An experiment to determine whether the universe is expanding

In the 19th century the German physicist Joseph von Fraunhofer (1787-1826) discovered that the solar spectrum contains a number of dark bands.  Fraunhofer made a detailed study of the wavelengths of these lines and later it was discovered independently by Bunsen and Kirchhoff that each chemical element has a characteristic set of these so called absorption lines.  The problem was then how to match up the lines in the solar spectrum with the absorption lines of all the different elements.  The spectral lines for a particular element are rather like a barcode.  When observing an object at a distance however the observer sees a single set of spectral lines which is formed from the combination of spectral lines from each of the elements present.  The problem was how to disentangle this mass of spectral lines to determine the constituent elements of the sun and the stars.

Cecilia Payne (1900 – 1979) studied astronomy at Newnham College, Cambridge.  At the time Cambridge did not award degrees to women, so Cecelia moved to the United States where she to join the graduate program at Harvard Observatory.  She was persuaded to write up her studies as a PhD thesis for which she was awarded her degree by Ratcliffe which is now part of Harvard.  In her thesis she overturned the then conventional wisdom that the composition of the sun was similar to that of the earth and showed that stars are made largely of hydrogen with smaller amounts of helium also present.

It was thus possible to detect the presence of hydrogen in distant stars by looking for the characteristic spectral lines.  But there was a problem: the spectral lines were not quite where they should be in the spectrum; they appeared shifted slightly towards the red end of the spectrum.

In the early 1900s Vesto Silpher (1875 – 1969) discovered that most spiral nebulae displayed this red shift, but it was Edwin Hubble (1889 – 1953) who discovered the relationship between the red-shift of these nebulae and their distance from the earth.  Hubble first encountered the red shift during the 1920’s and he went on to catalogue the red shift for different objects but also to independently estimate the distance to these objects.  Hubble was meticulous and took many readings from objects at different distances from the earth. He was able to estimate the distance to these objects by measuring the intensity of stars called Standard Candles. These are stars which are thought to have the same luminosity, so their brightness seen here on earth gives an indication of their distance.  He then plotted how the red shift varied with distance and discovered that there was a more or less linear relationship as best as he could tell from the data.  Despite the fact that the method of using Standard Candles to measure distance is somewhat imprecise, nevertheless Hubble’s results were convincing.

Red shifts can have a number of causes, but the one that scientists hit upon to explain Hubble’s results was related to the Doppler Effect.  The Doppler shift, the change of frequency due to movement, was first described in relation to sound waves.  Its first occurrence in relation to light was described by the French physicist Armand-Hippolyte-Louis Fizeau in 1848, who pointed to the shift in spectral lines seen in stars as being due to the Doppler Effect.  Doppler had discovered that objects which emit waves appear to do so at a higher or lower frequency depending on whether they are moving towards or away from the observer.  Most people are familiar with the often quoted example of a police siren, which has a higher note as the police car is approaching and a lower note as it recedes.  This is the Doppler Effect as it applies to sound.

The same effect occurs with light and other electro-magnetic radiation and forms the basis of inventions such as Doppler radar which is able to look for these minor changes in the frequency of microwave radiation to detect moving objects against background clutter.  The British astronomer William Huggins used the Doppler shift to estimate the velocity of a star moving away from the Earth in 1868.

A red shift is an apparent lowering of the frequency of the radiation and scientists reasoned that this must be caused by the fact that distance galaxies are receding.  Hubble’s analysis showed that the extent of the red shift varies with distance, galaxies which are further away displaying a larger red shift. A universe in which objects are receding proportional to their distance is consistent with a universe which is expanding.

If the universe is expanding then at some time in the distant past it must have been smaller.  Go far enough back in time and it must have been very small indeed; infinitesimally so; it is this idea that leads to the Big Bang, a point in time when the universe exploded into existence and continued to expand until it reached its present size.

The idea of a Big Bang was first proposed by the Russian mathematician and cosmologist Alexander Friedman.  He had solved Einstein’s field equations for a particular case which showed that the universe could be expanding.  Sometime later and independently, the Belgian physicist and Roman Catholic priest, Georges Lemaitre proposed the idea that the recession of the galaxies was consistent with an expanding universe, although both of these suggestions were largely ignored at the time.

For several years the idea of the Big Bang remained controversial with scientists divided into two camps one which favoured the big bang explanation and one which favoured an alternative so called steady state explanation.  It is interesting to note that both of these theories took for granted the idea that the universe was indeed expanding.  The idea that the universe could be stationary, that is neither expanding nor contracting, was dismissed as being irrelevant.  Two protagonists in particular fought a running and sometimes heated battle over the idea and its implications.  On the one hand was the camp led by astronomer Fred Hoyle (1915 – 2001), a dour Yorkshireman who objected as much on philosophical grounds as on scientific grounds to the idea of an expanding universe.  He was of the opinion that a universe that began with a Big Bang was consistent with a point in time of universal creation when the universe came into being and that such a moment of creation opened up the possibility of a creator god.  Hoyle refused to believe in any sort of god and so could not accept the idea of a Big Bang.

He did however accept the idea of an expanding universe and came up with an explanation which was dubbed the Steady State theory.  He likened the situation to that of a river estuary which grows wider as it reaches the sea.  An observer looking at this from a fixed reference point sees the river as expanding as it moves downstream.  To sustain this idea it is necessary to continually feed the system with fresh water from upstream and to drain away the water downstream.   Hoyle argued that matter was continuously being created somewhere in the universe and flowing past us here on earth in an ever expanding stream.

Somewhat ironically, it was Fred Hoyle himself who coined the term Big Bang.  Originally intended to disparage the idea; it has since stuck.

The rival camp was headed by George Gamow (1904 – 1968).  He used the idea of the Big Bang to explain the creation of matter in a process called Nucleosynthesis which he developed in association with physicists Ralph Alpher and Robert Herman.  Coincidentally their work also predicted the existence of a low level background radiation which would be found in the microwave part of the spectrum and it was the detection of this low level background radiation which finally settled the argument in favour of the Big Bang.

The matter appeared to be settled when, in 1964 two researchers at Bell Labs, Arno Penzias and Robert Wilson, intending to work on microwave astronomy accidentally discovered a low level microwave background radiation.  This discovery sealed the fate of the Steady State theory which had no explanation for the phenomenon.  Since then the Big Bang has come to be the accepted theory on the origin of the universe.

The Big Bang does however present a number of irreconcilable problems many of which are simply brushed aside by its advocates who argue that all of the Red Shift is as a result of universal expansion. Under such circumstances the age of the universe, that is the time since the Big Bang is calculated as the reciprocal of Hubble’s constant, which puts the age of the universe at around 13.8 billion years.  However, the use of other methods for calculating the age of the stars and galaxies appears to yield results which conflict with this value.  Calculation of the age of certain star clusters based on their mass and the rate at which they consume hydrogen in globular clusters puts the age at anything up to 18 billion years.  Although more recently scientists have tried to revise this estimate downwards in order to bring it more in line with the Hubble derived estimate for the age of the universe, this can be seen in part more as an attempt to massage the data to fit the theory.

The most distant objects in the universe are calculated to be more than 13 billion light years away from us based on their red shift. Among these very far distant objects is the galaxy UDFy-38135539 whose distance has been calculated at 13.1 billion light years (Shinga, 2010).  The light reaching us now from this distant source must have departed from UDFy-38135539 13.1 billion years ago, which at that time must have been 13.1 billion light years distant from us here on earth.  So just 700 million years after the Big Bang galaxy UDFy-38135539 was 13.1 billion light years distant, but if the Big Bang theory is correct, then just a few milliseconds after the Big Bang the universe was the size of a grapefruit and before that the size of a golf ball, which means that the material which made up galaxy UDFy-38135539 must also have moved from being a few centimetres from the proto earth to some 13 billion light years distant in an period of less than 700 million years.  Even averaging this out over the 700 million years, this would mean it moving at something approaching 18 times the speed of light.

The solution to this apparent dilemma has been to invent the idea of cosmic inflation – a period in time when the size of the universe supposedly increased by a factor of 1078 in a period of time which lasted from 10-38 seconds after the Big Bang to 10-32 seconds after the Big Bang.  The fact that this completely negates Einstein’s ideas that nothing can travel faster than the speed of light is conveniently overlooked.

There are problems too with the rate of expansion of the universe in the Big Bang theory.  The main one being that the rate of expansion would appear to be increasing.  Such an increase demands that energy be found from somewhere to fuel this increased rate of expansion.  The solution has been to invent the concept of a Dark Energy.  A source of energy that is invisible and as yet undetectable which somehow manages to drive this process.  I believe the correct expression for such Dark Energy is “Magic Fairy Dust”.

Yet more problems occur with the mass of the universe, which is insufficient to be consistent with most Big Bang theories, necessitation the invention of another type of Magic Fairy Dust, this time called Dark Matter.

The current Big Bang theory holds that the universe is expanding in all directions and has no centre.  A simple model based on an expanding balloon is often used to illustrate how this might happen in a two dimensional space.  The problem with this is that the balloon has a surface which is curved and so can be infinite but boundless, whereas the universe appears to be flat.  A flat universe which is expanding is inconsistent with a boundless universe.  If the universe is flat and it is expanding from some original event then it must have a boundary and if it has a boundary then it must have a centre.

So much for the difficulties with the Big Bang, of which there are many more, what of the ways in which we can prove whether or not it ever happened?

The energy of an individual photon is proportional to its frequency, the constant of proportionality being Planck’s constant. So a red shift, which represents a loss of the frequency of the photon, can also be thought of as a loss of energy.

In the current Standard Model in which the universe is thought to be expanding all of this energy loss takes place as the photon is emitted.  Energy loss due to the red shift is thus an event associated with the emission of the photon caused by the fact that the emitter is moving away from us, the observer.  After it has been emitted in this way the photon travels unmolested and unaltered across space until it is observed here on earth.  This is precisely the basis on which the expanding universe model us built and which therefore underpins the idea of the Big Bang.

If the universe is not expanding then this cannot be the case.  If distant objects are not moving away from us there can be no red shift associated with the emission event.  Instead the red shift must occur as a result of some other process which happens as it traverses the space between its origin and observer.

It is this difference between the idea of the red shift as an event or as a process which can provide a means to determine experimentally whether the universe is expanding or not. If we can determine the mechanism that underlies the red shift then we can ascertain the rate of expansion of the universe.  The trouble is that recession of the emitter is undoubtedly a possible cause of a red shift and that has been latched onto by the current theorists, but the question we seek to address is whether it is the cause of the red shift.

In “Shedding Some Light on the Nature of the Photon” I suggest that the velocity of the photon varies as a function of its frequency, with photons of a lower frequency (longer wavelength) travelling faster than higher frequency photons.  The velocity of the photon follows a simple mathematical law and is given by:

A graph of this function in Figure 1 shows the relationship more clearly.

Figure 1

Figure 1 Velocity of propagation vs Frequency

Figure 1

This plots the frequency on a logarithmic scale which allows us to see the familiar spectrum more clearly.  However if we were to plot frequency on a linear scale we get a slightly different picture of what is going on.  The characteristic is the quadrant of a circle.

There is already some evidence to support the idea that the velocity of light varies with frequency and it would appear that red light travels faster than blue light which is consistent with the ideas outlined here[i].

It is this difference in velocity with frequency which holds the key to measuring the distance to far away objects and the prospect of doing so with unprecedented accuracy.

Suppose a distant object emits a pulse of light containing a wide range of frequencies.  Assume for the sake of argument that each pulse is composed of photons of many different frequencies and that they all depart the object at exactly the same time.  If we measure the arrival time of the red and the blue photons then, based on the difference in the arrival time of the two colours, we can calculate the distance to the object.  If the object is one that emits such pulses in a regular repeating pattern, such as is the case with a pulsar, we can repeat the measurement over and over again.   With each such repetition the accuracy of the measurement improves and goes on doing so to an almost arbitrary degree.

There is one problem however and that relates to an issue which I touched on in “Sampling the Hydrogen Atom”.  In the unending sequence of red and blue pulses of light we have no way of knowing which red pulse and which blue pulse were emitted at the same time, and so the measurement could be off by an arbitrary whole number of cycles of the pulsar.  We can solve this problem by introducing a third frequency or colour.  If we measure not only the difference in the arrival times of red and blue light pulses, but also the difference in respect of say green light as well we obtain additional distance measurements which also contain this arbitrary error.  However with a judicious choice of frequencies only one distance will match all of the various delay periods that we observe.

If the red shift is an event associated with photon emission then the frequency of the photon remains constant throughout its journey across space and so therefore does its velocity.  Under these circumstances calculating the distance to the source of the emissions is simply a matter of multiplying difference in velocity of the photons by the interval between their arrivals at our detector here on earth.

If on the other hand the red shift is a process which takes place during the photon’s journey across space then the distance calculation becomes a little more complicated.  Photons which left the emitter would have done so with a higher frequency and therefore a lower velocity than when they arrive.  This is true for photons which are red on arrival and those which are blue on arrival.  The relationship between distance and time difference is quite complicated and depends on exactly how the photons lose energy with distance but the essential point is that the photons started out further up the spectrum and more important further apart in the spectrum and hence the speed difference at the start of their journey was greater.

This means that distance we associate with a particular time difference will be less if the photons lose energy during their journey than if they were to have lost all of their red shift energy at the very outset of their journey.

So in order to determine whether the red shift is associated with the emission of the photon or its transit it is necessary to compare the distance measured by this method with the known distance to the pulsar, but therein lies a problem.  We do not know the distance to the pulsar with any degree of accuracy.  Any measurements we do have are based on standard candles and extrapolation using the Hubble red shift and so are of dubious accuracy.

There is a way around this however and that is to make an exactly similar measurement only this time instead of using red blue and green light we use a different part of the spectrum, say UVA and UVB.  This too will lead to a measurement of the distance to the pulsar and this too will have two possible interpretations, one based on the red shift as an event and one based on the red shift as a process.  However, only one of these measurements will be consistent with the equivalent measurement made in the visible part of the spectrum.

In general we can make a whole series of measurements of the relative arrival times of pulses of electromagnetic radiation over a wide spectrum and then try to see which of the two models, the red shift event or the red shift process, best matches the characteristics of the photon over the entire spectrum.

[i] Anil Ananthaswamy The Light that Came Late New Scientist Vol 203 No 2721 15th Aug 2009 pp 26-29

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