Jesse, No, they do NOT have the same time coordinates in their respective frames because their clocks read different t-values. You simply cannot invent any frame that makes the actual difference in their ages go away. All you are doing is trying to ignore the effect by assigning a new arbitrary time to the meeting. That's fine but they are still really different ages so in that sense they can never actually be at the same clock time except by an arbitrary definition which ignores the fact of the trip and thus refuses to address the whole point of the trip.
Edgar On Friday, February 7, 2014 9:09:51 PM UTC-5, jessem wrote: > > > On Fri, Feb 7, 2014 at 3:24 PM, Edgar L. Owen <edga...@att.net<javascript:> > > wrote: > > Jesse, > > If as you say, the ""same point in time" in relativity just MEANS that > two events are assigned the same time coordinate" then the twins are NOT at > the same point in time because the two events of their meeting have > different time coordinates in their coordinate systems. > > > Huh? No they don't. If a given pair of events A and B have exactly the > same coordinates (both space and time coordinates) as one another in one > coordinate system, then A and B must have the same coordinates as one > another in EVERY coordinate system. Of course the actual value of the > shared time coordinate will differ from one coordinate system to another > (since this depends on things like where you arbitrarily set the origin of > your coordinate system), but 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), or are you just pointing out that the > shared time-coordinate is different in different systems, or that the > shared time-coordinate will not match the clock time for both of them? > > Incidentally, to speak of "their" coordinate systems is ambiguous since > they are not both inertial. Although physicists sometimes refer to the > inertial rest frame of an observer as "their own frame" or similar words > (though even this is purely a matter of convention, nothing stops a given > observer from assigning coordinates to events using a coordinate system in > which they are *not* at rest), there is no "standard" way to construct a > coordinate system for a non-inertial observers, there are an infinite > number of different coordinate systems they could use (even if you restrict > them to using a coordinate system where they remain at a constant position > coordinate, and where the time coordinate matches their own proper time). > > > > > That's the whole point of needing a separate present moment to account for > that. You can't just arbitrarily set a new clock time for the meeting and > ignore the actual clock time difference in ages.... > > > The *definition* of "same time" in relativity depends only on the > coordinate time, not the clock time of any particular clock which is not a > coordinate clock. So given this definition, yes you can ignore their own > clock times, because it isn't relevant. If your point is just "I don't like > this definition because it's different from how I would prefer to define > things" that's fine, but you can't claim that this way of speaking is > ill-defined or *internally* contradictory. > > > > > When measuring tapes cross with different readings they do cross at the > same point in space. > > > Yes, and that means if the point where they cross is the 30-cm mark on > tape #1 and the 40-cm mark on tape #2, then no matter what x-y coordinate > system you use to label different points on the surface where the tapes are > laid out, the 30-cm mark of tape #1 will have the same y-coordinate as the > 40-cm mark of tape #2 (and likewise for the x-coordinate). > > > > When twins with different clock times meet they meet at the same point in > time. > > > Yes, and that means that if twin #1 is turning 30 at the point in > spacetime where they meet, and twin #2 is turning 40 at that point, then no > matter what x-y-z-t coordinate system you use to label different points in > spacetime, the event of twin #1 turning 30 will have the same t-coordinate > as the event of twin #2 turning 40 (and likewise for the spatial > coordinates x,y,z). > > > > > It is NOT the same point in CLOCK time unless you redefine it as so by > imposing another coordinate system on it that ignores the fact of the trip. > > > > That's like saying "the point where the tapes cross is NOT the same point > in MEASURING TAPE space unless you redefine it as so by imposing another > coordinate system on it that ignores the fact of their paths in space." > > > > > But this is cheating because you ignore the real actual clock time > difference of the ages which don't go away. > > > That's like saying "but this is cheating because you ignore the real > actual measuring-tape difference of the position-markers which don't go > away." > > > > > The difference is that the tapes cross arbitrarily. > > > What makes their crossing "arbitrary"? To flesh this out a bit, I'm > imagining flexible cloth measuring tapes that can be used to measure length > along curving paths, not just straight-line ones. And 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. > > > > > The correct time analogy would be that the twins could start out with > UNsynchronized clocks. > > > Not with the modification above, saying that at the first point where the > tapes diverge from a common point, their markings at that point are > identical. > > > > > > 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. > > > > Likewise, the different in *intervals* measured along each tape between > the two crossing-points is real and absolute, regardless of what markings > the tapes "originally" had at the first crossing-point. But to make things > simpler, I'm assuming they both have the same marking at that first > crossing-point. > > So your tape analogy doesn't address the problem. Only a common present > moment does. > > > See above, I think the tape example is a spatial analogy to the twin > example where every measurable fact about the twins has an analogue with > the tape. It's even possible to define a spatial analogue of time dilation, > and of integrating the time dilation as a function of coordinate time in > order to find the total elapsed aging of each twin when they reunite...but > detailing the spatial analogue would take some time so I'll only go into it > if you think it would actually help you understand how relativity can be > understood in a goemetric manner. > > Jesse > > > > > > On Friday, February 7, 2014 12:51:32 PM UTC-5, jessem wrote: > > > > > On Fri, Feb 7, 2014 at 12:27 PM, Edgar L. Owen <edga...@att.net> wrote: > > Jesse, > > Well you just avoid most of my points and logic. > > > Can you itemize the specific points you think I'm avoiding? > > > > But yes, I agree with your operational definition analysis. That is > EXACTLY my point. That what our agreed operational definitions define is a > COMMON PRESENT MOMENT, and NOT a same point in spacetime, because the logic > of it does not support it being in the same point in space, only in the > same point of time > > > Huh? Even if one accepts p-time, that "operational definition" still must > be seen as a merely *approximate* way of defining the same point of p-time, > not exact, just like with "same point in space" or "same point in > spacetime". If I bounce some light off you, surely you agree that the event > of it reflecting off you occurred at a slightly earlier point in p-time > that the event of reaching my eyes (or instruments)? Likewise if I feel our > palms meet in a handshake, I don't actually begin to feel it until a > slightly later moment of p-time than the moment our palms first made > physical contact, and likewise for any shift or movement you might make > with your hands. If you want to talk in a non-approximate way, all our > experiences are slightly delayed impressions of events that occured in the > past, regardless of whether we're talking about p-time or coordinate time. > > On this subject, could you address the question I asked in another post > about whether you think there's any empirical way to determine whether two > events in the past occurred at the same p-time, or whether the assumption > of p-time simultaneity is a purely metaphysical one and that there's no way > of knowing whether a specific pair of events we have records of actually > > ... -- You received this message because you are subscribed to the Google Groups "Everything List" group. 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