A Review of Redshift and Its Interpretation in Cosmology and Astrophysics”
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“A review of redshift and its interpretation in cosmology and astrophysics” R. Gray and J. Dunning-Davies, Department of Physics, University of Hull, Hull HU6 7RX, England. email: [email protected] Abstract The interpretation of redshift in cosmology and astronomy yields a great deal of information about the universe in which we live, but much controversy surrounds the correct interpretation of the phenomenon. This article discusses the history of the redshift, and how its interpretation varies between different cosmological theories, including the Big Bang theory and some of its most famous rivals, the Steady State theory and Tired Light theory, and aims to highlight a few of the problems still existing. Some notions not normally associated with astronomy and astrophysics are mentioned also in the hope that a somewhat broader view of this important topic may be investigated. Introduction Redshift is a very important, and somewhat controversial, phenomenon with respect to cosmology and astronomy. The phenomenon occurs when the electromagnetic radiation that is emitted or reflected from an object is shifted toward the less energetic (higher wavelength) end of the spectrum. Using this phenomenon allows a start to be made on attempting to understand features of our galaxy and even of the universe as a whole. However, there is a large number of interpretations of the observed redshift and this brings into question the true nature of the observations and their meaning. One particular case where this is especially relevant is in the theories surrounding the origins of our universe. Nowadays, the Big Bang model for the origin of the universe often appears to be accepted as established fact1, its popularity in the scientific community apparently overshadowing all other theories. But, is this model necessarily correct? What evidence truly supports this theory over others? Is it, in fact, fair for this theory to receive so much acclaim, when rival theories seem to be dismissed without being afforded the same privileges of additions and corrections to their problems? These questions are amongst those to which this article aims to draw attention; there may not be a definite known answer, but a broader view of the problems surrounding these topics may allow an open-minded reader the opportunity their own decision as to whether or not to believe “conventional wisdom”. It is intended to discuss the history of redshift and its astronomical and cosmological interpretations, including the origins of the redshift-distance relationship theory and Hubble’s Law, making mention of the Doppler effect and how the two are related. This should cover the “relativistic Doppler Effect”, Einstein’s general relativity equations, their solution by Schwarzschild, Friedmann’s equations and gravitational redshift. Discussion will follow of some of the views of our universe and, more specifically, of the theories for the origins of the universe and how the interpretation of the cosmological redshift is important to these theories. In particular, due to its popularity in the scientific community, the Big Bang theory will be considered in some detail, drawing comparisons between this theory and its rivals, such as the Steady State theory. A brief discussion of one or two alternative theories for the cause of the cosmological redshift will also be included. These may be linked with the theories of the origins of the universe, but will be discussed in more detail afterwards, and include the Compton effect, “intrinsic redshifts” and tired light theory. History and Origins of “Redshift” Theories regarding cosmological redshifts began with the development of wave mechanics in the 19th Century, and the exploration of phenomena associated with the Doppler effect. This effect is named after Christian Andreas Doppler, who offered the first known physical explanation for the phenomenon in 1842.2 The Doppler effect is one encountered on a day-to-day basis, though the average person may not understand fully what it is, or that they are even experiencing it. It is commonly attributed to sound 2 waves, as these are involved in the most commonly encountered occurrences of the effect. Doppler predicted that this effect should apply to all waves. This prediction turns out to be correct. The first Doppler redshift was described in 1848 by French physicist Armand- Hippolyte-Louis Fizeau, who pointed to the shift in spectral lines seen in stars as being due to the Doppler Effect. In 1868, British astronomer William Huggins was the first to determine the velocity of a star moving away from the earth by this method3. In 1871, optical redshift was confirmed when the phenomenon was observed in Fraunhofer lines using solar rotation, about 0.1 Å in the red4. Optical redshift was also verified in 1901 by Aristarkh Belopolsky in the laboratory using a system of rotating mirrors5. The earliest occurrence of the term “red-shift” in print (in this hyphenated form), appears to be by American astronomer Walter S. Adams in 1908, where he mentions "Two methods of investigating that nature of the nebular red-shift"6. The word doesn't appear unhyphenated, perhaps indicating a more common usage of its German equivalent, Rotverschiebung, until about 1934 by Willem de Sitter7. Beginning with observations in 1912, Vesto Slipher discovered that most spiral nebulae had considerable redshifts8. Then, in 1915, Albert Einstein developed his equations of General Relativity. These equations Gμυ = -(8 G/c2)Tμυ connect matter and energy with the geometry of spacetime. Each superscript stands for one of the 4 coordinates of spacetime; so what looks like one equation is actually 16 equations (since some are repeated, there are really 10 equations)9. In essence, these formulae describe the laws of conservation, e.g. conservation of energy and momentum. These equations were solved by Karl Schwarzschild in 1916. The metric found by Schwarzschild is commonly given in the vast majority of textbooks as [1] It describes the spacetime geometry surrounding a spherically symmetric object of mass M, situated at the spatial coordinate r = 0. This metric gives an excellent description of the spacetime geometry around objects like the sun and the earth, that are, to a good approximation, spherical and forms the basis for an examination of the three classic tests of Einstein's theory of general relativity: 1) the perihelion advance of Mercury, 2) the bending of starlight by the sun and 3) the “gravitational redshift”. Later, Edwin Hubble discovered an approximate relationship between the redshift of nebulae, such as those observed by Slipher, and the distance to them, with the formulation of his Hubble’s Law10. This law is simply a statement that the redshift in light coming from a distant astronomical entity (for example, a galaxy) is proportional to its distance. These observations corroborated Alexander Friedmann’s work from 1922, in which he derived the famous Friedmann equations11, a set of equations that governs the 3 expansion of space in homogeneous and isotropic models of the universe within the context of general relativity. This is considered to be the first observational basis for the expanding space paradigm and today serves as one of the most often cited pieces of evidence in support of the Big Bang theory. However, it may be interesting to note that Hubble, even up to his final lecture before the Royal Society, always held open the possibility that the redshift did not mean velocity of recession but might be caused by something else1. Doppler Shift: A Little More Detail As explained above, the Doppler shift is a phenomenon in which the frequency and wavelength of a wave change for an observer moving relative to the source of the waves. If a source of light is moving away from an observer, then a redshift can be observed; conversely, if a source of light is moving toward an observer, a “blueshift” is observed. If the source moves away from the observer with velocity v, then, ignoring relativistic effects, the redshift is given by z v/c where c is the speed of light in a vacuum. In the classical Doppler effect, the frequency of the source is not modified, but the recessional motion causes the illusion of a lower frequency. However, for a more complete view of the effect, one must consider relativistic effects associated with motion of sources close to the speed of light. This “relativistic Doppler effect” is different from the non-relativistic Doppler effect as the equation includes the time dilation effect of special relativity and does not involve the medium of propagation as a reference point. They describe the total difference in observed frequencies and possess the required Lorentz symmetry. The revised expression for the redshift is This phenomenon was first observed in a 1938 experiment performed by Herbert E. Ives and G.R. Stilwell, called the Ives-Stilwell experiment12. Since the Lorentz factor is dependent only on the magnitude of the velocity, this causes the redshift associated with the relativistic correction to be independent of the orientation of the source movement. However, in contrast to this, the classical part of the formula is dependent on the projection of the movement of the source into the line of sight which yields different results for different orientations. Consequently, for an object moving at an angle θ to the observer (zero angle is directly away from the observer), the full form for the relativistic Doppler effect becomes and for motion solely in the line of sight (θ = 0°), this equation reduces to 4 For the special case when the source is moving at right angles (θ = 90°) to the detector, the relativistic redshift is known as the “transverse redshift”, and a redshift is measured, even though the object is not moving away from the observer.