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? 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.
