D O C U M E N T 2 4 5 A P R I L 1 9 2 6 2 5 7 . . . . . . . (3) Can this be derived from the field equations? I do not know. I hope that it will be possible to recognize this fact as a consequence of the field equations—as they now stand. I cannot go into this now (see 6. below) but I remark that this problem can- not under any circumstances be avoided, even if we do consider the field within the particles. We simply accept it as a fact, as a given property of the field. If the first of equations (3) holds, we say that particles T1 and T2 are electrically alike otherwise we say that they differ electrically. 5. And now we come to the question of the essential difference between both kinds of electricity. Let us imagine that the mass of a particle is determined by the field in an analogous manner to the charge (I am sending you, at the same time, an offprint of a notice that recently appeared and that treats the issue of mass in the simplest case).[7] Let us consider the ratio . The pertinent experimen- tal fact can be formulated as follows: “If we have two particles of different charge, then the ratio for one of them is 2,000 times greater than that for the other” . . . . . . . . . . . . . . . . . . . . . . . . (4) It makes sense that this formulation would take the mentioned experimental findings sufficiently into account we must merely define the positive particles as those corresponding to the larger value of the ratio, in order to arrive at the standard formulation. 6. Is the problem thereby eliminated? We do not know whether proposition 4 can be derived from the present field equations. However, it is by no means plausible that it cannot be derived from them. This is where the nonlinearity of the equations plays a role. If we had linear equations, it would be impossible to derive from them a proposition of the form (4) or even of the form of (3). This is because, in the linear case, the proposition holds that no necessary relations can exist between residues[8] —and charge and mass appear as such. In other words: no relations between residues can be derived from linear equations. For if a field is given by the quantities f and another by the analogous quantities F, and if these fields manifest singularities σ and Σ in different places (i.e., for different values of the coordinates), then the field which is given by λ f + μ F and where λ and μ are either A3 A1 A2 2 A1A2 + + = or A3 A1 A2 2 A1A2 –+= holds Mass Charge ---------------- - M L ---- -= M- L ---- M- L ----
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