On Fri, Feb 7, 2014 at 3:24 PM, Edgar L. Owen <edgaro...@att.net> 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 >> happened simultaneously in p-time? >> >> >> >>> and that same point in time is obviously not anything that relativity >>> predicts, because no matter what set of coordinates you choose, relativity >>> always gives 2 different real answers for the ages of the twins. >>> >> >> >> I don't know what part of this you're not understanding, "same point in >> time" in relativity just MEANS that two events are assigned the same time >> coordinate, relativity doesn't deal with any absolute notion of >> simultaneity of distant events whatsoever. And relativity definitely does >> predict situations where clocks show different readings at the same >> coordinate time--do you deny this? >> >> Like I said earlier, there is a direct spatial analogy here that makes >> perfect sense if you don't assume p-time from the start. If two different >> measuring tapes cross, and the point where they cross is at the 30 cm mark >> on one tape and the 40 cm mark on the other, and there's a Cartesian >> coordinate grid on the surface under them which says this point has an >> x-coordinate of 50, wouldn't you say that the measuring tapes DO cross at >> the "same point in space"? Would the fact that the tapes themselves show >> two different readings at that point negate this? >> >> As for your last paragraph you seem to agree that both our operational >>> definitions DO support the notion of a same present moment, just not that >>> time flows. >>> >> >> How do you figure? My last paragraph was just clarifying what I meant by >> arguments "dependent on conscious experience" vs. arguments defined in >> terms of straightforward experiments whose results we can all observe and >> agree on. Nowhere did I say anything in support of an absolute "same >> present moment". >> >> >> Jesse >> >> >> >> On Friday, February 7, 2014 8:49:32 AM UTC-5, jessem wrote: >>> >>> >>> On Fri, Feb 7, 2014 at 7:57 AM, Edgar L. Owen <edga...@att.net> wrote: >>> >>>> Jesse, >>>> >>>> OK, here's the detailed analysis of how I see the current state of this >>>> issue that I promised: >>>> >>>> >>>> A few points: >>>> >>>> 1. Since you asked let me repeat my 'operational definition' of the >>>> present moment that I used before. The twins meet, shake hands and compare >>>> watches. That is the operation definition. >>>> >>>> That is essentially the same as your reflected light operational >>>> definition with which I have no problem. >>>> >>>> 2. However it is important to note that that works not just for the >>>> twins together, but for every single twin by himself. Because any twin or >>>> observer can shake his own hand, look at his own watch, or note that the >>>> light reflected from a mirror in his hand takes minimal time to return. >>>> >>>> Therefore what is true for the twins together is also true for each >>>> twin separately, and is true for every observer in the universe as well. >>>> >>>> 3. So what is it that is true? You say it is "being at the same point >>>> in spacetime". Call that relationship R1. I use the term that everyone else >>>> does and has throughout history, namely "being in the (same) present >>>> moment". Call that relationship R2. >>>> >>>> >>>> So let's use a thought experiment to examine the difference between R1 >>>> and R2: >>>> >>>> Imagine a line of a billion twins. By both our definitions every two >>>> adjacent twins will be in what you call relationship R1 and I call R2. And >>>> this will be true of the adjacent twins on both sides of every twin. >>>> >>>> In your terminology every twin will be "at the same point of spacetime" >>>> with both the one to the right and to the left. >>>> >>>> In my terminology every twin will be "in the same present moment" with >>>> both the one to the right and to the left. >>>> >>>> Note that these relationships are transitive, so they necessarily >>>> cascade through the whole line of twins. What that means is that twin #1 >>>> must have that same relationship with twin #1 billion. >>>> >>>> But clearly it is NOT true that twin 1 is "at the same point in >>>> spacetime" as twin 1 billion because he not at the same point in space. >>>> However twin 1 can be in the same present moment as twin 1 billion, because >>>> that is just a time relationship that does not require a same space >>>> location. >>>> >>>> Thus our agreed operational definition leads to a contradiction with >>>> your terminology but not mine. >>>> >>> >>> Well, in my discussion I believe I alternated between two subtly >>> different definitions--one which said the light-signal-return-time actually >>> went to zero, and another which said that it was "negligible". The first >>> definition was an ideal theoretical description--and if the twins in your >>> thought-experiment were ideal point-like observers who could literally have >>> the time delay of light signals approach zero at the moment on each of >>> their clocks where they met, then you could have a billion of them meeting >>> in such a way and the fact of delay time approaching zero would really be >>> completely transitive. But the second definition was just an approximate >>> practical one. "Negligible" is obviously a fuzzy term which depends on how >>> precise your instruments are--if the twins are standing 0.3 meters apart >>> and they use the light test, a sufficiently sensitive instrument will >>> reveal it actually takes about 2 nanoseconds between emitting a light flash >>> and getting back the reflection. Likewise if they shake hands, sufficiently >>> good equipment would show a much larger delay between the moment their >>> hands touch and the moment the train of nerve impulses set off by the touch >>> reaches the brain (and the atoms of their hands don't really "touch", so >>> there would even be some sub-nanosecond delay between a motion in an atom >>> in the palm of one hand and its effect on the motion of an atom in the palm >>> of the other hand). For a normal experiment like the twin paradox, we won't >>> get any noticeably inaccurate results if we model them as meeting at the >>> same point in spacetime when sufficiently accurate measurements might show >>> them a light-nanosecond apart. But your row-of-twins scenario is obviously >>> constructed in a way where we'll get wrong conclusions if we treat >>> "negligible" the same as "zero", since if you stack up a bunch of zeros you >>> still always get zero, but if you stack up a bunch of "negligible, >>> unmeasurable" differences you eventually get a measurable difference. >>> >>> I'm sure you would run into the same problem if I asked you for a >>> practical operational definition of "same point in space"--any such >>> practical difference is going to ignore very small gaps that are too small >>> for our measuring-instruments to discern (or just aren't worth worrying >>> about in our calculations), but obviously if you stack up a sufficient >>> number of small things with small spatial gaps you may get an arbitrarily >>> large spatial distance between both ends of the stack. >>> >>> >>>> >>>> >>>> Now one final point: You criticize me for relying on "conscious >>>> experience" presumably when it comes to the twins shaking hands and >>>> comparing watches. >>>> >>> >>> No, when I talked about "conscious experience" I meant the vague >>> qualitative sense we have that time seems to "flow", that things seem to >>> come into existence (from our perspective at least) and go out of them. I >>> didn't mean the perceptions of well-defined experiments that anyone can >>> observe the result of from the outside without knowing anything about the >>> inner experience of the person performing it, like a comparison of watches >>> or a shaking of hands. >>> >>> 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 everything-li...@googlegroups.com. >> To post to this group, send email to everyth...@googlegroups.com. >> 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 everything-list+unsubscr...@googlegroups.com. > To post to this group, send email to everything-list@googlegroups.com. > 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. 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