heusdens
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Originally posted by FZ+
There are clouds and I cannot see the stars. Godel's paradox provides that even if there were no clouds, I cannot see all the stars.
The fact that one can not see all the stars are not caused by Godels paradox (this is a paradox applied to any formal system, and says that any formal system can not be both complete and consistent) but by the fact that:
- Our eyes and instruments are not sensitive enough to capture all the light emitting objects, so we only see the objects that emit enough light that can be captured on earth. Far away objects because of their distance therefore leave not enough light to be seen on earth.
- The universe has a horizon, caused by the fact that light from far away objects has not had enough time to reach us. This is a phenomena closely linked to the expansion of the universe.
There is however another nice paradox attached to this, and which shows that the night sky is in effect dark (except for the dots of light from galaxies and stars), which could not be the case if the universe was infinite in size and infinite in time, and homogenous.
We assume the universe however to be homogeneous, and all parts of the universe containing (on the large scale) the same amount of matter and light emitting matter. Space dust does not contribute to the darkness, cause that would re-emit the light.
So one of the propositions would have to be false: either the universe is finite in size, or the universe has not existed for an eternity, at least not in it's present form with light emitting matter in forms of galaxies and stars.
The nice feature of this is that initially the cause of the darkness of the night sky was assumed to be caused by the redhsift of light. Which means that in another part of the spectrum, the night sky is in fact luminant, and which has shown to be the case at around 2.7 Kelvin. The initial value was derived from theoretical calculations, and was around 3 K (this is the temperature of surrounding space, or also known as the Cosmic Background Radiation - CMBR).
Later investigations showed that this explenation was wrong, and the CMBR is now considered as the remnants of the photons in the early universe, a short time after the Big Bang, when the temperature and density sank low enough to allow photons to travel freely.