Mathematics of Physics and Engineering

120 Theory of Relativity

to conclude that

At 0 A£i

R(h) RihY

Hint: r(ti) - r(t 0 ) = r(h + Ati) - r(t 0 + At 0 ).

(2.4.47)

By observing the light from distant galaxies, Hubble determined that
Ato < A^i or 1/Ato > 1/Ati, that is, the frequency of the received radi-
ation shifts toward the lower-frequency, or red, part of the spectrum. By
(2.4.47), this observation implies R(t 0 ) < R(h), that is, the Universe is
expanding.