24/04/2024

In Folha, Viana addresses 'The Three-Body Problem'.

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Reproduction of Marcelo Viana's column in Folha de S. Paulo.

Netflix recently released a series whose title refers to a theme I know well: " The Three-Body Problem ." The reference goes back to the work of mathematician and physicist Isaac Newton (1643–1727), who created modern physics , reigning supreme until the advent of Albert Einstein 's (1879–1955) Theory of Relativity.

Newton postulated that all bodies attract each other through a force that is proportional to the product of their masses and inversely proportional to the square of the distance between them. For small bodies, this force is imperceptible, but on the scale of planets, stars, and galaxies, it plays a decisive role in the organization of the universe.

The law of gravitation can be expressed through a mathematical relationship called a differential equation. Newton showed how to solve this equation when considering only two bodies – the Sun and the Earth, for example. In this way, he confirmed the law formulated by Johannes Kepler (1571–1630) according to which the planet moves in an elliptical trajectory with the star at one of the foci of the ellipse.

But the equation of gravitation is much more difficult to solve when we consider three or more celestial bodies. Great mathematicians and physicists contributed to the advancement of this problem, most notably Henri Poincaré (1854–1912), and the advent of computers also provided new ways to solve this equation in practice. But the "three-body problem" remains synonymous with something difficult.

In the series, Earth is under threat of invasion by aliens from a solar system four light-years away: traveling at 1% of the speed of light, they will arrive in 400 years. They come from a system formed by three stars, around which, it is presumed, the aliens' planet orbits: therefore, there are four bodies, not three. This is not the only inaccuracy in the series.

The authors know that, according to Einstein's Theory of Relativity, nothing—neither object nor information—moves faster than light. But there is a dramatic need for aliens to communicate regularly with Earth.

Enter the phenomenon of quantum entanglement: a proton is sent to Earth while another proton entangled with it remains in the star fleet. The idea is that, because they are entangled, whatever happens to one proton will be immediately reflected in the other, allowing instantaneous communication between the invaders and Earth.

To read the full text, visit the newspaper's website.