On Monday, January 20, 2025 at 2:13:21 PM UTC-7 Jesse Mazer wrote:
On Mon, Jan 20, 2025 at 3:30 PM Alan Grayson <agrays...@gmail.com> wrote:
Below is what Brent wrote to describe his plots: notice that he uses the
car moving at 0.8c. But respect to what? He doesn't say.
I would actually quibble with his statement "In both diagrams the car is
moving to the right at 0.8c", since in the diagram for the car's frame the
car isn't moving at all, but I'm sure if asked to clarify he'd say he just
meant that both diagrams show a scenario where the car has a velocity of
0.8c relative to the garage, so this doesn't actually lead me to be
confused about his scenario the way some of your statements do (in part
because you refuse to give a straightforward numerical example like Brent
did). And everything else in his quote does clearly specify whether he is
talking about what's true in "the car's reference frame" or in "the
garage's reference frame" (naming the frame of a specific object as I have
asked you to do), he uses variations of those phrases several times.
And then he contracts the car from the garage frame. Is garage frame moving
or at rest? He doesn't say. So much presumably ambiguous non standard
terminology and not a peep out of you.
Here you seem confused about what I am saying is "non standard
terminology"--I think it's GOOD that Brent doesn't declare one frame to be
"moving" and the other to be "at rest", because that is precisely the sort
of confusing non-standard terminology YOU use that I'm objecting to! In the
standard terminology, one wouldn't say a given frame is "at rest" or
"moving" except as part of a longer phrase that specifies some other object
or frame those words are supposed to be relative to, like "the car is
moving relative to the garage frame" or "the garage is moving relative to
the car frame" or "the car is at rest relative to the car frame", with
these phrases just telling you something about the velocity of the named
object in the named frame.
Let's do this; since this discussion has reached the point of tedious
worthlessness, let's terminate it. AG
As I said, one easy way to avoid terminological confusion would be to
answer my simple request for a numerical example: "give me a specific
number for the rod's speed in the Earth's inertial rest frame, its
direction (in the +x or -x direction), and the initial position of each end
of the rod at t=0 in the Earth frame".
Is there some reason you are unwilling to give me a few numbers for
velocity and initial position of the rod in the Earth frame to work with?
If you did, I could then show you with a little simple algebra what happens
when we use the LT to transform these numbers into the rod's frame, proving
that when we do this the length of the rod is predicted to be EXPANDED
rather than contracted, compared to its length in the Earth frame.
*Yes, two reasons. Firstly, you can use Brent's numbers which he uses in
his plots; and secondly, it seems as if your results contradict length
contraction, so they are suspect. As for standard terminology, since motion
is relative, what's wrong with saying the rod is moving relative to the
Earth, towad the Earth, at some speed v, so the Earth can be imagined as at
rest? AG *
Jesse
"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."
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