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## Main Question or Discussion Point

Doran/Lasenby define a proper interval as:

[tex]

\delta \tau = \int \sqrt{\frac{dx}{d\lambda} \cdot \frac{dx}{d\lambda}} d\lambda

[/tex]

(c=1, x= (t,x1,x2,x3) is a spacetime event, and the dot product has a +,-,-,- signature)

and say that this is called the proper time.

I can see that this would be preferred as a parameterization in the same way that arc length is a natural parameterization of a curve (takes out zeros in the derivatives if one ``stalls'' for a while along the curve with respect to some specific parameterization).

However, calling this "time" seems slightly perverse to me since it looks to me (from an math point of view) as not much more than arc length with respect to this particular dot product.

Except for a particle is at rest, I can't imagine why one would want to call this parameterization time (unless its just because spacetime-arc-length is a mouthful). Can anybody else account for why this may be a reasonable choice of nomenclature?

[tex]

\delta \tau = \int \sqrt{\frac{dx}{d\lambda} \cdot \frac{dx}{d\lambda}} d\lambda

[/tex]

(c=1, x= (t,x1,x2,x3) is a spacetime event, and the dot product has a +,-,-,- signature)

and say that this is called the proper time.

I can see that this would be preferred as a parameterization in the same way that arc length is a natural parameterization of a curve (takes out zeros in the derivatives if one ``stalls'' for a while along the curve with respect to some specific parameterization).

However, calling this "time" seems slightly perverse to me since it looks to me (from an math point of view) as not much more than arc length with respect to this particular dot product.

Except for a particle is at rest, I can't imagine why one would want to call this parameterization time (unless its just because spacetime-arc-length is a mouthful). Can anybody else account for why this may be a reasonable choice of nomenclature?