Questions on world-line
in [Relativity]
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From: kenseto on 22 Aug 2006 11:16 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: Igor on 22 Aug 2006 12:53 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.
From: Dirk Van de moortel on 22 Aug 2006 12:56 "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? A worldline is not at all specific to SR. When you have a coordinate system (including a clock), and when you know the spatial coordinates - for example ( x(t), y(t), z(t) ) - of the point of an object (or a point object, or a particle) as a function of time, then you can "draw" the set of events that shows the history and future of the object in a diagram that includes time on an equal footing as (perhaps a subset of) the spatial axes. This way, the set of points (events actually) defines a line in the diagram. That line is a worldline. For a given point object each coordinate system has a different worldline. An alternative way (more abstract and perhaps preferable) is to define the worldline of an object as the set of all its events, independently of any coordinate system. In that case the point object has a unique worldline that is described by different equations in different coordinate systems. Dirk Vdm
From: surrealistic-dream on 22 Aug 2006 13:17 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 http://www.csupomona.edu/~ajm/materials/twinparadox.html
From: Sorcerer on 22 Aug 2006 13:31
"Dirk Van de moortel" <dirkvandemoortel(a)ThankS-NO-SperM.hotmail.com> wrote in message news:qHGGg.35352$tc4.487567(a)phobos.telenet-ops.be... [anip] xi, x'? Androcles |