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Multiverse Theories: A Philosophical Perspective

by Simon Friederich
Cambridge, 2021, 200 pages
reviewed by T. Nelson

ccording to Simon Friederich, much of the rationale for a multiverse is the idea that the universe is fine-tuned for life. It turns out that this ‘fine tuning’ is not so fine as many people think. For instance, the strong nuclear force could vary by 50% in either direction. Electrons would have to be twelve times heavier to make life impossible and the weak force seems not to matter much at all. What it really means, as far as I can tell, is that the universe is tuned in such a way that the universe continues to exist.

That, of course, makes fine-tuning seem a lot less mysterious, but suppose fine tuning were really some big mysterious thing. Then what? Well, the Intelligent Designers have an answer: God set the parameters so we could exist. And so Friederich launches into a long but fair discussion of what famous creationists like Behe and Dembski and philosophers like Richard Swineburne claim and the philosophical problems therewith. (Maybe too fair: he doesn't take sides as to whether God is a ‘she/he’ or just a ‘she’.)

Why is it that they can't get God's sex right, but never fail to call Satan a ‘he’ ? Hmmm?

Friederich makes extensive use of Bayes' Rule to discuss the probability that God, perhaps realizing he was on a roll, would have created a bunch of other universes. The general idea is that if the probability of a universe where humans could exist is too low, God would have had to make a lot of them to compensate. Bayes' Rule is supposed to calculate how many we need based on prior information. Unfortunately, we have only one piece of prior information: one universe does indeed exist. That doesn't tell us much about the multiverse other than that there could possibly be one, the idea being that, according to the Anthropic Principle, if there were no universe we probably wouldn't be here to ask the question.

All this comes to a head in the discussion of Nick Bostrom's thought-puzzles, which have evidently been extensively discussed by philosophers. Here is the Sleeping Beauty puzzle (modified a bit here but retaining the basic idea):

You are Sleeping Beauty in a coma for two days. A philosopher will wake you up either once or twice depending on a flip of a coin (heads=once, tails=twice) and start telling you about how wonderful Bayes' Rule is and how it tells you things that seem wildly counterintuitive. Each time you wake up, you will push that horrible memory out of your mind and forget that you woke up. Let's assume you don't have any other sources of information such as a calendar or the number of lipstick stains on the philosopher, so you don't know which time you're waking up. When you first awaken, what is the probability that the outcome was Heads?

The puzzle appears simple, but there's a huge literature on it with solutions ranging from 1/3 to 5/8. But in fact it can't be answered because, while it sounds precise, the question is actually ambiguous about when self-locating information is available. Friederich does not venture to tell us what he thinks the correct answer is. This is wise, because there isn't one: you get a different answer depending on your interpretation of the problem.

And here is Bostrom's Doomsday puzzle.

Suppose you know there are either 200 billion or 200 trillion humans who are ever going to exist. You are No. 60 billion. Using Bayes' Rule again, you calculate that it is fifty times more likely that the correct number of humans is 200 billion and the humans are going to die out quite soon.

This argument tells us that using Bayes' Rule not only leads to counterintuitive conclusions, the entire approach of using it to gain information is, as Friederich puts it, “problematic.” This approach of using Bayes' Rule is called self-locating indifference and it clearly doesn't work. This is not a problem, though, he says, because answering questions like this is already impossible.

So, what we have here is a whole book that concludes what we should have known from the beginning: that while philosophy may be great at helping us think clearly, it doesn't have a chance in hell of answering the multiverse question.

In the last two chapters, the author finally starts talking about David Lewis's modal realism, the Everett interpretation of quantum mechanics, and Max Tegmark's claim that the universe is made out of mathematics. But by that time I felt as if I had fallen into a coma, thinking my life had come up tails.

feb 06 2022

Conversations on Quantum Gravity

by Jácome (Jay) Armas, ed. Cambridge, 2021, 707 pages
reviewed by T. Nelson

h God, I hear you saying, not another seven hundred page tome on quantum gravity. Oh yeah, baby! But fear not: this one has no math, hardly, and it's absolutely fascinating.

It's a collection of interviews with famous physicists and mathematicians, including Abhay Ashtekar, Robbert Dijkgraaf, Gerard 't Hooft, Juan Maldacena, Roger Penrose, Joseph Polchinski, Carlo Rovelli, Lee Smolin, Rafael Sorkin, Steven Weinberg, Edward Witten, and many others. As you might guess from these stellar names, their ideas about quantum gravity require a little background in physics to fully understand, and they often differ from each other. But in this book you'll learn a bit of physics by hearing where they disagree and what they're planning for the future.

Gravity, as we all know, is not just another force, but is a distortion in the geometry of space and time. So, according to Abhay Ashtekar, when you study quantum gravity you're actually studying quantum spacetimes. Ashtekar laments that ideas are no longer judged objectively in science: some string theorists are becoming intolerant, as if people in loop quantum gravity are just wasting their time. Some also look down on causal set theory.

The goal is to ‘quantify’ gravity, which is to say to make Einstein's relativity compatible with quantum mechanics. The leading candidate is string theory (or M theory), but there are others, including loop quantum gravity, causal dynamical triangulation, quantum Einstein gravity, and Asymptotic Safety. Each approaches the problem from a different perspective. They aren't as well studied as string theory but have strong and articulate advocates.

Mathematician Alain Connes, who is famous for his work on non-commutative geometry, has a remarkable skill for fooling us into thinking complicated math is exciting. For instance, I always thought of renormalization as just a dirty trick, a way of cheating to get rid of infinities in a theory. Connes says it has an elegant mathematical meaning. It is, he says, related to a procedure called Birkhoff decomposition, which provides certain numerical values.

When you put these values on the Riemann sphere you find that ε is a singularity. The mathematical way of dealing with this singularity is to perform the Birkhoff decomposition and simply evaluate the holomorphic part at ε = 0. . . . This indicates that, first of all, there is a conceptual meaning to renormalization. [p.139]

He says spacetime emerges as the product of two 4-dimensional spheres of Planckian size [the smallest possible size, therefore the highest possible energy]. Geometry doesn't make any sense above Planck energy, since volume is quantized. (Others disagree, saying things are too fuzzy at that scale.) Time emerges from symmetry breaking and quantum randomness generates time:

The meaning of this is that probably the quantum is not only at the origin of variability which is much more primitive than the passing of time but . . . entanglement is in fact a synchronization of clocks at the level of randomness.

More of Connes's ideas are in his book Triangle of Thoughts.

Other interesting ideas

Many of the physicists have different interpretations of what background independence means and whether string theory is or is not background-independent as its advocates claim. The majority of string theorists still say there are ten dimensions of space (plus one of time), but disagree at what scale they are ‘compactified’ such that we can only detect the current four. They also agree that string theory and gauge theory are mathematically equivalent [i.e., dual]. They strongly disagree on whether string theory or something else is better. Armas asks intelligent questions and gets great answers. Here are some of the salient ideas (paraphrased):

Hořava: String theory is more of a technology than a theory. Anisotropic scaling [a feature of Hořava-Lifshitz gravity theory, a lattice formulation of gravity that is similar to causal dynamical triangulation or CDT], may be an alternative to inflation. Graviton polarization is a scalar. At extremely high energies, particles might move infinitely fast, unbounded by the speed of light.

Loll: Spacetime has only two dimensions at the Planck scale.

Minwalla: AdS₅ × S⁵ (a theoretical construct in string theory) is gravity when N = ∞ but is quantum mechanics when N < ∞.

Penrose: Gravity is the only thing that affects the causal structure of spacetime. Data from IMAP now support the CCC (conformal cyclic cosmology) hypothesis. It is impossible for a strong quantum superposition to exist in spacetime.

Polchinski: The interior of a black hole might not even exist. Extra dimensions in string theory aren't a problem: there's no reason why some dimensions expanded [during inflation] and some didn't. The more realistic alternative to AdS, called de Sitter or dS spacetime, is not eternal but can always decay. String theory is consistent with Lorentz invariance, but LQG [loop quantum gravity] and other theories aren't even close. Supergravity is now part of string theory. The problems with string theory are the fault of nature, not string theory itself.

Polyakov: String theory is an unqualified success so far: its application to turbulent flow showed that Navier-Stokes equations were missing a 14th parameter. Maxwell's equations can also be recast into string theory. Strings propagate as if they were five-dimensional strings. There may be no spacetime at all at the Planck scale.

Reuter: Something like MOND [modified Newtonian dynamics] might emerge from quantum Einstein gravity [a theory similar to CDT but hypothesizing a continuum].

Rovelli: Dark matter might actually be Planck-size black or white holes stabilized by quantum gravity effects. Dark energy is no longer a mystery: it is the polynomial divergence of the mass of the Higgs boson. We need to understand quantum space and quantum time. Hořava-Lifshitz gravity is ruled out because Lorentz invariance is not broken at the Planck scale, contrary to its prediction. String theory is also ruled out by empirical data such as the failure to find supersymmetric particles. Critics of LQG are discussing an earlier version that has long been surpassed. LQG is like QCD [quantum chromodynamics, the standard theory of quarks] on a finite lattice, but the lattice is dynamic. So contrary to what people think, LQG is Lorentz-invariant, especially in its spin-foam formalism. LQG may predict a Big Bounce because there is a maximum possible amount of curvature. We may soon be able to measure Planck time discreteness.

Sen: The main problem in string theory is that it has 10⁵⁰⁰ different phases called vacua that can't be calculated. If there is no well-defined notion of time then we don't even know what we mean by vacuum. In string theory we start with 10 dimensions, where supersymmetry still exists, and compactify down to four, where it's broken. The natural scale for this breaking to happen is at the Planck scale. String theory successfully calculates the entropy of black holes accurately as Area / 4.

Silverstein: The famous number 10⁵⁰⁰ for the number of vacua actually refers to a subset of solutions known as Ricci-flat manifolds. If you abandon low-energy supersymmetry the number of possible solutions in string theory is even greater: maybe infinite.

Susskind: In biology, a small number of DNA bases [actually 830 --tn] can produce the same number (10⁵⁰⁰) of possible outcomes, but only one is viable. Is this an accident? Of course not. So why worry about the fact that there are 10⁵⁰⁰ solutions to string theory? The anthropic principle is silly. There is no doubt that the mathematical structure of string theory is consistent and there is also no doubt that it's not our universe.

Smolin: Whether gravity is quantized is now becoming testable. For example, photons of different energies appear to travel at slightly different speeds because the concept of locality is energy-dependent, which constrains quantum theories of gravity. The path integral in the spin foam version of LQG gives us a powerful connection between quantum mechanics, general relativity, and thermodynamics. This allows the derivation of classical general relativity from the theory. The Trouble with Physics [Smolin's popular book] was misunderstood. It was more a reply to philosopher Paul Feyerabend, who criticized science, than a critique of string theory.

With all the energy going into these competing theories, there is no doubt that the broken symmetries among them will be repaired and they will soon be unified into a single theory. Sadly, some of these great physicists, including Joseph Polchinski and Steven Weinberg, have already died.

mar 13 2022