On Monday, October 28, 2024 at 5:26:45 PM UTC-6 Alan Grayson wrote: On Monday, October 28, 2024 at 12:01:33 PM UTC-6 John Clark wrote:
On Mon, Oct 28, 2024 at 9:19 AM Alan Grayson <[email protected]> wrote: *> The link just says that the apparent paradox is resolved by a breakdown in simultaneity, but doesn't specify exactly what that means. I notice that an apparent paradox can be defined for length contraction, whereas I was trying to resolve it for time dilation, but so far I cannot define the problem with clarity. Do you have any suggestion in this regard? AG* *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, and due to contraction of the garage's length, he knows his car won't fit inside. 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. 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* My analysis above is incorrect. Without analyzing simultaneity, the frames *disagree* on whether the car will fit in the garage. From the frame of the car, its length remains what it is, but if traveling fast enough, the garage length is seen as smaller than the car, and it *won't fit* inside. OTOH, from the pov of the garage frame, the length of the garage is unchanged, but the car shrinks small enough if going sufficiently fast, and the car *will fit* inside the garage. So, I will re-read JC's analysis, and expect that when simultaneity is properly analyzed, both frames *will agree* on the outcome and the paradox is no more. AG *ca* -- 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/21f1df1b-9ca8-4435-8f5a-179208c4f969n%40googlegroups.com.
