On Mon, Oct 28, 2024 at 7:26 PM Alan Grayson <[email protected]> wrote:
*>> ME: The garage is 9 feet deep and has doors on the front and back that > can be closed and locked, but the car is 10 feet long so apparently it can > never fit in the garage. However from the point of view of somebody > standing still next to the garage the car is moving so fast that, due to > Lorentz contraction, the car is now only 8 feet long. And to prove that the > contraction is real and not just an optical illusion, as soon as the back > of the car has fully entered the garage the man quickly closes and locks > the front of the garage, at that exact instant from the garage man's point > of view, the car is in the garage AND simultaneously it is between BOTH of > two closed and locked doors. The man then quickly runs to the back of the > garage and unlocks and opens the back door which allows the card to > continue on at nearly the speed of light. So there is no paradox. **But > how would this look from the driver of the car's point of view? He would > see the car as being stationary and therefore 10 feet long, but the garage > is moving so fast due to Lorentz contraction the garage is now only 8 feet > deep not 9, and apparently making things even worse. However, what the car > driver sees is that as soon as the front of the car enters the garage the > garage man runs around to the back and opens the back door of the garage. > From the car driver's point of view at NO time is the car > simultaneously between BOTH of two closed and locked doors. So there is no > paradox, although the car driver and the garage man do not agree what is > "simultaneous" and what is not.* > * <https://groups.google.com/g/extropolis>* > > > > *> Two doors. Doors locked and then unlocked. Or whatever. You seem to > have an inclination for overly complicated analyses. Why not just say the > car driver knows the length of his car because he can simultaneously > measure its endpoints, * > *The car driver knows the length of his car because he knows what the speed of light is and he sent 2 intense but very short bursts of light to mirrors placed at the front and back of his car; the driver used the time he observed on his wristwatch, which in physics is called "Proper Time", to determine how long it took him to see the beams reflected in the mirrors. "Proper Time" may be poorly named, it's not really "proper", it's not the one true time, it's just the time measured by a clock that is stationary relative to an observer.* *The car driver used a similar method to determine how deep the garage was. He also used his wristwatch to determine if things happen at the same time or not. The garage man used the exact same method to determine the length of the car and the depth of the garage EXCEPT that he used his "proper time", the time the garage man saw on his wristwatch, which was different from the car driver's "proper time". * > * > In the garage frame, the car's length cannot be measured due to a > breakdown in simultaneity. So this observer hasn't a valid opinion whether > or not the car will fit inside.* > *If the garage man knew Special Relativity then he WOULD have a valid opinion, the car WILL fit inside the garage. And if he didn't know Special Relativity but actually performed the experiment then he wouldn't need Einstein, he would have enough information to derive Special Relativity for himself, in fact he'd have to if he didn't want to live with a logical paradox. * *> So, in this analysis the paradox is solved, and the car won't fit inside > the garage. **What do you find insufficient about this analysis? AG**c* *The thing that makes your analysis unsatisfactory is that it contradicts experimental results, if the garage man followed your line of thought he would conclude that the car could never fit inside his garage, but when he actually performed the experiment he found that he was wrong, the car COULD fit inside his garage with both doors closed. * * John K Clark See what's on my new list at Extropolis <https://groups.google.com/g/extropolis>* dbc -- 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/CAJPayv3PxPVAHPCaVuFczpOw%2BYGPA2sCaENRbQD4TaMX_E0TWQ%40mail.gmail.com.
