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[sci.astro] Cosmology (Astronomy Frequently Asked Questions) (9/9)
Section - I.17 Since energy is conserved, where does the energy of redshifted photons go?

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Author: Peter Newman <p.r.newman@uclan.ac.uk>

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
      relativity theory.

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.

User Contributions:

1
Keith Phemister
⚠
Sep 13, 2024 @ 11:23 pm
Copied from above: If the Universe were infinitely old, infinite in extent, and filled
with stars, then every direction you looked would eventually end on
the surface of a star, and the whole sky would be as bright as the
surface of the Sun.
Why would anyone assume this? Certainly, we have directions where we look that are dark because something that does not emit light (is not a star) is between us and the light. A close example is in our own solar system. When we look at the Sun (a star) during a solar eclipse the Moon blocks the light. When we look at the inner planets of our solar system (Mercury and Venus) as they pass between us and the Sun, do we not get the same effect, i.e. in the direction of the planet we see no light from the Sun? Those planets simply look like dark spots on the Sun.
Olbers' paradox seems to assume that only stars exist in the universe, but what about the planets? Aren't there more planets than stars, thus more obstructions to light than sources of light?
What may be more interesting is why can we see certain stars seemingly continuously. Are there no planets or other obstructions between them and us? Or is the twinkle in stars just caused by the movement of obstructions across the path of light between the stars and us? I was always told the twinkle defines a star while the steady light reflected by our planets defines a planet. Is that because the planets of our solar system don't have the obstructions between Earth and them to cause a twinkle effect?
9-14-2024 KP

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