A Physicist Responds to “The Three Body Problem”

I’ve not had much motivation to post recently: it seems like I read another article every week or so where some fool is making the same wrong conclusions about Quantum Mechanics or Relativity or AI, or all of the above, simultaneously. It gets exhausting to read. I also haven’t had time for constructing a post on my recent problem work in part because I’m prepping for a major exam.

But, I need some time to take a break and change my focus. So, I decided to write a bit about some things I saw in Liu Cixin’s “The Three-Body Problem” of which I read Ken Liu’s translation. If you’re not familiar with this book, I would highly recommend it. This book deservedly won the Nebula and Hugo awards –both– and it is one piece of science fiction that is truly worth going through.

One of my non-spoiling responses here is that it shows how another culture, namely the Chinese culture, can go to extremes with how it treats Scientists and Intelligentsia and all the different ways that this relationship can oscillate back and forth. It shows too the humanity of scientists, both for better and worse. Based on the structure of the story, it’s clear to me that the author has respect for the scientific disciplines which is usually not so present in western literature anymore. I was also quite happy that characters were not meaninglessly fed to the meat grinder in the way they are too often in many western books in the supposed name of ‘authenticity.’

With that said and my badge of worthiness placed, we will get to the actually purpose of this post… some places where Liu Cixin’s Science fiction Authoritis shows through.

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The great problem with many science fiction writers is that they know just enough to be dangerous, but not enough to be right. Where they fall apart is when they start to over-explain the phenomenology of what’s happening in their stories in order to ‘make it work.’ There are two places I will talk about where this happened in ‘3BP’.

The first is the Zither.

To start with, I loved the idea of the zither. It was a very classy, ingenious use for the cliche of the monofilament wire. Note first that this is a cliche (a ‘trope’ maybe, but I detest that word for its cliche overuse). In the form that appeared in 3BP, nanomaterial monofilament 1/1000th the thickness of hair is strung in strings like a zither between pilings across a straight section of the Panama canal as an ambush trap for an oil tanker being used by the villains. The strings are strung between the banks of the canal attached to chains that can be raised and lowered so that ships which aren’t the target can be allowed through the canal unhindered. When the target ship approaches, the monofilaments are pulled up across the canal by tightening the chains such that the filaments are held in an invisible web of horizontal strands above water line, spaced from each other by only a few feet, like a big hardboiled egg slicer. The author even makes allowances for how the monofilaments can be attached to the chains so as not to shred the anchoring when the target ship pushes against them. When the ship hits the zither, it sails silently through and continues on until the engine of the ship rips itself to pieces and causes the whole boat to slide apart in sections.

You have to admit, it’s a nifty trap. The monofilament in question is described as a material intended for use building orbital elevators and is dubbed ‘nanotechnology’ by the story.

The great stumbling point most people have about nanotechnology is that it is not tiny without limit since it exists in a scale gap of less than 1 micron and more than 1 nanometer. For comparison, hair is about 100 microns and the length of a carbon-carbon sigma bond is about 0.1 nanometers; the zither monofilaments are therefore about 100 nanometers. This is sort of a crossover regime where building structures by top-down bulk techniques, like photo etching, becomes hard, while building from bottom-up by chemistry is also hard. In general, this is into a big enough scale where quantum mechanical effects become small and statistical mechanics tends to dominate manipulation. At the nanoscale, everything we understand about how the basic level of material stuff holds together remains true. In a way, nanoscale is small, but not so small that objects are markedly described by quantum mechanics, but also not so big that they behave like bulk objects. That’s why ‘nano’ is difficult: it sits at an uncomfortable seam between classical and quantum universes where the tools for one or the other aren’t quite right for doing what needs to be done.

Cutting material is by a process called scission. The act of ‘scission’ is, by definition, the breakage of a long chain molecule into two shorter chain molecules. It means separating at least one chemical bond in order to free a unified mass into two independent parts. And, a chemical bond always has at least two electrons since the bond state must consist of spin-up and spin-down parts in order to cancel out angular momentum… and that’s pretty much the theme of chemistry: stable states mostly have angular momentum canceled. There are some special exceptions, but these do not define the rule. Still, since you can’t subdivide an electron, splitting a bond means intact electrons residing somewhere who are no longer in a quantum mechanical ground state and also nuclei lacking complete valence shells. This means that the system, immediately after scission, will have a strong desire to rearrange by chemical reaction into a more stable state. What will it react with? Whatever is close by… in this case, the monofilament wire! This kind of process is part of why blades dull over time: for a conventional metal knife cutting a metal structure, the structure is literally ‘cutting’ the knife too and blunting its edge. With a nanofiber, there isn’t much mass to wear away.

This is one of the difficulties in scaling up nanotechnology: they usually become fragile!

Overlooking this fragility issue, one can argue that the process of making this nanofiber yielded a structure that is exceptionally strong and perhaps robust to chemical processes occurring around it. This is presumably what you would want in such a material that would be useful for building orbital elevators. If you want a tether from Earth up into orbit, you could bundle many of these fibers together and add coatings on the surface to help render them inert to chemistry. Many materials used in construction of advanced structures work in a manner like this: you’ve certainly heard of “Composites!”

Now then, singling one of these fibers out and stringing it across the Panama canal produces a second major issue. The energy necessary to allow the zither to slice apart the ship comes from the kinetic energy of ship coasting along the water way: the ship hits the zither and the monofibers of the zither redirect parts of the ship infinitesmally from each other so that their tensile strength is not great enough to resist going different directions from each other… causing them to rend apart microscopically. This redirection is arrested because the parts separated from one another can’t pass through the bulk materials holding them in place. This ‘motion’ is then completely incoherent and can only be tabulated as heat deposited into the material bulk at the location of the nanofilament. So, part of the kinetic energy of the ship’s motion is deposited as heat around the monofilament cut. This might not be quite a huge problem but that the monofilament has an intrinsically tiny mass and therefore a miniscule heat capacity: its electrical structure has relatively few valence modes where it can stuff higher energy vibrational states. Moreover, the fiber is located at the origin of the heat and the materials heating up surround it from all sides, so there is no other place where the fiber can dump heat except linearly along its own body. If the heat doesn’t dissipate through the hull of the ship fast enough, how hot can the fiber get before its electrical structure starts sampling continuum states? However tough the fiber is, if it can’t dump the heat somewhere, its temperature might well rise until it literally ionizes into a plasma. For such tiny mass, only a little heat input is a substantial thing.

This is a difficulty, but one a clever writer can probably still explain away (maybe better left as a black box). You might argue that the fiber can cope with this abuse by conducting the heat along its length and then radiating it into the air or emitting it as light. That might work, I suppose, but it would mean increasing complexity in the structure of the nanomaterial. Not an impossibility, but now the fiber glows at least as a black body and is no longer invisible! For anybody familiar with super-resolution microscopy, emission of light can make visible objects tinier than the optical resolution limits.

Maybe the classiest way would be to convert the fiber into a thermoelectric couple of some sort and get rid of the heat using an electrical current. Some of the well known modern nanofibers, the fullerenes and such, are also very good electrical conductors because of their bonding structures. In reality, this would also probably limit the cutting rate: the rate of heat deposition in the line must not exceed the rate at which the cooling mechanism can suck heat away! An unfortunate fact about very thin conductors is that their resistance tends to be high, meaning that the conduction rate goes up as the channel of the conductor is thickened… and you are unfortunately crippled by using a nanofiber, which is very skinny indeed. I won’t mention superconductors except to say that they have a limited range of temperatures where they can superconduct… using a superconductor in a thermoelectric couple is asking for trouble.

My big complaint about the zither boils down to that: heat and wear. Because of the difference of the applications, a material which is suitable to the purpose of building an orbital elevator is not necessarily suitable to building a monofilament cutter. I would also offer that a real monofilament cutter would be specifically engineered to the task and not a windfall of a second technology. The applications are just too different and don’t boil down to merely ‘strength’ and ‘tiny size.’

Having addressed the zither, I’ll talk about a second major point which suffered from too much description and too little plausibility. I’ll try to describe this part of the story without giving away a major plot point.

In this section of the story, someone is trying to use a colossal factory hovering in orbit above the planet to take a proton and expand it from a point-like object into a three dimensional structure. The author makes the case that a simple object, like a proton, which is essentially point-like when viewed from our place in spacetime, is actually an object with extensive higher dimensional structure and that some technological application can be carried out where this higher dimensionality can be expanded so that it can be manipulated in our three dimensional space. He even makes the case that these higher dimensions contain considerable volume and may be big enough to harbor entire universes. As he repeatedly emphasizes, a whole universe of complexity, but only a proton’s worth of mass.

To start with, I have little to say about the string theory. For one thing, I don’t really understand it. A major argument in string theory is that the tiniest bits of space in our universe can actually have seven or eight additional dimensions hidden away where we three dimensional creatures can’t see them. Perhaps that’s true, but as yet, string theory has made no predictions that have been verified by experiment. None!

From the standpoint of a person, it’s certainly true that a proton might seem point-like, but this is actually false! Unlike an electron, which is truly dimensionally point-like for all that physics currently understands of it, a proton has a known structure that occupies a definable three dimensional volume. The size here is tiny, at only about 10^-15 meters, but it is a volume with a few working parts. A proton is constructed of two “Up” quarks and a “Down” quark that are held together by nuclear strong force (making the proton a baryon with spin 1/2, and so abiding Fermi statistics).

I have considered that perhaps the application of a ‘proton’ in the story is perhaps a missed translation and that the author really wanted a dimensionless particle like a quark (which are never observed outside of particulate sets of two or three) or an electron (which can be a free particle). After writing the previous sentence, I spent some time looking at translator notes for this book and I found that the choice of the Chinese word for ‘proton’ facilitated a word play in the author’s native language that did not quite translate to English. I won’t detail this word play because it gives away a plot point of the book that is beyond the scope of what I wish to write about. A lesson here is that the author’s loyalty is definitely toward his literature above scientific truth.

One significant issue that must be brought up here is that ‘point-like’ is a relative description when you start talking about particles like these. An electron is fundamentally point-like, but it is also quantum mechanical, meaning that they tend to occupy finite volumes in space that vary quite strongly depending on the shape and boundaries of that space, as given by the wave function. Reaching in and ‘grabbing’ the electron reveals what appears to be a point, but that ‘point’ can be distributed in non-intuitive ways across the volume it occupies. We have no real capacity to describe that it has a shape and one might certainly consider that ‘point-like’ dimensionless object to be a singularity in exactly the same way that a black hole is a singularity. I have half a mind to say that the only reason an electron is not a black hole is because the diameter of the volume it occupies as described by the uncertainty principle is larger than its Schwarzschild radius. This statement is limited by the fact that Quantum Mechanics doesn’t play well with General relativity and the limits of the Schwarzchild radius may not coincide with the limits of the Uncertainty principle –both are physically true, but they each have a context where they are most valid and no unifying math exists to link one case directly to the other.

Now then, in 3BP, a point-like elementary particle with the mass and dimensionality of such a particle is shifted by a machine so that its higher dimensional properties are exhibited as a proportionate volume or geometric shape in three dimensions. In the first flawed experiment, the particle expands into a one dimensional thread which snaps off and comes wafting down everywhere onto the planet in nearly weightless tufts that annoy everybody. After the author spent such a time laboring over the invisible nature of a monofilament wire, he decided that a one dimensional thread could be visible! Note, a monofilament wire has a small but finite width, while a one dimensional line has no width at all! Which is ‘thinner?’ The 1D line is thinner by an infinite degree!

In the next flawed experiment, the higher dimensions of the point-like particle turn out to contain a super-intelligent civilization which realizes that the particle where they reside is about to be destroyed during the experiment. This civilization distends the structure of their particle into a huge mirror which they then use to focus the sunlight as a weapon onto the surface of the planet in order to attack their enemy, who they recognize to be the scientists running the experiment, and they start leveling cities! This is creative writing, but the author makes the explicit point that the mirror-structure formed from the elementary particle, while big, has only the mass of that particle, which is infinitesimal. If you’re versed in physics, you’ll see the first problem: light has momentum (Poynting vector!). When you reflect a beam of light, you change the direction of the momentum in that light. Conservation of momentum then requires the existence of a force causing the mirror to rebound. Reflecting enough light to thermally combust a city is a large intensity of light, easily megawatts per square meter. An electron has a minuscule mass at about ~10^-31 kilograms (0r 10^-27 if you insist on it being a proton). Force equals mass times acceleration and pressure equals force per area where light intensity can be easily converted to pressure and pressure to force. When you rearrange Newton’s second law to solve for acceleration, the big ‘force’ number ends up on top while tiny ‘mass’ number ends up on the bottom of the ratio, giving a catastrophically huge number for the value of the acceleration (conservatively on the order or 10^20 or 10^30 m/s^2 given intensity on the scale of only watts/m^2 where the mirror is only a square meter). That’s right, the huge mirror with the mass of a ‘proton’ accelerates away from the planet at a highly relativistic rate the instant light bounces off of it!

Yeah, I know, physicists and science fiction authors don’t often get along even though they both pretend to love each other.

I had significant problems with the idea of making a single electric charge into a reflective surface, but I’ve rewritten this point twice without being satisfied that the physics are at all instructive to my actual objection. In a real reflective surface, like a mirror, the existence of the reflected light wave can be understood as coherent bulk scattering from many scattering centers, which are all themselves individual charged particles. In this sort of system, the amount of reflected wave quite obviously depends on the amount of charged surface present to interact with incoming waves. The amount of surface available to reflect is conceptually dodgy when you’re talking about only a single charge, no matter how big of an area this charge is spread out to cover. This is why a half-silvered mirror reflects less intensity than a fully silvered mirror. Though I have failed in my own opinion to encapsulate the physical argument well, an individual charge has a finite average rate at which it can exchange information with the universe around it and reflecting photons en mass is an act of exchanging a great deal of information for such a tiny coupling. Since the quantum mechanics of scattering depends on a probability of overlap, the probability of simultaneously overlapping with many photons is small for only a single charge. The number densities are overwhelmingly different.

All said, the mirror is likely a very transparent mirror unless it has more than one charged particle’s worth of charge.

Despite all this analysis, I don’t believe that it detracts from the story. I really didn’t mind the flight of fancy in a well written piece of fiction. It’s unlikely that the casual reader will ever care.

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