An enquiry concerning the principles of natural knowledge

by Alfred North Whitehead

-system for space and time with the corresponding measurements in the

-system certainly are those suggested by common sense and in their results they agree very closely with the result of careful observation. These formulae are the ordinary formulae of dynamical treatises. For such transformations the Newtonian equations are invariant within the Newtonian group.

10.2 But, as we have seen, this invariance, with these formulae for transformation, does not extend to Maxwell's equations for the electromagnetic field. The conclusion is that—still assuming these formulae for transformation—Maxwell's equations apply to the electromagnetic field as referred to one particular consentient set of the Newtonian group. It is natural to suppose that this set should be that one with respect to which the stagnant ether is at rest. Namely, stating the same fact conversely, the stagnant ether defines this consentient set. There would be no difficulty about this conclusion except for the speculative character of the material ether, and the failure to detect the evidences of the earth's motion through it. This consentient set defined by the ether would for all practical purposes define absolute space.

10.3 There are however other formulae of transformation from the space and time measurements of set

to the space and time measurements of set

for which Maxwell's equations are invariant. These formulae were discovered first by Larmor for uncharged regions of the field and later by Lorentz for the general case of regions charged or uncharged. Larmor and Lorentz treated their discovery from its formal mathematical side. This aspect of it is important. It enables us, when we thoroughly understand the sequence of events in one electromagnetic field, to deduce innumerable other electromagnetic fields which will be understood equally well. All mathematicians will appreciate what an advance in knowledge this constitutes.

But Lorentz also pointed out that if these formulae for transformation could be looked on as the true formulae for transformation from one set to another of the Newtonian group, then all the unsuccessful experiments to detect the earth's motion through the ether could be explained. Namely, the results of the experiments are such as theory would predict.