Can somebody explain tachyons to me? Wikipedia isn't exactly the best resource for things like this. I just don't understand how something can travel superluminally; isn't the speed of light supposed to be the maximum possible speed? I realize that tachyons are theoretical, I was just wondering if someone could explain it a bit to me.

Here, i will explain it. This is the best way i have been able to explain tachyons to friends and alike: (I apologize the math has tex tags on the sides of the equations)

*Bradyonic Matter, Luxons and Tachyons*A Bradyon, also been known to be called as a Tardyon are particles with mass and a rest energy which concurrently never reach the speed of light. Because

they have what is called inertia and a gravitational mass (as shown by the Weak Equivalance Principle of General Relativity), it would reqire an infinite

amount of energy to accelerate, (let's say an electron) to accelerate to the speed of light. Since it would require more energy than what is visible in the

observable universe, this seems to be a ''barrier'' or a ''limit'' if you like in nature that can never be violated. The root word ''Brady'' means slow.

A Luxon is by classification, all particles of energy which have no inertial or gravitational mass, so they always move at light speed. This speed is roughly

186,350 miles per hour... which means this speed must remain constant in all inertial frames. The Bradyonic Matter can have speeds that vary however when

the speed of light is used to measure this. In this sense, we often think of the speed of light as a universal measuring stick.

A Tachyon is a hypothetical particle with a negative energy density. This negative energy allows them to move through spacetime with as little effort

or energy as possible.

The root word ''Tachy'' as in Tachcardia from fast heartbeat means -- obviously ''fast.'' Problems with the existence of tachyons do exist which makes their

existences questionable. A long time ago, there was a research group who proposed trying to generate & detect tachyons, which are not neutrinos.

It is alleged that particles traveling faster than light will generate Chernkov radiation, which is shifted as a color of blue.

Martin Gardiner wrote a Mathematical Games each month in Scientific American and is generally believed to be very knowledgable in physics.

Doctor Gardiner showed that the equations relating to Tacyons predicted the following (among other properties).

As mentioned above tacyons would generate Cherenkov radiation in a vacuum. Adding energy to tacyons slowed them down with the velocity of light as

the lower bound. In fact, a tachyon would find an infinite amount of energy at this lower bound limit, much like a Bradyon would find an infinite amount of

energy at the limit of lightspeed. Another strange prediction was that tachyons lost energy if they could be sped up. Hence, the existence of tachyonic matter

and their supposed fields seems... unlikely, but they are not completely ruled out (1).

*The facts of photon energy*What is the energy of the photon?

The energy of the photon is best said to be purely kinetic. Kinetic energy is derived from classical physics, where: [tex]E_k=\frac{1}{2}Mv^2[/tex].The key

equation to prove this is [tex]m^2c^4 = E^2 - p^2c^2[/tex], the contribution of [tex]mc^2[/tex] is called the rest energy, the stuff of rest matter, and all

other contributions to the energy are called kinetic energy. Since the photon has no rest energy, then the energy it can have must be a purely kinetical

energy.

A photon does not have any mass. It does contain however a non-zero momentum or as we often call it, a 4-momentum [tex]p^{\mu}[/tex] where [tex]p[/tex] is

for momentum, and for a photon it must be inforced to [tex]p=\frac{1}{2}\gamma Mv^2[/tex], as we shall soon see. The photon is said to move along what is

called a Null trajectory, [tex]p^{\mu}p_{\mu}=0[/tex], where in terms of its energy we have [tex]-E^2+|p|^2=0[/tex].For the given unit vector [tex]\hat{v}[/tex]

in the directionality of the motion of a photon (which is a unit of kinetic energy), we state that [tex]\rightarrow{p}=\hat{v}E[/tex], so the modulus of the

photon is given as [tex]|p|=E[/tex].

There has been some sensitive tests to experimentally-see whether the photon has a mass or not, and the lowest limit given is an absurd number of

[tex]10^{51}kg[/tex], but that should not be interpreted that the theory of photons work better with having a mass.

When calculating the energy of systems, we have an equation in relativity that provides a way to measure energy given as the famous [tex]E=Mc^2[/tex]. However

since in relativity we have the concept of an invariant mass, or a rest energy, we need to invoke the equation [tex]E=\gamma Mc^2[/tex], where the key

Greek symbol ''gamma'' [tex]\gamma[/tex] reduces the factor of [tex]M[/tex] to zero. So the mass is said to be zero in consequence. Gamma has a value of

[tex]\gamma=\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}[/tex]. Another way to derive the idea that photons have no mass but do have a momentum is by concluding mathematically

the following.

the equation [tex]E=(Mc^2)^2+p^2c^2[/tex] should be taken into consideration. Deriving that formula, you remove the [tex](Mc^2)^2[/tex] part and you get:

[tex]E=\sqrt{(Mc^2)^2(1+\frac{p^2}{(Mc)^2})}=Mc^2 \sqrt{1+\frac{p^2}{(Mc)^2}[/tex]

thus taking the tailor expansion of the sqaure root gives us:

[tex]E=Mc^2(1+\frac{p^2}{2(Mc)^2}+...)[/tex]

so that [tex]E=Mc^2+\frac{p^2}{2M}+...[/tex]

which derives the relation (which is an approximation)

[tex]p \approx \frac{1}{2}Mv^2[/tex] where it must be approximated for low velocities. If we are talking in terms of relativitic speeds, then

[tex]p=\frac{1}{2} \gamma Mv^2[/tex].

The energy of photon and its momentum are related to its frequency and its wavelength. The usual expression is given as:

[tex]E=\hbar \omega=h \nu=\frac{hc}{\lambda}[/tex]

Notes

(1) - They have a rest mass M that also has an imaginary value [tex](M^2<0)[/tex]. It turns out that [tex](E=M_g)[/tex], the observable mass-energy of

these light weight particles, becomes ''real'' and ''positive''. If a particle was able to defy the light-speed barrier so that v was greater than

[tex]c[/tex], then both [tex]g[/tex] and [tex]E[/tex] would become imaginary quantities, because [tex]\beta[/tex] would be larger than [tex]1[/tex] and

[tex](1 - \beta^2)[/tex] would be negative.We can create neurtino's from the decay of tritium. The basic underlining rule is through the relativistic

relation between energy and momentum [tex]E^2 = P^2 + M^2[/tex]... and we work out that it is mass squared that works out the neutrino mass from tritium

decay... but this mass squared can be seen in light of either a positive reult or a negative result, and if it is a tachyon, containing a very light weight

amount of imaginary matter of about [tex](i)(12 eV)[/tex], there is the big problem that nothing fuitful will arise out of this... because the theorists

do not believe. or cannot be sure if its qualities would be observable or known.