Lost in Math: A Book Review

I recently finished reading a thought-provoking book by theoretical physicist Sabine Hossenfelder, Lost in Math: How Beauty Leads Physics Astray. Hossenfelder writes in an engaging and accessible style, and I hope you will enjoy reading this book as much as I did. Do we have a crisis in physics and cosmology? You be the judge. She presents convincing arguments.

The basic premise of Hossenfelder’s book is that when theoretical physicists and cosmologists lack empirical data to validate their theories, they have to rely on other approaches—”beauty”, “symmetry”, “simplicity”, “naturalness“, “elegance”—mathematics. Just because these approaches have been remarkably successful in the past is no guarantee they will lead to further progress.

One structural element that contributes to the book’s appeal is Hossenfelder’s interviews with prominent theoretical physicists and cosmologists: Gian Francesco Giudice, Michael Krämer, Gordon Kane, Keith Olive, Nima Arkani-Hamed, Steven Weinberg, Chad Orzel, Frank Wilczek, Garrett Lisi, Joseph Polchinski, Xiao-Gang Wen, Katie Mack, George Ellis, and Doyne Farmer. And, throughout the book, she quotes many other physicists, past and present, as well. This is a well-researched book by an expert in the field.

I also like her “In Brief” summaries of key points at the end of each chapter. And her occasional self-deprecating, brief, soliloquies, which I find reassuring. This book is never about the care and feeding of the author’s ego, but rather giving voice to largely unspoken fears that theoretical physics is stagnating. And an academic environment hell-bent on preserving the status quo isn’t helping matters, either.

Anthropic Principle

Do we live in a universe fine-tuned for life? If so, is it the only possible universe that would support life? Recent work indicates that there may be more than one set of parameters that could lead to a life-supporting universe.

Beauty is in the Eye of the Beholder

Is our sense of what is “beautiful” a reliable guide to gaining a deeper understanding of nature? Or does it sometimes lead us astray? We know from history that it does.

In the past, symmetries have been very useful. Past and present, they are considered beautiful

When we don’t have data to guide our theory development, aesthetic criteria are used. Caveat emptor.

Experiment and Theory

Traditionally, experiment and observation have driven theory. Now, increasingly, theory drives experiment, and the experiments are getting more difficult, more expensive, and more time consuming to do—if they can be done at all.

Inflation

The rapid expansion of the universe at the time of the Big Bang is known as cosmic inflation, or, simply, inflation. Though there is some evidence to support inflation, that evidence is not yet compelling.

Mathematics

Mathematics creates a logically consistent universe all its own. Some of it can actually be used to describe our physical universe. What math is the right math?

Math is very useful for describing nature, but is math itself “real”, or is it just a useful tool? This is an ancient question.

Memorable Quotations

“I went into physics because I don’t understand human behavior.” (p. 2)

“If a thousand people read a book, they read a thousand different books. But if a thousand people read an equation, they read the same equation.” (p. 9)

“In our search for new ideas, beauty plays many roles. It’s a guide, a reward, a motivation. It is also a systematic bias.” (p. 10)

On artificial intelligence: “Being unintuitive shouldn’t be held against a theory. Like lack of aesthetic appeal, it is a hurdle to progress. Maybe this one isn’t a hurdle we can overcome. Maybe we’re stuck in the foundations of physics because we’ve reached the limits of what humans can comprehend. Maybe it’s time to pass the torch.” (p. 132)

“The current organization of academia encourages scientists to join already dominant research programs and discourages any critique of one’s own research area.” (p. 170)

Multiverse

The idea that our universe of just one of a great many universes is presently the most controversial idea in physics.

Particles and Interactions

What is truly interesting is not the particles themselves, but the interactions between particles.

Philosophy

Physicists and astrophysicists are sloppy philosophers and could stand to benefit from a better understanding of the philosophical assumptions and implications of their work.

Physics isn’t Math

Sure, physics contains a lot of math, but that math has traditionally been well-grounded in observational science. Is math driving physics more than experiment and observation today?

Quantum Mechanics

Nobody really understands quantum mechanics. Everybody’s amazed but no one is happy. It works splendidly well. The quantum world is weird. Waves and particles don’t really exist, but everything (perhaps even the universe itself) is describable by a probabilistic “wave function” that has properties of both and yet is neither. Then there’s the many-worlds interpretation of quantum mechanics, and quantum entanglement

Science and the Scientific Method

In areas of physics where experiments are too difficult, expensive, or impossible to do, some physicists seem to be abandoning the scientific method as the central pillar of scientific inquiry. Faith in beauty, faith in mathematics, faith in naturalness, faith in symmetry. How is this any different than religion?

If scientists can evaluate a theory using other criteria than that theory’s ability to describe observation, how is that science?

Stagnation

Some areas of physics haven’t seen any new data for decades. In such an environment, theories can and do run amok.

Standard Model (of particle physics)

Ugly, contrived, ad hoc, baroque, overly flexible, unfinished, too many unexplained parameters. These are some of the words used to describe the standard model of particle physics. And, yet, the standard model describes the elementary particles we see in nature and their interactions with extraordinary exactitude.

String Theory

String theory dates back at least to the 1970s, and its origins go back to the 1940s. To date, there is still no experimental evidence to support it. String theory is not able to predict basic features of the standard model. That’s a problem.

Triple Threat: Crises in Physics, Astrophysics, and Cosmology?

Physics: Sure, the Large Hadron Collider (LHC) at CERN gave us the Higgs boson, but little else. No new physics. No supersymmetry particles. Embarrassments like the diphoton anomaly. Do we need a bigger collider? Perhaps. Do we need new ideas? Likely.

Astrophysics: We’ve spent decades trying to understand what dark matter is, to no avail. No dark matter particles have been found.

Cosmology: We have no testable idea as to what dark energy is. Plenty of theories, though.


See Hossenfelder’s recent comments on the LHC and dark matter in her op-ed, “The Uncertain Future of Particle Physics” in the January 23, 2019 issue of The New York Times.


The book concludes with three appendices:

  • Appendix A: The Standard Model Particles
  • Appendix B: The Trouble with Naturalness
  • Appendix C: What You Can Do To Help

Hossenfelder gives some excellent practical advice in Appendix C. This appendix is divided into three sections of action items:

  • As a scientist
  • As a higher ed administrator, science policy maker, journal editor, or representative of a funding body
  • As a science writer or member of the public

I’m really glad she wrote this book. As an insider, it takes courage to criticize the status quo.

References
Hossenfelder, S., Lost in Math: How Beauty Leads Physics Astray, Basic Books, New York (2018).
Hossenfelder, Sabine. “The Uncertain Future of Particle Physics.” The New York Times 23 Jan 2019. https://www.nytimes.com/2019/01/23/opinion/particle-physics-large-hadron-collider.html.

The Anthropic Question

George F. R. Ellis writes in Issues in the Philosophy of Cosmology:

9.1 Issue G: The anthropic question: Fine tuning for life
One of the most profound fundamental issues in cosmology is the Anthropic question: why does the Universe have the very special nature required in order that life can exist?  The point is that a great deal of “fine tuning” is required in order that life be possible.  There are many relationships embedded in physical laws that are not explained by physics, but are required for life to be possible; in particular various fundamental constants are highly constrained in their values if life as we know it is to exist:

Ellis goes on to quote Martin Rees.

A universe hospitable to life—what we might call a biophilic universe—has to be special in many ways … Many recipes would lead to stillborn universes with no atoms, no chemistry, and no planets; or to universes too short lived or too empty to evolve beyond sterile uniformity.

Physics does not tell us anything (yet) about why the fundamental constants and other parameters have the values they do.  These parameters include, for example, the speed of light, the Planck constant, the four fundamental forces and their relative strengths, the mass ratio of the proton and the electron, the fine-structure constant, the cosmological density parameter, Ωtot, relative to the critical density, and so on.  And, why are there four fundamental forces?  Why not five?  Or three?

Also, why do we live in a universe with three spatial dimensions and one time dimension?  Others are possible—even universes with two or more time dimensions.

But it appears that only three spatial dimensions and one time dimension is conducive to life (at least life as we know it), as shown in the diagram above (Whittle 2008).

In fact, altering almost any of the parameters would lead to a sterile universe and we could not exist.  Is the universe fine-tuned for our existence?

Let’s assume for the moment it is.  Where does that lead us?

  1. As our understanding of physics advances, we will eventually understand why these parameters must have the values that they do. -or-
  2. We will eventually learn that some of these parameters could have been different, and still support the existence of life. -or-
  3. God created the universe in such a way that life could exist -or-
  4. We’re overthinking the problem.  We live in a life-supporting universe, so of course we find the parameters are specially tuned to allow life. -or-
  5. There exist many universes with different parameters and we just happen to find ourselves in one that is conducive to life. (The multiverse idea.)

#4 is the anthropic explanation, but a deeper scientific understanding will occur if we find either #1, #2, or #5 to be true.  #3 is problematic for a couple of reasons.  First of all, how was God created?  Also, deism has a long history of explaining phenomena we don’t understand (“God of the gaps”), but in time we are able to understand each phenomenon in turn as science progresses.

The anthropic explanation itself is not controversial.  What is controversial is deciding to what degree fine tuning has occurred and how to explain it.

In recent years, the multiverse idea has become more popular because, for example, if there were a billion big bangs and therefore a billion different universes created, then it should not be at all surprising that we find ourselves in  one with just the right set of parameters to allow our existence.  However, there is one big problem with the multiverse idea.  Not only do we have no physical evidence that a multiverse exists, but we may never be able to obtain evidence that a multiverse exists, due to the cosmological horizon problem1.  If physical evidence of a multiverse is not forthcoming, then in that sense it is not any better than the deistic explanation.

To decide whether or not there is only one combination of parameters that can lead to life we need to rule out all the other combinations, and that is a tall order.  Recent work in this field suggests that there is more than one combination of parameters that could create a universe that is hospitable to life (Hossenfelder 2018).

Thinking now about why our universe is here at all, it seems there are just two possibilities:

(1)  Our universe has a supernatural origin.

(2)  Our universe has a natural origin.

If our universe has a supernatural origin, then what is the origin of the supernatural entity (e.g. God)?  If, on the other hand, our universe had a natural origin (e.g. something was created out of nothing), didn’t something have to exist (laws of physics or whatever) before the universe came into existence?  If so, what created those pre-conditions?

In either case, we are facing an infinite regression.  However, we could avoid the infinite regression by stating that something has to exist outside of time, that is to say, it has no beginning and no ending.  But isn’t this just replacing one infinity with another?

Perhaps there’s another possibility.  Just as a chimpanzee cannot possibly understand quantum mechanics, could it be that human intellect is also fundamentally limited?  Are the questions in the previous two paragraphs meaningless or nonsensical in the context of some higher intelligence?

1We appear to live in a universe that is finite but very much larger than the region that is visible to us now, or ever.

References
G.F.R. Ellis, Issues in the Philosophy of Cosmology, Philosophy of Physics (Handbook of the Philosophy of Science), Ed. J. Butterfield and J. Earman (Elsevier, 2006), 1183-1285.
[http://arxiv.org/abs/astro-ph/0602280]

Sabine Hossenfelder, Lost in Math: How Beauty Leads Physics Astray (Basic Books, 2018).

M. J. Rees, Our Cosmic Habitat (Princeton and Oxford, 2003).

Mark Whittle, “Fine Tuning and Anthropic Arguments”, Lecture 34, Course No. 1830.  Cosmology: The History and Nature of Our Universe.  The Great Courses, 2008.  DVD.
[https://www.thegreatcourses.com/courses/cosmology-the-history-and-nature-of-our-universe.html]