Michel Jullian wrote:
----- Original Message ----- From: "Stephen A. Lawrence"
<[EMAIL PROTECTED]> To: <[email protected]> Sent: Friday, February
16, 2007 3:37 AM Subject: Re: [Vo]: FW: Einstein's Twin Paradox
...
This is not a paradox, and the "paradoxical" nature of the
problem was in fact resolved something on the order of a
century ago. The traveling twin accelerates; the stay-at-home
twin does not; thus, the symmetry is broken.
...
To be more precise the traveling twin is the only one who
accelerates _wrt the initial common frame of reference_, that's
what breaks the symmetry (otherwise one could argue that they
both accelerate wrt each other)
No you could not. Acceleration is absolute, not relative.
...
Not in the general sense Stephen. _Geometrically_, both twins
accelerate wrt each other, agreed?
You are talking about what we might call "coordinate acceleration",
which, I would claim, is a somewhat nonstandard use of the term
"acceleration".
It's _acceleration wrt an inertial frame of reference_ which is
absolute of course, hence my point. I wasn't contradicting you, just
highlighting a point which may not be obvious to everyone.
Acceleration, as I have generally seen the term used in casual
conversation (and in discussions of the twins paradox), is that which is
measured by an accelerometer. An accelerometer is a purely "local"
instrument (which, of course, can't tell the difference between gravity
and acceleration).
(d/dt)(dq/dt) where "q" is an arbitrary general coordinate is not
usually referred to simply as "acceleration". And, when the word
"acceleration" /is/ used that way, it often leads to interminable
pointless arguments about the difference between a "real force" and a
"fictitious force", as well as lengthy discussion of the true meaning of
"centrifugal force" :-)
Michel
