Olber’s Paradox

olberOlber’s paradox dates back to the 16th century and is often cited as evidence to support the idea that the universe had a finite beginning in the form of a Big Bang.  The paradox concerns the idea that a dark night sky conflicts with the idea that the universe is infinite, eternal and static.   It is named after the 19th century amateur German astronomer Heinrich Wilhelm Olbers (1758 – 1840) who described it in 1823, although it almost certainly precedes that and dates back at least to the English Astronomer Thomas Digges (1546 – 1595).

The paradox argues that an infinite, eternal and static universe would have a night sky which was bright and not the dark sky that is known to exist.  The essence of the argument is that any ray traced from an observer on earth out into such a space would ultimately end on a star and hence no matter what the direction an observer looked he would see a point of light.

At first sight it might be argued that this is an inevitable consequence of the inverse square law. The further away a star is from us here on earth, the less of its light reaches us. So if you look far enough into space, you will reach a point where there is virtually no light reaching us from that distance.  The problem however with this argument is that while the intensity of light from each star falls off as the inverse square of the distance to the star, the number of stars at any given distance increases in as the square of the distance, in other words in exact proportion to the attenuation due to the inverse square law.  The result is that we should expect the night sky to be bright.  All of the gaps that appear due to the inverse square law are filled by more stars the further away we look.

Another argument that has been put forward is that dust and other particles in the intervening space between us and distant stars would absorb some of the light, leading eventually to a dark night sky.   Once again there is a flaw in this argument.  The problem here is that the intervening dust would absorb energy from the light and that would raise its temperature, causing it to glow.  If all of the energy along a particular path were absorbed, sufficient to render that point a dark point in space, then the intervening path would have absorbed exactly that amount of energy such that it would glow as brightly as the distant star.

The currently held view is that the dark sky happens because the universe has a finite age.  The further one looks into space, the further back one looks in time.  Eventually the point is reached where one is looking back into a time from before the Big Bang.  Unless there happens to be an intervening star, then any ray traced from here on earth will not appear as a bright spot, but will be dark.  The population of stars in the universe is sufficiently sparse that the night sky then appears predominantly dark.

The Big Bang theory however introduces a new paradox.  If looking further into space involves looking back in time, then eventually the observer will see back sufficiently far to see the Big Bang itself, which was by definition a very hot, bright event.  The paradox is explained by invoking the expansion of the universe itself. Such an expansion is accompanied by a cooling effect, similar to that which happens when gas is expelled from an aerosol can. It is argued that the resulting cooling of the remnants of the Big Bang is now seen as the microwave background radiation.  The problem here is that light from 13.8 billion years ago originated in the big bang and so we should not be looking at the way the universe now is, cool and radiating microwave energy, but hot, exactly as it was at the time of the big bang.  The way that the big bang theory  gets around this slight inconvenience is to argue that there was a period of rapid inflation when the universe grew at enormous speed, pushing the constituents of the early universe apart far faster than the speed of light. That way we are seeing it as it was after this rapid expansion.

While the Big Bang may be consistent with the idea of a dark night sky, this is by no means the only explanation, indeed it is not even a very good explanation of the phenomenon since it requires that we overturn Einstein’s postulate that nothing can travel faster than the speed of light.

It is well understood that the further out into space we peer, the further back in time we are looking, this is the essence of the big bang explanation for Olber’s paradox.  So when we look at the sun for example we are not seeing it as it is now, but as it was 8 minutes or so ago.  This is the time it takes for light to travel from the sun to reach us here on earth.  Similarly when we look at a star which is say 50 light years away, we are seeing it as it was 50 years ago.  This is one reason why measuring cosmological distances using units of time, light years, makes sense.

However there is another phenomenon which is closely related and which is often overlooked.  Light from distant objects is shifted towards the red end of the spectrum.  With this so called Red Shift the further away the object is, the more the light from that object is shifted down the spectrum.  Looking at this from a slightly different perspective we can see that this is equivalent to saying that the further out into space we look the further up the spectrum we are looking.

A question then arises over the bandwidth of the photon which has to be limited in some way, otherwise we could expect photons with infinite frequency and infinite energy.  Infinite energy means enough energy in a single photon to destroy a star, enough energy in a single photon to destroy a galaxy, indeed it means enough energy to destroy all of the galaxies.  Clearly this is not the case and so there has to be a limit on the maximum energy that a single photon can carry.  In Shedding Some Light on the Nature of the Photon, a model is developed for the photon in which the bandwidth is seen to be limited by its inherent structure.

With photons having limited bandwidth and the further out into space we peer the further up the spectrum we are looking.  There must therefore come a point where we are looking so far out into space that we have reached the upper frequency limit of the photon and all we can see from beyond that point is black.  Hence the dark night sky.

Looking at it another way,  photons from this critical distance and beyond are red shifted to such an extent that they are no longer visible but are to be found in the part of the spectrum below the infra-red.  The critical distance at which this occurs then forms a visible event horizon from beyond which we cannot receive any visible light.  There are other similar event horizons for different frequencies, so for example there is a distance from beyond which we can never receive any X Rays and one for Ultra Violet.  In effect we are sitting at the centre of a series of such event horizons which form a set of concentric spheres.  We can only ever probe what lies beyond these event horizons by looking at lower and lower frequencies where, paradoxically, the resolution we can obtain gets less and less the further we look.

So here is a very simple rational explanation for the dark knight sky, one which does not require that we disbelieve Einstein’s theory of special relativity, one which does not requite that the universe started with a big bang, nor indeed that it is even expanding.  All that is necessary to fully explain Olber’s paradox is that there is a red shift, whatever its cause, and that the bandwidth of the photon has an upper limit.

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