of Occam’s razor, in that it postulates an enormous ensemble of empirically unobservable universes, just to explain our own. They further see the anthropic principle as a tautology, a fundamental retreat from the quest to understand why our universe is the way it is.

Here are some examples of these critics:

In his 2006 book Not Even Wrong, physicist Peter Woit concluded [Woit2006, pg. 264]:

Any further progress toward understanding the most fundamental constituents of the universe will require physicists to abandon the now ossified ideology of supersymmetry and superstring theory that has dominated the last two decades.

Also in 2006, Lee Smolin described these developments as a “crisis” for the field [Smolin2006, pg. 352]:

We physicists need to confront the crisis facing us. A scientific theory [string theory and the multiverse] that makes no predictions and therefore is not subject to experiment can never fail, but such a theory can never succeed either, as long as science stands for knowledge gained from rational argument borne out by evidence. There needs to be an honest evaluation of the wisdom of sticking to a research program that has failed after decades to find grounding in either experimental results or precise mathematical formulation. String theorists need to face the possibility that they will turn out to have been wrong and others right.

In a 2015 update, Smolin repeated his concerns, specifically condemning the multiverse and the anthropic principle [Smolin2015]:

Cosmology is in crisis. Recent experiments have given us an increasingly precise narrative of the history of our universe, but attempts to interpret the data have led to a picture of a “preposterous universe” that eludes explanation in the terms familiar to scientists. …

As a result, some cosmologists suggest that there is not one universe, but an infinite number, with a huge variety of properties: the multiverse. There are an infinite number of universes in the collection that are like our universe and an infinite number that are not. But the ratio of infinity to infinity is undefined, and can be made into anything the theorist wants. Thus the multiverse theory has difficulty making any firm predictions and threatens to take us out of the realm of science. … As attractive as the idea may seem, it is basically a sleight of hand, which converts an explanatory failure into an apparent explanatory success. The success is empty because anything that might be observed about our universe could be explained as something that must, by chance, happen somewhere in the multiverse.

In the above quotation, Smolin’s comment on the “ratio of infinity to infinity” echoes the “measure problem” of cosmology: the failure to develop a convincing measure theory of possible universes in the multiverse that would permit some meaningful computation of probabilities. For details, see this Quanta magazine article: [Wolchover2014].

Most recently, physicist Sabine Hossenfelder, in her 2018 book Lost in Math: How Beauty Leads Physics Astray, wrote [Hossenfelder2018],

The hidden rules [a preference for elegance and mathematical beauty] served us badly. Even though we proposed an abundance of new natural laws, they all remained unconfirmed. And while I witnessed my profession slip into crisis, I slipped into my own personal crisis. I’m not sure anymore that what we do here, in the foundations of physics, is science. And if not, then why am I wasting my time with it?

Other researchers have fought back, emphasizing that the multiverse and the anthropic principle are suggested in the mathematics of several of these underlying theories. More generally, they argue that resisting the multiverse smacks of the many similar denials of a larger-than-expected world in previous eras. Tom Siegfried, for example, wrote in his 2019 book The Number of the Heavens [Siegfried2019],

Denying the possibility of a multiverse ignores Descartes’s exhortation to “beware of presuming too highly of ourselves” by supposing that there are “limits to the world” we are capable of correctly imagining.

Woit has responded to Siegfried by noting that Siegfried collected arguments from string theory landscape proponents such as Carroll, Deutsch, Guth, Greene, Linde, Polchinski, Rees, Susskind, Tegmark, and Weinberg, but did not fully acknowledge criticisms from writers such as Baggott, Ellis, Hossenfelder, Smolin, Penrose and Richter, and he only briefly mentioned the lack of experimental confirmation in the latest results from the Large Hadron Collider. Thus Woit argued that Siegfried has only told one side of the story [Woit2019].

John Horgan, who for many years has written articles in Scientific American, added the following on Carroll’s and Siegfried’s recent books [Horgan2019]:

Science is ill-served when prominent thinkers tout ideas that can never be tested and hence are, sorry, unscientific. … Shouldn’t scientists do something more productive with their time?

Other leading physicists on the multiverse and the anthropic principle

Here are comments by some other leading figures in the field, pro and con:

  1. Paul Davies: Davies has criticized the multiverse as a flagrant violation of Occam’s razor. What’s more, he points out that if the multiverse exists, then not only would other universes like ours exist, but also vastly more universes where advanced technological civilizations acquire the power to simulate universes like ours on computer. Thus our entire universe, including all “intelligent” residents, could be merely avatars in some computer simulation. In that case, why should we take the “laws of nature” seriously? [Davies2007, pg. 179-185].
  2. George F. R. Ellis: “All in all, the case for the multiverse is inconclusive. The basic reason is the extreme flexibility of the proposal: it is more a concept than a well-defined theory. … The challenge I pose to the multiverse proponents is: can you prove that unseeable parallel universes are vital to explain the world we do see? And is the link essential and inescapable?” [Ellis2011].
  3. David Gross: Gross invoked Winston Churchill in urging fellow researchers to “Never, ever, ever, ever, ever, ever, ever, ever give up” in seeking a single, compelling theory that eliminates the need for multiverse-anthropic arguments [Susskind2005, pg. 355].
  4. Stephen Hawking: “I will describe what I see as the framework for quantum cosmology, on the basis of M theory [one formulation of string theory]. I shall adopt the no boundary proposal, and shall argue that the Anthropic Principle is essential, if one is to pick out a solution to represent our universe, from the whole zoo of solutions allowed by M theory.” [Susskind2005, pg. 353].
  5. Andrei Linde: “Those who dislike anthropic principles are simply in denial. This principle is not a universal weapon, but a useful tool, which allows us to concentrate on the fundamental problems of physics by separating them from the purely environmental problems, which may have an anthropic solution. One may hate the Anthropic Principle or love it, but I bet that eventually everyone is going to use it.” [Susskind2005, pg. 353].
  6. Juan Maldacena: “I hope [the multiverse-anthropic argument] isn’t true.” However, when asked whether he saw any hope in the other direction, he answered, “No, I’m afraid I don’t.” [Susskind2005, pg. 350].
  7. Joseph Polchinski: Polchinski, one of the leading researchers in string theory, saw no alternative to the multiverse-anthropic view [Susskind2005, pg. 350].
  8. Paul Steinhardt: “I consider this approach [the multiverse-anthropic view] to be extremely dangerous for two reasons. First, it relies on complex assumptions about physical conditions far beyond the range of conceivable observation so it is not scientifically verifiable. Secondly, I think it leads inevitably to a depressing end to science. What is the point of exploring further the randomly chosen physical properties in our tiny corner of the multiverse if most of the multiverse is so different. I think it is far too early to be so desperate. This is a dangerous idea that I am simply unwilling to contemplate.” [Steinhardt2006].
  9. Leonard Susskind: “The fact that [the cosmological constant] is not absent is a cataclysm for physicists, and the only way that we know how to make any sense of it is through the reviled and despised Anthropic Principle.” [Susskind2005, pg. 22].
  10. Gerard ‘t Hooft: “Nobody could really explain to me what it means that string theory has 10100 vacuum states. Before you say such a thing you must first give a rigorous definition on what string theory is, and we haven’t got such a definition. Or was it 10500 vacua, or 1010000000000? As long as such ‘details’ are still up in the air, I feel extremely uncomfortable with the anthropic argument. … However, some form of anthropic principle I cannot rule out.” [Susskind2005, pg. 350].
  11. Max Tegmark: As mentioned above, Tegmark has not only endorsed the multiverse suggested by others, but has also proposed that the multiverse ultimately consists of all logically consistent mathematical structures, which actually exist, although only a minuscule fraction contain sentient observers. [Tegmark2014].
  12. Steven Weinberg: “For what it is worth, I hope that [the multiverse-anthropic argument] is not the case. As a theoretical physicist, I would like to see us able to make precise predictions, not vague statements that certain constants have to be in a range that is more or less favorable to life. I hope that string theory really will provide a basis for a final theory and that this theory will turn out to have enough predictive power to be able to prescribe values for all the constants of nature including the cosmological constant. We shall see.” [Weinberg1993, pg. 229].

Many of the issues surrounding the multiverse, fine tuning and the anthropic principle were nicely summarized in two recent Quanta Magazine articles [Wolchover2013; Wolchover2014].

New paper questions string theory, inflation and the multiverse

In June 2018, a team of prominent string theorists led by Cumrun Vafa of Harvard University released a new paper that fundamentally questions the notion of a string theory-based multiverse with 10500 or more variations [Obied2018]. If their results are confirmed by other physicists and experimental evidence, they could seriously challenge string theory and even our entire conception of modern physics and cosmology [Moskowitz2018]. The Vafa result and its implications have been explained in detail in a very nice Quanta article by Natalie Wolchover [Wolchover2018a]. Here is a brief summary:

The main result of the Vafa team paper implies that as the universe expands, the vacuum energy density of empty space must decrease at least as fast as the rate given by a certain formula. The rule appears to hold in most string theory-based universal models, but it violates two bedrocks of modern cosmology: the accelerating expansion of the universe due to dark energy and the hypothesized “inflation” epoch of the first second after the big bang. In particular, Vafa and his colleagues argue that “de Sitter universes,” with stable, constant and positive amounts of vacuum energy density, simply are not possible under rather general assumptions of string theory. Such universes in general, and ours in particular, would reside in the “swampland” of string theory because they are not mathematically consistent. And yet here we are…

Just as significantly, the Vafa team result draws into question the widely accepted inflation epoch of the very early universe, when the universe is thought to have expanded by a factor of roughly 1030 or more. The trouble is, Vafa’s result implies that the “inflaton field” of energy that drove inflation must have declined too quickly to have formed a smooth and flat universe like the one we reside in.

String theorists and other physicists are divided about the Vafa team result [Wolchover2018a]. Eva Silverstein of Stanford University, a leader in efforts to construct string theory-based models of inflation, believes the result is likely false, as does her husband Shamit Kachru, co-author of the 2003 KKLT paper that is the basis of string theory-based models of de Sitter universes [Kachru2003]. But others, such as Hirosi Ooguri of the California Institute of Technology, are inclined to believe the Vafa result, since other “swampland” conjectures have withstood challenges and are now on a very solid theoretical footing [Wolchover2018a].

Potential explanations and experimental tests

One possible way out is that the accelerating expansion of the universe is not due to an ever-present positive dark energy, as currently believed, but instead is due to quintessence, a hypothesized energy source that gradually decreases over tens of billions of years. If the quintessence hypothesis is true, it could revolutionize physics and cosmology.

The quintessence hypothesis will be tested in several new experiments currently underway, and some others scheduled for the future, which will analyze more carefully whether the accelerating expansion of the universe is constant or variable [Wolchover2017]. One of these experiments is the Dark Energy Survey, currently underway, which analyzes the clumpiness of galaxies. The initial results so far, released in August 2017, find the universe is 74% dark energy and 21% dark matter, with everything else (stars, galaxies, planets and us) in the remaining 5%, all of which is pretty much consistent with our current understanding so far.

Another related experiment is the Wide Field Infared Survey Telescope (WFIRST) system, which is specifically designed to study dark energy and infrared astrophysics. The Euclid telescope, currently in development, will investigate even more accurately the relationship between distance and redshift that is at the heart of modern cosmology.

As mentioned above, the theory of cosmic inflation is also challenged by the Vafa team result. Along this line, experimental systems such as the Simons Observatory will search for signatures and other evidence of cosmic inflation. This evidence will be scrutinized carefully, though, in the wake of the widely hailed 2014 announcement of evidence for inflation that subsequently bit the dust, so to speak, in the sense that the results were later explained by dust in the Milky Way [Wolchover2015].

High stakes

Needless to say, if Vafa’s results are confirmed as correct, and the dark energy explanation for the accelerating expansion of the universe is reaffirmed by experimental evidence, then this may spell doom for string theory, and may fundamentally draw into question the multiverse and the anthropic principle.

But more is at issue than just whether this or that particular theory is correct. Many researchers in the field are fundamentally asking whether it is absolutely essential to have rigorous empirical testing for a theoretical line of research to be considered a legitimate branch of modern science and worth pursuing. Should the mathematical physics world stick to a very strict standard here, or is a bit more flexibility in order?

For example, string theory researchers have worked on the mathematics behind the theory for nearly 40 years. Yet despite numerous breakthroughs and advances, they are still not able to present a clear-cut experimental test, possible to conduct with present-day technology, that could definitively settle whether or not the theory is a valid description of nature. The Vafa team result, mentioned above, is perhaps the closest to a definitive test, but both sides still agree that more theoretical development and more rigorous empirical results are required to make a valid determination. If, say, ten more years elapse and theorists have still not produced a credible basis for experimental testing, will it still be prudent to continue large-scale investigations in the string theory arena? How much “rope” should be thrown to the string theory research world?

Almost everyone agrees, in the end, that empirical testing is the deciding touchstone for modern science. As Vafa explains [Wolchover2018a],

Raising the question [whether string theory is consistent with dark energy] is what we should be doing. And finding evidence for or against it — that’s how we make progress.

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