What does scalar phi represent in spacetime?

Trying to understand one-forms and vectors via Schutz's A First Course In General Relativity.

His example uses a spacetime diagram, a scalar field phi, a curve (worldline) parametrized using proper time and the tangent vector (4-velocity). I think I understand, but I can't see the physical significance of the scalar field phi. In plain English, in the spacetime diagram, what does or might phi represent?

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This doesn't answer your question, but: There is something mysterious and tantalizing about fundamental scalar fields. Why don't we have any? (Moot if the Higgs actually exists.) Scalar fields are invoked to create inflation. They can easily lead to classical violations of the energy conditions of GR. If we were going to design a universe to run on laws more Machian than GR, the best known way to do it would be Brans-Dicke gravity, which involves a scalar field. I'm tempted to make a new law of physics: no fundamental scalar fields. It would be a very powerful law. – Ben Crowell Jul 29 '11 at 1:42
@Ben: well, from the point of view of almost all physics, all you need is fermions (to get Pauli's exclusion to obtain variety of atoms) and gauge bosons. One only needs scalar fields for advanced stuff like electroweak SSB or the inflation you mention. Neither of which is relevant for the present universe barring the LHC and black holes (and possibly few other extreme objects) and one certainly imagine an universe without these objects (certainly the LHC). Similar question is why we need three generations of matter. Well, we don't, except for very subtle effects in high-energy regimes. – Marek Jul 29 '11 at 9:12

Moving up to 2+1 dimensions, it can again be a field of temperatures but now with time record included. So, your curve $\gamma$ records your wandering around the globe and ${\rm d} \phi \over {\rm d} \tau$ just tells you how the temperature you experience varies both in space and time.