Page:Über die Konstitution des Elektrons (1906).djvu/5

all dimensions in the direction of motion shall be contracted in the ratio

$(1-q^{2}/c^{2})^{\frac {1}{2}}$

while the transverse directions remain unchanged.

To this geometric fundamental assumption, he still added the physical one, that all molecular forces are changing the same way with velocity as the electrostatic forces, and that the "masses" of mechanics are changing the same way as the electromagnetic mass of the electron.

From the mentioned assumptions, a total independence of all observable phenomena from the absolute velocity was consequently given.

It cannot be overlooked, that this way of proving was unsatisfactory in one respect: A quantity for calculation is employed which shall be decisive for the shape of bodies, namely the "absolute velocity", or the "velocity relative to the luminiferous aether". This quantity actually cannot be defined by us at all, since the result of the now described calculation is, that there is no means to define this velocity even by a thought experiment. We cannot even give the amount of the deformation change belonging to the observable change of relative velocity $q$, as long as we don't know the absolute velocity $q_{0}+q$. For example, if the original length of a body is $l_{0}$, it thus becomes deformed by $q_{0}$ into

$l=l_{0}\left(1-{\frac {q_{0}^{2}}{c^{2}}}\right)^{\frac {1}{2}}$

and by $q_{0}+q$ into

$l'=l_{0}\cdot \left(1-{\frac {(q_{0}+q)^{2}}{c^{2}}}\right)^{\frac {1}{2}}.$

The length change $\delta l=l'-l$ corresponding to an observable increas of velocity, is thus not only a function of $q$, but also of $q_{0}$. As we have no right to assume, that our system of fixed stars to which we relate Earth's motion, is momentarily in absolute rest in the aether, we thus actually cannot say anything about the occurring deformations.

It is now very remarkable, that, starting from quite different