On Sun, Feb 9, 2014 at 2:53 PM, Edgar L. Owen <[email protected]> wrote:
> 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... > But weren't you trying to use the twin paradox scenario to make an *argument* in favor of p-time, rather than just assuming it from the start? If so, then I'm wondering if the argument just involves pointing to some broad conceptual understanding of what happens in the twin paradox scenario, or if you think there are specific numerical facts that don't have any good interpretation under a purely "geometric" understanding of spacetime (like the fact that they can be at the "same point in spacetime" but have elapsed different ages since their previous meeting). If it's the latter, then it's reasonable to point out that these numerical facts have exact analogues in purely geometric facts about the measuring tapes (like the fact that the tapes can cross at the "same point in space" but have elapsed different tape-measure distances since their previous crossing). Jesse > > 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]> 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.html and >> http://www.mail-archive.com/everything-list@googlegroups. >> com/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/everything-list@googlegroups. >> com/msg48058.html pointing 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/everything-list@ >> googlegroups.com/msg48261.html where 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]. > To post to this group, send email to [email protected]. > Visit this group at http://groups.google.com/group/everything-list. > For more options, visit https://groups.google.com/groups/opt_out. > -- 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]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/groups/opt_out.
