On Fri, Dec 6, 2024 at 1:13 PM Jesse Mazer <[email protected]> wrote:
*> When you say there is never a contradiction, do you deny we can pick > values for the rest length of the car and garage and their relative > velocity such if we use the Lorentz transformation, we find that B happens > before A in the car rest frame (so the car doesn't fit in that frame), but > A happens before B in the garage rest frame (so the car does fit in that > frame)? Or do you accept that point, but think there is some other way to > define the notion of "fits in the garage" that doesn't involve questions of > simultaneity?* *Two observers, such as the car driver and the garage man, would say the car fits in the garage if and only if they see that both doors on the garage are closed and simultaneously see that both the front and the back of the car are entirely in the garage. They both agree that there is a time when the front of the car is in the garage, and they both agree there is a time when the back of the car is in the garage, and they both agreed there was a time when both doors on the garage were closed, but they may disagree if there was ever a time when those 3 events occurred simultaneously.* *The faster the car goes the greater their disagreement about the length of the car and of the garage, and the greater their disagreement about the time when both doors were closed, and that resolves the logical contradiction. There is never an occasion when one observer sees the car crash into the back of the garage while the other observer does not. * *John K Clark See what's on my new list at Extropolis <https://groups.google.com/g/extropolis>* weq > > On Fri, Dec 6, 2024 at 7:45 AM John Clark <[email protected]> wrote: > >> On Fri, Dec 6, 2024 at 12:10 AM Alan Grayson <[email protected]> >> wrote: >> >> *>> from the garage man's POV the garage's length does not shrink but the >>> car's length does. In Special Relativity time is diluted by the factor γ >>> which is equal to 1 / √(1 - v²/c²) ; and an object's length will be >>> reduced by a factor of the inverse of γ. So Length contraction reduces the >>> length by 1/γ, and Time Dilation increases the time interval by γ. For >>> example, at 87% the speed of light length contracts to half its original >>> rest length, and time dilutes by a factor of two.* >>> *The bottom line is that when two observers are in relative motion, like >>> the garage man and the car driver are, they measure space and time >>> differently. An event has a position and a time, and the closing of both >>> garage doors is an event, so they will not agree if that event happened >>> simultaneously when the entire car was in the garage or not.* >>> >>> >>> >> >>> *> I don't think your proposed solution works. We're assuming the rest >>> frame length of the car is larger than the rest frame length of the garage.* >>> >> >> >> *As Jesse Mazer points out, if the car fits in the car driver's frame of >> reference then it always fits in the garage man's frame of reference. >> However if it doesn't fit in the garage men's frame of reference then it >> won't fit in the driver's frame of reference either; this can happen if the >> car is not going fast enough, and the asymmetry between the two viewpoints >> occurs because when the car driver and the garage man and the car and the >> garage are all in the same frame of reference (a.k.a. they are not moving >> with respect to each other) then they both agree that the car is longer >> than the garage. So there is never a contradiction, there is never an >> occasion where one of them predicts the car will fit in the garage and the >> other predicts it will not. * >> > > -- 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/CAJPayv3OPM1fawP6QA4daH3M3XWHKa6kqpbFd4ccEPkHg-k_aA%40mail.gmail.com.
