Minkowski/Twin Paradox: Examining an Objection to STR

[mrbeddow]

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...)

 

[mrbeddow]

*edit* I believe the commentary on this problem would consist of something like, "Well, this is all well and good but it's not taking into consideration the fact of STR's inconsideration of the possibility of traveling beyond the speed of light. STR is, as all theories are, susceptible to breaking down with more and more specific or far too general instances of it's application. So really, it is just speaking to what STR takes into account tongue-in-cheek."

 

[turin]

You need to focus on what SR says and what SR does not say; that is the basic flaw in the objection (which is the most common flaw in any objection to SR).

SR does not discount anything "tongue-in-cheek".

 

[Janus]

I would say that the problem is in the statement:

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”),

This ties in with what turin said. Does SR actually make this prediction?

 

[turin]

I didn't think that we were supposed to give solutions. Oh well.