Wednesday, October 17, 2012

gravitational interaction of photons

why do gravitational interactions of (CMB) photons with the cosmic large-scale structure such as gravitational lensing or the integrated Sachs-Wolfe effect conserve the Planckian shape of the photon energy distribution?

bonus question: what's $\sum_{i=0}^n{n\choose i}$ with the binomial coefficient ${n\choose i}=n!/i!/(n-i)!$?

4 comments:

  1. let me add an impromptu bonus question: could you construct other spectra that would be conserved by the iSW-effect?

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  2. bonus question: you can apply the general binomial formula in a funny way:
    \begin{equation}
    \sum_{i=0}^n{n \choose i} = \sum_{i=0}^n{n \choose i} 1 \times 1 = \sum_{i=0}^n{n \choose i} 1^i 1^{n-i} = (1+1)^n = 2^n
    \end{equation}

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    Replies
    1. and of course you're welcome to use this result for next week's bonus question!

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  3. i'm actually not quite sure as to why that is. my best guess would be the equivalence principle, because you can always get rid any gravitational effect by transforming into a free-falling frame. then, i'd say, one can use the fact that Planck-spectra are relativistically invariant.

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