Mass Tachyon

in lorentz invariant theory, same formulas apply ordinary slower-than-light particles (sometimes called bradyons in discussions of tachyons) must apply tachyons. in particular energy–momentum relation:

e

2


=
(
p
c

)

2


+
(
m

c

2



)

2





{\displaystyle e^{2}=(pc)^{2}+(mc^{2})^{2}\;}

(where p relativistic momentum of bradyon , m rest mass) should still apply, along formula total energy of particle:

e
=



m

c

2




1
−



v

2



c

2







.


{\displaystyle e={\frac {mc^{2}}{\sqrt {1-{\frac {v^{2}}{c^{2}}}}}}.}

this equation shows total energy of particle (bradyon or tachyon) contains contribution rest mass (the rest mass–energy ) , contribution motion, kinetic energy. when v larger c, denominator in equation energy imaginary , value under radical negative. because total energy must real, numerator must imaginary: i.e. rest mass m must imaginary, pure imaginary number divided pure imaginary number real number.

in modern formulations of theory, mass of tachyons regarded real.