Tachyon

--Mmutkoski3 (talk) 20:12, 5 December 2015 (EST)

A tachyon is a particle that always moves 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, 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 confirmed 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. 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.

Mathematics

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 relationship for bradyons also apply to tachyons: [math]\displaystyle{ E^2 = p^2c^2 + m^2c^4 }[/math]

According to the Lorentz invariant theory, all of the same math models that calculate accurate values for bradyons must also apply to tachyons.

The major difference is the theoretical applications of this. Often using math models with tachyons result in infinite or imaginary values.

One main example of the differences in math between bradyons and tachyons is the relationship between velocity and energy. The faster a bradyon moves, the more energy it has. However, the faster a tachyon moves, the less energy it has. As E approaches 0, v approaches infinity. Therefore, it would take infinite energy to lower the speed of a tachyon below the speed of light. The same way a bradyon's theoretical speed limitation is the speed of light, a tachyon can never go slower than this speed.

Examples

Relativistic model for total energy of a particle:

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

In the case of a tachyon, v would be greater than c, causing [math]\displaystyle{ \frac{v^2}{c^2} }[/math] to be greater than 1. This causes the value under the radical to be negative. This makes the energy of the tachyon imaginary. Because total energy has to be real, the numerator [math]\displaystyle{ mc^2 }[/math] must also be imaginary. This means the mass of the particle must be imaginary.

This is an example of the theoretical math behind tachyons, and a major reason why many scientists think they will never exist.

Connectedness

1. How is this topic connected to something that you are interested in? This topic relates heavily to relativity and theoretical physics. It is interesting to think about and is a gateway topic to higher level thought in the realm of special relativity.
2. How is it connected to your major? Computer science is about doing things faster than humanly possible. If it were possible to do things faster then time permits, it would be hugely applicable to computer science.
3. Is there an interesting industrial application? If tachyons were discovered, it could lead to human control of causality and time. There are infinite applications, but for now it is only theoretical.

History

In 1967, Gerald Feinberg wrote a paper titled Possibility of Faster-Than-Light Particles. In this paper, he coined the term "tachyon" and mapped out many of the theoretical mathematics behind the particle. In this paper, he also referenced fields with imaginary mass, which he used to explain tachyons mathematically.

In 2011, CERN claimed to have observed a particle move faster than the speed of light. However, later they stated that it was only due to faulty equipment.

See also

Einstein's Theory of Special Relativity

References

Possibility of Faster-Than-Light Particles by Gerald Feinberg

Science World: Tachyon

Scientific American: What is Known About Tachyons?

Wikipedia: Tachyon