Olbers's paradox, also known as the dark night paradox or Olbers and Cheseaux's paradox, is an argument in astrophysics and physical cosmology that says that the darkness of the night sky conflicts with the assumption of an infinite and eternal static universe. In the hypothetical case that the universe is static, homogeneous at a large scale, and populated by an infinite number of stars, any line of sight from Earth must end at the surface of a star and hence the night sky should be completely illuminated and very bright. This contradicts the observed darkness and non-uniformity of the night sky. [1]
The darkness of the night sky is one piece of evidence for a dynamic universe, such as the Big Bang model. That model explains the observed non-uniformity of brightness by invoking expansion of the universe, which increases the wavelength of visible light originating from the Big Bang to microwave scale via a process known as redshift. The resulting microwave radiation background has wavelengths much longer (millimeters instead of nanometers), which appear dark to the naked eye and bright for a radio receiver.
Other explanations for the paradox have been offered, but none have wide acceptance in cosmology. Although he was not the first to describe it, the paradox is popularly named after the German astronomer Heinrich Wilhelm Olbers (1758–1840).
The first one to address the problem of an infinite number of stars and the resulting heat in the Cosmos was Cosmas Indicopleustes, a 6th-century Greek monk from Alexandria, who states in his Topographia Christiana : "The crystal-made sky sustains the heat of the Sun, the moon, and the infinite number of stars; otherwise, it would have been full of fire, and it could melt or set on fire." [2]
Edward Robert Harrison's Darkness at Night: A Riddle of the Universe (1987) gives an account of the dark night sky paradox, seen as a problem in the history of science. According to Harrison, the first to conceive of anything like the paradox was Thomas Digges, who was also the first to expound the Copernican system in English and also postulated an infinite universe with infinitely many stars. [3] Kepler also posed the problem in 1610, and the paradox took its mature form in the 18th-century work of Halley and Cheseaux. [4] The paradox is commonly attributed to the German amateur astronomer Heinrich Wilhelm Olbers, who described it in 1823, but Harrison shows convincingly that Olbers was far from the first to pose the problem, nor was his thinking about it particularly valuable. Harrison argues that the first to set out a satisfactory resolution of the paradox was Lord Kelvin, in a little known 1901 paper, [5] and that Edgar Allan Poe's essay Eureka (1848) curiously anticipated some qualitative aspects of Kelvin's argument: [1]
Were the succession of stars endless, then the background of the sky would present us a uniform luminosity, like that displayed by the Galaxy – since there could be absolutely no point, in all that background, at which would not exist a star. The only mode, therefore, in which, under such a state of affairs, we could comprehend the voids which our telescopes find in innumerable directions, would be by supposing the distance of the invisible background so immense that no ray from it has yet been able to reach us at all. [6]
The paradox is that a static, infinitely old universe with an infinite number of stars distributed in an infinitely large space would be bright rather than dark. [1]
To show this, we divide the universe into a series of concentric shells, 1 light year thick. A certain number of stars will be in the shell, say, 1,000,000,000 to 1,000,000,001 light years away. If the universe is homogeneous at a large scale, then there would be four times as many stars in a second shell between 2,000,000,000 and 2,000,000,001 light years away. However, the second shell is twice as far away, so each star in it would appear one quarter as bright as the stars in the first shell. Thus the total light received from the second shell is the same as the total light received from the first shell.
Thus each shell of a given thickness will produce the same net amount of light regardless of how far away it is. That is, the light of each shell adds to the total amount. Thus the more shells, the more light; and with infinitely many shells, there would be a bright night sky.
While dark clouds could obstruct the light, these clouds would heat up, until they were as hot as the stars, and then radiate the same amount of light.
Kepler saw this as an argument for a finite observable universe, or at least for a finite number of stars. In general relativity theory, it is still possible for the paradox to hold in a finite universe: [7] Though the sky would not be infinitely bright, every point in the sky would still be like the surface of a star.
The poet Edgar Allan Poe suggested that the finite age of the observable universe resolves the apparent paradox. [8] More specifically, because the universe is finitely old (more precisely the Stelliferous Era is only finitely old) and the speed of light is finite, only finitely many stars can be observed from Earth (although the whole universe can be infinite in space). [9] [10] The density of stars within this finite volume is sufficiently low that any line of sight from Earth is unlikely to reach a star.
However, the Big Bang theory seems to introduce a new problem: it states that the sky was much brighter in the past, especially at the end of the recombination era, when it first became transparent. All points of the local sky at that era were comparable in brightness to the surface of the Sun, due to the high temperature of the universe in that era; and most light rays will originate not from a star but the relic of the Big Bang.
This problem is addressed by the fact that the Big Bang theory also involves the expansion of the universe, which can cause the energy of emitted light to be reduced via redshift. More specifically, the extremely energetic radiation from the Big Bang has been redshifted to microwave wavelengths (1100 times the length of its original wavelength) as a result of the cosmic expansion, and thus forms the cosmic microwave background radiation. This explains the relatively low light densities and energy levels present in most of our sky today despite the assumed bright nature of the Big Bang. The redshift also affects light from distant galaxies.
The redshift hypothesised in the Big Bang model would by itself explain the darkness of the night sky even if the universe were infinitely old. In the Steady state theory the universe is infinitely old and uniform in time as well as space. There is no Big Bang in this model, but there are stars and quasars at arbitrarily great distances. The expansion of the universe causes the light from these distant stars and quasars to redshift, so that the total light flux from the sky remains finite. Thus the observed radiation density (the sky brightness of extragalactic background light) can be independent of finiteness of the universe. Mathematically, the total electromagnetic energy density (radiation energy density) in thermodynamic equilibrium from Planck's law is
e.g. for temperature 2.7 K it is 40 fJ/m3 ... 4.5×10−31 kg/m3 and for visible temperature 6000 K we get 1 J/m3 ... 1.1×10−17 kg/m3. But the total radiation emitted by a star (or other cosmic object) is at most equal to the total nuclear binding energy of isotopes in the star. For the density of the observable universe of about 4.6×10−28 kg/m3 and given the known abundance of the chemical elements, the corresponding maximal radiation energy density of 9.2×10−31 kg/m3, i.e. temperature 3.2 K (matching the value observed for the optical radiation temperature by Arthur Eddington [11] [12] ). This is close to the summed energy density of the cosmic microwave background (CMB) and the cosmic neutrino background. However, the steady-state model does not predict the angular distribution of the microwave background temperature accurately (as the standard ΛCDM paradigm does). [13]
Suppose that the universe were not expanding, and always had the same stellar density; then the temperature of the universe would continually increase as the stars put out more radiation. Eventually, it would reach 3000 K (corresponding to a typical photon energy of 0.3 eV and so a frequency of 7.5×1013 Hz), and the photons would begin to be absorbed by the hydrogen plasma filling most of the universe, rendering outer space opaque. This maximal radiation density corresponds to about 1.2×1017 eV/m3 = 2.1×10−19 kg/m3, which is much greater than the observed value of 4.7×10−31 kg/m3. [4] So the sky is about five hundred billion times darker than it would be if the universe was neither expanding nor too young to have reached equilibrium yet. However, recent observations increasing the lower bound on the number of galaxies suggest UV absorption by hydrogen and reemission in near-IR (not visible) wavelengths also plays a role. [14]
A different resolution, which does not rely on the Big Bang theory, was first proposed by Carl Charlier in 1908 and later rediscovered by Benoît Mandelbrot in 1974.[ citation needed ] They both postulated that if the stars in the universe were distributed in a hierarchical fractal cosmology (e.g., similar to Cantor dust)—the average density of any region diminishes as the region considered increases—it would not be necessary to rely on the Big Bang theory to explain Olbers's paradox. This model would not rule out a Big Bang, but would allow for a dark sky even if the Big Bang had not occurred.[ citation needed ]
Mathematically, the light received from stars as a function of star distance in a hypothetical fractal cosmos is[ citation needed ]
where:
The function of luminosity from a given distance L(r)N(r) determines whether the light received is finite or infinite. For any luminosity from a given distance L(r)N(r) proportional to ra, is infinite for a ≥ −1 but finite for a < −1. So if L(r) is proportional to r−2, then for to be finite, N(r) must be proportional to rb, where b < 1. For b = 1, the numbers of stars at a given radius is proportional to that radius. When integrated over the radius, this implies that for b = 1, the total number of stars is proportional to r2. This would correspond to a fractal dimension of 2. Thus the fractal dimension of the universe would need to be less than 2 for this explanation to work.
This explanation is not widely accepted among cosmologists, since the evidence suggests that the fractal dimension of the universe is at least 2. [15] [16] [17] Moreover, the majority of cosmologists accept the cosmological principle,[ citation needed ] which assumes that matter at the scale of billions of light years is distributed isotropically. Contrarily, fractal cosmology requires anisotropic matter distribution at the largest scales.
The Big Bang is a physical theory that describes how the universe expanded from an initial state of high density and temperature. It was first proposed as a physical theory in 1931 by Roman Catholic priest and physicist Georges Lemaître when he suggested the universe emerged from a "primeval atom". Various cosmological models of the Big Bang explain the evolution of the observable universe from the earliest known periods through its subsequent large-scale form. These models offer a comprehensive explanation for a broad range of observed phenomena, including the abundance of light elements, the cosmic microwave background (CMB) radiation, and large-scale structure. The uniformity of the universe, known as the flatness problem, is explained through cosmic inflation: a sudden and very rapid expansion of space during the earliest moments.
Physical cosmology is a branch of cosmology concerned with the study of cosmological models. A cosmological model, or simply cosmology, provides a description of the largest-scale structures and dynamics of the universe and allows study of fundamental questions about its origin, structure, evolution, and ultimate fate. Cosmology as a science originated with the Copernican principle, which implies that celestial bodies obey identical physical laws to those on Earth, and Newtonian mechanics, which first allowed those physical laws to be understood.
The cosmic microwave background is microwave radiation that fills all space in the observable universe. It is sometimes called relic radiation. With a standard optical telescope, the background space between stars and galaxies is almost completely dark. However, a sufficiently sensitive radio telescope detects a faint background glow that is almost uniform and is not associated with any star, galaxy, or other object. This glow is strongest in the microwave region of the radio spectrum. The accidental discovery of the CMB in 1965 by American radio astronomers Arno Penzias and Robert Wilson was the culmination of work initiated in the 1940s.
The universe is all of space and time and their contents. It comprises all of existence, any fundamental interaction, physical process and physical constant, and therefore all forms of matter and energy, and the structures they form, from sub-atomic particles to entire galactic filaments. Space and time, according to the prevailing cosmological theory of the Big Bang, emerged together 13.787±0.020 billion years ago, and the universe has been expanding ever since. Today the universe has expanded into an age and size that is physically only in parts observable as the observable universe, which is approximately 93 billion light-years in diameter at the present day, while the spatial size, if any, of the entire universe is unknown.
Observations show that the expansion of the universe is accelerating, such that the velocity at which a distant galaxy recedes from the observer is continuously increasing with time. The accelerated expansion of the universe was discovered in 1998 by two independent projects, the Supernova Cosmology Project and the High-Z Supernova Search Team, which used distant type Ia supernovae to measure the acceleration. The idea was that as type Ia supernovae have almost the same intrinsic brightness, and since objects that are farther away appear dimmer, the observed brightness of these supernovae can be used to measure the distance to them. The distance can then be compared to the supernovae's cosmological redshift, which measures how much the universe has expanded since the supernova occurred; the Hubble law established that the farther away that an object is, the faster it is receding. The unexpected result was that objects in the universe are moving away from one another at an accelerating rate. Cosmologists at the time expected that recession velocity would always be decelerating, due to the gravitational attraction of the matter in the universe. Three members of these two groups have subsequently been awarded Nobel Prizes for their discovery. Confirmatory evidence has been found in baryon acoustic oscillations, and in analyses of the clustering of galaxies.
This timeline of cosmological theories and discoveries is a chronological record of the development of humanity's understanding of the cosmos over the last two-plus millennia. Modern cosmological ideas follow the development of the scientific discipline of physical cosmology.
The ultimate fate of the universe is a topic in physical cosmology, whose theoretical restrictions allow possible scenarios for the evolution and ultimate fate of the universe to be described and evaluated. Based on available observational evidence, deciding the fate and evolution of the universe has become a valid cosmological question, being beyond the mostly untestable constraints of mythological or theological beliefs. Several possible futures have been predicted by different scientific hypotheses, including that the universe might have existed for a finite and infinite duration, or towards explaining the manner and circumstances of its beginning.
The Big Crunch is a hypothetical scenario for the ultimate fate of the universe, in which the expansion of the universe eventually reverses and the universe recollapses, ultimately causing the cosmic scale factor to reach zero, an event potentially followed by a reformation of the universe starting with another Big Bang. The vast majority of evidence indicates that this hypothesis is not correct. Instead, astronomical observations show that the expansion of the universe is accelerating rather than being slowed by gravity, suggesting that a Big Freeze is more likely. However, some physicists have proposed that a "Big Crunch-style" event could result from a dark energy fluctuation.
A non-standard cosmology is any physical cosmological model of the universe that was, or still is, proposed as an alternative to the then-current standard model of cosmology. The term non-standard is applied to any theory that does not conform to the scientific consensus. Because the term depends on the prevailing consensus, the meaning of the term changes over time. For example, hot dark matter would not have been considered non-standard in 1990, but would have been in 2010. Conversely, a non-zero cosmological constant resulting in an accelerating universe would have been considered non-standard in 1990, but is part of the standard cosmology in 2010.
The observable universe is a ball-shaped region of the universe consisting of all matter that can be observed from Earth or its space-based telescopes and exploratory probes at the present time; the electromagnetic radiation from these objects has had time to reach the Solar System and Earth since the beginning of the cosmological expansion. Initially, it was estimated that there may be 2 trillion galaxies in the observable universe. That number was reduced in 2021 to several hundred billion based on data from New Horizons. Assuming the universe is isotropic, the distance to the edge of the observable universe is roughly the same in every direction. That is, the observable universe is a spherical region centered on the observer. Every location in the universe has its own observable universe, which may or may not overlap with the one centered on Earth.
Observational cosmology is the study of the structure, the evolution and the origin of the universe through observation, using instruments such as telescopes and cosmic ray detectors.
In physical cosmology, structure formation describes the creation of galaxies, galaxy clusters, and larger structures starting from small fluctuations in mass density resulting from processes that created matter. The universe, as is now known from observations of the cosmic microwave background radiation, began in a hot, dense, nearly uniform state approximately 13.8 billion years ago. However, looking at the night sky today, structures on all scales can be seen, from stars and planets to galaxies. On even larger scales, galaxy clusters and sheet-like structures of galaxies are separated by enormous voids containing few galaxies. Structure formation models gravitational instability of small ripples in mass density to predict these shapes, confirming the consistency of the physical model.
In physics, a homogeneous material or system has the same properties at every point; it is uniform without irregularities. A uniform electric field would be compatible with homogeneity. A material constructed with different constituents can be described as effectively homogeneous in the electromagnetic materials domain, when interacting with a directed radiation field.
The history of the Big Bang theory began with the Big Bang's development from observations and theoretical considerations. Much of the theoretical work in cosmology now involves extensions and refinements to the basic Big Bang model. The theory itself was originally formalised by Father Georges Lemaître in 1927. Hubble's Law of the expansion of the universe provided foundational support for the theory.
In cosmology, a static universe is a cosmological model in which the universe is both spatially and temporally infinite, and space is neither expanding nor contracting. Such a universe does not have so-called spatial curvature; that is to say that it is 'flat' or Euclidean. A static infinite universe was first proposed by English astronomer Thomas Digges (1546–1595).
The expansion of the universe is the increase in distance between gravitationally unbound parts of the observable universe with time. It is an intrinsic expansion, so it does not mean that the universe expands "into" anything or that space exists "outside" it. To any observer in the universe, it appears that all but the nearest galaxies recede at speeds that are proportional to their distance from the observer, on average. While objects cannot move faster than light, this limitation applies only with respect to local reference frames and does not limit the recession rates of cosmologically distant objects.
Cosmic infrared background is infrared radiation caused by stellar dust.
The chronology of the universe describes the history and future of the universe according to Big Bang cosmology.
Conformal cyclic cosmology (CCC) is a cosmological model in the framework of general relativity and proposed by theoretical physicist Roger Penrose. In CCC, the universe iterates through infinite cycles, with the future timelike infinity of each previous iteration being identified with the Big Bang singularity of the next. Penrose popularized this theory in his 2010 book Cycles of Time: An Extraordinary New View of the Universe.
The Puritan Thomas Digges (1546–1595?) was the earliest Englishman to offer a defense of the Copernican theory. ... Accompanying Digges's account is a diagram of the universe portraying the heliocentric system surrounded by the orb of fixed stars, described by Digges as infinitely extended in all dimensions.
The simple observation that the night sky is dark allows far-reaching conclusions to be drawn about the large-scale structure of the universe. This was already realized by J. Kepler (1610), E. Halley (1720), J.-P. Loy de Chesaux (1744), and H. W. M. Olbers (1826).
{{cite book}}
: |work=
ignored (help)