Questions on world-line
in [Relativity]
|
From: Ahmed Ouahi, Architect on 22 Aug 2006 16:47 The flecked river Which kept flowing and never The same way twice flowing Through many places As if it stood still in one -- Wallace Stevens -- Ahmed Ouahi, Architect Best Regards! "kenseto" <kenseto(a)erinet.com> wrote in message news:JdFGg.64268$vl5.40512(a)tornado.ohiordc.rr.com... > 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? > > Ken Seto > >
From: kenseto on 23 Aug 2006 08:58 <surrealistic-dream(a)hotmail.com> wrote in message news:1156267045.611522.11170(a)h48g2000cwc.googlegroups.com... > > 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. > > Not true. SR treats accelerations as absolute, but velocites and > positions as relative. > > > There is only > > relative motion then how does an individual object have world-line? > > > > Ken Seto > > With the exception of the worldline of a particle moving at light > speed, the worldline of a particle is a specific 'curve' (or piecewise > collection of curves and/or line segments) in a specific spacetime > diagram. This curve is generally timelike and not an invariant of a > Lorentz transformation. In other words, the worldline in one spacetime > map according to one inertial frame will not be the same worldline in a > spacetime diagram in another inertial frame, though some properties are > preserved under a Lorentz transformation (e.g., straight lines are > mapped into straight lines; lightlike lines are mapped to themselves). > Thus, generally but not always, the attributes of the curve in the > spacetime diagram DEPEND on the relative motion of the object to the > inertial reference frame. > > For an example of how the diagram (set of worldlines) changes when the > frame of reference changes, see You did not answer my question: What is the motion of an object that cause it to have a world-line??? Ken Seto
From: kenseto on 23 Aug 2006 09:01 "Timo A. Nieminen" <timo(a)physics.uq.edu.au> wrote in message news:Pine.WNT.4.64.0608230531570.1380(a)serene.st... > 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? > > Consider two points in space, A and B. Consider a displacement vector from > A to B. This only depends on the relative positions of A and B. However, > the (x,y,z) we might choose to represent the vector with very much depend > on our choice of coordinate system. > > Likewise, R(T1) - R(T2) only depends on the relative 4-positions of the > two events. The (x,y,z,t) depend on the chosen coordinate system. Relative > motion of the object and the origin of the chosen coordinate system > affects the (x,y,z,t) description of the world line, but can't affect the > geometry of the world line. You did not answer my question: What is the motion of an object that cause it to have a world-line??? Ken Seto > > How is this different between SR and Galileian relativity? In Galileian > relativity, transformations of time are separate from transformations of > the spatial coordinates, leaving only translations, reflections, and > changes of scale in t. Still, the same basic principles hold. Surely, in > a theory (perhaps something called IRT that has been posted on this ng) > that is a covering theory of SR, in the same way that SR is a covering > theory of Galileian relativity, this would be the same? > > -- > 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 >
From: kenseto on 23 Aug 2006 09:04 "Mike" <eleatis(a)yahoo.gr> wrote in message news:1156277943.578929.7420(a)b28g2000cwb.googlegroups.com... > > 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. > > Not exactly but ok for starters. > > > > Questions: > > 1. Does this mean that the world-line of an object is the result of the > > individual motion of the object? > > You do not need the term "individual". nd you must add ...motion of the > object in spacetime (not quite but ok for starters) > > It seems you are setting up a straw man argument using the word > "individual". > > > 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? > > Here we go again. The straw man is here. SR does not "say" anything > about "individual" motion. The subject of individual motion is > traditionally a subject of metaphysics and fundational physics > questions not dealt by experimental physics. Despite that, your > question is meaningless anyway. The other name for Relativity is > "Theory of Absolutes", suggested by Planck but rejected by Einstein > because he thought, although it was the correct name, it was too late > to change it. > > You probably confuse absolute motion with individual motion. Absolute > motio is motion WRT an absolute media, such as an absolute spacetime. > Individual motion exists in both absolute and relational spacetimes. In > the former it can be measured WRT the absolute media. In the latter it > can only be measured WRT another body in motion. That you need another > body to measure the motion of a body does not negate individual motion. > Actually, "it takes two to tango". You did not answer my question: What is the motion of an object that causes it to have a world-line??? Ken Seto
From: Paul B. Andersen on 23 Aug 2006 09:39
Igor wrote: > surrealistic-dream(a)hotmail.com wrote: >> Not true. SR treats accelerations as absolute, but velocites and >> positions as relative. > > Wrong. There is a Lorentz transformation for acceleration also. No, it's correct. But the acceleration that is absolute is the proper acceleration, that is the acceleration measured in the instant inertial rest frame of the object. It is the acceleration that is measured by an accelerometer. This acceleration is absolute, that is independent of frames of reference. The co-ordinate acceleration is however frame dependent. Example: If you travel in space with a rocket with constant thrust, you will have a constant proper acceleration. (Assume the mass of of the ship is constant.) Your accelerometer shows a constant acceleration of - say 1g. This acceleration is absolute, independent of frames of reference. But your co-ordinate acceleration measured in some inertial frame is NOT constant. As your speed in this frame of reference (after a year or so) approaches c, your co-ordinate acceleration approaches zero. >> With the exception of the worldline of a particle moving at light >> speed, the worldline of a particle is a specific 'curve' (or piecewise >> collection of curves and/or line segments) in a specific spacetime >> diagram. This curve is generally timelike and not an invariant of a >> Lorentz transformation. > > Wrong again. The worldline is invariant regardless of whether it is > spacelike, timelike, or lightlike. An interval between two events is timelike if it is possible for a massive object to be present at both events. 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". Paul |