Tachyon

A tachyon is a particle that is moving faster than the speed of light. Tachyons are currently only theoretical, and many scientists believe that they could not exist based on our understanding of the physics in this universe. Tachyons were first proposed by Gerald Feinberg in a paper he wrote in 1967 which coined the term tachyon and outlined a baseline for some of the theoretical physics surrounding them.

The Main Idea

Tachyons always move faster than the speed of light, while its complements, luxons, always move at the speed of light (ex. photon), and bradyons, which always are moving slower than light. Both of these complements exist, while tachyons are still only hypothetical. Most physicists believe that tachyons could not exist because their existence would break the barrier of the speed of light and therefor disrupt causality. For example, if tachyons did exist, Einstein postulated that it would be possible to build a device known as a tachyonic antitelephone, which would allow the transmission of messages faster than the speed of light, and therefor into the past. This would allow someone to answer a question before it was even asked, breaking the relationship of cause and effect we know as causality.

Research continues in an attempt to find the theoretical tachyon, however there has been no recorded success.

Appearance

Tachyons by definition move faster than light, therefore it would be impossible to see one approaching because it is moving faster than the photons reflecting off of it. The tachyon arrives to the viewing point before the light reflected off of it, and then continues on. Once it has passed the viewing angle, the viewer can now see two images of the tachyon.

The image in front of the view will be the image of the tachyon going the opposite direction than it came. This is because light reflected from the tachyon when it was closest to the viewer reaches the viewer first, followed by the light reflected longer and longer ago. This creates the appearance of the tachyon moving away from the viewer in the direction from which it came.

The second image of the tachyon is the right reflected from it as it departs in the direction it is actually moving in. This is reflected back to the viewer. Therefor, the viewer will see two images of the tachyon, both of which are departing in opposite directions. The image in front of the viewer will be blue shifted, while the image departing in the same direction as the tachyon will be red shifted. Both images will be distorted depending on the shape of the tachyon. In the simplest case, the tachyon is a tiny sphere and the image is represented by the animation above.

A Mathematical Model

Mathematically, tachyons are represented with space-like four-momentum. Tachyons would have imaginary mass, meaning that their mass is a negative number when squared. Because it is space-like, it can only exist in that space of the energy-momentum graph. This means that it would be impossible for the tachyon to slow down to speeds below that of light.

The energy-momentum relation for bradyons also apply to tachyons: [math]\displaystyle{ E^2 = p^2c^2 + m^2c^4 }[/math] What are the mathematical equations that allow us to model this topic. For example [math]\displaystyle{ {\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net} }[/math] where p is the momentum of the system and F is the net force from the surroundings.

Examples

Relativistic model for total energy of a particle:

[math]\displaystyle{ E = \frac{mc^2\root(1-\frac{v^2\c^2})} }[/math]

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