Jesse, A simple example:
Suppose A and B. Assume no relative motion but A is in a gravitational well that makes his clock runs 1/2 the speed of B's clock. Assume both clocks were synchronized when the gravitational field at A suddenly turned on. In this simple case both A and B were in the same present moment prior to the gravitational field turning on and both their clocks t and t' read time=0 when it turned on. After the field turns on then whenever tx2 = t' then A and B will be in the same moment of p-time. Note that will be ALL the time, because all observers are always at the same moment of p-time. But it is simple to determine what A and B were doing at all past moments of p-time by this method. This simple example will at least illustrate the method which can be applied to all other relativistic calculations. Note that all observers and everything is always at the same universal moment of p-time, so it's just a matter of figuring out what their various clock time t-values are or were at that synchrony. But from an observational test it's always simple to know what clock time of your comoving clock and all clocks in that same frame. All you have to do is look at the clocks and read them and whatever they read is always the clock time reading of the current moment of p-time, because everything always is in that moment. In fact it is only possible to read a clock IN the present moment, so you know that whatever clock you actually read, that is always the clock time of that clock that corresponds to the current p-time moment. Edgar On Saturday, February 8, 2014 5:28:08 PM UTC-5, jessem wrote: > > > > > On Sat, Feb 8, 2014 at 4:01 PM, Edgar L. Owen <[email protected]<javascript:> > > wrote: > > 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'. > > > And what if there *are* gravitational differences, if there are sources of > gravity nearby and they are at different points in space? Gravity is dealt > with using general relativity, and in general relativity there is no > coordinate-indepedent way to define the "relative motion" of observers at > different points in space (see discussion at > http://math.ucr.edu/home/baez/einstein/node2.html for details). And the > only coordinate-independent definition of "acceleration" is proper > acceleration (what an observer would measure with an accelerometer that > shows the G-forces they are experiencing), but all observers in freefall > have zero proper acceleration, so if you think there is a > "gravitational/acceleration difference" between an observer orbiting far > from a black hole and one falling towards it close to the event horizon, > you can't quantify it using proper time. > > > > > 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. > > > HOW would you "back calculate" it though? Even if we set aside my > questions about gravity above and just look at a case involving flat SR > spacetime, your answer gives no details. If you have any procedure in mind, > could you apply it to a simple example? Let's say Alice is sent on a ship > that moves away from Bob on Earth on the day they are both born, and the > ship moves with speed of 0.8c relative to the Earth, towards a planet 12 > light-years away in the Earth's frame. Alice arrives at that planet when > she is 9 years old, and at that point the ship immediately turns around and > heads back towards Earth with a relative speed of 0.6c. Alice experiences > the return journey to take 16 more years, so when she returns to Earth she > is 25 years old, but Bob is 35 years old when they meet. Can you show me > how to back-calculate how old Bob was when he was in the same moment of > p-time as Alice turning 9 and her ship reaching the planet and turning > around? > > > > 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. > > > I have never asked you for a p-time "value", I'm only interested in the > question of which events are simultaneous in p-time. I don't think your > answers so far have made it clear that you have any well-defined procedure > for determining this, see my questions above. > > Jesse > > > > > 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]> 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. > > Therefo > > ... -- 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.
