On Thu, Dec 12, 2024 at 4:55 PM Alan Grayson <[email protected]> wrote:
> > > On Thursday, December 12, 2024 at 2:45:17 PM UTC-7 Brent Meeker wrote: > > > > > On 12/12/2024 3:51 AM, Alan Grayson wrote: > > > > On Thursday, December 12, 2024 at 3:18:38 AM UTC-7 Alan Grayson wrote: > > On Thursday, December 12, 2024 at 3:08:37 AM UTC-7 Jesse Mazer wrote: > > On Thu, Dec 12, 2024 at 2:28 AM Alan Grayson <[email protected]> wrote: > > > > On Wednesday, December 11, 2024 at 11:44:11 PM UTC-7 Jesse Mazer wrote: > > On Thu, Dec 12, 2024 at 1:02 AM Alan Grayson <[email protected]> wrote: > > On Tuesday, December 10, 2024 at 11:15:16 PM UTC-7 Brent Meeker wrote: > > Do I not only have provide a diagram I also have to explain it in detail > just to end this silly thread?? > > First note by comparing the two diagrams that the car is longer than the > garage, 12' vs 10'. So the car doesn't fit at small relative speed. What > does "fit" mean? It means that the event of the front of the car > coinciding with the right-hand end of the garage is after or at the same > time as the rear of the car coinciding with the left-had end of the > garage. In both diagrams the car is moving to the right at 0.8c so > \gamma=sqrt{1-0.8^2}=0.6. Consequently, in the car's reference frame, the > garage is contracted to 6' length and when the rear of the car is just > entering the garage, the front is *simultaneously*, in the car's > reference frame, already 6' beyond the right-hand end of the garage. > > > > Then in the garage's reference frame the car's length is contracted to > 0.6*12'=7.2' so at the moment the front of the car coincides with the right > end of the garage, the rear of the car will simultaneously, in the garage > reference system, be 2.8' inside the garage as shown below. > > > *If the car is contracted in garage's reference frame, why is the car's > length plotted at its initial value of 12' If this issue is so silly, I'd > think your diagram wouldn't raise this question. AG * > > > The first diagram where the car has length 12 is showing the car's > reference frame, not the garage frame--the garage frame is the second > diagram. > > Jesse > > > *It says "GARAGE" so it must mean garage frame. AG * > > > Both diagrams say "garage" next to the red worldlines (the front and back > of the garage) and "car" next to the blue worldlines (the front and back of > the car), they are labels to tell you which worldlines belong to which > object. And in the first diagram you can see the blue worldlines > representing the car have position coordinates which don't change as you > vary the time coordinate (move up and down the graph vertically), so that's > the diagram representing the car rest frame. > > Jesse > > > *TY. I'll look at those diagrams again. Incidentally, I just posted my > solution to the alleged length contraction paradox. I can't prove it > because there's no test possible, but I'm confident I am correct. AG* > > > *Using Brent's parameters, the car will crash into the end door of the > garage because, with a gamma factor of .6, corresponding to v = .8c, the > length of the garage is reduced from 10' to 6', whereas the car's length is > reduced from 12' to 7.2', still longer than the length of the garage.* > > You've got them both moving at 0.8c in which case the car will not crash > into the door because it's not moving relative to the door. > > Brent > > > *In the car's frame, the garage is not moving but its length is contracted > to 6'. AG* > The car and garage have a relative speed of 0.8c, so naturally that means that in the car's rest frame, the garage is moving at 0.8c. You can directly see that in the first diagram where the garage worldlines are slanted rather than vertical (are you familiar with how plots of position vs. time work, where if time is the vertical axis than a vertical line represents an object at rest and a non-vertical line represents an object in motion, with its velocity corresponding to the slope of the line?) Jesse > * You can believe it for the same reason you believe that the distance to > Andromeda will be reduced by 40% for a traveler whose v = .8c. The reason > the contrary result seems plausible is quite subtle, and I will try to > address this subsequently, but it has to do with an asymmetry between the > frames of reference. 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