On 1/12/2025 8:38 AM, Alan Grayson wrote:
That's the sort of question that gets you a troll reputation. The events are clearly labelled and the axes have time and position variables. If you can't read the diagram you won't understand a written explanation any better.On Saturday, January 11, 2025 at 8:48:21 PM UTC-7 Brent Meeker wrote: On 1/10/2025 11:29 AM, John Clark wrote:On Fri, Jan 10, 2025 at 2:15 PM Alan Grayson <agrays...@gmail.com> wrote: />>>If I believe in SR, then I can use length contraction to establish the car won't fit in garage in car's frame./ *>> That depends entirely on what you mean by"the car won't fit inthe garage". In the above I've told you exactly what I mean by the term. What do you mean? * /> What do I mean; what any sane person would mean; that the car's length is fixed from the pov of the car's frame when car is moving, but the garage's length is shortened from an initial condition where it starts out shorter. AG / *That's all very nice but that's not what I asked. What _exactly_ do you mean by "the car won't fit in the garage" if it's not "the front of the car is fully within the garage while _SIMULTANEOUSLY_ the back of the car is also fully within the garage"?*I think you meant "the car *will *fit in the garage." But there's been so much unproductive back and forth on this thread, which I thought I had put to bed, that I'm going to try again and to make everything even more graphic and explicit. Here's the spacetime diagram in the reference frame of the garage (which we would ordinarily refer to a stationary): * *Here we see that the car, whose proper length is 10', traveling at 0.8c is Lorentz contracted to a little over 6'. We start with the entrance open and the exit closed and we see that we can close the entrance door before we have to open the exit door because there is a brief period in which the car is fully within the 8' garage, the red trapezoid. If the distances are in feet then the times are in nano-seconds. So the exit door can stay closed for about 2.5 nano-seconds after the entrance door closes, as measured in the garage reference frame. For those 2.5 nano-seconds the car is fully inside the garage. Now consider that same events in the car's frame of reference. Keep in mind the technical meaning of "event" is a point in spacetime, not a "happening" as in casual parlance. So points in the above diagram, like "FRONT ENTERS" are events and the Lorentz transformation preserves events but it in general changes their spacetime relation. Here is the Lorentz transformation, point-by-point, of the above diagram. The two diagrams are physically identical; differing only in being viewed from different states of motion: Specifically in this case the time order of "REAR ENTERS" and "FRONT EXITS" is reversed. This is typical of space-like separated events: their order is different in different reference frames. So from the car's point of view there is a period of about 7 nano-seconds during which both doors are open and so the car sails thru without hitting a door.* *BrentWhen you write the time order of events is reversed, presumably in the car frame, does this mean the rear of the car enters the garage before the front enters (which is physically impossible)? If not, what do you mean? AG
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