TAP 704- 4: Relativity and the expanding Universe
The expanding Universe according to general relativity
According to general
relativity, the Big Bang
was not an explosion of
matter into empty space.
Both space and matter came into existence together about 14 billion years ago.
Imagine a balloon with dots drawn on
it to represent galaxies, and slowly
blow it up.
As the balloon grows, the
space between the
galaxies grows. The
galaxies do not move
within the surface.
In the real Universe - unlike in the balloon model - the
galaxies themselves do not grow: their gravity holds
them together.
General relativity pictures the expansion of space-time as if it were an expanding balloon.
The cosmological red-shift...
Think of an electromagnetic wave drawn on the balloon, travelling from one galaxy to another.
A light wave travels from galaxy 1 to galaxy 2. The galaxies are a distance demitted apart
when the wave is emitted.
The Universe expands.
 emitted
d emitted
Space is stretched and the wave with it.
received
dreceived
When the light is received, the galaxies are a distance dreceived apart.
Wavelengths are red shifted because space-time stretches as the light travels through it.
The expansion of space is related to the cosmological red shift.
Practical advice
The balloon model of the expansion of space-time is a good analogy of the predictions of
general relativity. The problem with drawing galaxies (more correctly, clusters of galaxies) on
a balloon is that the galaxies themselves expand as space-time does. This does not happen
in reality because of the gravitational attraction between the galaxies within a cluster. A
different model can be made by gluing cotton wool galaxies to the balloon which then do not
expand as the balloon does – however, these galaxies do stick out from the space-time fabric
in a rather unrealistic way!
The cosmological red shift, from which measurements of the Hubble constant are made, is
seen using this model as being due to the expansion of space-time. The recession of distant
galaxies is not then due to their velocities through space but rather to the expansion of the
space-time between them. Hubble’s original data were interpreted as being due to an actual
velocity of the galaxies away from each other; today’s interpretation is rather different.
Alternative approaches
A Modellus model animating stretching wavelengths in an expanding Universe.
Modellus
Modellus is available as a FREE download from http://phoenix.sce.fct.unl.pt/modellus/ along
with sample files and the user manual
Social and human context
The origins and future of the Universe are of constant fascination to humankind.
External reference
This activity is taken from Advancing Physics, chapter 12, 170O