Multiverse scientists use string theory to support the Varied Multiverse Premise. This essay will evaluate whether or not string theory truly supports the notion that the constants vary between universes. To do so, we’ll first need to give a little context on how string theory fits into the picture of modern physics and the pursuit of a final theory of everything (one theory that explains everything else in the universe). Then we’ll discuss some of the basic elements of string theory relevant to the multiverse.
Highlights of this essay:
Below is an essay version of the ideas presented in Episode 5 of Season 2 of the Physics to God podcast. You can hear the audio version above.
Final Theory of Everything
Let's start with a little context to help understand string theory. The Standard Model of quantum mechanics describes all the known particles and forces in the universe, with the important exception of gravity which is understood by a different theory called general relativity. Quantum mechanics has undergone hundreds of successful tests and predictions, making it the most accurate scientific theory ever.
Despite its success, it’s known that the standard model of quantum mechanics is not the final theory physicists dream about. This is because a final theory has to explain everything, and since the Standard Model leaves out gravity, it’s obviously not the final theory. That’s where string theory comes in.
String Theory
String theory is probably the most popular attempt by physicists to remedy the Standard Model’s incompleteness by including gravity - and many physicists believe that string theory is the best candidate for a final theory of everything.
It’s important to note that, as of yet, neither string theory nor any other theory that goes beyond the standard model has found any experimental support. In fact, the lack of highly anticipated experimental confirmation, most notably the failure of the particle collider at CERN to find any corroboration of string theory, has caused more and more physicists to question the viability of string theory entirely. We’ll talk a bit more about that later. For now, let’s try to understand what string theory is all about.
String theory posits that every fundamental particle (like an electron) is really an extremely tiny one-dimensional string. The idea of dimensions will be important, so let’s explain what it means.
A string - whether straight, curved, or even a closed loop - is one-dimensional. This is because you only require one number to specify the location of an object on a string. For example, you can say that an object is situated three centimeters from the left end of the string. Compare this to 3-dimensional space which requires three numbers to specify where something is. For example, to give an object’s exact location on Earth, you must specify its longitude, latitude, and altitude.
The fundamental strings of string theory are hypothesized to be the smallest possible objects, and the way each string vibrates determines its specific properties, such as its mass and charge.
One way to think about this is by comparison to the notes of a guitar string. Just as the different ways a guitar string vibrates result in different sounds, so too the different vibrational patterns of the fundamental strings determine their distinct properties.
There was a lot of excitement in the latter part of the 20th century about string theory’s potential to be the long-sought-after theory of everything. Yet, despite string theory’s initial promise as a final theory, there was a catch. For string theory to be formulated in a mathematically consistent manner, it required the existence of at least nine dimensions of space.
At first glance, this would seem to present a significant problem - you don’t have to be an expert in physics to see that there are only three spatial dimensions - not nine. Nevertheless, adherents to string theory account for the extra six dimensions by positing that they’re curled up and compacted so small that we can't observe them.
The standard analogy for these hidden dimensions is an ant on a rope. From a distance, a rope appears as a one-dimensional line on which the ant can only move back and forth. If this were the case, then we’d be able to specify the exact location of the ant by one number which says where it is along the length of the rope.
However, if we zoom in closer, we see that there’s another hidden dimension to the rope. That is, it’s also possible to circle the thickness of the rope. Not only can the ant move back and forth along the rope, but it can also move around the circumference of the rope. Therefore, to specify the exact location of the ant, we would need two numbers: one which says where the ant is along the length of the rope and another which says where it is on the circumference of the rope. Thus, even though the rope appears from afar to be one-dimensional, this is because its second dimension is hidden. Similarly, although our universe appears to be three-dimensional, string theory claims that it actually has (at least) nine dimensions, six of which are hidden.
In its early stages, string theory faced a major problem because there were five different versions of string theory, each having nine spatial dimensions. Since the five versions were different, it seemed that they couldn’t all be correct. After all, there can only be one ultimate final theory of everything - not five!
You may be wondering why this is a problem. Granted that all five versions can’t be true, but maybe our universe is governed by one of the five versions? And maybe this one version is the final theory of everything?
To answer this question, consider the following. Physicists' dream was to find one unique final theory that would intrinsically explain everything else. But if there are many different versions of this theory, it doesn’t explain itself! We’d still be left with the question of why we observe this ultimate law of nature and not a different ultimate law.
To appreciate this point in more depth, you can check out Series One Essay 7 where we really develop the idea of a unique final theory.
To solve the problem of five different versions of string theory, physicist Edward Witten proposed a unification of the five different versions. He showed that they weren’t truly five different theories, but were really five special cases of one other theory that had one more extra dimension, for a total of ten spatial dimensions. Witten called this new theory, M-Theory, and it’s believed to supersede the prior versions of string theory.
The Problem with String Theory’s Hidden Dimensions
Although Witten’s new theory has never been completely worked out or verified, it breathed new life into the hope that string theory would be the final theory everyone was dreaming about. However, physicists discovered a major problem, intimately tied up with the unobservable hidden dimensions essential to string theory, that seriously challenged this hope.
When studying the hidden spatial dimensions of string theory, it turned out that their configurations are very important. Depending on how the hidden dimensions are curled up and compacted, the theory results in very different properties for the fundamental particles - specifically different values for their constants (like mass and charge).
Let's try to simplify this abstract point. The different ways that string theory’s hidden dimensions can theoretically be curled up can be compared to the different ways that a rope can be tied into differently shaped knots. If each knot has its own unique set of complex twists and turns, the different knots would drastically affect the properties of the paths that our ant can take along the rope.
Taking the analogy a step further, let’s imagine that we assign a number to each and every knot. This number corresponds to the number of times the rope crosses over itself in making that knot. Just like the specific shape of the knot influences the number of crossings, so too string theory claims that the shape of the hidden dimensions influences the values of the constants of nature.
Returning to string theory, there are currently known to be many different possible ways that the very small unobservable spatial dimensions can be compacted and hidden away. In fact, there are thought to be at least 10^500 such ways - that’s a 1 with five hundred zeros. The set of all these different configurations for the extra dimensions is called the string theory landscape. With all these possibilities, string theory can explain just about any universe with any set of constants.
While it might sound like a good thing for a theory to be able to explain any possible universe, it was a major cause for chagrin amongst string theorists, causing the theory to come under heavy criticism. The first problem is that a scientific theory needs to make credible predictions that can be compared to experiments. Since string theory can’t uniquely determine the configuration of these extra dimensions, just about any phenomenon can be “explained” by string theory. This is a major problem. How are scientists supposed to verify that these hypothetical hidden dimensions are real if string theory is intrinsically unable to make any unique predictions? If it can explain almost anything, then in truth it explains nothing at all.
Putting this problem aside, the existence of 10^500 different versions of string theory presents a serious problem for an alleged final theory that’s trying to uniquely explain our one particular universe. It’s way worse than just five versions of string theory. After all, 10^500 different versions are the complete opposite of one unique theory that couldn’t possibly be different. With 10^500 different versions, we’re still left with the mystery of why our one universe has this particular shape for the hidden dimensions such that it results in one set of values for the constants of nature and not some other. This is the type of problem a unique final theory isn’t supposed to have!
It seemed that until string theorists could show some compelling reason why our universe has just one particular configuration out of the 10^500 different theoretical possibilities in the landscape, string theory would remain beautiful mathematical speculation with no hopes of fulfilling physicists’ dream of a unique final theory for our one physical universe.
Let's see how physicist Leonard Susskind, one of the founders of string theory, described scientists’ recognition of string theory’s failure to be a unique final theory because of their inability to determine which of the possible shapes for the hidden dimensions is correct - what Susskind calls a vacuum selection principle that chooses just one single vacuum (The Cosmic Landscape pg. 274):
Until recently string theorists were blinded by this old paradigm of a theory with a single vacuum. Despite the fact that at least a million different Calabi-Yau manifolds could be utilized for compactifying (rolling up and hiding) the extra dimensions implied by String Theory, the leaders of the field continued to hope that some mathematical principle would be discovered that would eliminate all but a single possibility. But with all the effort that was spent on searching for such a vacuum selection principle, nothing ever turned up. They say that “hope springs eternal.” But by now most string theorists have realized that, although the theory may be correct, their aspirations were incorrect. The theory itself is demanding to be seen as a theory of diversity, not uniqueness.
Though Susskind expressed this problem regarding the shape of string theory’s hidden dimensions, the problem of string theory’s failure to be a unique final theory can be seen in the context of Feynman’s mystery of the constants that we introduced in Series One Essay 2.
The mystery was: what caused the constants to have their specific values and not some other possible values? Again, this has nothing to do with fine tuning but is just a fundamental problem of how a theory of everything can determine a specific number like 1/137. String theory allegedly had the potential to solve this mystery and show that only one law of nature with only one set of constants is possible.
However, the discovery of 10^500 different shapes for the hidden dimensions showed that string theory didn’t solve this problem. All it did was to shift the mystery of the constants to the mystery of the hidden dimensions. That is, what caused our universe’s unobservable and unverified hidden dimensions to have their particular shape and not some other shape?
Besides this problem with string theory, there’s one more - the problem of fine tuning. That is, almost all possible shapes of the hidden dimensions would yield a universe with no atoms, molecules, planets, stars, and so on. Given that so many other shapes are inherently possible, what caused our universe to have such a fortunate fine tuned choice of a shape for its hidden dimensions?
To be fair, unlike the first two problems, fine tuning is not a problem specific to string theory. The standard model of quantum mechanics also has the problem of fine tuning - since almost all values of the constants of nature would result in a universe with no complexity, order, and structure, so what caused our universe to have such a fortunate fine tuned choice of constants when so many other constants were possible?
Nevertheless, the point is that the problem of fine tuning remains in string theory, but it now expresses itself as fine tuning of the shape of the hidden dimensions instead of fine tuning of the values of the constants. String theorists have simply reformulated the question using string theory terminology without solving it in the slightest.
Let’s now summarize the three problems that emerged with the realization that string theory can have 10^500 different possible shapes for the hidden dimensions:
It's difficult, if not impossible, for string theory to make any concrete predictions that can be compared to experiment - something critical for a scientific theory.
It signified the failure of string theory to be the much-dreamed-about final theory of everything.
There is still no explanation for the fact that the shape of string theory's hidden dimensions is fine tuned to produce a universe with complexity, order, and structure.
The Marriage of String Theory and Multiverse
Because of these problems, in Leonard Susskind's groundbreaking 2005 book, The Cosmic Landscape: String Theory and the Illusion of Intelligent Design, he arranged a marriage between string theory and the eternal inflation multiverse. This union was meant to solve the second and third problems. That is, to rescue string theory as a potential theory of everything, and to solve the fine tuning problem through what Susskind calls the “populated Landscape”.
The string theory landscape is the abstract set of all possible configurations of the hidden dimensions, meaning all the different possible ways the hidden dimensions can be curled up. Susskind suggested that this landscape is “populated”, meaning that these configurations are all actually realized in different universes in the eternal inflation multiverse.
The idea is that since the shapes of the hidden dimensions can in theory vary, where one universe has its hidden dimensions with one shape and another universe has a different shape, Susskind posited that there’s a natural mechanism that causes every universe in the multiverse to have a different shape for its hidden dimensions and thereby different values for its constants. If this is true, the populated landscape can solve two of the three problems. Let’s start with the fine tuning problem.
As we discussed in Series One Essay 3, Susskind, like many multiverse scientists, was particularly moved by the 1998 discovery of the precise fine tuning of the cosmological constant, which was observed to be the incredibly small number of around 3x10^-122. If it had been even a tiny bit bigger or smaller there would be no galaxies, stars, or planets in the universe.
Susskind recognized that such extreme fine tuning naturally points to an intelligent fine tuner, and that an infinite varied multiverse is the only other reasonable alternative to explain the mystery of this fine tuning. However, an infinite varied multiverse needs to justify the Varied Multiverse Premise - that the constants change from universe to universe - and that’s where string theory and the shape of the hidden dimensions come in.
The line of reasoning is as follows: Without assuming string theory, the known and tested laws of physics (the standard model) provide no justification whatsoever for the claim that the values of the constants change from universe to universe. However, because string theory maintains that the values of the constants are dependent upon the shape of the extra dimensions and it’s plausible that there’s some natural mechanism that causes the configuration of the hidden dimensions to change from universe to universe, it likewise becomes more plausible that the constants vary from universe to universe.
In trying to support his populated landscape paradigm through arguing by elimination that no other good possibility exists, Susskind wrote as follows (on page 356):
What are the alternatives to the populated Landscape paradigm? My own opinion is that once we eliminate supernatural agents, there is none that can explain the surprising and amazing fine-tunings of nature...The populated Landscape, together with the rich diversity predicted by string theory, is the only known explanation of the extraordinary special properties of our universe which allow our own existence.
Incidentally, that quote from Susskind is another nice illustration of the hidden premise many scientists harbor - that an intelligent cause is not a theory to be taken seriously. Of course, if that hidden premise were dropped, there’s no need to posit an infinite varied multiverse to explain fine tuning.
Nevertheless, Susskind’s point is that if the populated landscape is actually true, different universes in the multiverse would have different values of the constants. If so, even though our universe appears fine-tuned by an intelligent cause, this is a mere illusion stemming from an observer bias. Instead, we just happen to be in one of the few lucky universes in an infinite multiverse with perfectly shaped hidden dimensions that yield fine tuned constants which could produce intelligent observers like us. Despite our universe’s special appearance, the overwhelming majority of other universes in the multiverse would have differently shaped hidden dimensions which result in constants that aren’t fine tuned at all and would have nothing resembling intelligent observers.
All this assumes that not only is there an infinite number of universes via eternal inflation, and that string theory is true, but also that all the different universes have different configurations for the hidden dimensions, thereby giving different values to the constants. If string theory were true but all the universes had the same shape for the hidden dimensions, nothing would be gained in terms of solving fine tuning.
In other words, if the hidden dimensions throughout our universe always have the same shape, it’s certainly conceivable that all the other universes in the multiverse also have the same shape and thereby all have the same constants.
Nevertheless, to be fair to multiverse scientists, the fact that in string theory the values of the constants are contingent on the shape of the hidden dimensions makes it more plausible to assume that they and the derived constants change from universe to universe.
Putting that aside, Susskind’s move to unite string theory with eternal inflation does more than just explain fine tuning of the constants but also has the potential to solve the second problem we mentioned above - that is, it can restore string theory’s original promise of being a theory of everything.
Susskind realized that if the eternal inflation multiverse theory was real, then string theory having many different possible configurations might not be so bad after all; it might even be a good thing! While a theory with 10^500 different possibilities is a poor explanation for one universe with one set of constants, it may be a great explanation for a multiverse with more than 10^500 different universes. Thus, string theory could still be a theory of everything - all we have to do is to change our understanding of “everything” from the one fine tuned universe we observe to an infinite varied multiverse we can’t observe and for which we have no actual evidence.
While the populated landscape can potentially solve the second and third problems of explaining fine tuning and rescuing string theory’s ability to be a theory of everything, Susskind’s solution still doesn’t solve the first problem - that is, it doesn’t enable string theory to make clear predictions that can be experimentally tested.
In fact, there were certain “predictions” that some versions of string theory made about expected observations in high-energy collisions. The failure to observe these predictions in the large hadron collider at CERN over the past decade has dealt a major blow to string theorists and is a major cause of why string theory has become much less popular as of late.
You may be wondering what we mean when we say that it made predictions that weren’t observed. Didn't we say that string theory doesn’t make predictions? And if it made false predictions, why is it less popular? Shouldn’t it be clear that it’s just wrong?
Well, because string theory isn’t unique and has so much flexibility, string theorists are always able to tweak their theory so that any failed prediction can be explained away. That’s why its predictions weren’t really concrete and why you can’t ever really prove string theory wrong. Nevertheless, there was an expectation that the collider at CERN would find certain things, and it didn’t - what a 2012 article in Scientific American called the “nightmare scenario”. This cast further doubt on string theory, even among some of its ardent supporters. We’ll come back to this issue in a later essay when we discuss the multiverse and the scientific method.
Before moving on, there’s an important caveat to the populated landscape. As of yet, string theorists have been unable to show that even one of the different possible configurations of the unobservable dimensions can accurately describe our actual observable universe. Nevertheless, they assume that since 10^500 is such a big number, one of them probably contains a universe exactly like ours.
Brian Greene explains this problem in his book The Hidden Reality (pg. 186). He writes as follows:
For this line of thinking to be credible, though, we need at a bare minimum to know not only that there are bubble universes in which the cosmological constant has the right value, but also that in at least one such bubble the forces and the particles agree with what scientists in our universe have measured. We need to be sure that our universe, and all its detail, is somewhere in the landscape...To date no one has found an example that reproduces the features of our universe exactly. But with some 10^500 possibilities awaiting exploration, the consensus is that our universe has a home somewhere in the landscape.
Summary of the Evidence
Before moving on, let’s review where we’re at in our argument. Series One presented the fine tuning argument that showed how the fine tuned constants indicate that our universe has an intelligent cause. This argument places the burden of proof on multiverse scientists to justify an infinite varied multiverse as an alternative to an intelligent fine tuner. For multiverse scientists to meet this burden of proof, they must justify that there are infinitely many universes and that the constants vary from universe to universe. Even if one accepts eternal inflation’s support for the first premise - that there exists an infinite number of universes - have multiverse scientists provided good justification for the second premise - that the constants vary from universe to universe?
This was the topic of the past two essays. Last time, we assessed their first justification - assuming there is no intelligent cause, there is simply no explanation for fine tuning other than the constants changing from universe to universe. We showed that this line of reasoning is guilty of assuming its conclusion. In assessing whether or not our universe’s fine tuned constants indicate an intelligent cause, there’s no legitimate justification for eliminating an intelligent cause from the outset, and then drawing a conclusion about the varied constants. Rather, scientists need independent evidence that the constants change in different universes.
This essay discussed string theory - the only other justification multiverse scientists use to establish the Varied Multiverse Premise. However, using string theory to support the Varied Multiverse Premise makes multiverse contingent upon the truth of string theory. While string theory is, or at least was, a popular theory, it has no experimental confirmation and is extremely difficult, if not outright impossible, to test.
This creates a problem that’s articulated by physicists George Ellis and Joe Silk in their article, Scientific Method: Defending the Integrity of Physics, published in the science journal, Nature. They argue: “Fundamentally, the multiverse explanation relies on string theory, which is as yet unverified, and on speculative mechanisms for realizing different physics in different sister universes. It is not, in our opinion, robust, let alone testable.”
This being the case, supporting the Varied Multiverse Premise by string theory, which is itself an unverified theory, significantly weakens scientists’ justification for multiverse as an explanation for fine tuning.
While some scientists have reservations about string theory because it makes big claims and has never been experimentally verified, for the purpose of our argument we’ll nevertheless grant that multiverse scientists can use string theory to meet the burden of proof for the Varied Multiverse Premise.
We’re now in a position to combine eternal inflation with string theory and summarize multiverse scientists’ strongest justification for the first two premises that are needed to explain fine tuning without an intelligent fine tuner.
First, they support the Infinite Multiverse Premise by assuming that the theory of inflation and the model of eternal inflation are true.
Second, they support the Varied Multiverse Premise by assuming that string theory is true and that there’s a natural mechanism that allows the shape of the hidden dimensions (and thereby the values of the constants) to vary from universe to universe.
While we’ll grant all this to multiverse scientists, we want to point out the many weaknesses in their alleged supports for the first two premises. They need to assume all of the following points:
An actual physical infinity like the infinite universes of eternal inflation is possible.
Inflation is true, even though there are competing alternative theories that explain the same data.
Eternal inflation, because it’s the simplest model, is the right way to model inflation, even though there are models of inflation that don’t yield an infinite number of universes.
String theory is real, even though it makes many big and unverified claims like the existence of hidden dimensions, and it’s not clear that there is even a single version of string theory that is capable of explaining our universe.
The shape of the hidden dimensions changes from universe to universe, even though as Ellis and Silk note this is based on “speculative mechanisms for realizing different physics in different sister universes”.
You may argue that multiverse scientists haven't provided solid enough justification for an infinite number of unobservable parallel universes with different values for the constants of nature. After all, that’s quite the claim and the evidence they’ve provided isn’t exactly airtight.
But keep in mind that we’re accepting it for the purpose of continuing our argument. We want to show that even if we grant multiverse scientists these two premises - multiverse still fails to explain fine tuning. We won’t need to argue scientific points with scientists, such as whether eternal inflation and string theory are valid theories. We want it to be clear that multiverse is not a good explanation even if we grant them these points. Ultimately, we’ll show that even in their own framework, the eternal inflation/string theory multiverse fails at the crucial test of establishing the Typical Universe Premise and falls prey to the measure problem - and that won’t require us to argue with them about anything scientific.
The next five essays will be lighter on the science and will be the core of this series about analyzing and rejecting the multiverse. The next essay will explain what goes wrong if multiverse scientists only have the first two premises, and thereby show why they need to posit and justify the all-important third premise. The next four essays will build up to the devastating measure problem. So stay tuned.
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