Olber’s paradox

Why isn't the night sky as uniformly bright as the surface of the Sun?

If the Universe has infinitely many stars, then it should be uniformly bright in all directions. 

Why is the night sky dark?

or

E4.1

Newton’s model of the universe assumed that the universe was infinite (in space and time) uniform and static.

Olber’s paradoxIf the Universe is eternal and

infinite and if it has an infinite number of stars, then the night sky should be bright.

Very distant stars contribute with very little light to an observer on Earth but there are many of them. So if there is an infinite number of stars, each one emitting a certain amount of light, the total energy received must be infinite, making the night sky infinitely bright, which it is not.

E4.1

universe is infinite in extent • contains an infinite number of stars uniformly distributed • is static and exists forever

n – density of stars, t – thickness of the shell at distance d from Earth; number of stars in shell = density x volume = n 4d2 t• brightness of one star decreases as 1/d2 ; b = L/4 πd2

• brightness of shell is constant;assuming that luminosity L is the same for all stars, the received energy per sec per unit area from all stars in the thin shell is:

22 4

4L d nt Lnt const.d

• amount of light we receive from shell does not depend upon how far away the shell is

• adding all shells to infinity; each contributing a constant amount of energy• sky would be uniformly bright; (the total energy received must be infinite)

Olber’s paradoxIf we consider the Universe finite and expanding, the

radiation received will be small and finite mainly for 2 reasons:

There is a finite number of stars and each has a finite lifetime (they don’t radiate forever)

andBecause of the finite age of the Universe, stars

that are far away have not yet had time for their light to reach us.

Also,The Universe is expanding, so distant stars are

red-shifted into obscurity (contain less energy).

E4.2

THE BIG BANG MODEL

E4.3-4.7

Doppler effect

In astronomy, the Doppler effect was originally studied in the visible part of the electromagnetic spectrum. Today, the Doppler shift, as it is also known, applies to electromagnetic waves in all portions of the spectrum. Also, because of the inverse relationship between frequency and wavelength, we can describe the Doppler shift in terms of wavelength. Radiation is redshifted when its wavelength increases, and is blueshifted when its wavelength decreases.

E4.3

Doppler effectIn astronomy, the Doppler effect was originally

studied in the visible part of the electromagnetic spectrum. Today, the Doppler shift, as it is also known, applies to electromagnetic waves in all portions of the spectrum.

Astronomers use Doppler shifts to calculate precisely how fast stars and other astronomical objects move toward or away from Earth.

E4.3

Doppler effectWhy is Doppler effect

so important?

In 1920’s Edwin Hubble and Milton Humanson realised that the spectra of distant galaxies showed a redshift, which means that they are moving away from Earth. So, if galaxies are moving away from each other then it they may have been much closer together in the past

Matter was concentrated in one point and some “explosion” may have thrown the matter apart.

E4.4

Background radiationIn 1960 two physicists, Dicke and Peebles, realising

that there was more He than it could be produced by stars, proposed that in the beginning of the Universe it was at a sufficiently high temperature to produce He by fusion.

In this process a great amount of highly energetic radiation was produced. However, as the Universe expanded and cooled, the energy of that radiation decreased as well (wavelength increased). It was predicted that the actual photons would have an maximum λ corresponding to a black body spectrum of 3K.

So, we would be looking for microwave radiation.

E4.5

Background radiationShortly after this prediction, Penzias and Wilson were working with a microwave aerial and found that no matter in what direction they pointed the aerial it picked up a steady, continuous background radiation.

E4.5

Background radiationIn every direction, there is a very low energy and

very uniform radiation that we see filling the Universe. This is called the 3 Degree Kelvin Background Radiation, or the Cosmic Background Radiation, or the Microwave Background. These names come about because this radiation is essentially a black body with temperature slightly less than 3 degrees Kelvin (about 2.76 K), which peaks in the microwave portion of the spectrum.

E4.5

Background radiation

Why is the background radiation an evidence for the Big Bang?

The cosmic background radiation (sometimes called the CBR), is the afterglow of the big bang, cooled to a faint whisper in the microwave spectrum by the expansion of the Universe for 15 billion years (which causes the radiation originally produced in the big bang to redshift to longer wavelengths).

E4.6

Big BangThe Big Bang Model is a broadly accepted theory for

the origin and evolution of our universe.It postulates that 12 to 14 billion years ago, the

portion of the universe we can see today was only a few millimetres across.

It has since expanded from this hot dense state into the vast and much cooler cosmos we currently inhabit.

We can see remnants of this hot dense matter as the now very cold cosmic microwave background radiation which still pervades the universe and is visible to microwave detectors as a uniform glow across the entire sky.

E4.6

Big BangThe singular point at which space, time,

matter and energy were created. The Universe has been expanding ever since.

Main evidence:Expansion of the Universe – the Universe is expanding (redshift) it was once smaller it must have started expanding sometime “explosion” Background radiation evidence of an hot Universe that cooled as it expandedHe abundance He produced by stars is little there is no other explanation for the abundance of He in the Universe than the Big Bang model.

E4.6

Fate of the UniverseUniverse

Closed Open

Enough matter density is not enough to allow an infinite expansion gravity will stop the Universe expansion and cause it to contract (Big Crunch)

Not enough matter density is such that gravity is too weak to stop the Universe expanding forever

Flat

Critical density Universe will only start to contract after an infinite amount of time

E4.8

Critical densityThe density of the Universe that separates a universe that will expand forever (open universe) and one that will re-colapse (closed universe).Critical density is the density of the Universe which produces a flat universe, i.e. it would take an infinite amount of time to stop expansion of it.

So, how do we measure the density of the Universe?

E4.9

Critical density is the density of the Universe that would be necessary to stop the expansion after an infinite amount of time

Critical densityIf we take in account all the matter (stars) that we

can see then the total mass would not be enough to keep the galaxies orbiting about a cluster centre.

So, there must be some matter that can not be seen – dark matter. This dark matter cannot be seen because it is too cold to irradiate.

According to the present theories dark matter consists in MACHO’s and WIMPS

E4.9

MACHO’s

WIMP’s

Massive compact halo objects – brown and black dwarfs or similar cold objects and even black holes.

Non-barionic weakly interacting massive particles (neutrinos among other particles predicted by physics of elementary particles)

It seems that there is also what is called “dark energy”…

E4.11

E4.11

Precision Cosmology

“…as we know, there are known knowns; there are things we know we know. We also know there are known unknowns; that is to say we know there are some things we do not know. But there are also unknown unknowns -- the ones we don't know we don't know.”