Translation:Two Objections Against the Theory of Relativity and their Refutation

By..

I.

Of all apparently paradox consequences that stem from the time-transformation of the theory of relativity, there is probably none, against which the common sense of anyone (who is still unfamiliar with the matter) is more reluctant, than the one according to which the time indication of a clock shall be dependent on its state of motion. Already in his fundamental paper, has driven this paradox to the extreme by a thought experiment, recently explained in a particular nice way by  in a lecture that is also very readable in other respects.

With a small modification this can be represented as follows:

A bundle of clocks, physically exactly equal and equally set, shall be moving with uniform velocity at the same path, all adjacent so close, that they can be considered as simultaneously lying at the same point. Thus they all accordingly measure the proper time (in the an sense) of the worldline corresponding to their motion. In a particular moment, however, their paths will be separated, and only after the completion of a certain time, they simultaneously come together at the same spacepoint again, to execute a common motion again. At their encounter, differences exist in their indications that constantly remain. During the time of separation, the rate of that clock is most advanced which was at rest in a valid reference system in the meantime; namely there is always one, and only one valid reference system, for which the locations of separation and re-encounter lie in the same geometric point.

The opposition against this, which at first will probably be raised in the mind of everyone, has recently caused two authors to object at this place. rejects this consequence and thinks, that there is an error in 's consideration. Contrary to this, proves in a particularly striking way, that the discussed fact follows from the relativity laws, however, he thinks that it contradicts the "unconditional" relativity principle, and it would show the inequality of different "strides" (Schreitungen) in a particular clear way.

We want to examine this objection, by using 's four-dimensional world as the basis of this study. The principle of relativity claims the equivalence of all time-like directions in it. 's experiment, however, is represented by a curved worldline, which (in a worldpoint $$A$$) decomposes into a row of curves, and all of them will be re-united at a worldpoint $$B$$ to a single line. Of all curves connecting the points $$A$$ and $$B$$ having time-like direction throughout, the straight connection has the longest proper time; that is the meaning of 's consideration. That of all time-like directions, one is preferred in this way, is to be admitted; however, this preference is not based on the natural laws employed, but only on the choice of world-points $$A$$ and $$B$$, i.e. on the special assumptions of our example.

At the end, an analogy shall be allowed. One of the most important physical findings is the physical equivalence of all directions in (three-dimensional) space; and one of the most elementary geometric laws says, that two points determine a straight line, and thus a direction as well. It would be in accordance with the previous objection against the relativity theory, when one would try to refute that law of the isotropy of space by the aid of that geometric theorem.

II.

Another indication for the existence of the aether is seen by in the occurrence of border-strides (Grenzschreitungen), occurring with the speed of light in every reference system. For small velocities he admits the validity of the relativity laws as very probable (gravitation may probably be neglected at this place); but beyond of this border he expects totally new phenomena, from which the state of motion of the aether can be recognized.

By a very striking terminology, distinguishes the standpoint of the "conditional" and the "unconditional" principle of relativity. Both are in full agreement as regards the mathematical formulation of the "relativity laws" for subluminal velocities. However, they are principally different as regards the assessment of the relativity principle. As to the first standpoint, it is only a mathematically convenient calculation-rule; since at this very place a preferred reference system at rest in the aether exists, whose time is "the time", while the time of all other systems is only "local time" according to 's terminology. It is quite correct at this place, to speak about velocities of every amount, and, since the speed of light indeed represents a limitation for the relativity laws, to expect principally new knowledge from superluminal velocities.

However, as to the second of the mentioned standpoints, the equivalence of all reference systems is a law of nature; yet they are only equivalent, when the times connected to them are completely equally valid. Now, already and maybe even better  and the author of this rebuttal have shown, that the existence of superluminal velocities must cancel the unambiguity of the assignment of cause and effect. (The conditional relativity principle, however, escapes from this conclusion, since it can re-establish the unambiguity by means of the passage from the local time to "the" time.) Thus it is a consequence of the unconditional relativity- and the causality-principle, that strides don't occur beyond 's border-strides. Thus when says: "For the judgment of what is happening with matter when the borders of the area were exceeded, any clue is missing until today", he consequently executes his standpoint of the conditional relativity principle. However, to derive from that an objection against the view of the "unconditional" relativity principle, as it was done by in § 15, is impossible. And when writes : "Yet, as soon as the validity  of the relativity principle will be concluded from the observations, so that (as previously described) a natural limitation of the ordinary states of motion must be assumed, is is impossible to avoid the conclusion, that just not all strides are equivalent for the world process", then this conclusion is totally inadmissible in the system of the unconditional relativity principle. Because this view necessarily must deny the occurrence of superluminal velocities for matter. To conclude different validities of the possible strides from the non-existence of certain imaginable strides, is not allowed.

For the rest it seems to me, as if the whole question after the existence of the aether and absolute time could be banned out of the physical discussion; as long as no totally new facts can be demonstrated by experiment, as for example the existence of superluminal velocities or a contradiction between the phenomena of gravitation and the relativity principle, it cannot be physically distinguished between both mentioned standpoints. Concerning all quantities accessible to measurement, they exactly give the same results. By that it should not be said, that this questions would be of no interest, on the contrary it seems to me as of high philosophical importance; yet exactly because of that it should be reserved to treatment by philosophical methods.

, December 1911.

(Received December 6, 1911.)