- #1
mrbeddow
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2. Consider the following objection to STR: “Since time-dilation and length-contraction are reciprocal, STR actually contradicts the frame-invariance of physical age differences, that is, the plain physical facts. For instance, so there can be no ambiguity about “age comparisons”, let us replace “Bob” and “Bubba” in Kosso’s version of the twin paradox (“Mitch’s Paradox”) by identical masses of a radioactive substance, call them respectively “Pile1” and “Pile2”, always at rest with respect to one another, and let us replace “Richard” with a third mass, “Pile3”, moving at a constant velocity v relative to piles 1 and 2 (in the positive x direction) and passing Pile 1 (event A) before Pile 2 (event B). Assume that at event A Piles 1 and 3 have exactly the same number of undecayed particles left (they are the same age, an invariant physical fact). Then at event B, STR says both that Pile 3 has more particles left than Pile 2 (i.e. Pile 3 is “younger”) and, by reciprocity, that Pile 2 has more particles left than Pile 3 (i.e. Pile 3 is “older”), which is absurd. Thus, however useful STR may be in predicting experimental results, it cannot be conceptually coherent.”
(a) Set up a minkowski space-time diagram (with one spatial dimension) indicating the world lines and sample simultaneity lines of the three piles and showing events A and B. Do this, however, by taking Pile 2 as at rest in the “stationary frame” of the diagram.
(b) Comment on the above objection to STR. (1-2 pp)
(I'm afraid I have no attempt at a solution because I am not exactly sure what Mitch's paradox, or, rather, the "Twins Paradox" entails. Otherwise, I can handle representing this with a Minkowski diagram...I think...I am a philosophy major...)
(a) Set up a minkowski space-time diagram (with one spatial dimension) indicating the world lines and sample simultaneity lines of the three piles and showing events A and B. Do this, however, by taking Pile 2 as at rest in the “stationary frame” of the diagram.
(b) Comment on the above objection to STR. (1-2 pp)
(I'm afraid I have no attempt at a solution because I am not exactly sure what Mitch's paradox, or, rather, the "Twins Paradox" entails. Otherwise, I can handle representing this with a Minkowski diagram...I think...I am a philosophy major...)