This article is from the Astronomy FAQ, by Joseph Lazio (firstname.lastname@example.org) with numerous contributions by others.
By Peter Newman <email@example.com>
The energy of a photon is given by E = hc/lambda, where h is Planck's
constant, c is the speed of light, and lambda is its wavelength. The
cosmological redshift indicates that the wavelength of a photon
increases as it travels over cosmological distances in the Universe.
Thus, its energy decreases.
One of the basic conservation laws is that energy is conserved. The
decrease in the energy of redshifted photons seems to violate that
law. However, this argument is flawed. Specifically, there is a flaw
in assuming Newtonian conservation laws in general relativistic
situations. To quote Peebles (_Principles of Physical Cosmology_,
1995, p. 139):
Where does the lost energy go? ... The resolution of this
apparent paradox is that while energy conservation is a good
local concept ... and can be defined more generally in the
special case of an isolated system in asymptotically flat space,
there is not a general global energy conservation law in general
In other words, on small scales, say the size of a cluster of
galaxies, the notion of energy conservation is a good one. However,
on the size scales of the Universe, one can no longer define a
quantity E_total, much less a quantity that is conserved.