2017-02-14 09:38:58 UTC
Banesh Hoffmann, Relativity and Its Roots, p. 105: "In one case your clock is checked against two of mine, while in the other case my clock is checked against two of yours, and this permits us each to find without contradiction that the other's clocks go more slowly than his own."
In an alternative scenario where the traveling twin CAN perform the checking procedure, the stationary twin is aging SLOWER, that is, remains YOUNGER (according to Einstein's relativity). This is easy to see in both the one-way travel case and to-and-fro travel case:
1. One-way travel case: In the following picture the single moving clock lags behind the multiple stationary clocks, but if the single clock were stationary and the multiple clocks moving, the single stationary clock would lag behind the multiple moving clocks:
Accordingly, the stationary owner of the single clock would get younger and younger than traveling owners of moving clocks.
2. To-and-fro travel case: Let us imagine that all ants spread out on the closed polygonal line have clocks and travel with constant speed:
For this scenario, Einstein's relativity predicts that the clock of a single STATIONARY ant located in the middle of one of the sides of the polygon will show less and less time elapsed than moving clocks consecutively passing it. In terms of the twin paradox, the single stationary ant gets younger and younger than traveling brothers it consecutively meets.
Clearly Einstein's relativity is an inconsistency (it predicts that stationary clocks run both faster and slower than moving clocks) and should be immediately discarded:
W.H. Newton-Smith, THE RATIONALITY OF SCIENCE, 1981, p. 229: "A theory ought to be internally consistent. The grounds for including this factor are a priori. For given a realist construal of theories, our concern is with verisimilitude, and if a theory is inconsistent it will contain every sentence of the language, as the following simple argument shows. Let 'q' be an arbitrary sentence of the language and suppose that the theory is inconsistent. This means that we can derive the sentence 'p and not-p'. From this 'p' follows. And from 'p' it follows that 'p or q' (if 'p' is true then 'p or q' will be true no matter whether 'q' is true or not). Equally, it follows from 'p and not-p' that 'not-p'. But 'not-p' together with 'p or q' entails 'q'. Thus once we admit an inconsistency into our theory we have to admit everything. And no theory of verisimilitude would be acceptable that did not give the lowest degree of verisimilitude to a theory which contained each sentence of the theory's language and its negation."