Jesse, With regards to your contention in your first paragraph below it may express the correct view of frame DEPENDENT simultaneity, but that is NOT the point I'm making. I'll try to explain more clearly. This example is revised to attempt to conform with your previous objections so please bear with me. I'll keep it short...
Take twins who start and finish a trip with the same proper ages. Define their trips as symmetric in the sense they both experience exactly equivalent proper accelerations at the exact same moments by their own proper clocks. (This is a new definition of symmetric.) This is why their ages must be the same when they meet. Now first I still maintain that in this case it is simple logic to conclude that there is a 1:1 correlation of their proper times during the trip, but I think we can now do better than that. Take the beginnings and ends of every phase of their acceleration changes, beginning with the start of the trip, as event markers. Now you, yourself, tell us that the proper times between every one of these markers is invariant. Now the question is whether these two invariant proper time sequences are synchronized or not. Whether there is a 1:1 correlation of proper times as each twin passes through these event markers that are defined identically in terms of each twin's proper acceleration? You point out that from the POV of all arbitrary frames they won't be, BUT the point is we MUST use a frame that MAINTAINS the real and actual symmetry to determine the ACTUAL REALITY of this situation. In any frame that PRESERVES that symmetry the observer WILL conclude that the proper times of both twins between all markers will be exactly the same, and thus the proper times of the twins at every one of these symmetric markers will be equal. Thus we do have a natural 1:1 correlation between the proper times of the twins that is also consistent with the direct observational agreement of proper times at start and finish, which we must account for in any accurate analysis. So my point is that there is a REAL AND ACTUAL SYMMETRY between the trips of the twins, and thus to get an accurate view of that real symmetry we must analyze it in a frame that preserves that symmetry. And when we do this we DO achieve a 1:1 correlation of proper ages during the trip, which must obviously be correct if they are to meet with the same ages. My whole approach depends on recognizing the difference between what is REALLY HAPPENING to someone as opposed to how any other observer may VIEW what is happening to that OTHER person. It is always what is actually happening to someone that is the reality irrespective of other's VIEWS of that reality. You consistently present the correct relativistic analysis of relativistic VIEWS without recognizing there is an ACTUAL REALITY involved that can be properly analyzed only by frames that recognize and preserve that reality. Do you agree that if we choose a frame that preserves the real and actual symmetry of the trip that we do get EQUAL proper times between all markers on the twins respective trips? And thus that we CAN establish a 1:1 correlation of proper times in this case? Edgar On Thursday, February 27, 2014 7:11:08 PM UTC-5, jessem wrote: > > > > On Thu, Feb 27, 2014 at 6:43 PM, Edgar L. Owen <edga...@att.net<javascript:> > > wrote: > > Jesse, > > My understanding of the first part of your reply is though proper time is > "ONLY one's reading of one's own clock" (as I stated) it IS possible for > any other observer to calculate that proper time and always come up with > the same answer. Is that correct? > > > For a given clock C, it is possible for any observer to calculate the > proper time between events ON C'S OWN WORLDLINE, and everyone will get the > same answer (it is frame-invariant). But what is NOT frame-invariant is the > answer to a question like "what is the proper time on that distant clock > RIGHT NOW, at the same moment that my own clock shows some specific time > T"--in that case you aren't talking about a specific event on C's > worldline, you're talking about a specific event on your worldline (the > event of your clock showing time T), and asking which event on C's > worldline is simultaneous with that. Since simultaneity is frame-dependent > in relativity, there is no frame-invariant answer to this second type of > question. > > > > > If so that's precisely what I've been claiming all along! That it's always > possible for any observer to calculate any other observer's PROPER TIME. > Why did I get the strong impression you were claiming that wasn't so from > your previous replies? That is precisely the whole crux of my case, and > precisely what I've been claiming.... > > In my view that is exactly what is necessary to establish a 1:1 > correlation between proper times. If everyone can always calculate > everyone's proper times including their own in an UNAMBIGUOUS INVARIANT WAY > then why isn't it possible to establish a 1:1 correlation between them? > Please give me a clear and simple proof that it's not.... > > > > By "unambiguous invariant way", which of these do you mean? > > 1. If they all agree to use a particular reference frame to define > frame-dependent things like simultaneity and velocity, then they can agree > on which proper times on each worldline are simultaneous, giving a 1:1 > correlation. > > 2. They have a way to define a 1:1 correlation between proper times that > does NOT depend on agreeing to use any particular reference frame. > > Please tell me whether you would select 1 or 2 (or some third option that > is somehow different than either one). > > > > > > I'm not sure whether it's necessarily relevant here but note that the > "event markers" that define proper ages are already actual physical > worldline event points defined by the earth's orbit and rotation. > > > > But we have been discussing scenarios involving observers zipping around > in space, so events on Earth would not be at the same point in spacetime as > events on their own worldlines. > > > > So the very definition of a proper age is already IN TERMS OF worldline > markers. We don't have to specify new markers to make things work. Proper > time is ALREADY NECESSARILY defined in terms of event markers such as > physical clock ticks. We don't need any new ones. > > > I agree that clock ticks can count as "markers", but sometimes you're > dealing with problems where you want to calculate what a clock reading at a > point on some observer's worldline will be without knowing it in advance. > If you have a network of coordinate clocks, you can also use readings on > coordinate clocks at the moment the traveling observer passes right next to > them as event markers, and ask questions like "what is this observer's > proper time at a coordinate time of t, i.e. at the moment the coordinate > clock he's right next to at that moment reads t". > > > > > Do you also agree that proper time RATES are calculable by other observers > and invarian? Not just the times, but the rates as well? > > > No, there is no frame-invariant notion of "clock rate" in relativity. The > only way to talk about rates is to look at the rate a clock is ticking > relative to coordinate time in some coordinate system, and obviously this > can differ from one coordinate system to another. > > Jesse > > > > > > > > On Thursday, February 27, 2014 4:49:17 PM UTC-5, jessem wrote: > > > > On Thu, Feb 27, 2014 at 4:05 PM, Edgar L. Owen <edga...@att.net> wrote: > > Jesse, > > Remember we are talking ONLY about PROPER TIMES, or actual ages. These DO > NOT HAVE any MEANING IN OTHER FRAMES than that of the actual frame of the > observer in question. > > > No, you couldn't be more wrong about that last statement. Any physics > textbook will tell you that the proper time between two events on a > worldline is a frame-independent quantity that can be calculated in ANY > frame, in fact this is one of the most important frame-independent > quantities in both special and general relativity (for example, in general > relativity the curvature of spacetime is defined in terms of the "metric" > which gives proper time along all possible timelike worldlines in the > spacetime, and proper distance along all possible spacelike worldlines). > > A simple example: say in Alice's rest frame, there are two markers at rest > in this frame 20 light-years apart, and Bob moves inertially from one > marker to the other a velocity of 0.8c in this frame. What is the proper > time on Bob's worldline between passing the first marker and passing the > second? In Alice's frame we could calculate this by first noting it should > take 20/0.8 = 25 years of coordinate time in this frame for Bob to get from > one to the other, and then the time dilation equation tells us that if he's > moving at 0.8c his clock should be slowed by a factor of sqrt(1 - 0.8^2) = > 0.6 in this frame, so Bob's own clock should tick forward by 25*0.6 = 15 > years between passing the first marker and the second. That is BOB'S PROPER > TIME, AS CALCULATED IN ALICE'S REST FRAME. > > You could of course calculate the proper time in Bob's rest frame too. In > this case, you have to take into account length contraction--the markers > are moving at 0.8c relative to Bob's frame, so if the distance between them > was 20 light-years in their own rest frame, in Bob's frame the distance > between them is shortened by a factor of sqrt(1 - 0.8^2) = 0.6, so in Bob's > frame the second marker is 20*0.6 = 12 light-years away at the moment he is > passing the first marker. Thus, if the second marker is moving towards him > at 0.8c, it will take 12/0.8 = 15 years of coordinate time in this frame to > reach him after the first marker passed him. And since he is at rest in > this frame, his clock ticks at the same rate as coordinate time, so his > clock should also tick foward by 15 years between passing the first marker > and passing the second. That is BOB's PROPER TIME, AS CALCULATED IN BOB'S > REST FRAME, and you can see that we get exactly the same answer as when we > calculated his proper time using Alice's rest frame. > > After looking over this example, please tell me if you AGREE or DISAGREE > that in relativity the proper time between two specific events on a > worldline can be calculated using any frame we wish (in the manner above), > and we'll always get the same answer regardless of what frame we use. > > > > So your comments that an observer's age will be measured differently in > other frames, while obviously true, is NOT the observer's PROPER AGE or > PROPER TIME. Every observer has one and only one proper age, that is his > proper age to himself, NOT to anyone else, not in any other frame. > > > Every observer has a proper age at any specific event on their worldine, > like the event of Bob passing one of the markers in my example above. But > this proper age is not associated with any particular frame, it's a > frame-independent quantity that can be calculated in whatever frame you > wish, and no matter what frame you use to perform the calculations you'll > always get exactly the same answer. > > > > That holds for all your comments about age effects of acceleration being > different in different frames. Of course they can be but that is NOT PROPER > ACTUAL AGE. > > > But you are not pointing to a specific event on his worldline and asking > his proper age at that point, you are asking what his age *would* have been > if he hadn't accelerated. This involves looking at TWO worldlines--one of > the actual person wh > > ... -- 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. 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