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"I managed to get a quick PhD — though when I got it I knew almost nothing about physics. But I did learn one big thing: that no one knows everything, and you dont have to."
Steven WeinbergConsider... [the formula given by special relativity for the magnitude — Steven Weinberg
"Consider... [the formula given by special relativity for the magnitude of the ]P \equiv m_0 \sqrt{g_{ij}\frac{dx^i}{d\tau}\frac{dx^j}{d\tau}}...where d\tau^2 = dt^2 - g_{ij} dx^i dx^j. [This holds because in] a locally inertial Cartesian coordinate system, for which g_{ij} = \delta_{ij}, we have d\tau = dt\sqrt{1 - \mathbf {v}^2} where v^i = \frac{dx^i}{dt}... [The P] is evidently invariant under arbitrary changes in the spatial coordinates, so we can evaluate it... in Robertson-Walker coordinates. ...[T]o save work ...adopt a spatial coordinate system in which the particle position is near the origin x^i = 0, where \tilde{g}_{ij} = \delta_{ij} + \mathit0(\mathbf{x}), and we can therefore ignore the purely spatial components of \Gamma_{jk}^i of the . General relativity gives [the momentum]... with a metric g_{ij} = a^2(t)\delta_{ij}...P(t) \propto 1/a(t)... for any non-zero mass, however small... Hence, although for photons both m_0 and d\tau vanish... [the momentum relation] is still valid."
Steven Weinberg
Steven Weinberg
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Steven Weinberg was an American theoretical physicist. He shared the 1979 Nobel Prize in Physics with Abdus Salam and Sheldon Glashow "for their contributions to the theory of the unified weak and electromagnetic interaction between elementary particles, including, inter alia, the prediction of the weak neutral current".
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