# Why does general relativity use coordinate systems?

1. Nov 22, 2014

### zeromodz

If you look at Newtonian gravity, there is no major deal with coordinate systems. I am guessing we use coordinate systems because in general relativity we think of coordinate systems as different frames of references and that all frame of references must have the same laws of physics. Is that why?

2. Nov 22, 2014

### Staff: Mentor

Newtonian mechanics has coordinate systems as well, but they are all easy to relate to each other and you know exactly how the coordinate system looks everywhere. In GR spacetime gets warped, so local coordinate systems become important.

All inertial frames of references have the same physics, but that concept is common for both theories.

3. Nov 22, 2014

### pervect

Staff Emeritus
Both GR and Newtonian physics use coordinate systems and in much the same way, except that the coordinate systems in GR are generalized coordinates, and the coordinates in Newtonian physics usually are not. One COULD use generalized coordinates with Newtonian physics, but the math required to deal with generalized coordinates is not taught in high school. It's usually taught at the graduate level in college. A bit of the math needed to deal with a few special cases (such as polar coordinates) is snuck in a bit earlier, not very rigorously, but it's not very rigorous nor does it handle totally arbitrary coordinate systems.

One of the things this means in practice is that a change of a coordinate by one unit in GR does not in general (or even usually!) represent a change in distance of one unit - coordinates do not directly measure distance. This is the easy part, sometimes it seems that attempts to explain this fall on deaf ears, and I'm not quite sure why. The procedure for getting distances out of coordinate changes in GR involves using the metric.

Some authors banish the idea of the observer from GR, calling it "confusing" and ambiguous". I'll give a quote from one such paper by Misner, "Precis of General Relativity", http://arxiv.org/pdf/gr-qc/9508043v1.pdf

The reason for this banishing of the observer suggested by Misner is explained further in the paper where he explains what he calls "the conceptual model". The reason he gives is basically that space-time is curved, and that the curvature gives rise to effects are not intuitive. In fact, in the presence of curvature, the idea of coordinates remains the same (contrary to the original poster's question), but the idea of "observers" in "frames" becomes a bit harder to define. I would not say the concepts of "an observer" or "a frame" are impossible to define, personally, but I find that by the time the definition is precise enough to be useful, it's lost 95% of the audience :(.

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