Just so you know, the way I make the diagrams is I start by entering the
loci of the object (e.g. the exit door of the garage) as stationary at
equal time intervals (e.g. nano-seconds) and then I Lorentz transform
using the matrix for L(v).
Brent
On 1/24/2025 2:19 PM, Jesse Mazer wrote:
On Mon, Jan 20, 2025 at 4:13 PM Jesse Mazer <[email protected]> wrote:
On Mon, Jan 20, 2025 at 3:30 PM Alan Grayson
<[email protected]> 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.
Since I gave a similar numerical example in my recent comment at
https://groups.google.com/g/everything-list/c/QgVdhXi3Hdc/m/SG_JbWiYDQAJ
I'm going to re-use it with a few modifications to prove my point
above: if we start with the equations for the worldlines of the back
and front end of a rod which is moving in the Earth frame, and then
use the LT to calculate the equations for the worldlines of the ends
of the rod in the rod's own frame, we will see the its length in the
rod frame is EXPANDED compared to the Earth frame, not contracted.
Say that relative to the Earth frame, the rod is moving at 0.6c in the
+x direction and is 8 light-seconds long as measured in this frame, so
the equation for the back of the rod could be x = 0.6c*t and the
equation for the front of the rod could be x = 8 + 0.6c*t. Now if we
want to know the equations in the rod's own frame, we can substitute
those expressions for x into the Lorentz transformation's position
transformation equation, x' = gamma*(x - v*t). Since the rod frame has
v=0.6c as measured in the Earth frame, we have gamma=1/sqrt(1 - 0.6^2)
= 1.25, so the LT equation can be written as x' = 1.25*(x - 0.6c*t).
Now, if you take the equation for the back of the rod in the unprimed
(Earth) frame, x=0.6c*t, and substitute that in for x in the LT
equation x' = 1.25*(x - 0.6c*t), you get x' = 1.25*(0.6c*t - 0.6c*t) =
0, meaning in the primed (rod) frame the back end of the rod has a
fixed position x' = 0 which doesn't change with time (the rod is at
rest in the primed frame).
And if you take the equation for the front of the rod in the unprimed
(Earth) frame, x = 8 + 0.6c*t and similarly substitute it into x' =
1.25*(x - 0.6c*t), you get x' = 1.25*(8 + 0.6c*t - 0.6c*t) = 1.25*8 =
10, meaning in the primed (rod) frame the front end of the rod is
fixed at x' = 10.
So you can see that if we start with the coordinates for a rod that in
the unprimed (Earth) frame has a length of 8 light-second and is
moving at 0.6c, and then we apply the LT equations, we end up with the
coordinates for a rod that's 10 light-seconds long and at rest in the
primed (rod) frame.
Jesse
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