Hi all, and thanks in advance. I am an old guy learning GR for fun. Reading Weinberg's "Gravitation and Cosmology". PhD in math 1998, so I read all books like I read math books: every character, every word, every line, every page extremely carefully.(adsbygoogle = window.adsbygoogle || []).push({});

I am stuck on the stupidest thing. On p.72, he writes out a quadratic equation for the time ##dt## for a photon to travel a distance ##d\vec{x}##:

$$0 = g_{00}dt^2 + 2g_{i0}dx^i dt + g_{ij}dx^i dx^j$$

(##i=1,2,3##.), which follows immediately from (3.2.9) or (3.2.6). He then gives the solution in (3.2.10) using the quadratic formula.

What stumps me is that he has used the minus (-) square root instead of the (+) square root. How does he know to do that? If you test it using the simplest coordinate transformation ##x^α=ξ^α## and hence the metric ##g_{μν}=η_{μν}##, then of course he IS right, because ##g_{00} = -1##. But the ##g_{μν}## could be anything, so how does he justify taking the negative square root?

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# A Help with Weinberg p. 72 -- time dt for a photon to travel a distance d⃗x

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