On Sat, Jan 25, 2025 at 4:03 AM Alan Grayson <[email protected]> wrote:
> > > 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 <[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. > > > *Yes, two reasons. Firstly, you can use Brent's numbers which he uses in > his plots; * > OK, looking at Brent's original post with the diagrams at https://groups.google.com/g/everything-list/c/_O3VOdJ-KUU/m/24R401SnBAAJ he shows the car to have a length of 12 in its own frame, and to be moving at 0.8c in the +x direction in the garage frame (so gamma = 1/sqrt(1 - 0.8^2) = 1/0.6, and the length contraction equation says length is contracted by 1/gamma so length of the car in the garage frame is 0.6*12 = 7.2), and the worldline of the back end of the car passes through the point x=0, t=0 in the garage frame. So, you similarly want the rod to have a length of 12 in its frame, to be moving at 0.8c in the +x direction in the Earth frame so it has a contracted length of 7.2 in the Earth frame, and the back end passing through x=0, t=0 in the Earth frame. If so, I'll just make some small modifications to the other numerical example I have you a couple posts back at https://groups.google.com/g/everything-list/c/ykkIYDL3mTg/m/hH75rNWuDQAJ -- Let the unprimed frame be the Earth frame, and the primed frame be the rod's frame. In the Earth frame, the BACK end of the rod has velocity 0.8c and passes through x=0, t=0, so its equation for position as a function of time for the BACK must be x = 0.8c*t. And in the Earth frame the FRONT of the rod is also moving at 0.8c and is always in front of the back by 7.2 (the rod's length in this frame), so its equation for position as a function of time for the FRONT must be x = 7.2 + 0.8c*t Now if we want to know the equations in the rod's own (primed) 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=0.8c as measured in the Earth frame, we have gamma=1/0.6, so the LT equation can be written as x' = (x - 0.8c*t)/0.6 Now, if you take the equation for the BACK of the rod in the unprimed (Earth) frame, x = 0.8c*t, and substitute that in for x in the LT equation x' = (x - 0.8c*t)/0.6, you get x' = (0.8c*t - 0.8c*t)/0.6 = 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 = 7.2 + 0.8c*t, and similarly substitute it into x' = (x - 0.8c*t)/0.6, you get x' = (7.2 + 0.8c*t - 0.8c*t)/0.6 = 7.2/0.6 = 12, meaning in the primed (rod) frame the FRONT end of the rod is fixed at x' = 12. If the BACK has fixed position x' = 0 in the rod frame and the FRONT has fixed position x' = 12, that means the rod has a length of 12 in this frame. So you can see that if we start with the coordinates for a rod that in the unprimed (Earth) frame has a length of 7.2 light-second and is moving at 0.8c, and then we apply the LT equations, we end up with the coordinates for a rod that's 12 light-seconds long and at rest in the primed (rod) frame. > *and secondly, it seems as if your results contradict length contraction, > so they are suspect.* > No, those results agree with length contraction. The length contraction is written as a relation between the object's "proper length" L_0 in the frame where the object is at rest (in this case, the rod's frame), and the contracted length L in some other frame where the object is in motion (in this case the Earth's frame)--the equation is just L = L_0/gamma, and gamma > 1 so this always means L is smaller than L_0. So, if you start from the frame where the rod is moving and the length is L, and use the LT to transform into the frame where the rod is at rest (using the rod's frame as what you called the 'target frame' for the LT), in order to agree with the length contraction equation the LT should predict a LONGER length L_0 in the target frame. > *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 * > The standard terminology is to define length and rest relative in terms of the coordinates of whichever frame you are explicitly talking about. So it's fine to say something like "in the Earth frame, the rod is moving and the Earth is at rest" as long as you would likewise say "in the rod frame, the rod is at rest and the Earth is moving". But what is non-standard is to say something like "I am going to define the Earth as at rest and the rod as moving throughout this discussion, and will continue to define them this way even when I am talking about how things are relative to the rod--for example, I will say 'the Earth is at relative rest wrt the rod' even though in the rod frame, the Earth has a nonzero coordinate velocity". If I'm understanding correctly, something like that was the logic behind your statement in the post at https://groups.google.com/g/everything-list/c/ykkIYDL3mTg/m/cZ_dWIcwDAAJ that "The spaceship is in one frame, at relative rest WRT the rod; the rod is in another frame, in relative motion WRT to the spaceship" (the Earth later took the place of the spaceship in how you described the example). So if I do understand the logic of that statement correctly, what's wrong with it is just that physicists don't talk about rest and motion that way, there are agreed-upon conventions and inventing your own alternate conventions creates unneeded confusion. 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/CAPCWU3J-MjbmgNi-5RKDUb75uiP1%3DN9nQEczXP_0MkSkHmE39A%40mail.gmail.com.
