Chen Li


Book Review: The Invisible Universe: Why There's More to Reality than Meets the Eye

This is a review of The Invisible Universe: Why There’s More to Reality than Meets the Eye by Matt Bothwell.

§1 Astronomy 101

The first 6 chapters are Astronomy 101 to me. I have read about them in several textbooks, but when these clues forming a linear process, it’s something else. (I will come back to this “linear process” later in §2.) Here’s something interesting to me in these chapters.

  • The restrictions of human eyes: (1) wavelength: $380–700 \space \mathrm{nm}$. (2) $220 \space \mathrm{frames/s}$ or maybe higher, see FPS : Human eye can see how many frames per second?.
  • The piano metaphor, that the full spectrum of light of different wavelength is like the full notes on a piano with only one note that human can hear/see, is beautiful. I have an analogue of that metaphor myself, consider a guitar, this time the wavelength can go to infinity, since $f_n=nv/2L$1. But does the frequency of light reach infinity? Theoretically there is no such limit, but in practice we haven’t observe it. It wouldn’t travel to earth or it would just pass through us. Well, according to GZK limit, there is a limit for protons, but I don’t know about photons.
  • A Tediously Accurate Map of the Solar System feels like the rolling credit for a movie which is about how human can never leave the Solar System.
  • Cosmic Background Explorer is legendary! It’s shocking that Ron Howard did not make a movie about it.
  • I have always known the cover of Unknown Pleasures by Joy Division is a pulsar, but I didn’t know it’s CP1919 (Cambridge Pulsar). See the picture below. The fact that this pulsar was discovered in the UK is probably why they chose it as the cover. See, I told you the origin of Rock’n’Roll is not America. :D
  • The person who coined the term “the Big Bang” on BBC radio (as a rejection of the Big Bang), Fred Hoyle, is also the person who came up with the idea of Triple-alpha process, which is the formation of carbon in stars. And carbon is what makes life on earth.

§2 Dark Matter

Thanks to the effort that the author put to make a linear process out of history, chapter 7 is amazing. It totally worth the effort mentioned in the final chapter. And it’s probably the best detective novel ever, since murder is kind of boring compared to all these twists and turns:

  1. The speculation of Dark Matter is historical. We calculated there’s a planet Neptune because Uranus moves a little odd according to Newton’s law.
  2. And these evidences suggests that there are a lot more material that we can’t observe in the universe: (1) speedy galaxy clusters, (2) fast-rotating galaxies, (3) gravitational lensing.
  3. However, could it be that we understand Gravity wrong? Since Mercury precession used to be wrongly explained until General Relativity. And we proposed two possible theory: (1) MOND (Modified Newtonian Dynamics fudge factor), (2) TeVeS (tensor-vector-scalar gravity theory).
  4. “The Bullet Cluster, … , turns out to be the perfect arena for pitting dark matter and MOND against each other.” Due to a difference in cross section, which means that dark matter has a small cross section and stars, gas have a big cross section, Dark Matter stays.2 Bullet_cluster
  5. So what is Dark Matter?
  6. It could be MACHO (MAssive Compact Halo Object), which was later ruled out.
  7. It could be WIMP (Weakly Interacting Massive Particle), which has to be (1) non-baryonic in the Standard Model, (2) weakly interacting, meaning that only Gravity and Weak Nuclear Force are possible.
  8. The author didn’t point it out, but the murderer is probably neutrino.3 See Sterile neutrino. I later found out that Interpreting Reactor Antineutrino Anomalies with STEREO data rejects this hypothesis. But the results from LSND and MiniBooNe are odd, so it’s kind of suspicious.4

Anyway, the murderer is still out there, you kids should watch out.

Cosmic Microwave Background (CMB) is also an evidence of Dark Matter, see Microwave background observations. You can calculate the percentage of Dark Matter from the power spectrum of CMB:

Power spectrum of temperature fluctuations in the Cosmic Microwave Background

§3 More

In chapter 8, the author talked about LIGO mission, which is another detective novel. The fact that a observatory has a secret supervision team that inserts false signal is a triumph of humanity, unironically. It’s kind of like after the failure of Hitomi, a more organized team for XRISM is created. See Detailed Design of the Science Operations for the XRISM mission. I wouldn’t say these are the best solutions, but it’s a good thing that we’re trying. The detector itself has all kinds of flaws, but team management is actually the biggest engineering challenge.

In chapter 9, the author said that the final destination of our universe is a battle between ice (the Big Chill) and fire (the Big Crunch). I am curious if this is a A Song of Ice and Fire reference. Also, Dark Energy has nothing to do with Dark Matter. Dark Energy is basically just $\Lambda$ constant.

And in the final chapter, Conclusion: The complete picture: visible and invisible, what the author is trying to say is that we should be multi-messenger astronomer these days. Yeah, I guess with the help of ChatGPT, it’s possible to handle all those literatures. And I am always a little sad that the Nobel-Prize-winning LIGO detection is not multi-messenger.


  1. See Strings, standing waves and harmonics↩︎

  2. The author quote that “The ‘duck test’ says that if something looks like a duck, swims like a duck, and quacks like a duck, then it probably is a duck.” Duck is somehow good for metaphor, I don’t know why. I later wrote about the Duck-Rabbit picture in Book review: Existential Physics: A Scientist’s Guide to Life’s Biggest Questions↩︎

  3. The moment this came to my head is memorable. It was on a train, and I was listening to Ti Amo by Laura Branigan. After reading Love and Math: The Heart of Hidden Reality by Edward Frenkel, I found out that he also had this kind of “Eureka” moment on a train. His idea is true, while mine still needs to be tested by experiment. ↩︎

  4. I later got in touch with the author, and it is recommended to read this review article Sterile Neutrino Dark Matter. Thanks for his help! ↩︎