I empathize with your battles with instructors. I tested on the standardized achievement tests as a junior year in college level in science, when I
was in 5th Grade (the old way they would express the results - I guess I should have asked "which college?"
). And of course, my school
administrators did exactly what was necessary such a situation, ...they asked me how I was able to cheat. I had already been declared stupid long
ago, so that was the simplest explanation, and no other could be considered. So... I remained a dummy in their eyes, until my high school guidance
counselor convinced the school to try an alternative, and they put me in chemistry and physics my frosh year. After that my world changed
dramatically. All the 'straight A' students from my class? Well, two are terrified and disillusioned engineers at Mega-Corp USA, and the rest are
selling real estate/insurance back in my home town or are unemployed. Sometimes, as I might infer from your OP, sometimes intelligence involves not
just following rules.
That being said however, I am not sure that one can, solely from the formula for kinetic energy, validate a condition wherein objects conventionally
move as tachyons. This is a formula for deriving the kinetic energy of a closed system mass, based on velocity of the system mass, not a formula for
deriving velocity based on total system Energy.
The best we can hope for inside a system energy contribution to velocity, is to establish that an electromagnetic wave is Lorentz Invariant, and
therefore can travel at or near the speed of light and through space. This includes both its electrical and magnetic aspect; however neither moves
faster than the speed of light as you cite.
Newton, and a good part of the science community for some time, presumed that gravity moved instantaneously relative to the space between two masses;
however was proved wrong by recent experiments by by Ed Fomalont of the National Radio Astronomy Observatory (NRAO), and Sergei Kopeikin of the
University of Missouri. Sadly, gravity also is bound by the speed of light.
The equation you seek is E = m[1−(v/c)²]−½ which is the relativistic equation regarding the relation of velocity to mass and Energy. Here,
once velocity v
of mass m
exceeds the speed of light c
then E becomes an imaginary number. Keeping E real provides the
formulation for an asymptotic limit to the velocity of mass m, which is c - with a hyperbolic contribution of energy E being required to take a mass
close to that limit.
However, if you are attempting to force a construct which leaves no option aside from the relative velocity of two particles exceeding the speed of
light, then consider that the Universe is measured by the best estimates, to be 13.8 billion years old, while the size of the visible universe is 15
billion light years. So, if I am a particle on the East ordinate of the inflative Universe moving outward from original singularity, what is my
relative velocity compared to a particle on the West ordinate of the inflative Universe moving outward in the opposite direction? These two particles
moved 15 billion light years apart from each other in 13.8 billion years.
edit on 1-8-2013 by TheEthicalSkeptic because: (no reason given)