## Wednesday, February 20, 2013

### Hubble slow motion

does time pass slower in distant galaxies? if you could observe a planetary system at high redshift and observe the orbits of planets (or any other dynamical system driven by gravity), would the observation be consistent with a lower gravity instead of a slower passage of time? what about atomic processes like chemical reactions or radiative processes?

bonus question: can you show that for a real-valued matrix $A$ the matrix exponential $\exp(A)$ transforms according to

\exp(R^{-1}AR) = R^{-1}\exp(A)R

with any invertible matrix $R$?

because of the associativity of the matrix product, $(R^{-1}AR)^i = R^{-1}AR\ldots R^{-1}AR = R^{-1}A\ldots AR = R^{-1}A^iR$.