On Wed, Dec 18, 2024 at 2:07 AM Alan Grayson <[email protected]> wrote:
> > > On Tuesday, December 17, 2024 at 11:11:11 PM UTC-7 Jesse Mazer wrote: > > On Tue, Dec 17, 2024 at 11:34 PM Alan Grayson <[email protected]> wrote: > > On Tuesday, December 17, 2024 at 9:05:09 PM UTC-7 Jesse Mazer wrote: > > On Tue, Dec 17, 2024 at 10:52 PM Alan Grayson <[email protected]> wrote: > > On Tuesday, December 17, 2024 at 6:57:28 PM UTC-7 Alan Grayson wrote: > > I > > On Tuesday, December 17, 2024 at 2:33:46 PM UTC-7 Brent Meeker wrote: > > On 12/17/2024 9:25 AM, Alan Grayson wrote: > > > Yes, you look at it just in terms of lengths, which is what I did in the > first pair of diagrams. But the relativity of simultaneity is another > way to look at the same problem, which is what I showed in my last posting. > > > *Another way, but not the only way. AG * > > > We seem to be on the same page concerning use of length contraction to > explain the > differing results in the frames under consideration. But I remain unclear > how the > disagreement of simultaneity can also give the same results. For example, > suppose > from the pov of the garage frame, the car fits in the garage for > sufficient v, with room > to spare, but the front and rear end EVENTS do not Lorentz transform into > simultaneous > events in the car frame. Can't there be other ways for the car to fit, > using another set > of events which* are* simultaneous in the car frame? AG > > > For any pair of events on the worldlines of the front and back of the car > which are simultaneous in the car frame, rhe distance between that pair of > events in the car frame is always 12. > > > OK, AG > > > And for any pair of events on the worldlines of the front and back of the > *garage* which are simultaneous in the car frame, the distance between that > pair of events in the car frame is always 6. > > > Don't follow. AG > > > Can you say more about what you don't follow about this comment? Given the > two garage worldlines, we can find pairs of events along those two > worldlines that are simultaneous in the car frame, no? (just draw a > horizontal line in the first of Brent's diagrams, which was drawn from the > POV of the car frame, and the points where your horizontal line intersects > the two slanted red garage worldlines will be such a pair) Is that the part > you don't follow, or do you not follow why the distance between any such > pair would be 6 in the car frame? > > Jesse > > > Truthfully, I don't follow these arguments using worldlines > Can you try to be specific about what aspect of it you find hard to follow? First of all, do you feel you have a good grasp of plots of position vs. time in classical physics, where there is no disagreement about simultaneity or time or distance intervals, or do you need a refresher on the classical graphs before trying to follow the relativistic ones? Do you understand for example why if we had a classical graph with various lines or curves representing the worldlines of objects, with time on the vertical axis and position on the horizontal axis, then if we wanted to know the position of all the objects at a particular time, that would involve drawing a horizontal line of fixed time coordinate (a classical line of simultaneity, which doesn't change from one frame to another) and seeing where the horizontal line intersects with the worldlines of the objects? but what I can say is that it's more or less uniformly assumed in the > physics community, that the problem is solved, whatever the problem is -- > and now I'm not sure! -- by the claim that simultaneous events in one > frame, are not simultaneous in the other -- the frames being the car and > garage frames. Now, in Brent's recent plots, he seems to show, or believe, > that when the car fits perfectly, from the pov of the garage frame due to > contraction of the car, that the front and back events ARE simultaneous in > the car frame. So, if what I've written is correct, why does the consensus > opinion conclude that the problem's solution depends on something which > isn't true; namely, an alleged disagreement about simultaneity? AG > Are you saying you think Brent's plots contradict the idea that frames disagree about simultaneity? If so you are misunderstanding something important here--in Brent's plots, if you look at the particular pair of that are simultaneous in the garage frame where the car fits, those same events are *not* simultaneous in the car frame, although in the car frame you can find a *different* pair of events that are simultaneous. Which post and/or plot of Brent's were you referring to? Also do you understand that an "event" is always located at a specific position and time coordinate on a given plot, and to see where that same event lies on the other plot, you have to use the Lorentz transformation? Like if a little firecracker went off at position x and t in the first frame, in the second frame the event of the firecracker going off would have to be plotted at x'=gamma*(x-vt) and t'=gamma*(t-vx/c^2). > Finally, since using length contraction and Brent's initial conditions of > the lengths of the car and garage as 12' and 10' respectively, is there any > objection to the conclusion that from the car's frame, it never fits in the > garage, and if so, is there any paradox implied that the frames disagree on > whether the car will fit, or not, in the garage? AG > In an imaginary alternative physics where different frames had no disagreement about simultaneity but different observers still all believed the length contraction equation should apply in their frame, then this would be a genuine paradox/physical contradiction, because different frames would end up making different predictions about local events. Think about it this way--if there were no disagreement about simultaneity, there could be no disagreement about the *order* of any two events (this would be the case even if observers predicted moving clocks run slow like in relativity). But if observer #1 thinks the car is shorter than the garage, he will predict the event A (the back of the car passing the front of the garage) happens before event B (the front of the car reaches the back of the garage), and if observer #2 thinks the car is longer than the garage, he will predict B happens before A. If there were no disagreement about simultaneity this would lead them to different predictions about readings on synchronized clocks at the front and back of the car/garage at the moment of those events, specifically whether the clock at A would show a greater or lesser time than the clock at B. 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/59086494-1deb-497e-94a0-e8ec74fd9fb8n%40googlegroups.com > <https://groups.google.com/d/msgid/everything-list/59086494-1deb-497e-94a0-e8ec74fd9fb8n%40googlegroups.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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