Re: Problem with Fermi-Walker Transport in the Physics FAQ file
- From: Dono <sa_ge@xxxxxxxxxxx>
- Date: Tue, 31 Jul 2007 00:05:46 -0700
On Jul 30, 11:00 pm, "John M. Dlugosz" <11lrha...@xxxxxxxxxxxxxx>
wrote:
I'm editing some of the Physics FAQ files, some just to fix the 10-
year-old converted HTML, general copyediting, and such. But when the
muse descends ...
In the page on "Bell's Spaceship Paradox", my initial effort was to
supply all the illustrations that are left to the imagination of the
reader. I'm also expanding and clarifying the text.
My draft in progress can be seen at <http://www.dlugosz.com/files/
PhysFAQ-edit/Relativity/SR/spaceship_puzzle.html>.
My question to the group concerns Figure 4. I followed the
instructions in the original text, seen in the paragraph before the
figure, and the two lines intersect! Based on the following
paragraph, that should not happen, and the ship that starts out on the
right should remain on the right, but draw ever closer in the lab-
frame.
What is going on here? Clearly the "K" in this formula is not at all
related to the "k" used earlier, since the directions say "K>1" and
the earlier "k" is the x-distance between ships in the lab-frame at
launch. The units of space would make ">1" nonsense (one what?).
In the Figure, the vertical height is 1 unit (-0.0325 through 0.9625)
and the function iterates over t in that range. K=2. The original
curve (and the left curve here) is the same function with K=1. Now,
on the left curve, as with all the previous figures, note that the
hyperbola appears just a few pixels right of the t axis. The function
as written would give an x intercept of 1, so the illustration would
have to be as wide as it is tall before you even start to see the
curve. The two ships differ in their starting position, so the curves
are shifted left by a different constant x for each ship. In Figure
4, the right curve is also shifted left to the same starting position
as the second ship is always drawn at, though the natural position of
the stated function is even farther right (intersects the x axis at
x=K).
Is that an issue? The text does NOT say that the ships have to be a
minimum distance apart to begin with, so I should think not. Point
is, there is something that the text is not explaining, or perhaps a
simple error in a symbol somewhere.
Could someone who understands this please take a close look at it?
Thanks,
--John
John
I couldn't see the page in cause, the link malfunctioned. Either way,
wiki provides a reasonable (not the bset) explanation here:
http://en.wikipedia.org/wiki/Bell%27s_spaceship_paradox#Analysis
.
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