On Sun, Jan 19, 2025 at 5:04 PM Brent Meeker <[email protected]> wrote:
> > > > On 1/18/2025 8:54 PM, Jesse Mazer wrote: > > > > On Sat, Jan 18, 2025 at 8:58 PM Brent Meeker <[email protected]> > wrote: > >> >> >> >> On 1/18/2025 4:56 PM, Alan Grayson wrote: >> >> >> >> On Saturday, January 18, 2025 at 5:44:46 PM UTC-7 Brent Meeker wrote: >> >> >> >> >> On 1/18/2025 4:32 PM, Alan Grayson wrote: >> >> >> >> On Saturday, January 18, 2025 at 4:28:06 PM UTC-7 Brent Meeker wrote: >> >> >> >> >> On 1/18/2025 5:42 AM, Alan Grayson wrote: >> >> >> >> On Saturday, January 18, 2025 at 6:13:27 AM UTC-7 John Clark wrote: >> >> On Fri, Jan 17, 2025 at 1:41 PM Alan Grayson <[email protected]> wrote: >> >> *> IMO SR can handle curved spacetime. All one has to do is make the >> partitions very fine, so we're approximating inertial motion along very >> short paths. AG * >> >> >> *All one has to do? Well yes but that's easier said than done, it took >> Einstein 10 years of grueling work to figure out exactly how to do it, and >> the effort nearly killed him, he got sick, lost 50 pounds and figured he >> would die soon. Fortunately he did not. One of the most difficult things he >> had to figure out was how to measure distance in 4D non-Euclidean spacetime >> that was curved in any given way that was useful and never produced >> self-contradictory results. Mathematicians insist that distance must have >> the following properties:* >> >> >> >> >> *1) Non-negativity: d(x,y) ≥ 0 2) Identity of indiscernibles: d(x,y) = 0 >> if and only if x = y 3) Symmetry: d(x,y) = d(y,x) 4) Triangle inequality: >> d(x,z) ≤ d(x,y) + d(y,z)* >> >> *After years of false starts and dead ends Einstein eventually found a >> measuring stick that worked, it's called the Metric Tensor. * >> >> *John K Clark See what's on my new list at Extropolis >> <https://groups.google.com/g/extropolis>* >> >> >> Sorry to consume so much bandwidth here. I have one question about the LT >> and one about the Metric Tensor (MT) which will hopefully resolve most of >> my confusions. >> >> I'll pose the LT question in the context of the TP. If the stationary >> twin at rest on the Earth uses the LT to calculate the clock reading at >> some time on the traveling twin's clock, or its clock rate using two or >> more time readings, what relationship, if any, does this have on what the >> traveler twin's clock actually reads, >> >> Actually reads when? >> >> and what he observes as his clock rate? >> >> He observes his clock rate to be one second per second. >> >> >> *IOW, using the LT, the stationary twin knows precisely what the >> traveling twin will measure for his clock rate, but the traveling twin >> detects nothing. You gotta luv it. AG* >> >> >> >> *It's the same as length contraction, nobody ever measures time dilation >> with their own clock. Brent* >> >> >> *So the claim that the LT yields what the target frame -- in this case >> the frame of the traveling twin* >> >> That doesn't even parse. Frames doesn't measure anything. >> > > I assume you'd agree an inertial frame's coordinates are often defined in > intro textbooks in terms of local measurements on a system of rulers with > clocks attached to different markings, all mutually at rest (and with the > clocks synchronized in their rest frame using the Einstein convention), as > in the illustration at > http://www.upscale.utoronto.ca/GeneralInterest/Harrison/SpecRel/SpecRel.html#Exploring > -- even if such systems are not constructed in practice, this is a way to > conceive of an inertial frame's coordinates as physical "measurements" > which could be done in principle. And if we know the coordinates assigned > to events by the ruler/clock system corresponding to some frame A, and want > to know the coordinates that'd be assigned to the same events by a > ruler/clock system corresponding to some different frame B, we can just > apply the Lorentz transformation to the coordinates in A to get the right > answer for the coordinates in B--Alan's confusion here (one of them, > anyway) is that he thinks there are situations where the Lorentz > transformation would give the wrong answer, and it seems like he > misinterpreted your comment above as supporting that. > > When you said "nobody ever measures time dilation with their own clock", > did you mean that if there's a clock B in motion relative to me, I can't > measure its time dilation with a *single* clock A at rest relative to me? > > No I meant that one doesn't measure time dilation in their own frame. > It's always relative. > Do you just mean one doesn't measure any time dilation of a clock in that clock's own rest frame? I'd of course agree with that, but I was making the different point that an observer measuring a clock B in motion relative to themselves (using their own clocks at rest relative to themselves to measure it) can measure the time dilation of clock B in their frame, by comparing readings on B with readings on their own clocks as B passes by multiple clocks. And naturally this does not mean that B's time is dilated in any objective frame-independent sense, it's a frame-dependent measurement. > Personally I don't like to invoke ruler/clock systems. I think they muddy > explanations because they introduce simultaneity, *as measured in the > ruler/clock system*; while it's important to realize there is no physical > significance to "simultaneous" for spacelike events. > Sure, assigning coordinates in an inertial frame using such a ruler/clock system always depends on a purely conventional definition of simultaneity in that frame (the Einstein synchronization convention), but it would still be a type of physical measurement (and other measurements of frame-dependent quantities, like velocity, also depend on conventions). Alan seems to interpret you as making a broader claim that the coordinates obtained by the Lorentz transform can't be assigned meaning in terms of any kind of physical measurement whatsoever, but I assume that's not what you're saying. Jesse > But to clarify for Alan, presumably you'd agree I could in principle > measure the time dilation of clock B in my frame with local measurements on > a system of multiple clocks of the kind I mentioned, which are all at rest > relative to me and pre-synchronized by the Einstein convention? > > Jesse > -- > 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 view this discussion visit > https://groups.google.com/d/msgid/everything-list/CAPCWU3JhKnYMTDjMn%2B44kBTuSnbDKXVJep8Tkxu4D4YOHwt_SQ%40mail.gmail.com > <https://groups.google.com/d/msgid/everything-list/CAPCWU3JhKnYMTDjMn%2B44kBTuSnbDKXVJep8Tkxu4D4YOHwt_SQ%40mail.gmail.com?utm_medium=email&utm_source=footer> > . > > > -- > 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 view this discussion visit > https://groups.google.com/d/msgid/everything-list/a1730360-b733-4ba5-9268-e166876ba274%40gmail.com > <https://groups.google.com/d/msgid/everything-list/a1730360-b733-4ba5-9268-e166876ba274%40gmail.com?utm_medium=email&utm_source=footer> > . > -- You received this message because you are subscribed to the Google Groups "Everything List" group. 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