Jesse, The crux of my answer to the crossed tapes question was that yes that would be true of clock time but not for p-time. Again you are using the question to argue against clock time simultaneity. And I agree with that 100%. It's just not p-time...
Edgar On Sunday, February 9, 2014 2:22:20 PM UTC-5, jessem wrote: > > > > On Sun, Feb 9, 2014 at 1:21 PM, Edgar L. Owen <[email protected]<javascript:> > > wrote: > >> Jesse, >> >> It's not clear to me what you mean by, "in every coordinate system the >> time-coordinate of A = the time-coordinate of B. Are you actually >> disagreeing with that (please answer clearly yes or no)". >> >> The way I understand that the answer is clearly NO. The whole idea of >> relativity is that the time coordinates (clock times) of A and B are NOT in >> general the same in either A nor B's coordinate systems, or any other >> coordinate system. >> > > I think I see where you are confused--the term "time coordinate" does NOT > in general mean the same thing as "clock times" in relativity, it only does > if the clock in question is a coordinate clock (part of a ruler/clock > system as I described), or happens to agree exactly with a coordinate clock > at the same point in spacetime. The time on a clock which isn't a > coordinate clock is referred to as a "proper time" for that clock, not a > "time coordinate". So with that clarification on the terminology used by > physicists, would you agree with my quoted statement above? > > >> >> And I did answer your crossing tapes example in detail showing how it is >> not relevant for p-time. I'm beginning to wonder if you actual read my >> posts... >> > > I asked for an answer to the specific question of whether there is any > quantitative feature of the twin paradox scenario that doesn't have a > quantitative analogue in the measuring tape scenario. Before the most > recent post of yours that I was responding to when I asked this question, > the only earlier posts of yours I can remember directly responding to the > issue of spatial analogies are the ones > http://www.mail-archive.com/[email protected]/msg48047.htmland > http://www.mail-archive.com/[email protected]/msg48049.html, > but both of them featured variation on the broad conceptual objection > that any spatial situation like cars on a road or wires in ice must > themselves exist in time, but I addressed this issue in my own post at > http://www.mail-archive.com/[email protected]/msg48058.htmlpointing > out that we could restrict ourselves to talking about spatial > features at a single moment in time, a point which you didn't respond to. > > In any case, a broad conceptual objection like "spatial scenarios always > exist in time" doesn't answer my question about whether there are any > particular quantitative features of the twin paradox scenario that don't > have particular quantitative spatial analogues in the measuring-tape > scenario. The only post I can think of where you made a stab at pointing to > such a particular quantitative aspect was in the post I was directly > responding to when I asked the question, the one at > http://www.mail-archive.com/[email protected]/msg48261.htmlwhere > you said "The clock readings are arbitrary depending on how they were > originally set, just like the crossing point of the two tapes. But the > difference is ages is real and absolute." But I responded to this at > http://www.mail-archive.com/[email protected]/msg48294.html, > saying: > > "I'm imagining that they actually crossed once before, then took > different paths to their second crossing-point. At the first point where > they cross, let's imagine that both tapes have exactly the *same* marking > at that point, and after that they follow different paths until their paths > cross again. This corresponds to the fact that both twins have the same age > at the common point in spacetime that their paths diverge from, and then > different ages at the next common point in spacetime where they unite." > > You didn't respond to this. To spell the analogy out more clearly, the > twin's worldlines meet at two points, the first where they depart and their > clock readings are identical, the second where they reunite and their clock > readings are different. And even if they hadn't synchronized their clocks > initially, we could still point out that the total *elapsed* time on each > clock between meeting-points, i.e. [time-reading at second meeting] minus > [time-reading at first meeting], is different for each twin. This is how we > know there is a real physical difference in proper time (aging) along their > two paths through spacetime between the meetings. > > Likewise, the two measuring tapes cross at two points, the first where > their markings are identical, the second where their markings are > different. And even if we hadn't arranged things so the markings at the > first point were identical, we could still point out that the total > *elapsed* distance on each measuring tape between the two crossing-points, > i.e. [marking at second crossing] minus [marking at first crossing], is > different for each measuring tape. This is how we know their is a real > physical difference in path length along their two paths through the 2D > plane between the crossing-points. > > So you see, the quantitatively measurable features of the twin paradox > scenario described in the first of the two paragraphs above all have direct > analogues in the measuring tape scenario on the second paragraph. So, you > have not yet answered my question and pointed to a quantitatively > measurable feature of the twin paradox scenario which *doesn't* have an > analogue in the measuring tape scenario. Such a fact could involve clock > readings at particular events, elapsed aging/clock time between two events, > or coordinates assigned to events (for the last one, assume the measuring > tapes are laid out on a large sheet of graph paper with Cartesian > coordinates assigned to the corners of each square on the graph, so that we > can assign coordinates to any point along the measuring tape which can > differ from the reading on the tape itself at that point). If you think > there is one, please point it out; if you don't claim there is one, please > spell that out clearly. > > Jesse > -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. 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