Questions on world-line
in [Relativity]
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From: Igor on 22 Aug 2006 14:34 surrealistic-dream(a)hotmail.com wrote: > 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. Wrong. There is a Lorentz transformation for acceleration also. > > 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. Wrong again. The worldline is invariant regardless of whether it is spacelike, timelike, or lightlike.
From: dwhig265 on 22 Aug 2006 15:22 Igor wrote: > 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. DWH says: He may be correct in that that is what SR says but it is incorrect to say SR is correct if it says there is no absolute motion and $10,000 says I can prove it. You are Khavkine are you not? > > >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.
From: Timo A. Nieminen on 22 Aug 2006 15:51 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. 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 22 Aug 2006 15:57 "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?
From: Mike on 22 Aug 2006 16:19
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". Mike > > Ken Seto |