IB Physics

Option F - Astrophsyics

Cosmology

olber's paradox / big bang / development of the universe

Olber's Paradox

If we look out into space, we do not see an edge. It seems to carry on much the same in all directions. The constellations all seem to remain the same. From these observations, Newton assumed that the universe is infinite, uniform and static. This view, however, was difficult to reconcile with a seemingly simple question, ‘Why it is dark at night?’ If the universe is what Newton assumed it is, then the night sky should be bright since there are a huge number of stars shining.

If stars were identical then those at the same distance away would be the same brightness. The stars further away would be dimmer but there would be more of them.

The instensity (or as we call it here, apparent brightness, b, in Wm-2) of the light we get from a star with the power (which we call the absolute luminosity, L, in W) decreases with the square of its distance d from us:

Assume now that all stars in the universe have the same luminosity, L, and that they are uniformly distributed in the universe, with a constant number, N, of stars per volume unit (this is not true in detail, stars are sticking together as galaxies, but on a large enough scale this would on average be true).Then we study a spherical shell which is thin (compared to the size of the universe).

One solution could be that the universe is not infinitely old, so light from distant galaxies that are traveling very fast with respect to Earth, has not yet reached us. This contradicts Newton’s assumption of a static infinite universe, since in this case the universe is evidently expanding. The faster stars travel the greater is the red shift, so we could perhaps not even see the electromagnetic waves the most distant stars emit, since they don’t appear in the visible spectrum. Another solution is that the light could be absorbed before it reaches us. However, if something was in the way and absorbed the light, then it will heat up and eventually reradiate the energy. The universe may not be infinite and there is a ‘cosmic edge’, then the stars do not carry on forever but there is a limit to the universe. If we are receiving light from a finite number of stars, then the night sky will be dark.

The universe may not be static. When adding up the contributions of each shell of stars, we assumed that the light from the far shells would add to the light from the near shells. But light has a finite velocity, so it would take time for light to travel from further shells.

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The Big Bang

The ‘Big Bang’ theory was developed over some years, based on observations made about deep space. The initial proposal of the theory is mainly accorded to Georges Lemaître, who suggested the idea of an explosion of a primeval atom, implying that all the matter in the universe was at the same point about 15 billion years ago. This theory was then further developed by George Gamow, in opposition to the ‘Steady State’ theory proposed by Fred Hoyle. In fact, the name ‘Big Bang’ was coined by Hoyle, in derision of the theory. However, the name stuck, and the ‘Big Bang’ theory went of to become the dominant theory of the origin and evolution of the universe.

The ‘Big Bang’ theory itself states that both space and time originated with the ‘Big Bang’ itself. In this case, it is important to note that the universe itself is not expanding into anything; even a void. It is simply expanding. There is also no such time as ‘before the Big Bang’, as time itself was created in the Big Bang.

The observations that supported the ‘Big Bang’ theory as well as the ‘Steady State’ theory were made by Edward Hubble, and relate to the Hubble constant; that is that the universe is expanding, as observed through the redshift of almost all the galaxies. This indicates that all of the galaxies are moving away from us.

Although that observation would seem to indicate that we, or rather, the Earth, are at the centre of the universe, this is not the case. It only appears to be this way as we are observing from the Earth. If we were on a different galaxy, we would see our own galaxy moving away in the same manner as we are observing that galaxy moving away. This can be related to the idea of painted dots on the surface of a balloon; as the balloon is inflated, all of the dots move away from each other equally.

Ultimately, however, what gave the Big Bang theory weight above all others was the discovery of Cosmic Microwave Background Radiation. This was discovered by Penzias and Willams in 1965. They discovered that the radiation was coming in all directions in space, when they built Dicke radiometer, originally intended for astronomy and satellite communication experiments. The presence Cosmic Microwave Background Radiation was predicted by Ralph Alpher and Robert Henman in 1948. They estimated the temperature of the cosmic microwave background to be 5 K though later, they re-estimated it at 28 K.

WMAP image of the cosmic microwave background radiation

This discovery supports the Big Bang theory in two major ways; firstly the early universe was in thermal equilibrium and the radiation from then had a black body spectrum, which has traveled through space, becoming increasingly redshifted up to this point in time. This reduces the temperature of the black body spectrum and the radiation should be visible from every point in space. Secondly, as the radiation travels throughout the universe, space has expanded, causing the wavelength to decrease. All these observations are in accordance with the Big Bang theory.

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Development of the Universe

Future of the Universe

If the Universe is expanding at the moment, what is it going to do in the future? Remember that our current model of the Universe is that it is infinite. We can not talk about the size of the Universe, but we can talk about the size of the observable Universe. At the moment the furthest object that we can see is about 12 billion light years away. What is going to happen to the size of the observable Universe? As a result of the Big Bang, other galaxies are moving away from us. If there were no forces between the galaxies, then this expansion could be thought of as being constant.

The expansion of the Universe cannot, however, have been uniform. The force of gravity acts between all masses. This means that if two masses are moving apart from one another there is a force of attraction pulling them back together. This force must have slowed the expansion down in the past. What it is going to do in the future depends on the current rate of expansion and the density of matter in the Universe.

An open Universe is one that continues to expand forever. The force of gravity slows the rate of recession of the galaxies
down a little bit but it is not strong enough to bring the expansion to a halt. This would happen if the density in the Universe were low.

A closed Universe is one that is brought to a stop and then collapses back on itself. The force of gravity is enough to
bring the expansion to an end. This would happen if the density in the Universe were high.

A flat Universe is the mathematical possibility between open and closed. The force of gravity keeps on slowing the expansion down but it takes an infinite time to get to rest. This would only happen if universe were exactly the right density. One electron more, and the gravitational force would be a little bit bigger. Just enough to start the contraction and make the Universe closed.

From top to bottom: geometry in a closed universe, an open universe and a flat universe.

Critical Density

The theoretical value of density that would create a flat Universe is called the critical density. Its value is not certain because the current rate of expansion is not easy to measure. It is round about 5 x 10-26 kg m3 or 30 proton masses every cubic metre. If this sounds very small remember that enormous amounts of space exist that contain little or no mass at all.

The density of the Universe is not an easy quantity to measure. It is reasonably easy to estimate the mass in a galaxy by stimating the number of stars and their average mass. This calculation results in a galaxy mass which is several orders of magnitude too small. We know this because we can use the mathematics of orbital motion to work out how much mass there just be keeping the outer stars in orbit around the galactic centre.

In effect, we can see only 10% of the matter that must exist in the galaxy. This means that much of the mass of a galaxy and indeed the Universe itself must be dark matter - in other words we cannot observe it because it is not radiating sufficiently for us to detect it.

Machos, Wimps and Other Theories

Astrophysicists are attempting to come up with theories to explain why there is so much dark matter and what it consists of. There are a number of possible theories:

  • the matter could be found in Massive Astronomical Compact Halo Objects or MACHOs for short. There is some evidence that lots of ordinary matter does exist in these groupings. These can be thought of as low-mass failed' stars or high-mass planets. They could even be black holes. These would produce little or no light.

  • some fundamental particles (neutrinos) are known to exist in huge numbers. It is not known if their masses are zero
    or just very very small. If they turn out to be the latter then this could account for a lot of the missing mass.

  • there could be new particles that we do not know about. These are the Weakly Interacting Massive Particles. Many experimenters around the world are searching for these so-called WIMPs.

  • perhaps our current theories of gravity are not completely correct. Some theories try to explain the missing matter as simply a failure of our current theories to take everything into account.

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