[Bill S (OP)]

I've had a shot at answering this and would appreciate comments.

A timeline is a list of events in chronological order. Obviously, the events are “real” in the sense that they can be experienced sequentially in our 3+1 dimensional Universe, but the timeline, itself, has no independent existence, and is simply a useful contrivance for the measurement and recording of change.  Consequently, a point on a timeline has no intrinsic spatial dimensions, and may be expressed as zero-dimensional in time

A worldline is the conceptual path that an object takes in 4-dimensional spacetime.  It is distinguished from, for example, a trajectory by the essential inclusion of time as a dimension.  Thus, the trajectory of an arrow, from bow to target, may be expressed without reference to the time involved in that journey.  The same journey, expressed as a worldline, would include time, and would, therefore, denote the relative speed of the arrow. Graphically, it would be shown as an inclined line within a light cone.  This cone would be bounded by lines showing the path that a single flash of light, from a specific source, would trace, travelling at “c” through space. 

Unlike a timeline, a worldline always has an object, physical or conceptual, that gives it meaning.  Each of us has a worldline, which we follow from conception to death and arguably beyond.  Thus, it can be reasoned that a worldline is a physical entity, because, in this case, it has a physical object that is present throughout its history.

[Halc]

Pretty much a good description, but I'll comment on it since you ask.

I've had a shot at answering this and would appreciate comments.

A timeline is a list of events in chronological order. Obviously, the events are “real” in the sense that they can be experienced sequentially in our 3+1 dimensional Universe, but the timeline, itself, has no independent existence, and is simply a useful contrivance for the measurement and recording of change.  Consequently, a point on a timeline has no intrinsic spatial dimensions, and may be expressed as zero-dimensional in time

Good description.  Events are not all points, so many (most?) events have dimentions.  The two world wars were some 25 years apart, but years in duration each.  In physics, and especially relativity, events as points are more commonly referenced.  Discussion of world wars isn't particularly physics.

A worldline is the conceptual path that an object takes in 4-dimensional spacetime.  It is distinguished from, for example, a trajectory by the essential inclusion of time as a dimension.  Thus, the trajectory of an arrow, from bow to target, may be expressed without reference to the time involved in that journey.

I have a hard time with this statement.  We have a guy firing an arrow at a target backlit by the setting sun, ok?  There is the location in space where the bow and arrow part company, and there is the location in space where the arrow hits the target.  On what side of the other are these two locations in space?  The trajectory seems to depend on this relationship between those two locations in space.
So relative to the archer, he's shooting into the sunset, so the target location is west of the location of the shot being fired.  The trajectory is westward.
Relative to Earth, the spin is far faster than our guy can fire the arrow, so the 2nd location is east of the former.  That's an eastward trajectory.
Relative to the solar system, the Earth is booking along and the archer is at the trailing edge at sunset, so the arrow trajectory is straight down.  Relaive to the galaxy, maybe the trajectory is downish and NW.  I don't know.  Depends on the time of year.

Point is, the trajectory of the arrow is very much dependent on the reference frame, and that frame corresponds to the orientation of the time dimension.  You need to reference time, even if only implicitly.

The same journey, expressed as a worldline, would include time, and would, therefore, denote the relative speed of the arrow. Graphically, it would be shown as an inclined line within a light cone.  This cone would be bounded by lines showing the path that a single flash of light, from a specific source, would trace, travelling at “c” through space. 

Good description of the worldline, except there is no specific event at which the flash of light belongs.  Worldlines don't have light cones.  Events do.  The inclination of anything's worldline can change at any time, so it doesn't have a constant inclination.  The inclination is very dependent on how you assign the 4 axes.  They can be arbitrarily assigned, but need to be mutually orthogonal.

The arrow's worldline slope (inclination) changes abruptly as it is fired, and changes abruptly again as it reaches its target and resumes the slope it had before being fired.

Unlike a timeline, a worldline always has an object, physical or conceptual, that gives it meaning.

Agree.  A worldline can be abstract.  The center of mass of Jupiter and Saturn forms a worldline that snakes through spacetime, with no physical object to instantiate it.  It is an an abstract worldline of an abstract concept.

Each of us has a worldline, which we follow from conception to death and arguably beyond.

I don't think a worldline is something followed.  That implies a current location, that I've left the other portions or haven't come to them yet.  That is a flowing time model, not a spacetime one.  Flowing time models don't have worldlines.  There is just 3D space that changes state.
I am present at all of my worldline, by definition, therefore it doesn't seem that I'm following that line any more than I'm following a line from my feet to my head.

[yor_on]

Try this Bill
http://www.astro.ucla.edu/~wright/relatvty.htm

[Bill S (OP)]

Thanks for that, Halc.  It highlights the fact that as a non-scientist I don’t always express things very appropriately.  E.g. when I said “a point on a timeline has no intrinsic spatial dimensions” I didn’t mean to imply that the events to which these points relate had no dimensions.  That was why I said “intrinsic dimensions”.  Must think about re-wording.

You make some interesting points about the flight of the arrow.  I was not thinking at that depth.  What I meant by: “the trajectory of an arrow, from bow to target, may be expressed without reference to the time involved in that journey” was that one could describe the flight in terms of the distance between bow and target and the shape of the arc, without reference to time or speed.

[Bill S (OP)]

Thanks, Yor_on, the link looks good. I’ll just have to try to find time to study it, and refine my wording.

[geordief]

I've had a shot at answering this and would appreciate comments.

A timeline is a list of events in chronological order. Obviously, the events are “real” in the sense that they can be experienced sequentially in our 3+1 dimensional Universe, but the timeline, itself, has no independent existence, and is simply a useful contrivance for the measurement and recording of change.  Consequently, a point on a timeline has no intrinsic spatial dimensions, and may be expressed as zero-dimensional in time

A worldline is the conceptual path that an object takes in 4-dimensional spacetime.  It is distinguished from, for example, a trajectory by the essential inclusion of time as a dimension.  Thus, the trajectory of an arrow, from bow to target, may be expressed without reference to the time involved in that journey.  The same journey, expressed as a worldline, would include time, and would, therefore, denote the relative speed of the arrow. Graphically, it would be shown as an inclined line within a light cone.  This cone would be bounded by lines showing the path that a single flash of light, from a specific source, would trace, travelling at “c” through space. 

Unlike a timeline, a worldline always has an object, physical or conceptual, that gives it meaning.  Each of us has a worldline, which we follow from conception to death and arguably beyond.  Thus, it can be reasoned that a worldline is a physical entity, because, in this case, it has a physical object that is present throughout its history.

I enjoyed your description,although I don't think timelines and worldlines are really comparable except  in the way you have attempted to contrast one against the other**

From my lowly vantage point I have also struggled with understanding worldlines  (with me it is all theory and no practice)

One thing I think I have gleaned from the responses to my  queries is that  they are locally defined (you don't extend them indefinitely and try to fashion an entire universe with them  like a kind of infinitely entangled web)

I have in the past been pulled up  by other  posters in my use of  the word "events".
I assumed ,perhaps a little like you that "something happened" at an "event".

I have been corrected  to a  new understanding that an "event" is just a point on a 4D  co-ordinate map  (nothing has to actually "happen" there-although it might)

So to return to your "timeline vs worldine" question , I actually think both lack "physicality"  and tbh  I am not sure (now that I rethink it)  that they are not equivalent concepts.


**oops ,I seem to have changed my mind during my reply;I seem to have decided they are equivalent.

[Halc]

Thanks for that, Halc.  It highlights the fact that as a non-scientist I don’t always express things very appropriately.  E.g. when I said “a point on a timeline has no intrinsic spatial dimensions” I didn’t mean to imply that the events to which these points relate had no dimensions.  That was why I said “intrinsic dimensions”.  Must think about re-wording.

You're find.  Points are dimensionless, yes.  The arrow example clearly has duration, such as from letting go of the string to the arrow and string separating.  At the target there is first contact and ending when it matches the speed of the target.  Both 'events' have a duration, even if a small fraction of a second.  For the purposes of our discussion, that duration is acceptable.  We only wanted to know the trajectory of the thing.

You make some interesting points about the flight of the arrow.  I was not thinking at that depth.  What I meant by: “the trajectory of an arrow, from bow to target, may be expressed without reference to the time involved in that journey” was that one could describe the flight in terms of the distance between bow and target and the shape of the arc, without reference to time or speed.

A westbound arrow seems to be a significantly different flight than one that goes straight down, but the difference between the two was only an adjustment to the time axis.  That's what I was trying to point out.

[yor_on]

One thing Bill, when it comes to his description of 'skewed worldliness' he forgot to write ' in this model ' everything can be explained geometrically. I would take ... " Thus the "twin paradox" is no more paradoxical than the statement that a man who drives straight from LA to Las Vegas will cover fewer miles than a man who drives from LA to Las Vegas via Reno." ... with a pinch of salt. But it's still a very good description.

The twin paradox is most definitely weird to me :) It's also so that he goes from a 'global view' describing it. As if SpaceTime was contained in a 'box', in where everything inside can be described through taking into consideration a geometry. That you find Lorentz transformations to work does not tell you that it must be a 'box' we live in. It tells you that there is a logic.

I think I agree with Einstein on that using mathematics instead of describing it geometrically is better. I suspect it gives one less preconceptions about what this 'box' would be.

[guest4091]

Bill S;

I think you did well overall with the essence of the definitions. How much time do you spend forming all these questions?

A timeline is a list of events in chronological order. Obviously, the events are “real” in the sense that they can be experienced sequentially in our 3+1 dimensional Universe, but the timeline, itself, has no independent existence, and is simply a useful contrivance for the measurement and recording of change.  Consequently, a point on a timeline has no intrinsic spatial dimensions, and may be expressed as zero-dimensional in time

Some clarification while considering SR graphics (Minkowski spacetime diagrams, or Hermanns, since verboseness is wasteful, redundant, and boring).
Any point is dimensionless. (Notice how they are fudged by representing them with a blob of medium, but how else could you see them!)
A timeline is specific to an observer at a given speed, and implies a local clock that moves with him.
The point denotes the distance vt from the origin. On the plus side, Minkowski brought time into the 20th century, with his revision of t with ct, a distance.
Now the graph plots object speed vs light speed, vt/ct = v/c. It's a speed profile in the form of a history of positions for a given object. Yes, it has no independent existence, since each position occurs at a different time.
No different from a trajectory or planetary orbit. It would be problematic since each observer perceives a different path depending on their motion!

A worldline is the conceptual path that an object takes in 4-dimensional spacetime.  It is distinguished from, for example, a trajectory by the essential inclusion of time as a dimension.  Thus, the trajectory of an arrow, from bow to target, may be expressed without reference to the time involved in that journey.  The same journey, expressed as a worldline, would include time, and would, therefore, denote the relative speed of the arrow. Graphically, it would be shown as an inclined line within a light cone.  This cone would be bounded by lines showing the path that a single flash of light, from a specific source, would trace, travelling at “c” through space.

This is the abstract, 'lines on paper', theory perpetuated by academy. Its advantage is in calculations for physical processes. Its disadvantage is metaphorical interpretation such as 'moving through time'.  Before someone asks, yes, a Hermann is also 'lines on paper', but its purpose is a geometric application of the Lorentz/SR coordinate transformations, where the worldline is supposed to represent what you describe in the following.   

Unlike a timeline, a worldline always has an object, physical or conceptual, that gives it meaning.  Each of us has a worldline, which we follow from conception to death and arguably beyond.  Thus, it can be reasoned that a worldline is a physical entity, because, in this case, it has a physical object that is present throughout its history.

What's missing is "perception is reality confined to the mind".
The worldline is just as fictitious as the timeline, orbit, path of Lewis and Clark expedition, etc. for the same reasons mentioned above. They are histories, a sequence of ordered events, but cannot be experienced as a single event. Using the simple SR train experiment, the passenger observes the stone drop vertically to the floor when released, as the train moves along, but the bystander observes the stone fall along a curve to the floor. How can the one stone have multiple trajectories? It can't, but each observer can have different perceptions, and that is their reality.
Even though there is a physical object present throughout its history, the object is changing along the way. You are not the same person physically or mentally at death as at birth. Identification is accomplished via names, fingerprints, social security, etc., i.e. things that are assumed to remain constant.

[Bill S (OP)]

Geordie, thanks for the kind comment.

One thing I think I have gleaned from the responses to my  queries is that  they are locally defined (you don't extend them indefinitely and try to fashion an entire universe with them  like a kind of infinitely entangled web)

I understand that Wheeler and Feynman did a lot of work on the idea of advanced and retarded radiation, in the 40s. This seems to have involved an infinitely “entangled” web, but I believe the idea was eventually consigned to the “recycle bin.  Can’t say I’m sorry about that, it did some odd things with time.

Some other points I want to come back to when time permits.

[Bill S (OP)]

  I would take ... " Thus the "twin paradox" is no more paradoxical than the statement that a man who drives straight from LA to Las Vegas will cover fewer miles than a man who drives from LA to Las Vegas via Reno." ... with a pinch of salt. But it's still a very good description.

That line of reasoning seems to fit better in a discussion as to whether or not gravitational lensing can give rise to past directed time travel.  Jenny Randles thinks it can, but that’s not for this thread.  A future one, perhaps?

The twin paradox is most definitely weird to me

The “terrible twins” have given rise to a lot of discussion, and will probably continue to do so.  Michael Huemer’s explanation is the one that helped me most.  It might be worth looking specifically at that, at some time.

[Bill S (OP)]

How much time do you spend forming all these questions?

No straightforward answer to that. Mostly, I'm thinking while doing other things, then, when I find a few moments, I post some of those thoughts; often in a hurry.