146 RELATIVITY, THE SPECIAL THEORY
and thus obtained what he called a 'new manner of expression' for the Lorentz
force: whereas in 1895 Lorentz [L2] had introduced Eq. 7.16 as a new
assumption (see Eq. 6.13), Einstein obtained this force kinematically from the
purely electric force acting on a charged particle that is instantaneously at rest.
He also gave an expression for the kinetic energy W of the particle for the case
where accelerations are small and therefore no energy is given off in the form
of radiation. In that case,a relation which led him to comment: 'When v = c, W becomes infinite.
Velocities greater than light have ... no possibilities of existence.' (During
1907 Einstein had a correspondence with W. Wien on this question.)
[Remark. This conclusion is perhaps not quite correct. The precise statement
is: If a particle moves with a velocity smaller (larger) than c in one inertial frame,
then it moves with a velocity smaller (larger) than c in all inertial frames. (The
relative velocity of inertial frames is < c by definition.) Thus c is a velocity bar-
rier in two respects. According to Eq. 7.9, c is the upper (lower) limit for a particle
moving with sublight (superlight) velocity. Several physicists have speculated
about the weird properties of 'tachyons,' the name coined by Gerald Feinberg [F2]
for hypothetical superlight-velocity particles.* Tachyons can appear in our cosy
sub-c world only if they are produced in pairs. Tachyon physics is therefore nec-
essarily a topic in quantum field theory. The quantum theory of free tachyons has
been developed to some extent [F2]. The theoretical description of interactions
involving tachyons is thus far an open problem.]- Relativity Theory and Quantum Theory. The June paper also contains the
transformation law for the energy £ of a light beam:
(where 4> is defined as in Eq. 7.12) as well as the following comment by Einstein
on the similarities between Eqs. 7.12 and 7.18: 'It is remarkable that the energy
and the frequency of a light complex vary with the state of motion of the observer
in accordance with the same law.'
Three months earlier, Einstein had completed a paper which contains the
relation
E = hv (7.19)
between the energy and the frequency of a light-quantum [E7]. It is therefore of
interest that Einstein would call the similarities in transformation properties of E*See, e.g., [B2] and [F2] also for references to earlier literature.