> You are talking about what we might call "coordinate acceleration"
Yes indeed Stephen, we might call it thus, although just "acceleration" is better and simpler. Time derivative of velocity in an arbitrary frame, not just an inertial one. That's the most general definition of "acceleration", that's why I said "Not in the general sense": ac·cel·er·a·tion n. 1. a. The act of accelerating. b. The process of being accelerated. 2. Abbr. a Physics The rate of change of velocity with respect to time. But enough bickering. Talking about "centrifugal force", you do know that by running around a bucket of water you incurve the water as if it was centrifuged don't you? :) Michel ----- Original Message ----- From: "Stephen A. Lawrence" <[EMAIL PROTECTED]> To: <[email protected]> Sent: Friday, February 16, 2007 4:09 PM Subject: Re: [Vo]: FW: Einstein's Twin Paradox > > > 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 >> >
