# Why didn't Lorentz conclude that no object can go faster than light?

Based on Lorentz factor $$\gamma = \frac{1}{\sqrt {1-\frac{v^2}{c^2}}}$$ it is easy to see $$v < c$$ since otherwise $$\gamma$$ would be either undefined or a complex number, which is non-physical. Also, as far as I understand this equation was known before Einstein's postulates were published. My question is: why didn't Lorentz himself conclude that no object can go faster than speed of light? Or maybe he did, I do not know. I feel I am missing some context here.

• Just because an intermediate result is a complex number doesn't mean it can't be used to model/predict real-world results. Further, many simple physical laws turn out "later on" to be first-order approximations to reality, e.g. $F = mv$ vs. $F = \dot{p}$ – Carl Witthoft Feb 20 '19 at 12:59
• I found this answer to the same question on physics.se quite interesting, I am guessing it may be of interest to others as well. – eirikdaude Feb 20 '19 at 13:19

While Lorentz (before 1905) himself didn't directly address the question whether light speed is a universal limiting speed, there were many physicists before Einstein who argued that the speed of light cannot be reached, at least in the context of electrically charged particles. For instance, since 1881 the concept of electromagnetic mass was used, according to which the inertia of a particle increases at higher velocity due to its electromagnetic self-energy. J.J. Thomson concluded in 1893:

[p. 21] When in the limit v = c, the increase in mass is infinite, thus a charged sphere moving with the velocity of light behaves as if its mass were infinite, its velocity therefore will remain constant, in other words it is impossible to increase the velocity of a charged body moving through the dielectric beyond that of light.

Or G.F.C. Searle in 1897, whose computation were based on the so-called "Heaviside ellipsoid", according to which the spherical fields of moving charges become ellipsoids:

.. when v = c the energy becomes infinite, so that it would seem to be impossible to make a charged body move at a greater speed than that of light.

In 1899 and 1904, Lorentz completed his electron model which includes the Lorentz factor as well as alternative formulas for electromagnetic mass. This, together with Searle's concept of the Heaviside ellipsoid, brought Wilhelm Wien in 1904 to the conclusion that the Heavisde ellipsoid prohibits faster than light motion, because the Lorentz factor $$\sqrt{1-(v^{2}/c^{2})}$$ becomes imaginary.

Henri Poincaré (1904) came closest to Einsteins postulate of the constancy of the speed of light, by writing:

From all these results, if they were confirmed, would arise an entirely new mechanics, which would be, above all, characterized by this fact, that no velocity could surpass that of light, [Because bodies would oppose an increasing inertia to the causes which would tend to accelerate their motion; and this inertia would become infinite when one approached the velocity of light.] any more than any temperature can fall below absolute zero. No more for an observer, carried along himself in a translation he does not suspect, could any apparent velocity surpass that of light; and this would be then a contradiction, if we did not recall that this observer would not use the same clocks as a fixed observer, but, indeed, clocks marking 'local time.'

There he alluded to the relation between the "apparent" speed of light as a limiting speed, the relativistic mass (which includes the Lorentz factor), the relativity principle, and "local time" based on Poincaré-Einstein synchronisation in contradistinction to "true time" in the aether.

However, Einstein (1905) was the first to note, that all these relations follow from the relativity principle and light speed constancy alone, and are directly related to space and time, without any reference to the aether - which is precisely what we now call special relativity. This laid the basis of Minkowski's spacetime formulation of relativity.

• There's some good history there, Batiatus. Thanks. – John Duffield Feb 24 '19 at 17:22