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 could equally >> well agree to calculate things from the perspective of a totally different >> frame. >> >> >> Now to your replies to my post beginning with your first paragraph. >> >> Certainly there are equations that do what you say they do, but I don't >> see why what I say isn't correct based on that. Why do you claim it is >> impossible to just take proper acceleration and calculate what my age would >> have been if there was not any proper acceleration? >> >> >> I don't claim it's impossible, just that it can only be done relative to >> a particular frame. I can make statements like "I am now 30, but in frame >> A, if I hadn't accelerated I would now be 20" and "I am now 30, but in >> frame B, if I hadn't accelerated I would now be 25". >> >> >> >> An observer knows what his proper acceleration is, and he knows how much >> various accelerations are slowing his proper time relative to what it would >> be if those accelerations didn't happen. >> >> >> "Slowing his proper time" only has meaning relative to a particular >> frame, there is no frame-independent sense in which clocks slow down (or >> speed up) due to acceleration in relativity. >> >> >> >> He has a frame independent measure of acceleration. He knows that >> particular acceleration will slow his proper time by 1/2 so he can define >> and calculate an 'inertial time' whose rate is 2x his proper rate. >> >> >> Given the exact same proper acceleration, there may be one frame A where >> at the end of the acceleration his clock has slowed by 1/2 (relative to the >> time coordinate of that frame), and another frame B where it has slowed by >> 1/3, and even another frame where it has *sped up* by a factor of 10. Do >> you disagree? >> >> >> >> You seem to think it would be necessary to MEASURE THIS FROM SOME FRAME >> for the concept to be true. It's not an observable measure, it's the >> CALCULATION of a useful variable. Therefore there is NO requirement that >> it's measurable in any frame because it's a frame independent concept, a >> calculation rather than an observable. >> >> >> Calculations are always calculations of the values of particular >> numerical quantities, like the "rate" a clock is ticking. So, what matters >> is whether the quantity in question is frame-dependent (like velocity, or >> rate of clock ticking) or frame-independent (like proper time at a specific >> event on someone's worldine), there is nothing inherent in the notion of >> "calculations" that make them frame-independent. >> >> Also, *all* calculated quantities in relativity can also be >> "observables"--it's straightforward to observe frame-independent quantities >> like proper time (just look at the clock the observer carries), and >> frame-dependent ones can also be "observed" if you have a physical grid of >> rulers and coordinate clocks as I have described before (for example, to >> find the "rate" a clock is ticking relative to a coordinate system, you >> look at the time T1 it reads as it passes next to a coordinate clock that >> reads t1, and the time T2 it reads as it passes next to another coordinate >> clock that reads t2, and then you can just define the average rate over >> that interval as [T2 - T1]/[t2 - t1], and if the difference between T2 and >> T1 approaches 0 this approaches the *instantaneous* rate at T1). >> >> >> >> >> Therefore I don't see any reason to accept your criticism in this >> paragraph. If you disagree, which I'm sure you will, then explain why this >> concept of inertial time is not frame independent and valid. Perhaps a >> clear example would help? >> >> >> >> If you disagree with my statement above that different frames can disagre >> ... > > -- > 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. 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]. 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