The Three-Body And Other Scientific Problems

The new Netflix hit show “Three-Body Problem” that first aired in March, swept countless viewers into a fantastic voyage where physics, technology and aliens are mixed together. The show is based on a book by the Chinese author Liu Cixin, published in 2006, which is the first of the “Remembrance of Earth’s Past” trilogy.

It seems that lately physics is cinematically revitalized: after all, one of the biggest movies of last summer, “Oppenheimer”, dealt with the physics of the atom bomb and the physicists who developed it. In contrast, “Three-Body Problem” includes a lot of science fiction and yet, it has a kernel of truth that appears every now and then. Here we will discuss some physical concepts that inspired the show, most of them receiving such exposure to the wider audience through the small screen for the first time. Let’s get started, but stay alert - there are spoilers.

Swept countless viewers into a fantastic voyage where physics, technology and aliens are mixed together. The book that the show “Three-Body Problem” is based on | Shutterstock, Ralf Liebhold

Three-Body Problem

We will start, how else, from the beginning - the name of the show. The three-body problem is one of the oldest problems in celestial body mechanics, dealing with the question: how does the Sun, Earth and the Moon affect each other while traveling in space? While the question how two objects interact through gravity was analytically solved by Issac Newton 350 years ago, and is currently taught to physics undergrads, the behavior of a three body system is very difficult to resolve using pen and paper. So difficult that in most cases it is impossible. 

In classical mechanics, to fully describe the motion of a body you must know its location and speed in any given moment. Each body has three location components and three speed components - lengthwise, widthwise, and heightwise. When there are three bodies, with six coordinates each, you get eighteen coordinates. But a three-body system is characterized by tens of quantities that remain constant through the motion, such as the total energy of the system and other quantities that were found to remain constant. Multiplicity of the forces acting on each body in the system and a variety of motion possibilities alongside the constraints of the constant quantities, result in a state where it is very difficult to calculate the trajectory of each of the bodies.  

The behavior of a three-body system is very difficult to resolve with pen and paper. Trajectories of three bodies in such a system |, Dnttllthmmnm

Newton successfully used approximations to estimate the moon's perigee, which is the minimal distance between it and the earth, but he was subsequently found to be wrong when his estimation was twice the actual distance. Following him, the best minds of France, mathematician Jean le Rond d'Alembert and his sworn enemy Alexis Clairaut, continued working on the problem but made no significant progress and the field reached a proverbial dead end.   

That is until, as the song goes, on a damp morning in 1878, American physicist Geroge Hill rephrased the problem. He formulated an equation that would later be known as Hill’s equation, and stated that the problem is similar to mass that is attached to a spring or a ball swinging on a wire through the effect of gravity - which is known in physical terms as “harmonic oscillator”. Usually, in a harmonic oscillator the frequency of the motion is constant, but in this case the frequency of the movement of the trajectories is in itself a periodic function in time. 

This problem was the foundation of much of our understanding regarding periodic trajectories, a very important concept in mechanics: trajectories that start and end in the same location and at the same speed. These are trajectories that are characterized by steady movement, in contrast to chaotic trajectories, which are sensitive to slight shifts in locations and initial velocities of the bodies, and their movement is clearly disordered.  

This was the source of the need to characterize the stability of trajectories. One of the earliest and handiest tools developed, as early as in the 19th century, is called “Poincaré maps” after French mathematician Henri Poincaré who invented them. These maps present a certain section of the trajectory to understand its nature; instead of drawing the entire trajectory, you examine its location and velocity at different intervals that sustain a defined mathematical condition, like passing through the starting location. From the obtained form you can determine whether the trajectory is periodic, periodic-like or chaotic. The three-body problem is currently studied using advanced algorithms and even neural networks. These provide huge collections of possible solutions for the problem, which has applications in theoretical chemistry, with proper adjustments. 

One of the earliest and handiest tools developed to characterize the stability of trajectories is called “Poincaré maps” after French mathematician Henri Poincaré | Bill Sanderson / Science Photo Library

In the TV show humanity interacts with aliens that arrive from an even more complex system, a four-body system - three suns and a planet - named Alpha Centauri, which is presumably a chaotic system. If so, how can life exist on it? In reality the Alpha Centauri system is actually not chaotic. It is composed of two large stars - Alpha Centauri A and B, as well as a small star called Proxima Centauri. Since Proxima is very small compared to its two larger brothers, the system presents a three-body problem which is more like a two-body problem with a slight disturbance, and in practice - the trajectory of Proxima is periodic with a fifteen day cycle. We now know that it has at least three planets. The first of them to be discovered is relatively similar to earth and its surface temperature is roughly zero degrees celsius, which could presumably sustain life, but it also has increased magnetic activity and is saturated with X ray radiation. These two are not recommended for sustaining life, at least as we know them. 

Proxima Centauri has at least three planets, including one that is relatively similar to earth. Illustration of the scenery on the surface of Proxima Centauri B, with the three stars of the system in the skies. | Mark Garlick / Science Photo Library

Communication Via Quantum Entanglement

In the series, the communication between humans and the aliens, and even worse - the espionage and monitoring inflicted on us by the aliens, are achieved through tiny supercomputers, the size of a proton, called Sophons. Two such Sophons are located with the aliens and two Sophons are sent to earth, and they convey information to each other through a quantum entanglement mechanism.    

This term originates from a foundational manuscript from 1935, composed by Albert Einstein and his colleagues Boris Podolsky and Nathan Rosen - who later immigrated to Israel and was one of the most important physicists in the Technion. In their manuscript, called EPR according to the initials of their names, the three claimed that quantum mechanics is incomplete and it should be rid of the probabilistic component that governs it; their claim was demonstrated by a thought experiment, called “spooky action at a distance”.

In this experiment you take two particles that were “born” together with defined qualities that are opposite to each other, and you move them apart immeasurably. Allegedly, measuring the quality of particle A will immediately, faster than the speed of light, provide us with information about the quality of particle B, as the qualities are opposite and synchronized, even if there is a great distance between them. This is in fact the concept of entanglement, and it seems to oppose quantum mechanics, where experiments cannot affect each other from a great distance, which goes to say that all physics is local. 

In the experiment you take two particles that were “born” together with defined qualities that are opposite to each other, and you move them apart immeasurably. Illustration of quantum entanglement | Victor de Schwanberg / Science Photo Library

Years later Irish physicist John Stewart Bell demonstrated that you can settle this paradox with the existence of hidden variables - constraints that are meant to express the differences between quantum mechanics and classical mechanics. He showed that if a quantum system upholds the principle of locality, the influence of one experiment on the other does not occur immediately. Additionally, physical qualities are defined by their very existence with no need for measurements, which is called the principle of intrinsicness. These conclusions were known since as “Bell’s Inequality” 

While classical mechanics is intrinsic and local, quantum mechanics violates these constraints; it cannot be intrinsic and local at the same time. This violation was measured experimentally by physicists Alain Aspect, John Clauser and Anton Zeilinger in systems with entangled photons, which resulted in them winning the Nobel Prize in Physics in 2022.

Despite this, according to current knowledge, quantum entanglement does not enable information transfer that is faster than the speed of light, not even theoretically. This is not the place to go into the complexities of why quantum teleportation alone does not allow for transfer of information. The term teleportation might be deceiving due to its cultural context, but in this context it refers to the collapse of a quantum state at one location and creation of an identical state at a different location, at the same moment. To extract information from this process you require additional information transfer in a classical form, which is limited to the speed of light. 

According to current knowledge, quantum entanglement does not enable information transfer that is faster than the speed of light. Illustration of measuring entangled particles, one in China and the other in Austria | Jose Antonio Peñas / Science Photo Library

Nuclear Propulsion

Jewish-Polish mathematician Stanislaw Ulam took part in the Manhattan Project for the development of the American nuclear bomb, where he worked shoulder to shoulder with Robert Oppenheimer, Edward Teller, Enrico Fermi and others who participated in this achievement. Following the war, with the launch of the nuclear era, Ulam thought of an interesting concept where nuclear power will not be harnessed for military uses, but for interstellar travel. 

In 1995 the concept began to materialize, when Ulam and his colleague Frederick Reines - who discovered the neutrino at the time and later won a Nobel prize for it - suggested building airplanes and rockets that are propelled by nuclear explosions. The concept gained momentum when it reached the desk of president Eisenhour. In the following years “Project Orion”, which was funded by the American government, examined this concept from a theoretical perspective. However, in 1963 the Treaty Banning Weapon Tests in the Atmosphere, in Outer Space and Under Water was accepted. This put an end to the project and it was abandoned in 1965. But the Americans kept working on the concept tenaciously under different headers, the main one being Rover Project. After investing a fortune into it, the program was canceled without a single nuclear propulsion rocket launched.    

Ulam and Reines proposed building airplanes and rockets that are propelled by nuclear explosions. Illustration of the rocket from project Orion, which did not come to fruition | NASA 

The concept of nuclear propulsion resurfaced during the Clinton administration, and was quickly taken off the table; and it resurfaced again lately - this time a date was set for the preliminary experiments, led by Lockheed Martin company and other collaborators. Not particularly fictional science. 

One of the concepts that were presented in these programs included the use of a space sail that will harness the energy that is discharged from a series of nuclear explosions. This concept is also mentioned in the show and it is far from delusional. Space sails are an old concept, where the pressure created by electromagnetic radiation, so far from the Sun, is used to propel an object that is attached to the sail. This as well is no longer science fiction. 

The concept of nuclear propulsion resurfaced again lately and this time a date was set for the preliminary experiments. Illustration of a spaceship propelled by the power of nuclear explosions | Christian Darkin / Science Photo Library

Nano-Fibers

One of the protagonists in the show, a scientist named Auggie, runs a company that produces fibers that are a nanometer in diameter. She is forced to stop her research when she receives a message from the aliens, but later she is able to resume it and use these fibers to take revenge on people who maintain continuous communication with the aliens.  

These fibers are presented as being able to cut straight through diamonds; but diamonds are rightfully known as the toughest material in nature. While theoretically the existence of tougher materials is conceivable, in practice - diamonds take the lead. Thus, it is positive that any nano-fiber, strong as it may be, cannot easily cut diamonds into slices.  

A material that might be able to challenge the toughness of diamonds is Graphene - single-layer carbon atoms. When graphene is rolled into nano-tubes, it is revealed as a material with interesting qualities like hardness and flexibility, but it still cannot be used for cutting. The tubes are also usually relatively short, just a few centimeters, as longer tubes already start to present defects. 

Current nano-fiber research is wide and addresses many fields. Amongst others, polymeric nano-fibers were suggested a long time ago as a practical application in the robotics industry, to mimic human tissues. Additional applications that were experimentally validated are in the electro-optics industry and photovoltaic cells. Cutting walls or sides of ships, as done by Auggie in the show, is not the focus of scientific interest, at least for now.    

 When graphene is rolled into nano-tubes it is revealed as a strong and flexible material, at least at a microscopic level, but it still cannot be used for cutting. Graphene nano-tube | Robert Brook / Science Photo Library