CosmologyThe Origin and Future of the UniversePart I

Olbers’ Paradox

Remember?

Hubble’s distance measurements confirmed a model of the Universe in which stars are grouped into galaxies…..

….. and local clusters of galaxies were distributed uniformly in space…..

….. and that galaxies more than 500 million light-years away are generally too faint to be seen but this does not negate the possibility of this pattern continuing throughout the Universe

So what’s the problem?

Well! Astronomers had established a cosmological model which was static, uniform and infinite – just like Newton had perceived…..

…until Heinrich Olbers came along…

Olbers’ Paradox

If the Universe is infinite, it follows that there must be an infinite number of stars in all directions which, in turn, means that the sky should be equally bright in all directions and the sky would be exceedingly bright!

We know that this is not so!

Olbers’ Paradox

If the Universe is static and not infinite then it would eventually collapse under its own gravitational forces!

We know that this is not so!

Olbers’ Paradox

That the Universe must be infinite and yet can not be infinite is known as Olbers’ Paradox

Olbers’ Paradox

Newton and Olbers both believed that:

Space is infinite and extends in all directions

The Universe is static

And then Hubble came along!

Hubble’s Law

Hubble discovered that the Universe is expanding and this negated the ‘truths’ which were until then believed

How did Hubble achieve this?

Towards Hubble’s Law

Vesto Slipher had discovered that dark lines in the spectra produced by the light from other galaxies had shifted towards the red end of the spectrum

These dark lines were otherwise easily identifiable as those representing particular elements

Towards Hubble’s Law

These red-shifts were explained in terms of the Doppler Effect

The bigger the red-shift, then larger the speed of recession: viz. the greater the speed with which the galaxy and the Earth are moving apart

The Doppler Effect

If a source is emitting light of wavelength λ metres travelling at c metres per second then one wave will be emitted in a time of λ/c seconds

If the source moves at v metres per second then it will have moved away (or towards) the observer a distance of v.λ/c metres during the production of one wave

This change in wavelength Δλ is given by:Δλ = v. λ/c

The Doppler Effect

This means that the fractional change in wavelength is calculable as shown:

Δλ/λ = v/c

Remember - v = speed of source and that c = speed of light

Remember – this equation is only valid where v is small compared with c

Hubble’s Law

Hubble discovered that there is a pattern between recessional speeds and the distance away of the galaxies:The recessional speed of a galaxy is directly proportional to its distance from the Earth

This is Hubble’s Law and implies that the whole Universe is expanding

Hubble’s Law

Hubble’s Law

Does this mean that the Earth is at the centre of the Universe if all cosmological bodies are moving away from the Earth?

No it does not for the following reason…..

Hubble’s Law

If two galaxies are distance d apart then in a time Δt the galaxies move a distance of Δd further apart; two galaxies a distance 2d apart would move a distance of 2Δd further apart

This would be true wherever you are in the Universe

So what of Olbers’ Paradox?

Owing to the fact that it was suggested now that the Universe is expanding and not static, a solution to Olbers’ Paradox exists…..

So what of a Big Bang?

As it had been shown that galaxies are all moving apart from each other at speeds which are directly proportional to their distances apart, it suggests that there must have been a time when all of the galaxies in the Universe were in the same place…..

So what of a Big Bang?

…..so the Universe must have started with a great explosion which we know as the Big Bang

It is possible to calculate when this Big Bang occurred: viz. if the recessional speed of a galaxy is 0.25 x speed of light and the distance away is 5 x 109 light years then the age of the Universe is equal to (5 x 109)/0.25 = 2 x 1010 years

The Hubble Constant

Hubble’s Law can be written as (speed of recession/distance) = H0

H0 is known as the Hubble Constant and is gradient of the graph linking recession speed to distance away of the galaxies; it is also the inverse of the age of the Universe…..

Viz. 1/H0 = age of the Universe

The Age of the Universe

The data obtained from the Hubble telescope, launched in the early 1990s, compared with other data has led to the general acceptance that the age of the Universe is around 12 (plus or minus 2) billion years

The Big Bang

In 1965 Cosmic Microwave Background Radiation was discovered

This was discovered as coming from all directions in space, at all hours of day and night and at the same strength (to within 0.01%)

The Big Bang

The existence of this microwave radiation and the fact that it corresponded to a black body temperature of 2.7K supported the idea that the Universe started with a Big Bang

The Big Bang

When the Big Bang occurred the Universe would have been very hot and, therefore, there would have been a lot of radiation with very short wavelengths

As the Universe expanded this radiation would have stretched to longer wavelengths and correspondingly lower energies

The Big Bang

It was predicted more than twenty years earlier that there should be microwave background radiation corresponding to a temperature just above absolute zero (0)K and the discovery of this radiation made the Big Bang theory more plausible

The Big Bang

The visible matter in the Universe is approximately 70% hydrogen and 27% helium

Since the Universe has existed, hydrogen burning in the stars could not have converted more than 2–3% of the hydrogen into helium

The Big Bang

There must have been a time when the temperature was so high that hydrogen-helium conversion (hydrogen burning) took place at a faster rate – Big Bang

The Big Bang theory thus became the standard model of the origin of the Universe