With Restrictions Why Can Tachyonic States Not Exist ?

[maddog]

I remember in QM classes when I first learned about the Schroedinger equation and the use of <x*Hx> notation where it is often chosen to use the |x> Ket vector notation, solving for x. Equally one could do the algebra on the left and use the Bra vector <x| as well. I chimed in, yes you can use either one fine. Once chosen, what about the other vector phenomenologically, that is. Would not the other state being a Complex conjugate state be Tachyonic in nature ?

 

If we restrict causality to be only locally conservered, that is in a time-like fashion and allow virtual states (those in which in a Feynman Diagram is not observed) be not required to be constrained to be a "real" state - would not allowing Tachyons in this way not violate our known physical laws. Regarding Antimatter, it's time sense is already backwards. This would also not violate the CPT theorem. This then could address entanglement.

 

Interestingly enough, a symmetry develops: for real matter (v < c) - Bradyons has a Reimannian geometric view while Tachyons (v > c) have Lobachevskyian or Hyperbolic geometric view. The mass of a Bradyon is real and the Energy increases with velocity. Symmetrically, a Tachyon has an imaginary mass (or in general Complex) and Energy decreases with increasing velocity. Thus for both classes, Energy goes asymptotic as velocity approaches c.

 

I am wondering if the supersymmetric partners long sought after are actually Tachyonic in nature. We haven't found any yet they are thought to exist. At the same time, Tachyons are thought to give off Cherenkov radiation and thus would be seen, yet do not (so far).

 

In EM, if you measure the E potential of wire at a point in space near the wire (constant flux) - this full hairy equation is a complex equation. The prof will tell you to only be worried about the Real term. The Imaginary term is irrelevant. I asked why, they always say don't ask. A lot of hand waving.... Viola! Only real values now.

 

What if Time itself were a Complex variable. For the most phenomena you only need the real term. You only get into the other part when dealing with anomalies. Tachyonic states come up in most string theories (M-Theory). A lot of time and energy is spent attempting to eliminate them. Why not embrace them and deal with the addition ?

 

maddog

Edited May 31, 2012 by maddog