On Tue, Dec 24, 2024 at 12:12 AM Alan Grayson <[email protected]> wrote:
> > > On Monday, December 23, 2024 at 3:04:58 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 * > > | - In both frames, set the origin of our coordinate system to be the > point where the back of the car passes the front of the garage--then that > point will have coordinates x = 0 and t = 0 in the garage frame, x' = 0 and > t' = 0 in the car frame. > > *OK.* > > --In the garage frame, at t = 0 the front of the car is at the same > position as the back of the garage, at position x = 20, so that's the > position and time of the event of the front of the car passing the back of > the garage in the garage frame. > > > *OK. * > > --In the car frame, at t' = 0 the back of the garage must be at x' = > 16 (since we know the front of the garage is at position x' = 0 at time > t'=0, and using Lorentz contraction in the car frame we know the garage > has length 16 in this frame), and the front of the car is at rest at x' = > 25, so a distance of 25-16 = 9 from the back of the garage, which in this > frame has already passed the front of the car at that moment. > > ? > > > You agreed above that in the car frame, the front of the garage was at > position x' = 0 at time t' = 0, yes? And you also agreed that in the car > frame, the garage has length 16, yes? So why would you have any doubt that > if the front end of the garage is at position x' = 0 at time t' = 0 in the > car frame, then the back end must be at position x' = 16 at the same time > t' = 0 in the car frame? That's just what "length" in a given frame means, > the distance between the two ends of an object at a single moment in time > in that frame. To put it another way, if this was just a classical 1D > problem and I told you a rod had length 16 and at t' = 0 the front end was > at position x' = 0, and it was moving in the -x direction, would you have > any doubt the back end would be at x' = 16 at the same moment? > > Or do you agree that this is straightforward, but have questions about why > the front of the car would be at rest at x' = 25 (this also seems > straightforward since you agreed its back end is at x' = 0 and its length > is 25)? Or why, granted the back end of the garage is at x' = 16 and the > front end of the car is at x' = 25 at this moment, the distance between > them at this moment must be 9? > > > *In the car's rest frame, the back end of garage is at x' = 16, but in the > garage's rest frame, front of car is x = 25 (not x'), so you can't subtract > apples from oranges. AG * > No, the car's rest length is 25, so that's its length in the *car's* rest frame, by definition. Since the back of the car is at rest at x' = 0 in this frame, the front must be at rest at x' = 25 in this frame. Meanwhile the car is moving at 0.6c in the garage's rest frame so its length is Lorentz-contracted down to 25/1.25 = 20, meaning at t = 0 the front of the car is at x = 20 in the garage's rest frame. 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/CAPCWU3LNurWevxoxd%2BxtMJfmqeDwwJxxidPQ42f-b%3D%3DnsG3Vxw%40mail.gmail.com.
