# Worldlines - no need for ref frames?

1. Sep 22, 2006

### pivoxa15

"In Principle, worldlines allow us to relate events on one another - to do sciecne without using reference frames at all".

This was in Wheeler and Taylor's Intro to SR book.

My question is, isn't this false? Because worldlines exist in a spacetime diagram. Vertical being time and horizontal is space. One reference frame is always needed, which normally is the one that does not move wrt space. Hence it registers the greatest proper time. All other worldlines are created wrt to this stationary reference frame (i.e. the speed and directions of the particles that translate to worldlines are calculated or measured wrt to the stationary frame). So one reference frame must be needed hence contradicting the statement?

Last edited: Sep 22, 2006
2. Sep 22, 2006

### robphy

I think what they are trying to say is that
the physics involved relies only on the worldlines and their [Minkowski-]geometric relations to events and other figures.... and not on the choice of axes (choice of reference frame) used to draw the picture. By direct analogy, the properties of Euclidean geometry rely on the figures themselves and not on the choice of axes used to draw the picture.

3. Sep 22, 2006

### pivoxa15

So they are trying to say that no matter which frame you are in, you will calculate the same major results such as the proper time for different moving objects moving wrt you. All reference frames are arbitary and there are quantities that are independent of all ref frames.

Correct?

4. Sep 25, 2006

### lightarrow

Interval ds is independent of ref. frame:

ds^2 = (ct)^2 - (dx^2 + dy^2 +dz^2).

If only one spatial dimension x is involved: ds^2 = (ct)^2 - dx^2.

But I think this is only valid with inertial ref. frames (or when you can ignore acceleration effects), that is in a Minkowskian space-time, that is, in a "flat" space-time. A lot of people here can correct me.

Last edited: Sep 25, 2006
5. Oct 6, 2006

### pess5

Well, I'm not sure what the meaning was supposed to be wrt everything after the dash there? Doesn't sound right "as worded" here.

Without a worldline, a Minkowski worldline diagram is pretty much useless. It's like defining the location of something with no point of reference anywhere anytime. Space & time w/o any observer.