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On Not Finishing Kaku’s “Physics of the Impossible”

Posted by jns on 7 March 2012

I read a lot of popular-science books. You know I do this partly to support the Science Booknotes and Science Book Challenge projects at Scienticity. I often remark to myself how thoroughly I enjoyed a book that I chose arbitrarily at my library, maybe because the title appealed to me or the book spine was the right color for me that evening. The implication for me, I’m happy to say, is that there is a great deal of really very good writing about science for the non-specialist. It’s satisfying to review these books and let other potential readers know about the great ideas they discuss.

Sometimes, of course, I select a book that turns out not to suit my taste for some reason. Generally speaking I prefer not to review a book I didn’t care for because I don’t see the point of a negative review about a book whose subject matter didn’t really appeal to me or whose author wrote in a style that I found unsympathetic. After all, many others might find the book worthwhile or tune in to that author’s particular style, and I’d much rather have a review in our booknotes collection setting out positive reason why a potential reader might choose to read a particular title.

Then there is the small but difficult category of books that I never finish reading because, for some reason or another, I find them too overwhelmingly irritating. For instance, I never finished reading Stephen Jay Gould’s The Hedgehog, the Fox, and the Magister’s Pox (my booknote) because his writing was so bad, and so badly edited, that I conjectured that it had been written by pod people who had taken over his body. Happily, these are rare events, but sometimes it seems important to write about them.

What to do, then, when I find an author known for his (or her) enthusiastic and entertaining advocacy and popularizing for science whose writing exhibits a notable disregard for precision about scientific facts and, furthermore, who seems to have a superficial or incorrect understanding of parts of his or her subject matter?

When I read a book that I plan to write about, I keep a folded sheet of paper inside the back cover where I make notes of interesting ideas, things to mention, and possible quotations for use in a review. I also make a note of trouble spots in the text: unclear or badly written explanations, confusion over facts of science, and such things. When I have filled the pages with errors the author has made and I’m only on page 30 of the book, I know I have trouble on my hands, and a quandary. I can easily stop reading the book, but I have to decide whether to write about it or not. Is there a useful point — beyond venting my spleen — to writing about bad science writing?

I have such a case on hand with Michio Kaku’s Physics of the Impossible*, in which the (apprently) well-known science popularizer talks about the physics and possibility of such science-fiction staples as invisibility cloaks, force fields, time travel, and such topics. It’s a very appealing idea, I thought, but I had to stop reading; there were simply too many errors–some serious errors–of science to continue, all before I reached page 30, less than one-tenth of my way through the book.

Let’s begin by going through some of the problems that I had in these early pages.

1. Conflating Historic Events

“Growing up, I remember my teacher one day walking up to the map of the Earth on the wall and pointing out the coastlines of South America and Africa. Wasn’t it an odd coincidence, she said, that the two coastlines fit together, almost like a jigsaw puzzle? Some scientists, she said, speculated that perhaps they were once part of the same, vast continent. But that was silly. [...] Later that year we studied the dinosaurs. Wasn’t it strange, our teacher told us, that the dinosaurs dominated the Earth for millions of years, and then one day they all vanished? No one knew why they had all died off. Some paleontologists thought that maybe a meteor from space had killed them, but that was impossible; more in the realm of science fiction [pp. xi--xii]

The idea that the continents might once have fitted together is a very old one, evident to most anyone who ever looked at a world map. These days we have at hand the well-established theory of plate techtonics to explain how it all could have happened, and certainly did happen. In the earlier twentieth century geologists and others began thinking more seriously about the idea of continents moving, but it was experimental results in the late 1950s and early 1960s that finally overthrew “conventional wisdom” that the continents couldn’t just move around. Plate techtonics was well established as scientific orthodoxy by 1965.

The Alvarez Theory, the idea that the extinction of the dinosaurs was brought about by the impact with Earth of a large body from space, was first proposed by Luis and his son Walter Alvarez following on Walter’s discovery of a thin sedimentary layer of iridium that dated closely to the time when dinosaurs disappeared. That theory did not appear until 1980. For many years afterwards the idea that an asteroid impact wiped out the dinosaurs was widely thought preposterous; before that time it hadn’t even been thought of. By now, of course, it’s widely familiar to the general public.

I hope you see my difficulty by now. The author writes that his teacher taught him that 1) some scientists speculated that continents drifted, an assertion that only makes sense prior to 1965, when Plate Techtonics was established; and 2) that some scientists though maybe an asteroid had killed the dinosaurs, an idea that no one had thought of until 1980. He writes that his teacher taught him these things in the same year, even though the closest in actual time that they may have come to each other is 15 years. In other words, this makes a good story but it’s highly unlikely that these two events took place in the same year.

2. Confusing Words and Ideas

This problem is more subtle. In the first chapter Kaku has a section on “force fields”, a common technology of science-fiction worlds for decades. Kaku unfortunately takes the words too literally and conflates the notion of a science-fiction “force field” with some combination of the ideas of “forces” and “fields” as they are used in physics, and so he spends some time talking about the four fundamental forces of the universe (gravitation, electromagnetism, the weak force, and the strong force) and discusses to some extent how each of these is formulated mathematically as “field theories”. But one does not get “force fields” by simply combining these two concepts. He confuses the reader over these pairs of words used differently in two different realms, and then leaves the reader with the mistaken impression that “force fields” might become reality just as soon as physics catches up and discovers a new field theory for a “fifth force”. None of this has anything useful to do with the concept of a “force field” as it’s deployed by science-fiction authors.

3. Casual Writing Leads to Mistaken Readings

In another space I’ll write about what I think should be the prime directive of any writer about science : First, Do Not Mislead. Writing about science for a popular audience is an awesome responsibility; scientifically literate readers can fend for themselves, but if the author has in mind an audience of nonspecialists, it is vital that the author take the utmost care with describing and explaining facts from science, because the nonspecialist reader can easily invent his or her own mistaken notion of how nature works when presented with sloppy, incomplete, or imprecise exposition. I expect popular science writers to

  1. Get it right, and
  2. Say it clearly.

Here are just some examples of statements that I felt violated the Prime Directive in Kaku’s writing. First, from the section on “Magnetic Levitation”:

“One common property of superconductivity is called the Meissner effect.” [p. 14]

When a superconductor in a magnetic field is cooled from its normal (non-superconducting) phrase to its superconducting phrase, it “expels” the external magnetic field from it’s interior, which is to say that it creates on its surface electrical currents that themselves create a magnetic field that just cancels the externally imposed field within the superconductor. This is known as the “Meissner Effect”, named for Walther Meissner. This is a defining characteristic of superconductors, a property necessarily exhibited by every superconductor. I find it odd to refer to it as a “common property of superconductivity”, as though it’s an incidental property seen in only some, perhaps many, superconductors, but suggesting that it is not a universal property.

In a section on “Invisibility”, discussing the possibility of an “invisibility cloak”:

“But today the impossible may become possible. New advances in “metamaterials” are forcing a major revision of optics textbooks. [p. 17]

Actually, the manufactured metamaterials that Kaku refers to, surprising and ingenious as they are, behave according to well-understood principles, requiring no “revision”, just an increase in understanding how to manufacture materials with desirable optical properties. This is misleading and a type of sensationalism that doesn’t serve the cause of increasing science literacy.

Later in the section on “Invisibility”, Kaku turns to a discussion of electromagnetic fields, namely, James Maxwell’s great advance in physical theory in the 19th century:

“(…If he [Maxwell] had lived longer, he might have discovered that his equations allowed for distortions of space-time that would lead directly to Einstein’s relativity theory. [p. 19]

Now, here is a frequent problem with those who write about science. There are, in fact, two distinct theories of Einstein commonly referred to as “relativity” : the theory of “Special Relativity”, from 1905, and the theory of “General Relativity”, from 1916. Special relativity is a theory of electrodynamics, basically a theory of light, which also introduced the idea of four-dimensional “space-time” and that most famous of equations, E=mc^2. General relativity is a theory of gravitation, a geometrical theory that treats gravity as deformations in space-time.

Usually the context makes clear which “relativity” the author meant. But here our only guide is that Kaku speaks of “distortions of space-time”. In special relativity travel at high velocities bring about time dilations and length contractions (“Lorentz Transformations”), i.e., distortions of space-time. In general relativity, gravitational effects are produced by the distortions of space-time caused by mass.

Carelessness here has caused a confusion that can’t be untangled and therefore does nothing to enlighten the nonspecialist reader who may not distinguish the two “relativity” theories so easily to begin with.

4. Errors of Physical Fact

These were the most troubling errors that confronted me in reading the first sections of Kaku’s book. Troubling because it betrays the trust between the nonspecialist reader and the authoritative voice of the author to make statement of physical fact, or to give descriptions of physical systems, that are imprecise or simply incorrect. I find it even more troubling when the author is a physicist who should be expected to get it right.

Back to the pages of discussion about Maxwell’s Theory of Electrodynamics, the author writes:

Maxwell began with Faraday’s discovery that electric fields could turn into magnetic fields and vice versa. He took Faraday’s depictions of force fields and rewrote them in the precise language of differential equations, producing one of the most important series of equations in modern science. They are a series of eight fierce-looking differential equations. Every physicist and engineer in the world has to sweat over them when mastering electromagnetism in graduate school [p. 18].

While it is certainly true that every physicist and engineer had to sweat over the equations in graduate school–probably even using the same, nearly universally taught textbook–the italicized phrase (my italics) would raise any student’s eyebrows. Whether the equations are “fierce-looking” or not is a matter of taste (I think they’re rather elegantly simple myself), there are in fact only four equations, two for the electric field and two for the magnetic field.

I nearly dropped the book when I read this — I couldn’t imagine how any physicist could have come to refer to “eight” equations. Now, while it’s true that the electric and magnetic fields are written in modified form when they occur in materials, rather than vacuum, the equations stay the same. That there are two each for the electric and magnetic fields is fundamentally characteristic of the entire field theory.

Slightly further on, Kaku offers this analysis of the property of optical transparency in materials:

Maxwell’s theory of light and the atomic theory give simple explanations for optics and invisibility. In a solid, the atoms are tightly packed, while in a liquid or gas the molecules are spaced much farther apart. Most solids are opaque because light rays cannot pass through the dense matrix of atoms in a solid, which act like a brick wall. Many liquids and gases, by contrast, are transparent because light can pass more readily between the large spaces between their atoms, a space that is larger than the wavelength of visible light. For example, water, alcohol, ammonia, acetone, hydrogen peroxide, gasoline, and so forth are all transparent, as are gases such as oxygen, hydrogen, nitrogen, carbon dioxide, methane, and so on.

There are some important exceptions to this rule. Many crystals are both solid and transparent. But the atoms of a crystal are arranged in a precise lattice structure, stacked in regular rows, with regular spacing between them. Hence there are many pathways that a light beam may take through a crystalline lattice. Therefore, although a crystal is as tightly packed as any solid, light can still work its way through the crystal.
Under certain circumstances, a solid object may become transparent if the atoms are arranged randomly [as in a glass]. [pp. 25--26]

It’s at this point that I threw up my metaphorical hands in despair and stopped reading the book. This “explanation” of transparency is so totally wrong I hardly know where to begin.

Light, namely, propagating electromagnetic waves, only interact with matter via the electromagnetic field (with a notable exception in General Relativity that doesn’t impinge on this discussion); in other words, light waves are sensitive to electrical charges, electrical currents, and magnetic fields. They sense the electrical charge of the electron “cloud” around an atomic nucleus; they might sense the positive charge of protons in a nucleus if they can get close enough for it to have an effect. Electromagnetic waves–light waves or photons, pick your favorite representation–do not interact with the mass of matter itself. Whether atoms are heavy or not heavy makes no difference, the light doesn’t sense the mass. Hold that thought.

Now, while it is true that the atoms in a liquid or solid are much closer together than they are in a gas, the atoms are still so physically small and so distantly separated relative to their physical sizes–not to mention that the components of an atom are vastly tinier than the “size” of the atom itself–that most of matter, whether solid, liquid, or gas, is still empty space. Even in a crystal or a glass this is true. Physically, the mass of atoms occupies exceedingly little of the space of the object they make up. By “exceedingly little” I mean this: the volume of the atomic nucleus is only about 1/1,000,000,000,000th the approximate volume of the atom itself.

I hope it’s becoming clear by this point that how close the atoms are together has relatively little bearing on how much “space” in matter is taken up by substantial parts of the atoms. The simple deduction, then, is that material objects are not more transparent or less transparent because the atoms are closer or further apart such that they “block” the light. The light does not run into the atoms and get blocked by their physical size. They are in no sense like a “brick wall” in any way that I can imagine makes sense.

The transparency of any given substance is determined by the not-so-simple interaction between light waves of particular frequencies (or “colors”) and the electric fields (predominantly) created in the substance by the particular configuration of its atoms. Gases do tend to be relatively transparent because the wide separation of their atoms creates a weakly interacting electric field. Nevertheless, some gasses do have colors because their atoms absorb certain wavelengths of light preferentially, through light waves being absorbed and/or emitted by the atomic electrons. Crystals have complicated and varied optical properties — transparency, opacity, colors in gemstones, birefringence, polarization rotations, etc. — depending sensitively on the periodically varying electric field inside the crystal that is produced by the regular (crystalline) placement of the atoms; but do keep your mind on the electric field inside the crystal, not the atoms “blocking” the light. There are also materials that are mostly opaque to visible light but that can be transparent in wavelengths of light that our eyes do not detect. The optical properties of materials is a rich field with lots of interesting effects and phenomena; get a taste for it, if you like, by looking up “transparency” in Wikipedia.

Looking up “transparency” is apparently something that author Kaku didn’t bother to do when he should have. His explanation of the phenomenon I find so confused and misleading that I feel his writing does a serious disservice to the nonspecialist who reads his book hoping for understanding from a scientist who knows what he’s talking about. This is why I stopped reading the book at this point, and why I have chosen to write about it.

One or two of the objections I noted earlier on amount to very little. I frequently find one or two little errors in any book I read, but it’s usually just something to note with some amusement and then move on; rarely does a misstatement or error like that cause me serious concern, and I rarely comment on them in my review of a book. A whole string of them, page after page, however, convinces me that the author is a sloppy writer or has a very superficial knowledge of the subject at hand. When the writer is a working scientist writing about science, I am totally confounded. As for these bigger errors I’ve just discussed — they are inexplicable. It is the author’s responsibility to realize the limits of his or her knowledge or understanding and find ways to avoid or correct problems in his or her writing.

These are the reasons why I simply cannot recommend this book to a general reader. That the book seems to have reached some level of popularity disturbs me : such poorly conceived and executed writing about science undermines the efforts of the many excellent writers about science — scientists, historians, journalists, and others — writing with more care and accuracy about their subject.
* Michio Kaku, Physics of the impossible : a scientific exploration into the world of phasers, force fields, teleportation, and time travel. New York : Doubleday, 2008. xxi + 329 pages.

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