On Thu, Feb 27, 2014 at 6:43 PM, Edgar L. Owen <[email protected]> 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 <[email protected]> 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 who had done some acceleration, and another hypothetical >> worldline he would have had if he had not accelerated (this need not be >> purely hypothetical, you could imagine he had a twin who was moving >> alongside him before he accelerated, but continued to move inertially when >> he accelerated). And you're asking which event on the second inertial >> worldline lines up with some specific event on the worldline that >> experienced acceleration (like the event of his accelerometer first showing >> that he has stopped accelerating and is experiencing 0 G-force once again). >> It's impossible to answer that question in relativity without picking a >> specific frame with a specific definition of simultaneity, which allows us >> to match up the event on the non-inertial worldline with some specific >> event on the inertial worldline, and then calculate the age on the inertial >> worldline at that event. >> >> >> >> >> >> So I have to disregard all those comments because they don't apply to >> PROPER TIMES OR ACTUAL AGES. Proper time is ONLY one's reading of one's own >> clock, NOT one's own clock viewed from some other frame. >> >> Correct? >> >> >> Incorrect. It's true that proper time is ONLY one's reading of one's own >> clock, but only at some specific named event on one's worldline (like >> passing a marker), and one's own clock reading at that event can be >> calculated from the perspective of ANY frame, there is absolutely no need >> to use one's comoving frame to calculate it. >> >> >> >> >> Now a very basic question. Do you agree or disagree that all PROPER TIMES >> run at the same rate unless some effect causes them to run at different >> rates? Again this is NOT how clocks appear to run in any other frames but >> their OWN. >> >> >> >> Are you DEFINING the "rate" that proper time "runs" in terms of the rate >> of a clock in its own frame? And are you talking only about clocks that >> move inertially in flat SR spacetime free from gravity, so that "own frame" >> just means the clocks' own inertial rest frame? PLEASE ANSWER THESE >> QUESTIONS YES OR NO. If "yes" to both then I agree with your statement, if >> "no" then I can't make sense of your statement as written, since as I said >> there is no frame-independent definition of "clock rate" in relativity, and >> there is no convention telling us which coordinate system is meant by the >> phrase "own frame" if you aren't talking about an inertial clock in SR >> spacetime. >> >> Jesse >> >> >> >> >> >> >> >> >> >> On Thursday, February 27, 2014 3:07:41 PM UTC-5, jessem wrote: >> >> >> >> On Thu, Feb 27, 2014 at 2:38 PM, Edgar L. Owen <[email protected]> wrote: >> >> Jesse, >> >> First the answer to your question at the end of your post. >> >> Yes, of course I agree. Again that's just standard relativity theory. >> However as you point out by CONVENTION it means "the observer's comoving >> inertial frame" which is the way I was using it. >> >> >> Thanks, it seemed like you might have been suggesting there was some >> "natural" truth to calculations done in the comoving frame of two >> obserervers at rest relative to each other, even though they c >> >> ... > > -- > 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. > -- You received this message because you are subscribed to the Google Groups "Everything List" group. 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