faster than the speed of light

i had a small argument with my cus about "traveling faster than the speed of light"

special relativity works only for speeds less than the speed of light... and so far there are no proper observable or theoretical proof of particles or any other kinda of matter traveling faster than the speed of light...

by speed of light i am referring to the physical quantity, c which the speed of light in a vacuum... having a value of 299,792,458 m/s

he claimed that you can keep accelerating faster than the speed of light...

and i said... "ok lets model it..."

invariant mass (rest mass), m, is the absolute mass... m does not vary from one frame of reference to another... unlike relativistic mass which changes depending on the relative speed (see my blog post on my birth details... check the 4th comment)... we assume that earth is at rest with respect to a distant star and therefore earth mass is the invariant mass of the spacecraft...

we have a model for speed, v where 0< v < c, from special relativity...
speed ratio, β = ^v / _c
lorentz factor, γ = (1 - β²)^-1/2
kinetic energy of the frame of reference the space is given by E₀=γmc²

the space craft launches from earth... it accelerates from rest, where the magnitude of velocity half the speed of light...
v = c/2
β₁ = ^c/2 / _c = 0.5
γ = (1 - 0.5²)^-1/2 = 1.1547005384

kinetic energy is given by, E=γmc²
specific kinetic energy (kinetic energy per kg)= 103,779,308,880,000,000 J/kg = 104 PJ (P - peta - x10¹⁵)

so if the spacecraft weighed 100ton, E = 10,400,000 PJ

about 89 PW of solar power is absorbed by earth... the total human power consumption is 15 TW (0.015 PW)... 104 PJ is equivalent 2 hours of the total amount of total human energy consumption

okay so what happens after half the speed of light... well as v -> c, γ -> ∞ and E -> ∞

eg. say v = 0.99999999999c (99.99999999% of the speed of light)...
γ= 223,607
E=20,096,794,925,180,400,000,000 J/kg = 20,096,795 PJ/kg
and for a 100ton spacecraft, E = 2,009,679,500,000 PJ

calculate it yourself... you'd find that as v becomes even closer to c... the amount of energy required increases tremendously...

so on the basis of energy... approaching the speed of light would require massive quantities of energy...

also relativistic mass tends to infinity as v->c... to the amount of force required to accelerate further increases... i wont get in to that... its based in lorentz transformation... check wikipedia on "special relativity"...

my cus said... wait.. i cant remember what he said... will have to wait till he replies...