On Tue, Dec 24, 2024 at 3:22 PM Alan Grayson <[email protected]> wrote:
> > > On Tuesday, December 24, 2024 at 10:43:55 AM UTC-7 Jesse Mazer wrote: > > On Tue, Dec 24, 2024 at 6:13 AM Alan Grayson <[email protected]> wrote: > > On Tuesday, December 24, 2024 at 3:30:15 AM UTC-7 Alan Grayson wrote: > > On Tuesday, December 24, 2024 at 1:30:59 AM UTC-7 Alan Grayson wrote: > > On Tuesday, December 24, 2024 at 1:23:44 AM UTC-7 Brent Meeker wrote: > > On 12/23/2024 11:48 PM, Alan Grayson wrote: > > On Monday, December 23, 2024 at 11:03:36 PM UTC-7 Brent Meeker wrote: > > On 12/23/2024 9:36 PM, Alan Grayson wrote: > > On Monday, December 23, 2024 at 9:38:34 PM UTC-7 Alan > Grayson wrote: > > On Monday, December 23, 2024 at 9:33:36 PM UTC-7 > Brent Meeker wrote: > > All you have to do is solve for the speed at which the Lorentz contraction > is 10/12 so that the car is ten feet long in the garage frame. > > Brent > > > I know that. What I don't know is which question you're allegedly > answering. AG > > More important question; didn't you deny my claim that for a sufficient > velocity the car either fits or doesn't fit, as an objective fact that the > paradox seems to deny? AG > > If I was thinking clearly I did. An objective fact is not reference frame > dependent. > > Brent > > Obviously, you guys can only speak in riddles, > > If you would ever solve one the riddles you might learn something. > Telling you answer just leads to your saying you're not convinced and > around it goes. > > so I have to assume you can't answer the underlying question; > > Or you might assume you just too dumb or stubborn to learn the answer. > > Brent > > > You have no answer, just some plots pretending to be an answer. Just > riddles upon riddles. AG > > > Why I don't believe the gurus here have the answer; you'll note how easy > it is to pose the question, and how easy it is to offer a proposed > solution; namely, the disagreement about simultaneity. But that's obviously > not enough. As Quentin's behavior exemplifies; the mere statement of the > solution is hardly sufficient. One then needs an ARGUMENT connecting the > alleged solution, to the construction of the problem; that is, the paradox. > But Quentin is totally UNAWARE of this requirement, which his link fails to > provide, and then he's perfectly satisfied with accusing me as a troll. > You, Brent, allege the solution in your plots, which I admit I fail to see > the connecting argument just alluded to. But if you really understood the > solution, and pride yourself in your teaching skills of relativity, you > could offer a text solution, which should be a relatively short paragraph. > But that remains wanting. AG > > > Reviewing how time transforms using the LT, it does appear that for a > perfectly fitting car for which its time parameter is identical at its end > points, time does NOT transform to identical time parameters of the car's > end points in the car frame, since in the garage frame the spatial > parameter of the end points differ in the transformation equation. I'm not > entirely certain, but I think this establishes the disagreement concerning > simultaneity between the frames. Now, to resolve the paradox, requires an > ARGUMENT to, in effect, DECONSTRUCT the claim of a paradox depending on > this disagreement. AG > > > The argument is that both frames agree on all the local physical facts at > the front of the car as it reaches the back of the garage--in my example > they both agree that the physical clock at rest relative to the car there > reads -15 and the physical clock at rest relative to the garage there reads > 0. Their only disagreement is the *convention* they each use about which > physical clock to treat as canonical for the purpose of assigning an > abstract time-coordinate to that location in spacetime. > > > *What convention are you referring to? Einstein uses the same clocks in > each frame, which are synchronized at rest, and then go out of synch when > motion is initiated. He never refers to different clocks.* > Are you talking about the 1905 paper? He does in that paper imagine originally creating two rigid measuring systems at rest with each other and then imparting a velocity to one relative to the previous rest state (in section 3 starting at https://einsteinpapers.press.princeton.edu/vol2-trans/160 ), but this notion of them starting at rest relative to one another isn't an essential part of his argument, you could equally well imagine two rigid measuring systems that have been moving relative to each other forever (or at least for the whole duration we are considering in the problem), and he dispenses with this notion in other works where he discusses two measuring systems in relative motion (like the section of his book Relativity: The Special and General Theory at https://philosophie.ens.fr/IMG/EGS%20Einstein%20relativity%208-9.pdf ). And although both systems are equipped with the same *types* of clocks, they are not literally sharing the same individual clocks--there are some clocks at rest relative to the first rigid system, and a different set of clocks at rest relative to the second system. Finally, he doesn't imagine syncing the clocks beforehand and then seeing them "naturally" go out-of-sync when one system is imparted a velocity relative to the first, instead he talks about synchronizing each system's own clocks using his light-signal method *after* he talks about giving them a relative velocity, on the page at https://einsteinpapers.press.princeton.edu/vol2-trans/160 where he writes: "The origin of one of the two systems (k) shall now be imparted a (constant) velocity v in the direction of increasing x of the other system (K), which is at rest, and this velocity shall also be imparted to the coordinate axes, the corresponding measuring rod, and the clocks. ... Further, by means of the the clocks at rest in the system at rest and using light signals in the manner described in §1, the time t of the system at rest is determined for all its points where there is a clock; likewise, the time tau of the moving system is determined for all the points of the moving system having clocks that are at rest relative to this system, applying the method of light signals described in §1 between the points containing these clocks." > * And the LT has both clocks, whatever they might be, in its > transformation equations, namely t and t'. I've never seen of any choice > about which physical clock is treated as canonical. * > Yes, but in terms of physical clock readings, all frames agree that *both* of those readings t and t' are seen on clocks from different measuring systems that are passing through the region of the event in question, with the different measuring systems and their clocks having a relative velocity. Each frame simply *defines* the time coordinate of an event by the reading on the single clock at that location that is at rest in that frame, not by any of the other clocks that are in motion in that frame--that's all I mean by treating one clock as canonical. Trust me as someone who studied this stuff that this is the standard understanding of how inertial coordinate systems are defined physically, and that it's understood that the section of Einstein's original 1905 SR paper I quoted above is talking about this idea, whether or not you've ever seen it. > *Any clock seems satisfactory. But even if your argument holds, it's not > obvious how this would DECONSTRUCT the argument that the car fits in the > garage in one frame, but not in the other. AG* > It doesn't! It deconstructs the idea that this constitutes a paradox in the sense of contrary predictions about objective reality, once you realize that in relativity "objective reality" consists only of local physical facts, and that frames can disagree on the order of events (and thus on whether the car fits) without the slightest disagreement about any local physical facts. > > Once one realizes that they agree about all local physical facts at each > point in spacetime, > > > *Is measured time the same in both frames? Of course not. Does this mean > measured time is NOT a physical fact which is frame dependent? AG* > I referred not just to a "physical fact" but to an *objective* physical fact, i.e. one that doesn't depend on human conventions (as an analogy, if you choose a position for the origin of a spatial coordinate system and the orientation of your coordinate axes, there may then be a fact about the x-coordinate of some physical object in this system, but it depends on your conventional choice of how to position our coordinate system so it isn't an objective fact in my sense, for example if another physicist wasn't informed about our choice, we'd have no reason to expect them to independently arrive at the same coordinate system, and thus no reason to expect them to assign the same x-coordinate to that physical object). Measured time between events is not an objective fact in this sense (unless you are talking about proper time between two events along a specific timelike worldline that goes through both, but this can only make sense for events with a time-like rather than a space-like separation), it depends on which clocks you *choose* to use to assign coordinate time. 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/CAPCWU3LfGcqMmeVuDyJBWAoNBxVQES8bZdKUUsvBitrrorSgwA%40mail.gmail.com.
