Forgive me if this was already done but I would like to clarify the experiment. Let's assume a covered bridge with two sliding doors. The bridge is 10 m in length. There is also a car 12 m in length. The front sliding door is closed and the car drives onto the bridge until the front almost touches the door and stops. The driver of the car and the bridge operator both agree that the back of the car sticks out 2 m at the rear. They propose an experiment. The driver will drive through the bridge at near the speed of light. When the front of the car is almost at the front door the bridge operator will quickly close and then open the front door. And when the back the car is just inside the bridge he will do the same with the rear door. They complete the experiment and compare notes.
The bridge guy says that when he was about to close the front door he noticed that the rear of the car has already passed the rear door, so he opened and closed both doors at the same time. The driver disagrees. He sped up to the front door and saw it close and then open. He noticed in his rear view mirror that that back door was still open and the car still outside the bridge. As he sped through the front door (now open again) he notice the rear of the car moving past the rear gate, which then opened and closed behind him. To resolve the APPARENT paradox they have to account for length contraction and time dilation. The doors opened and closed simultaneously in the garage operator's frame but not the driver's Dirk On Monday, January 13, 2025 at 12:10:04 PM UTC-8 Brent Meeker wrote: > > > > On 1/12/2025 11:01 PM, Alan Grayson wrote: > > > > On Sunday, January 12, 2025 at 6:53:35 PM UTC-7 Brent Meeker wrote: > > That's a rather different paradox and of course the answer is nothing > would happen to the object. The mass increase and length contraction are > only *relative*: as measured by the observer the object is moving > relative to. > > Brent > > It's often stated that the transformed event, usually denoted as the > Primed Frame, is what is actually measured in the primed frame, such as the > E and B fields in E&M. But here is an example something NOT measured in > the primed frame, another is length. So it's hard to consistently interpret > what the LT does. AG > > > Motion is only relative. The same object at the same time has different > velocity relative to many other objects. It can't collapse into black hole > relative to one and not another. In it's own reference frame it must be > unaffected by inertial motion. In 2 dimensions here's the Lorentz > transformation of points I used in the garage/car paradox: > > (defun lorentz-2d (v) > "Returns a function that takes a point (t,x) and > returns the transformed point (t',x')" > (lambda (p) > (let ((t0 (car p)) > (x0 (cadr p)) > (g (gama v))) > (list (* g (+ t0 (* v x0))) ;; this is v*x0/c^2 where c=1 > (* g (+ x0 (* v t0))))))) > > > Brent > -- 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/503e96ba-ba77-4b8d-abcb-89443eef89b9n%40googlegroups.com.
