Wormhole (full version)

Wormholes are among the greatest mysteries of science. Such objects are hypothetical (they have never been proven), and were steamed from Albert Einstein's General Relativity equations. Essentially, wormholes are formed by two "mouths" and a "throat", which connect two points in spacetime, which would theoretically enable travel through space and time itself. However, when talking about wormholes (or any topic that involves more delicate matters), we must be especially careful not to fall into fiction and rather stick to scientific rigor.

Such objects are one of the science fiction favorites, being featured in several films, such as Interstellar, Star Trek, Donnie Darko, among others. In the case of Interstellar, there is a great deal of scientific rigor surrounding the film, which was achieved by the participation of the theoretical physicist Kip Thorne (who was also a close friend of Stephen Hawking).

Imagine an apple “inhabited” by a worm, which wants to leave point A on the surface of the apple and reach point B, opposite to point A, also on the surface of the fruit. If you walk through the shell, the shortest distance the annelid will have to travel will be the path described by the contour of the fruit. However, the worm has the possibility of a shorter path (a shortcut), which would be through the fruit. To cross the apple and reach the desired point, the invertebrate will have to dig, creating a tunnel/hole, and from that we have the analogy attached to the hypothetical cosmic objects.

Several types of wormholes were obtained as solutions of Einstein's field equation. More generally, we can divide them into intra-universe wormholes (whose connection leads from one place to another in the same universe) and inter-universe wormholes (which link one universe to another in a multiverse context, which also has no proof of its existence and remains hypothesized). More specifically, we can classify these space-time shortcuts as Lorentzian (studied within General Relativity and semi-classical gravitation) or Euclidian (studied in particle physics). The most common type of wormhole to be debated is the Lorentzian (most commonly called the Schwarzschild wormhole or Einstein-Rosen bridge).

The Einstein-Rosen bridges, formulated by Albert Einstein and Nathan Rosen, have a very peculiar hypothetical component, the so-called white hole. In short, the white holes would be "inverted" black holes, since instead of attracting/sucking nearby objects they eject/launch objects from within them. Consequently, a property that illustrates very well the distinction between these two celestial bodies is that while in the black hole nothing can come out, once within its event horizon, in a white hole nothing can go in once out of it, regardless the energy applied trying to force the body into it. An Einstein-Rosen bridge is formed by a black hole (composing one end/mouth), the “bridge” (which replaces the singularity) and a white hole (composing the other end/mouth), which would give connection to a mirror universe with time "moving" backward from the previously "normal" universe. However, Schwarzschild's wormholes were later shown to be unstable by physicist John Wheeler, meaning that they would collapse very quickly, making the crossing impossible. Despite being classified as non-transposable due to their high instability, they served as a basis for the development of ideas aimed at avoiding this problem.

A wormhole is spherical in shape and can be simply viewed with the following intuitive thought: Imagine that you have a sheet of paper with two points marked P1 and P2. The sheet will represent the fabric of spacetime and the points are arbitrary positions in space. The shortest distance between P1 and P2 in the plane will be, by definition, a straight line. The wormhole has the effect of folding the fabric of spacetime, thus enabling the points to overlap so that the distance between them becomes much shorter (“shortcut”).

It is theorized that, if they exist, wormholes could be manipulated to become stable through properties of a matter other than ordinary matter, called exotic matter. Such theorized particles have negative mass and therefore have a negative energy density, which would cause a repulsive/"anti-gravitational" effect (opposite to the attractive effect caused by positive mass particles) due to the "reverse" deformation in the spacetime fabric. If we had access to exotic particles, we could add them to the wormhole, where, with its “antigravity” effect, it would fight gravity (which induces the bridge to close) thus making the wormhole stable. In quantum mechanics, we have the so-called quantum vacuum fluctuations, which is the emergence and spontaneous disappearance of particles called virtual particles. Quantum fluctuations have been experimentally proven in an experiment known as the Casimir effect. This bizarre effect that enables particles to be created essentially out of nothing generates small flows of negative energy, which is analogous to the properties of exotic particles (making it somewhat possible to stabilize wormholes).

A transposable type of wormhole that dispenses exotic particles for their “sustenance” is derived from string theory (theory that basically attempts to unify physics) describing that in the early universe quantum vacuum fluctuations may have created several wormholes in the order of Planck length (the minimum length allowed which is in the order of 10 ^ -35 meters) with so-called cosmic strings (which also promote stability). With the period of inflation and the expansion of the universe, the "mouths" of these tiny wormholes were separated by enormous distances and scattered throughout the cosmos.

Suppose a curious (perhaps too much) astronaut finds a transposable wormhole with possible conditions for the human to get through it smoothly. Suppose also that the spacesuit has a wristwatch, which marks the same time as the astronaut's home-city. Our explorer checks the clock, which reads 10:05 AM and then enters the mysterious object and, after passing through the tunnel, exits through the other mouth. Once out, the astronaut somehow realizes that he is in a distinct galaxy. Checking the clock again it reads 10:15 AM. In just 10 minutes, the astronaut went through a path that light (which has the highest speed allowed in the universe) would take billions of years to reach. Special relativity states that nothing can exceed the speed of light. Did the explorer violate the fundamental laws of the universe by traveling trillions of kilometers in just a few moments? No, our astronaut is not bold enough. Relativity states that the speed of light cannot be exceeded "locally" meaning that no massive particle can reach or exceed the speed of light (which is approximately 300,000,000 m/s) on its own without using the shortcut used by the astronaut. For better illustration, if a photon (light particle) entered the wormhole with the astronaut, it would reach the other side much faster than the space man.

As mentioned, our hypothetical object of study indicates the possibility of time travel, however, under certain restrictions. In 1988, renowned scientists such as Yurt Sever and Kip Thorne worked on how to convert a wormhole transposable in space into a wormhole transposable in time. Physicists concluded that two paths would be possible for the realization of "time travel". In one case one of the mouths of our mysterious object would have to be accelerated up to a significant fraction of the speed of light and then would have to be brought back to the point of origin. In the other situation, one mouth is moved to a gravitational field of a sufficiently massive object. The theory of relativity predicts that in both cases there will be the effect of temporal dilation, the first caused by the speed comparable to that of light and the second caused by a gravitational field strong enough to bend the space-time fabric. The mouth that experienced one of the two possible cases will have its time measurement different from that of an observer outside these conditions, for that mouth, time will have "slowed down". Therefore, we will have mouths with distinct “ages”, an"older" (having experienced the “common” time passing) and a younger (having experienced time dilatation). An observer, passing through the "younger" entrance/mouth will come out of the "older" at a (past) time when the "older" was the same age as the "younger". As mentioned, there are conditions imposed, and it would not be possible to make a trip for any arbitrary time but only from when our wormhole had been “converted” into a time machine.

There are famous paradoxes stemming from the implications of time travel, such as the grandfather paradox, but these fall into a more philosophical field in descriptions and beliefs about what free will really is.

Despite being hypothetical objects that exist only in relativity equations, wormholes are nonetheless fascinating elements to study, with unique properties, providing inspiration to many science fiction writers.

Reference material: "A Brief History of Time" (Stephen Hawking) "Universe in a Nutshell" (Stepeh Hawking) / "The Science of Interstellar" (Kip Thorne)

https://en.wikipedia.org/wiki/Wormhole?fbclid=IwAR0TcfZvGWruIgRbyOldyllcFs1max7giWnrqzqscMC9UkdGszw1ShWPUmY