On Mon, Dec 23, 2024 at 10:07 PM Alan Grayson <[email protected]> wrote:
> > > On Monday, December 23, 2024 at 6:54:57 PM UTC-7 Alan Grayson wrote: > > On Monday, December 23, 2024 at 4:09:38 PM UTC-7 Jesse Mazer wrote: > > On Mon, Dec 23, 2024 at 4:10 PM Alan Grayson <[email protected]> wrote: > > On Sunday, December 22, 2024 at 10:05:54 PM UTC-7 Jesse Mazer wrote: > > BTW, since you seem to be interested in a scenario where the car and > garage are exactly matched in length in the garage frame, something which > isn't true in Brent's scenario, here's a different scenario you could look > at, where I'm again using units where c=1, let's say nanoseconds for time > and light-nanoseconds (i.e. distance light travels in one nanosecond) for > distance. > > --Car's rest length is 25, garage's rest length is 20, car and garage have > a relative velocity of 0.6c, so gamma factor is 1/sqrt(1 - 0.6^2) = 1.25 > > > *OK. * > > > --In garage rest frame, garage has length 20 and car has length 25/1.25 = > 20. In the car rest frame, the garage has length 20/1.25 = 16 and the car > has length 25. > > > *OK, assuming car is moving, but I wouldn't call that "in the car rest > frame" since you have garage length as contracted. AG * > > > BTW I forgot to reply to this line since it was an overall "OK", but just > wanted to note that this is the standard meaning of "[object's] rest frame" > in physics--it refers to the inertial coordinate system where the object, > in this case the car, has position coordinates that don't change with > coordinate time, so the car is said to be "at rest" in this coordinate > system. It is the garage, not the car, that is moving in the car's rest > frame, since the garage's coordinate position does change with time in this > frame--this relative perspective on who is "moving" and who is "at rest" is > just as true in classical mechanics as in special relativity (though of > course there is no length contraction accompanying motion in classical > mechanics), see the discussion of Galilean relativity at > https://www.physicspace.com.ng/2018/09/galilean-relativity-2.html with > Galileo's own discussion of an observer below decks of a windowless ship > who has no way of knowing if the ship is at moving smoothly over the water > or at rest relative to it. If you don't understand this sort of basic > observation about classical mechanics in an inertial coordinate system > (along with other basic observations like the classical relation between > 'length' and coordinates of endpoints of an object, or classical relation > between 'velocity' and the way position coordinates of an object change > with coordinate time), that's something you really need to bone up on a > little before tackling relativity. > > Jesse > > > IMO, the rest frame is defined as the initial conditions in this problem > when the car isn't moving, and is longer than the garage. When the car is > moving, we have been calling the other two frames, simply the car frame and > the garage frame. About local events, if one measures x, t in one frame, > which presumably are local events, and then transform to x', t' in another > frame using the LT, are the primed values local event in your definition of > local? Finally, if disagreement about simultaneity is alleged to solve the > paradox, why did Brent deny my claim that there must be one objective > reality; namely, that the car can, or cannot, fit in the garage? Is the > paradox we're discussing rooted in this disagreement about local events? > TY, AG > > > For clarification purposes; when t is measured using the readings on a > clock, and transformed to t' via the LT, do you agree that these times have > nothing to do with coordinate times in spacetime (which are just labels)? > AG > Time coordinates are always assumed to be *derived* from physical clock readings, but as I've told you several times, if different frames each have their own set of synchronized clocks then there will be *multiple* clocks in the neighborhood of the same local event, and different frames make different choices of which clock to take as "canonical" for the purpose of defining their time coordinates. In the most recent numerical example I gave, in the neighborhood of the event of the front of the car passing the back of the garage there was a clock at rest in the garage frame reading 0, and a clock at rest in the car frame reading -15, and both frames agree on both these local physical facts; but the garage frame takes the clock at rest in that frame as canonical and so assigns this event a coordinate label of t = 0, while the car frame takes the clock at rest in that frame as canonical and so assigns this event a coordinate label of t' = -15. Jesse > -- > 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/0c55a38c-e8ef-4574-927c-45baa09d2344n%40googlegroups.com > <https://groups.google.com/d/msgid/everything-list/0c55a38c-e8ef-4574-927c-45baa09d2344n%40googlegroups.com?utm_medium=email&utm_source=footer> > . > -- 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/CAPCWU3KUCM7TVUTwENHg9pDVtG%3DyY7rmLyQi6BXU9z39bf%2Brgg%40mail.gmail.com.
