Tachyon

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Since a tachyon moves always faster than light, it could not be observed approaching. Shortly after a tachyon passed by, two reflections could be seen from it, which are separated in opposite directions. The black line is the shock wave of Cherenkov radiation, represented only for an instant of time. The double image effect is both more important for an observer on the trajectory of a superplastic object (in this example, a sphere, represented in gray). The blue form of the right is the image formed by Doppler effect of the light reaching the observer, which is located on the vertice of the black lines of Cherenkov of the near sphere. The left image is formed by the light with corrimiento to the red light that leaves the sphere after it overlays the observer. Since the object arrives before its light, the observer sees nothing until the sphere begins to surpass the observer.

A tachyon (from the Greek ταχυόνιον takhyónion from ταχύς takhýs 'quick, swift') is any hypothetical particle capable of moving at superluminal speeds. Tachyons are attributed inexplicable properties today.

Physical description

In terms of Einstein's theory of special relativity, a tachyon is a hypothetical particle with a space-like quadri-momentum. This implies that if your energy and momentum are real, your apparent conventional rest mass would be an imaginary number. Therefore, Minkowski's (pseudo) norm of his four-momentum would be negative, since:

$sum_{a=0}^3 P^aP_a = frac{E^2}{c^2} - p_x^2 - p_y^2 - p_z^2 = m^2c^2$

The proper time experienced by a tachyon is also imaginary. A curious effect is that unlike real particles, the speed of a tachyon increases when its energy decreases. This is a consequence of special relativity since, hypothetically, a tachyon has negative square mass. According to Einstein, the total energy of a particle is the rest mass m times the speed of light squared and multiplied in turn by the Lorentz factor, that is, the total energy comes from given by the relation:

${displaystyle E={frac {mc^{2}}{sqrt {1-{cfrac {v^{2}}{c^{2}}}}}}}$

For ordinary matter, this equation shows that E increases with velocity, becoming infinite as v (velocity) approaches c, the speed of light. If m is imaginary, on the other hand, the denominator of the fraction needs to be imaginary to keep the energy as a real number. The denominator would be imaginary if the number in the square root is negative, which only happens if v is greater than c.

A tachyon is limited to the space type portion of the energy-momentum graph. Therefore, it can never go at speeds less than the speed of light. Interestingly, as his energy decreases, his speed increases.

If tachyons existed and could interact with ordinary matter, the principle of causality could be violated.

In the theory of general relativity, it is possible to construct space-times in which particles propagate faster than the speed of light, relative to a distant observer. An example is the Alcubierre metric. However, these would not be tachyons in the above sense, since they would not exceed the speed of light locally.

Field and string theories

In quantum field theory, a tachyon is the quantum of a field, usually a scalar field which has a negative mass squared. The existence of such a particle is a signification of the instability of the space-time vacuum, because the energy of the vacuum has a maximum instead of a minimum. A small impulse could cause a decay of exponential amplitudes which at the same time could induce tachyon condensation. The Higgs mechanism is an elementary example, but it's good to realize that once the tachyon field reaches its minimum potential, its quanta stop being tachyons and become Higgs bosons with positive mass.

Tachyons are found in many versions of string theory. In general, string theory states that what we see as "particles" —electrons, photons, gravitons, etc...— are actually different vibrational states of the same string. The mass of a particle can be deduced as from the vibration exerted by the string; in other words, the mass depends on the note the string is playing. Tachyons frequently appear in the spectrum of states of permissible strings, as meaning that in some states they have negative squared masses, and hence imaginary masses.

Imaginary mass

Starting from the equation of the Theory of Relativity:

$E = frac{mc^2}{sqrt{1 - frac{v^2}{c^2}}}$

Factoring the -1 in the denominator and operand:

$E = frac{mc^2}{sqrt{-1cdot(frac{v^2}{c^2} -1})}= frac{mc^2}{sqrt{-1}cdotsqrt{frac{v^2}{c^2} -1}}$

Variable change: $i = pmsqrt{-1}$ then multiplies the numerator and denominator by i:

$E = pmfrac{imc^2}{i^2sqrt{frac{v^2}{c^2} -1}}$

If a "tachyon mass" is formally defined by $M_t = im,$ you have:

$E = pmfrac{M_tc^2}{sqrt{frac{v^2}{c^2} -1}}.$

The root is analyzed and it is obtained that to be real, $c,}" xmlns="http://www.w3.org/1998/Math/MathML">v▪c{displaystyle v PHPc,} c," aria-hidden="true" class="mwe-math-fallback-image-inline" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b2e1ed5d04ee662e7d1a4168593c8e0deedc836e" style="vertical-align: -0.338ex; width:5.62ex; height:1.843ex;"/>$ , particle speed should be higher than c (light speed).

Interpretation

In quantum mechanics and quantum field theory an imaginary value of mass or energy can be interpreted as an unstable particle that decays into other particles, or as an unstable vacuum state that gives rise to other states. Specifically, the imaginary part of the energy is directly related to the disintegration time of said state. Thus, states with real energy, since their imaginary part is zero, can exist indefinitely. For states or particles with imaginary mass or energy, the decay time is inversely proportional to the imaginary part:

$tau_{des} = frac{2pi hbar}{|mbox{Im} E|}$

Being E the complex total energy and $hbar$ the constant of Planck (part of 2 pi) according to the quotient between the real and imaginary part of the energy μ = (Re E)/(Im E) unstable particles can be classified into:

Unstable particulate mass $1;}" xmlns="http://www.w3.org/1998/Math/MathML">μ μ ▪1{displaystyle mu 한1;} 1;" aria-hidden="true" class="mwe-math-fallback-image-inline" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/39ba7c39fd3c28ba9dd9ed190350b465e6ea9add" style="vertical-align: -0.838ex; width:6.308ex; height:2.676ex;"/>$ .
Resonances $mu approx 1$ .
Tachyonic particles $<math alttext="{displaystyle mu μ μ .1{displaystyle mu \leq1;} <img alt="mu$ .

Science Fiction

In science fiction there has been a masterful use of tachyons as a whole that answers the big question about how to travel and be the master of time. Some examples:

In Disney Channel's Best Friend Whenever television series, some episodes mention tachyons as residual particulates of travel in time that the protagonists Cyd and Shelby experience.
In the television series The Flash of the comic company DC Comics, Dr. Harrison Wells, also known as the Flash Reverse, or Eobard Thawne, uses tachyonic particles to boost its speed.
The popular character of the American comic company, DC Comics, The Flash (comic), has his temporary counterpart in the 27th century, when John Fox, a scientist, accidentally discovers the extraordinary properties of the tachyons by experiencing in his own body the risks of his "Theory of Speed by Rest", challenging the laws of physics considerably and using his hypervelocy to make temporary travels, through the curves.
It also appears in the film the 4 fantastics when it is ordered to look for a spatial anomaly which triggers the encounter of the character Silver Surfer, the search and the capture consisted of a tachyonic ray.
The tachyons are commonly used throughout the Star Trek series, and films such as Land of the Lost and K-Pax, in which his protagonist Prot claimed to travel at tachyon speeds.
In Expediente X (The X-Files), season 4 chapter 19 "Synchrony", reference is made to tachyons when an old man comes from the future to kill the group of scientists who made possible "the world without history, without hope, where everyone knew exactly what was going to happen."
The author of science fiction Philip K. Dick, who throughout his life had episodes of visions and hallucinations to which he tried unsuccessful to seek a rational explanation, became interested in the tachyons in the 1970s following the essay "Orden en el disorder" published in the magazine "Harper's" by Arthur Koestler in July 1974. In this work it was proposed that the Universe crosses a continuous process from chaos to total form. Dick relates this to the concept of tachyons as particles that travel in time in opposite direction to ours. The relationship between these two data was adapted to his own theory that his novels were anticipating the future in a way in which he himself could not have foreseen. In some of the letters then collected in Exegesis Dick suggests that the entire planet Earth receives, from heaven, a constant bombing of tachyons that, coming from the Future, bring with it information of a higher and more advanced state of order of the Universe. Dick theorized that some people somehow act as antennas by absorbing that information in a more or less conscious way. He also assumed that animals were sensitive to that information, which served them as a tool of evolution. This curious statement deduced her from the study of her cat's nocturnal behavior.
Tachyons are also used in Alan Moore's graphic novel WatchmenIn which the tachyons, according to Dr. Manhattan, are particles that travel backwards in what humans perceive as time.
In the film K-Pax, the character who starred Kevin Spacey, who said coming from space, also mentions the tachyons in one of his sessions with his psychiatrist, incarnated by Jeff Bridges, whose original version is the Argentinian Man looking at the southeast, by Eliseo Subiela (1986).
In the film "The Prince of Darkness" of 1987, mention is made of the use of a TV transmission from the future modulating tachyons, to warn those who receive such a message, about the coming of Satan to the world, that message arrived at random and those who received it considered it a dream, until they realized that among them they dreamed exactly the same. When traveling faster than the light, a video could be transmitted to the past
They have also been employed by the Russian-American writer Isaac Asimov in several of his stories, making reference to them in the transformations that matter suffers when the stars of his stories move at super-plastic speeds (the "high"), describing the transition of transformation as a tardio-tachion-tardion (e.g. in the story "Take a match").
In the book Flashforward (Records of the Future) by the writer Sawyer Robert J., reference is made to tachyons in experiments carried out by CERN scientists in particle accelerator.
The novel Timescape ("Cronopaisaje" in his Spanish translation) by Gregory Benford bases his plot on the use of tachyons as a means of intertemporal communication.
In the television series of the late Gene Rodenberry, Star Trek The New Generation and Star Trek Voyager, a regular use of tachyons is made to those who give them different employment according to circumstances.
In the Castle TV series (temporary 6, episode 5): as part of the plot use a tachyon generator which produces energy and allows time travel.
In the chapter The obstacles of Leela the adolescent mutant of the animation series Futurama Fry, Leela, Amy, Hermes, Zoidberg and the teacher rejuvenate due to the effect of the tachyons.
In the animated series of Max Steel (2013), TURBO energy is an unlimited energy based on tachyon energy.
In X-Men, the first Silver Samurai is a mutant with the ability to generate a tachyon field, with which you can surround anything. He commonly uses his power over his sword, allowing him to cut almost anything, except adamantium
In Stephen King's short novel "The Gods Word Processor" refers to the hypothetical discovery of tachyons.
In the Tomorrowland film (2015), reference is made to a Tachyon machine with which they can control them, thanks to which it can be seen back to the past and in front of the future.
In the Stellaris video game, the most powerful weapon you can investigate is the "Tachyon Dance", visually displayed as a blue beam when fired from a ship. You can also investigate the "Tachyon Sensors" that are the most advanced space sensors.
A video game called Tachyon is available in the Google Play Store.
On Takeshi Obata's sleeve (All you need is kill). Mimetics (terrestrial beings) can produce tachyons and create a temporary loop. In which the protagonist gets trapped.
In Alejandro Rocha Narváez’s novel “El Cristo Final” (2018), a modest and tormented secondary professor helps his friend Gonzalo Lecaros and other physicists to solve the difficult problem of penetrating the singularity that began the Universe, until before the first moment of the Big Bang, in his delusional obsession for “discovering the mind of God.” The professor proposed adapting the mechanism of Hawking radiation, assuming that, in the same way that all the particles of the universe were created, also under the enormous initial energies would have been generated virtual tachyon-antitachion pairs, some of which penetrated the horizon of events of origin while others were trapped in the evolution of the Universe, being possible to detect them by orbital telescopes similar to Planck (satellite), As well as these photon telescopes enabled the mapping of microwave background radiation, the new technology for the detection of cosmic tachyons would allow it after a decades-long exposure. And every tachyon that has sunk in the primordial singularity will inform of its mysterious properties by the quantum interlacing that it maintains with the anti-tachion detected in the present, revealing at last the unfathomable mystery of Creation.
The book of "The Adventures of The Tachyon for Space-Time" explores the possibility that the collapse of the black hole ends in a bottle of Klein. In these stories The Tachyon is a boy who could travel at superluminous speeds.

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