On 12/12/2024 3:51 AM, Alan Grayson wrote:
On Thursday, December 12, 2024 at 3:18:38 AM UTC-7 Alan Grayson wrote:
On Thursday, December 12, 2024 at 3:08:37 AM UTC-7 Jesse Mazer wrote:
On Thu, Dec 12, 2024 at 2:28 AM Alan Grayson
<[email protected]> wrote:
On Wednesday, December 11, 2024 at 11:44:11 PM UTC-7 Jesse
Mazer wrote:
On Thu, Dec 12, 2024 at 1:02 AM Alan Grayson
<[email protected]> wrote:
On Tuesday, December 10, 2024 at 11:15:16 PM UTC-7
Brent Meeker wrote:
Do I not only have provide a diagram I also
have to explain it in detail just to end this
silly thread??
First note by comparing the two diagrams that
the car is longer than the garage, 12' vs
10'. So the car doesn't fit at small relative
speed. What does "fit" mean? It means that
the event of the front of the car coinciding
with the right-hand end of the garage is after
or at the same time as the rear of the car
coinciding with the left-had end of the
garage. In both diagrams the car is moving to
the right at 0.8c so \gamma=sqrt{1-0.8^2}=0.6.
Consequently, in the car's reference frame,
the garage is contracted to 6' length and when
the rear of the car is just entering the
garage, the front is /*simultaneously*/, in
the car's reference frame, already 6' beyond
the right-hand end of the garage.
Then in the garage's reference frame the car's
length is contracted to 0.6*12'=7.2' so at the
moment the front of the car coincides with the
right end of the garage, the rear of the car
will simultaneously, in the garage reference
system, be 2.8' inside the garage as shown below.
*If the car is contracted in garage's reference
frame, why is the car's length plotted at its
initial value of 12' If this issue is so silly,
I'd think your diagram wouldn't raise this
question. AG *
The first diagram where the car has length 12 is
showing the car's reference frame, not the garage
frame--the garage frame is the second diagram.
Jesse
*
*
*It says "GARAGE" so it must mean garage frame. AG *
Both diagrams say "garage" next to the red worldlines (the
front and back of the garage) and "car" next to the blue
worldlines (the front and back of the car), they are labels to
tell you which worldlines belong to which object. And in the
first diagram you can see the blue worldlines representing the
car have position coordinates which don't change as you vary
the time coordinate (move up and down the graph vertically),
so that's the diagram representing the car rest frame.
Jesse
*TY. I'll look at those diagrams again. Incidentally, I just
posted my solution to the alleged length contraction paradox. I
can't prove it because there's no test possible, but I'm confident
I am correct. AG*
*Using Brent's parameters, the car will crash into the end door of the
garage because, with a gamma factor of .6, corresponding to v = .8c,
the length of the garage is reduced from 10' to 6', whereas the car's
length is reduced from 12' to 7.2', still longer than the length of
the garage.*
You've got them both moving at 0.8c in which case the car will not crash
into the door because it's not moving relative to the door.
Brent
*You can believe it for the same reason you believe that the distance
to Andromeda will be reduced by 40% for a traveler whose v = .8c. The
reason the contrary result seems plausible is quite subtle, and I will
try to address this subsequently, but it has to do with an asymmetry
between the frames of reference. AG*
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