Expanding Universe
The story of the discovery of the expanding universe is fascinating.
Here is an article which became
a book later on.
And
here is a Heise (German) article. In Wikipedia, the history is summarized:
- The red shift was discovered in 1912 by Vesto Slipher.
- Observational evidence of expansion of the universe came in 1924 with Knut Lundmark.
- A linear relation between distance and recession velocity was suggested by Georges Lemaitre in 1927.
- Observational confirmation of Lundmarks and Lemaitres findings by Edwin Hubble in 1929.
It is in this area of physics, where
tensors play an important role. The
metric tensor is what we called the
first fundamental form. If r is a parametrization or coordinate change then g = r
T r
is called the metric tensor or
first fundamental form. It is a symmetric matrix defined
at each point and a (0,2) tensor: it attaches to every pair of vectors column vectors
v,w a number ∑ g
ij v
i w
j.
We have seen that det(g)
1/2 is the
distortion factor when making a coordinate
change. If r is a parametrization into a larger dimensional space, it is still the
correct transported area or volume element like for example |r
u x r
v| in
the case of a parametrization of a surface or |r'| in the case of a parametrization of a
curve.
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