On Thu, Feb 27, 2014 at 2:38 PM, Edgar L. Owen <edgaro...@att.net> 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 disagree on the amount that a clock slowed down (or sped up) after a given proper acceleration, I can give you a numerical example. > > Another way to approach this is do you deny that if we drop a coordinate > grid on an area of EMPTY space that the coordinate clocks at the grid > intersections all run at the same rate? And if not, why? > Are you talking about an inertial coordinate grid of rigid rulers, or an arbitrary non-inertial coordinate grid where we can imagine different grid points connected by rubbery rulers that can stretch and compress over time? In the simpler case of an inertial grid, obviously all inertial coordinate clocks tick at the same rate relative to any other inertial coordinate system, though not necessarily relative to an arbitrary non-inertial system. And the clocks of an arbitrary non-inertial coordinate system need not tick at a constant rate relative to inertial systems. > And don't start making up other frames on me here. Just compare the proper > times of those coordinate clocks. Do they all run at the same rate or not? > > Since the whole question is whether the notion of "rate" is frame-dependent or frame-independent, you're ducking the whole issue if you refuse consider "other frames". I have always agreed that relative to any SINGLE frame, you can make definite statements about the rates of different clocks relative to one another, but since your conclusions will differ depending on what frame you pick, this tells us jack squat about what the rates are relative to an absolute "moving present", even if such a thing exists. Jesse > > > > > On Thursday, February 27, 2014 11:56:08 AM UTC-5, jessem wrote: >> >> >> >> On Thu, Feb 27, 2014 at 9:25 AM, Edgar L. Owen <edga...@att.net> wrote: >> >> Jesse, >> >> I haven't answered those questions out of any disrespect or rudeness but >> because I was working on a new explanation which I think does specifically >> address and answer all of them which I present in this post. I will be >> happy to answer any of your questions if you think they are still relevant >> after reading this post which I think solves the 1:1 age correlation to >> your satisfaction. >> >> >> That's the problem, you continually come up with new arguments and >> explanations that you think resolve the questions I asked and therefore >> mean you don't need to address them, but inevitably I disagree. Please just >> respect my judgment about what's relevant TO ME, and answer the questions >> that I ask ALONGSIDE any new arguments or explanations you might want to >> supply. You say above "I will be happy to answer any of your questions if >> you think they are still relevant after reading this post", so I will hold >> you to that by repeating a question I'd like you to answer at the end of >> this post. >> >> >> >> >> >> If you find any of the terminology confusing please let me know what you >> think it SHOULD be rather than just saying it's wrong. >> >> Twins A and B start at the same location in deep space. No acceleration, >> no gravitation. Their ages are obviously the same, and their age clocks are >> running at the same rate. >> >> They exchange flight plans and embark on their separate trips according >> to those flight plans. >> >> Now the only effects that will alter the rates of their age clocks are >> acceleration or gravitation. But each twin can continually measure the >> amount of acceleration or gravitation he experiences with a scale. >> >> >> >> Let's consider just the issue of accelerations in flat SR spacetime for >> now, since it's simpler. The problem with this statement is that although >> it's true each twin can measure their proper acceleration, there is no >> FRAME-INDEPENDENT equation in relativity for how a given acceleration >> affects the "rates of their age clocks", the only equations dealing with >> clock rates and acceleration in SR deal with how changes in coordinate >> velocity (determined by acceleration) affect the rate a clock is ticking >> relative to coordinate time in some specific coordinate system. >> >> >> >> So each twin can always calculate how much his age has slowed relative to >> what his age WOULD HAVE BEEN had he NOT experienced any gravitation or >> acceleration. Let's call that his 'inertial age', the age he WOULD have >> been had he NOT experienced any acceleration or gravitation. >> >> >> >> I see no way to define this in any frame-independent way. The only >> version of this that relativity would allow you to calculate is what your >> age would have been at a PARTICULAR COORDINATE TIME if you had remained >> inertial, and you can compare that to what your age is at that SAME >> COORDINATE TIME given your acceleration history. But this comparison >> obviously gives different results in different coordinate systems. So, I >> don't agree with your subsequent conclusion that this allows two twins to >> define a 1:1 correlation in their ages in a frame-independent way. >> >> There are a number of questions I asked in the last few posts that none >> of your answers have addressed, but I'll restrict myself to repeating one >> for now: >> >> 'Also, do you understand that even for inertial observers, the idea that >> an observer's own rest frame can be labeled "his view" or taken to describe >> "his observations" is PURELY A MATTER OF CONVENTION, not something that is >> forced on us by the laws of nature? Physicists just don't want to have to >> write out "in the observer's comoving inertial frame" all the time, so they >> just adopt a linguistic convention that lets them write simpler things like >> "from this observer's perspective" or "in his frame" as a shorthand for the >> observer's comoving inertial frame. Physically there is no reason an >> observer can't assign coordinates to events using rulers and clocks that >> are moving relative to himself though, lots of real-world experiments >> involve measuring-instruments that move relative to the people carrying out >> the experiment.' >> >> Do you agree with the above paragraph? >> >> Jesse >> >> >> >> </d >> >> ... > > -- > 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. > To post to this group, send email to everything-list@googlegroups.com. > 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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