Questions on world-line
in [Relativity]
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From: Ahmed Ouahi, Architect on 24 Aug 2006 10:42 However, when you do give a complicated image along anything you would like to attain, therefore, the behaviours along that matter would be always more complicated. Whether, the things which are already known, is that, any object along the universe has its own a motion, not only always a relative but most of the time also a depending . However, on the fact of its structure and its structuration and a definitely on the mass as on any excessivity of any force all along, especially of the object itself, whether could be an infinitesimal objet what is all about. -- Ahmed Ouahi, Architect Best Regards! "kenseto" <kenseto(a)erinet.com> wrote in message news:_FhHg.69400$vl5.11915(a)tornado.ohiordc.rr.com... > > "YBM" <ybmess(a)nooos.fr> wrote in message > news:44ece480$0$19781$636a55ce(a)news.free.fr... > > kenseto a ?crit : > > > "YBM" <ybmess(a)nooos.fr> wrote in message > > > news:44ec8a99$0$19782$636a55ce(a)news.free.fr... > > > > > >>kenseto a ?crit : > > >> > > >>>The point is: worldline or trajectory in spacetime requires some kind > of > > >>>motion to happen. In SR there is only relative motion.....does that > mean > > >>>that worldline of an object is the result of relative motion?? > > >> > > >>I should be dreaming... You are just about to get it ! > > > > > > > > > RFOTFLOL this idiot falls into the trap.....an object doesn't need any > > > reference to have a worldline. > > > > Well, I'm right not to have bet on that... not that I did believe it > > actualy. > > > > Back to basics : the worldline of Ken Seto is defined in a specific > > frame F as the set of the t-uples (x,y,z,t) tagging in F the events > > "at time t, Ken Seto is at coordinates (x,y,z)". > > This is not basic you are talking about relative motion between me and > frame F. In my frame of reference my coordinates are (0,0,0) at all time. > Why? Because SR and I assumed that I am in a state of rest and all the > objects around me are doing the moving. Even though that I assume that I am > in a state of rest I still have a worldline. This applies to all the object > that are at rest wrt me. > > Ken Seto > >
From: Igor on 24 Aug 2006 12:06 kenseto wrote: > "Igor" <thoovler(a)excite.com> wrote in message > news:1156353371.333406.159360(a)i42g2000cwa.googlegroups.com... > > > > kenseto wrote: > > > "Igor" <thoovler(a)excite.com> wrote in message > > > news:1156349832.759078.175940(a)74g2000cwt.googlegroups.com... > > > > > > > > kenseto wrote: > > > > > "Igor" <thoovler(a)excite.com> wrote in message > > > > > news:1156265582.026355.324580(a)p79g2000cwp.googlegroups.com... > > > > > > > > > > > > kenseto wrote: > > > > > > > In SR the world line is the path of an object in space with the > > > passage > > > > > of > > > > > > > time. > > > > > > > > > > > > Not quite. It's literally the path taken through spacetime. > > > > > > > > > > > > >Each object has its own world-line. > > > > > > > > > > > > Yes. > > > > > > > > > > > > > > > > > > > Questions: > > > > > > > 1. Does this mean that the world-line of an object is the result > of > > > the > > > > > > > individual motion of the object? > > > > > > > > > > > > Yes, through spacetime, but as opposed to what? > > > > > > > > > > > > > 2. SR says that there is no such thing as individual motion. > > > > > > > > > > > > Depends on what you mean by individual motion. If you mean > absolute, > > > > > > then you're correct. > > > > > > > > > > > > >There is only > > > > > > > relative motion then how does an individual object have > world-line? > > > > > > > > > > > > The world line is fixed in spacetime. It's invariant, so everyone > > > > > > agrees on the path. How you define the coordinate system, > however, is > > > > > > entirely up to you. That's where relative motion comes in. > > > > > > > > > > > The question is: how does an object have world line? What make it > trace > > > out > > > > > a world line? > > > > > > > > The best analogy would be a trajectory in spacetime. What makes a > body > > > > have a trajectory? In classical physics, all bodies have a unique > > > > trajectory, as opposed to QM, where their trajectories become smeared > > > > over many different paths. > > > > > > > The point is: worldline or trajectory in spacetime requires some kind of > > > motion to happen. In SR there is only relative motion.....does that mean > > > that worldline of an object is the result of relative motion?? > > > > The worldline is invariant. Motion is relative. That's all there is > > to it. Beyond that, I don't really understand what you're even asking. > > > What I am asking is: what motion of an object that gives rise to it > worldline? Is it the object's absolute motion (individual motion)? If not > why not? > > Ken Seto Ask Galileo. This is not just an issue with SR. You might want to reprase your question as "How can motion in space be relative and still have a well-defined trajectory?"
From: Dirk Van de moortel on 24 Aug 2006 12:20 "Paul B. Andersen" <paul.b.andersen(a)hiadeletethis.no> wrote in message news:ecka36$3j6$1(a)dolly.uninett.no... > Dirk Van de moortel wrote: >> "Paul B. Andersen" <paul.b.andersen(a)hiadeletethis.no> wrote in message news:echlqg$7t6$1(a)dolly.uninett.no... [snip] >>> The word line of an object is its path through space-time. >>> Any interval between events on this world line must thus per >>> definition be time-like. >>> There is no such thing as a "space-like world line". >> >> I'd prefer to say that there is no such thing as "an object with a >> space-like worldline". >> A light signal clearly has a light-like worldline, and a shadow or >> the spot of a laser can have a space-like worldline. > > In that case you would use an unconventional definition of "world-line". > >> That is of course, unless you prefer to call these lines lightlines >> and spotlines :-) > > Curves in space-time? > > I looked up a few definitions: > > Oxford English Dictionary: > Physics and Philos. the succession of points in space-time > that are occupied by a particle; > > http://www.answers.com/topic/world-line > "The path in space-time traveled by an elementary particle > for the time and distance that it retains its identity." > > In: > http://en.wikipedia.org/wiki/World_line > I find: > "In physics, a world line of an object (approximated as a point in space, > e.g. a particle or observer) is the sequence of spacetime events corresponding > to the history of the object." > and: > "In our definition above: world lines are time-like curves in spacetime." > but also: > "Sometimes, the term world line is loosely used for any curve in spacetime. > This terminology causes confusions. More properly, a world line is a curve > in spacetime which traces out the (time)history of a particle, observer or > small object." > > I use the "more proper" definition. :-) > And then "space-like world-line" is a contradiction in terms. Yes, of course. If it, like Wiki expresses it so eloquently, causes confusions, I will consider adjusting my preferences :-) Cheers, Dirk Vdm
From: YBM on 24 Aug 2006 13:08 kenseto a ?crit : > "YBM" <ybmess(a)nooos.fr> wrote in message > news:44ece480$0$19781$636a55ce(a)news.free.fr... > >>kenseto a ?crit : >> >>>"YBM" <ybmess(a)nooos.fr> wrote in message >>>news:44ec8a99$0$19782$636a55ce(a)news.free.fr... >>> >>> >>>>kenseto a ?crit : >>>> >>>> >>>>>The point is: worldline or trajectory in spacetime requires some kind > > of > >>>>>motion to happen. In SR there is only relative motion.....does that > > mean > >>>>>that worldline of an object is the result of relative motion?? >>>> >>>>I should be dreaming... You are just about to get it ! >>> >>> >>>RFOTFLOL this idiot falls into the trap.....an object doesn't need any >>>reference to have a worldline. >> >>Well, I'm right not to have bet on that... not that I did believe it >>actualy. >> >>Back to basics : the worldline of Ken Seto is defined in a specific >>frame F as the set of the t-uples (x,y,z,t) tagging in F the events >>"at time t, Ken Seto is at coordinates (x,y,z)". > > > This is not basic you are talking about relative motion between me and > frame F. In my frame of reference my coordinates are (0,0,0) at all time. > Why? Because SR and I assumed that I am in a state of rest and all the > objects around me are doing the moving. Even though that I assume that I am > in a state of rest I still have a worldline. This applies to all the object > that are at rest wrt me. So what ? In that case (Seto at rest in F), my definition works as well and gives { (x_s,y_s,z_s,t) / t \in R } where (x_s,y_s,z_s) is your constant spacial coordinates... BTW, you seem (in another post of this thread) to suggest that a worldline could be defined without refering to a frame. Please do so.
From: Timo A. Nieminen on 24 Aug 2006 14:27
On Wed, 23 Aug 2006, kenseto wrote: > "Timo A. Nieminen" <timo(a)physics.uq.edu.au> wrote: >> On Tue, 22 Aug 2006, kenseto wrote: >> >>> In SR the world line is the path of an object in space with the passage > of >>> time. Each object has its own world-line. >>> Questions: >>> 1. Does this mean that the world-line of an object is the result of the >>> individual motion of the object? >>> 2. SR says that there is no such thing as individual motion. There is > only >>> relative motion then how does an individual object have world-line? >> >> Consider an object, with position in a particular inertial coordinate >> system (aka inertial reference frame) given by r(t). It can only be in one >> place at a time, and is always somewhere at any time; thus r(t) is a >> function. The problem is that not only does r depend on choice of >> coordinate system, but so does t. >> >> So, what to do? Introduce a parameter that is independent of choice of >> coordinate system, such as the "proper time" T, and we can write >> R(T) = (r,t) >> as a 4-vector valued function. How can any individual object _not_ have a >> world line? [cut] > > You did not answer my question: What is the motion of an object that cause > it to have a world-line??? If that was your question, you should have asked it in the first place. You asked: "how does an individual object have world-line?" The answer is that motion really has nothing to do with it; an object has a world line if it is somewhere at any given time. -- Timo Nieminen - Home page: http://www.physics.uq.edu.au/people/nieminen/ E-prints: http://eprint.uq.edu.au/view/person/Nieminen,_Timo_A..html Shrine to Spirits: http://www.users.bigpond.com/timo_nieminen/spirits.html |