On Monday, December 23, 2024 at 9:06:31 PM UTC-7 Jesse Mazer wrote: On Mon, Dec 23, 2024 at 8:55 PM Alan Grayson <[email protected]> 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. This isn't really a matter of opinion, just standard terminology; in physics books (in classical mechanics as well as relativity) you will only ever see "rest frame" defined relative to specific objects, and you will never see any reference to "the" rest frame without it being defined relative to such an object, nor is the phrase "isn't moving" understood as meaningful unless you add something like "isn't moving relative to [some other frame or object]". Please don't make up your own terminology, *I'm definitely NOT doing that. Rather, that's how the frame names have been used throughout this discussion by members of this MB. AG* it'll just confuse things unnecessarily. Finally, note that nowhere in either my or Brent's formulations was it stated that the car initially was at rest relative to the garage, for the purposes of the problem you can assume the two have been in relative motion since a time of -infinity in both frames. You're also free to assume the car has been floating in space without accelerating for eternity and the garage accelerated to get close to it before coasting inertially, it should make no difference to the analysis of subsequent events (earlier when we were discussing the twin paradox you agreed that any acceleration prior to the period of time we are analyzing should make no difference). 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, x, t are not configurations of matter and energy in a local region, are they? That is the only definition of local event or physical fact I have been using. If you want to use x to refer to a marking on a specific physical ruler, and t to refer to a reading on a specific physical clock, then you have to specify the details about them in the problem (what they are at rest relative to, how the clock was synchronized, etc.), as I did when I introduced rulers and clocks into the problem. But normally x and t just refer to coordinate labels for events. 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? Fitting/not fitting not a local event by the definition I gave you (can you define 'fitting' in a way that refers only to configurations of matter and energy in the neighborhood of individual points in spacetime?), so if one takes the view that only local physical facts are the "objective reality", then this obviously doesn't qualify. 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/9fcf34c0-177e-4fba-b749-14ac3e52b594n%40googlegroups.com.
