Jesse, Yes, I think there is always a way to determine if any two events happen at the same point in p-time or not, provided you know everything about their relativistic conditions.
You do this by essentially computing their relativistic cases BACKWARDS to determine which point in each of their worldlines occurred at the same p-time. Take 2 observers, A and B. 1. If there is no relative motion or gravitational/acceleration differences you know that every point t in A's CLOCK time was in the same present moment as every point t' in B's CLOCK TIME when t=t'. So we know that whenever there are no relativistic effects between any A and B that we just use their synchonized clocks to determine they are in the same current moment of p-time. 2. In the case of the twins after they meet up again with A's age =30 and B's age =40. A: There are no more relativistic effects after the meeting so we know they are now in the same current point in p-time. B: We can back calculate that they were in a previous same point in p-time when their synchronized clocks and ages were still identical, i.e. from their birth to the start of the trip. 3. In the case of twins DURING the trip in relative motion we can always back calculate the relativistic effects to make a statement of the form "the twins were in the same current moment of p-time when A read his own clock as A-t and B's clock as B-t, AND B read his own clock as B-t' and read A's clock as A-t'. In this case A-t will NOT = A-t', and B-t will NOT = B-t', but they will have specific back calculable t values for every current p-time during the trip. Thus if we have all the details of that trip's motion we should always be able to back calculate to determine which clock times of any two observers occurred in the same current p-time SIMULTANEITY even when those observers cannot agree on CLOCK time simultaneity among themselves. So since p-time has no metric itself you can't just compare p-time t values because there are none. You have to back calculate clock times to determine in what current p-times they occurred. So that's how we determine whether any two events occurred a the same p-times or not. You should always be able to determine that even though you can assign a p-time t value because there are none because p-time doesn't have a metric. Edgar 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 <[email protected]<javascript:> > > 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 <[email protected]> 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 compari > > ... -- You received this message because you are subscribed to the Google Groups "Everything List" group. 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