Roger Penrose is well known for the Moore–Penrose pseudoinverse, the Penrose diagram, the Penrose–Rindler books on spinors and space-time, and the Penrose tile. He is also known for his argument that human consciousness is non-algorithmic.1 In Fashion, Faith, and Fantasy in the New Physics of the Universe, Penrose considers some recent developments in theoretical physics, appearing both as a stodgy conservative, reacting against flights of mathematical fantasy by string theorists, and as a maverick, with idiosyncratic ideas about quantum mechanics, gravity, and cosmology.
The book is organized into four chapters and an epilogue. The first chapter, “Fashion,” introduces particle physics. Penrose views string theory in particular as fundamentally wrong, but, as he notes, it has monopolized the attention, funding, and students of a generation. In the second chapter, “Faith,” Penrose questions the near-religious devotion to quantum mechanics of most physicists, arguing that gravitational effects must be included in any picture of the quantum world. In the third chapter, “Fantasy,” he argues against inflationary theories in cosmology, offering in its place his own theory of cyclic conformal cosmology. The epilogue is reserved for some of Penrose’s personal thoughts on theoretical physics.
Fashion
Penrose is passionate when criticizing string theory. Its “stranglehold on developments in fundamental physics,” he argues, “has been stultifying.”2 He objects, in particular, to supersymmetry, or SUSY, which pairs elementary particles to entirely imaginary partners, bosons to charginos, photons to photinos, and quarks to squarks. “Given the alarming nature of this proliferation of basic particles (and, perhaps, the seeming absurdity of the proposed terminology),” Penrose observes, “the reader may be relieved to hear that no such supersymmetric sets of particles have been yet observed!”3 Penrose thinks it unlikely that they exist and even if they do, he claims, they will not do much to help string theory.
If Penrose is critical of the proliferation of elementary particles, he still more critical of the proliferation of spatial dimensions in string theory. In 1907, Hermann Minkowski unified space and time into a four-dimensional Minkowski manifold, and in 1921, Theodor Kaluza attempted to reconcile electromagnetism with general relativity by moving to a five-dimensional space. The idea that the laws of physics can be made simpler by the expedient of multiplying dimensions has never lost its appeal to physicists. In string theory, there are at least eleven and as many as twenty-six space-time dimensions.
Penrose has two major objections to the extra-dimensional program of string theory. The fields inhabiting a given dimension have infinitely many degrees of freedom. With every extra dimension, there is an exponential increase in the way these fields can arrange themselves. How, Penrose asks, should we deal with the extra degrees of freedom when trying to get back to our 3+1 dimensional space-time? The usual answer involves the mathematical process of compactification, as when a two-dimensional sheet of paper becomes a one-dimensional scroll when rolled up. In string theory, compactification proceeds on Calabi–Yau manifolds. But how does one guarantee that these extra degrees of freedom are not excited after compactification? Even at very high energies, whatever is buried in those extra dimensions can be excited by an astronomical source.
What is more, Penrose adds in his second objection, solutions to the equations of string theory in extra dimensions are unstable. Their dynamic evolution must be singular. This means, as Penrose notes, “the extra dimensions must be expected to crumple up to something where curvatures diverge to infinity and further evolution of the classical equations becomes impossible.”4 Proofs of stability are famously difficult to achieve; even the fact that flat space-time is globally stable under gravitational perturbations has only been proven with great effort.5 All the obvious routes to the proof, as Demetrios Christodoulou and Sergiu Klainerman acknowledge, lead nowhere.
Penrose’s experience as an analytic geometer provide him with insights that have eluded others working in the field. It was, after all, Penrose, in his famous singularity theorem, who found a basic obstruction to global existence. The stability issue has been raised in the past.6 In fact, it goes back to the original work of Henri Poincaré and Aleksandr Lyapunov. In some cases, it has been answered.7 For all that, string theorists would do well to attend more to issues of stability.
The chapter ends with a discussion of the landscape and the swamplands. Our best current understanding of string theory tells us there is not one theory but many. Each possible vacuum state of a theory corresponds to a different universe, each with different physical properties. The result is the landscape. Some of these universes are inconsistent. When mathematically-consistent worlds are subtracted from the landscape, what remains is the swamplands.
The idea now seems to be that if we want to explain nature’s apparent “choice” of values for the different moduli that determine the nature of the actual universe that we experience, we are to argue as follows: it is possible to find ourselves only in a universe in which the moduli have values leading to constants of nature compatible with the chemistry, physics, and cosmology necessary for the evolving of intelligent life. This is an instance of what is referred to as the anthropic principle [emphasis original] … In my view, this is a very sorry place for such a grand theory to have finally stranded us.8
It has now become very fashionable to criticize string theory. In The Trouble with Physics Lee Smolin argued that string theory was overblown and overhyped.9 Peter Woit’s Not Even Wrong assigned string theory to the class of theories dismissed by Wolfgang Pauli: “Das ist nicht nur nicht richtig; es ist nicht einmal falsch!”10 Smolin and Woit published their critiques in 2006. Penrose delivered the lectures upon which the book is based in 2003, but waited until 2016 to publish them as a book. He never explains why.
Penrose says little about the standing of string theory within the larger physics community. In the past decade, string theory in particular and theoretical quantum gravity in general have fallen on hard times. There are fewer faculty openings and less funding available.11
Penrose seems to have been ahead of the curve.
Faith
Throughout Fashion, Faith, and Fantasy, Penrose’s objurgations are expressed in sacerdotal language. “The Quantum Revelation” is a section title, a refreshing if idiosyncratic change from the quantum revolution. Penrose defines faith in a way that is appropriate for an atheist, as an argument from authority. A better definition for faith, as the word is used in this book, might be: “Now faith is the substance of things hoped for, the evidence of things not seen.”12 This is surely the kind of faith routinely shared among physicists. As Joseph Polchinski argues in remarks noted by Penrose, “the existence of magnetic monopoles seems like one of the safest bets that one can make about physics not yet seen.”13 Polchinski’s faith may be misplaced, but it is not blind, nor is it based on any authority.
Penrose has set his sights on the “dogma of quantum mechanics,” which he compares to Hans Christian Andersen’s little mermaid.
I have depicted the mermaid sitting on a rock, with one half of her body under water and the other in the open air. The lower part of the picture depicts what is happening beneath the sea … This represents the strange and unfamiliar world of the quantum-level processes. The upper part of the picture depicts the kind of world that we are more familiar with, where different objects are well separated and constitute things that behave as independent objects. This represents the classical world, acting according to the laws we have become accustomed to, and had understood—prior to the advent of quantum mechanics—as precisely governing the behavior of things. The mermaid herself straddles the two, being half fish and half person. She represents the link between the two mutually alien worlds.14
Penrose does not like that these two worlds are divided. He too has a faith, which is almost religious, in the sense that it is a system of beliefs about the nature of the world. There is only one world and only one theory: “We expect that—indeed we may [have] a faith that—physics as a whole must be a unity. [emphasis original]”15 Quantum theory requires unitary wave-function dynamics and probabilistic measurement.
This is the problem.
The solution adopted by most practitioners of quantum mechanics is that of the Copenhagen school. The wave function collapses when we make a measurement. Penrose remains unconvinced. Physics, in his view, should be objective, and human agency should play no fundamental role. Nor is he persuaded by fashionable theories of decoherence, the argument that measurement is nothing more than the uncontrolled interaction of a quantum system with its environment.
It is this almost religious desire for an objective, observer-independent theory that has led many otherwise respectable physicists to Hugh Everett III’s many-worlds interpretation of quantum mechanics. Here no measurements ever take place, but at the metaphysical cost of requiring an exponentially increasing number of branching and unobserved worlds.16
Most philosophical discussions of the foundations of quantum mechanics ignore the dramatic progress achieved in controllable quantum systems.17 For those following recent developments in quantum information theory, the role of the observer is, more than ever, central. Quantum Bayesians have pushed hard on the subjectivity of quantum theory.18
Having erased the information measured by an observer, quantum information theory has made it possible to reverse the collapse of the wave function.19 In quantum information theory, physicists leverage quantum phenomena to perform tasks in computation, control, and estimation. This makes the most sense when the information controlled by an observer is precisely specified.
Penrose searches elsewhere for solutions and, unsurprisingly, finds one in gravity, the area of his life’s work. Quantum mechanics is a linear theory; gravity, fundamentally nonlinear. This strikes Penrose as key. We have no well-developed theory of quantum gravity, but Penrose, following Lajos Diósi, has argued for a criterion under which the nonlinearities of the gravitational field lead to spontaneous collapse of the wave function.20 This results in an effective breakdown of the superposition principle of quantum mechanics. Others have had similar ideas. Giancarlo Ghirardi, Alberto Rimini, and Tullio Weber have proposed their own objective collapse theory.21 The spontaneous collapse time is predicted to be Planck’s constant divided by the gravitational self-energy difference of a massive object being quantum superimposed between two possible positions.
Curiously enough, Penrose does not mention experiments carried out in 2008 by Nicolas Gisin’s group. In this optical interferometer experiment involving two entangled photons, the detection of a photon triggered the movement of a massive mirror designed to satisfy the Diósi–Penrose criterion.22 The mirror’s movement should have been enough to collapse the photon’s wave function. Tests revealed a violation of Bell’s inequality, indicating that while their mechanism may still be invoked to explain the individual collapses, it cannot explain the non-local correlations between the two photon measurements. The local gravitational collapse model has thus been ruled out experimentally.
No experiment is entirely free of wiggle room, but if gravity is to be invoked as a mechanistic form of wave-function collapse, it should be able to collapse non-locally entangled states in a way that quantum mechanics predicts. This is precisely what this local mechanism cannot do. Furthermore, if gravity is behind all wave-function collapses, how then it is possible to make measurements when massive objects are not moved? In most cutting-edge quantum experiments, the system is probed off-resonantly by light, which is subsequently amplified. Yet very precise theories of quantum wave-function collapse and quantum measurement can be tested that have nothing to do with gravity.23
If we do discover a deeper theory of quantum measurement and quantum physics, it will take us even further away from a classical worldview, and be even stranger than the quantum physics we currently know.
Fantasy
Penrose views as fanciful most current theories in cosmology. The Big Bang was an incredible idea, one that Albert Einstein rejected until the mid-1930s. But Big Bang cosmology is far less incredible than inflationary models of the universe, brane worlds, and the multiverse. Having dismissed these theories as fantasies, Penrose introduces one of his own. His cyclic conformal cosmology expresses the idea that Big Bangs come in perpetual cycles, one bang giving rise to another, as in a drumroll.24
[T]here are some key aspects to the nature of our actual universe that are so exceptionally odd (though not always recognized as such) that if we do not indulge in what may appear to be some outrageous flights of fantasy, we shall have no chance at all of coming to terms with what may well be an extraordinary fantastical-seeming underlying truth.25
Once again, there is an ironic tension; Penrose goes to some lengths to attack the fanciful cosmologies of contemporary physics, and then proposes an improvement on hot Big Bang cosmology that is just as fanciful.
Flight into the Unknown
At the conclusion of his book, Penrose tells us what he really thinks. On the one hand, he admits to being quite conservative about physics—hence his aversion to multidimensional spaces, and his concerns about speculative high energy physics and quantum theories of gravity. On the other hand, he does not hesitate to advance eccentric ideas he instinctively feels may be right, such as the deep connections between four-dimensional space-time, geometry, and his own twistor theory.
[W]hen I heard that string theory … had moved itself in the direction of requiring all those extra spatial dimensions, I was horrified … I found it impossible to believe that nature would have rejected all those beautiful connections with Lorentzian 4-space – and I still do.26
