Olbers' Paradox - by Eduardo Manuel Alvarez:
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Introduction
Olbers' Paradox
Analysis of Proposed
Solutions
Final Explanation
Conclusion
References
Introduction
During a warm summer night last January, two couples of friends, my wife
and I were having a great time while dining out in the open at the
pavement of an enjoyable little downtown restaurant. Suddenly, at the
final coffees, all lights were off. An unusual complete blackout had
occurred.
Having realized that the best thing to do was just waiting for the
lights to come back (instead of “rapidly disappearing”, like
someone actually suggested) the amicable chat resumed under a complete
darkness. Gradually, a myriad of stars began to materialize above our
dark-adapted eyes, while a voluptuous Milky Way unquestionably assumed
the leading role of such great spectacle. Less than ten minutes later
everyone had become completely engrossed by the marvellous scene over
our heads.
Knowing my great fondness for astronomy, all kind of questions were
immediately shot over me, mostly the usual trivial ones. My ego was
being nicely fed. Suddenly all the fun ended up, not by lights coming
back but for a damned unexpected question: “Please, tell me, if there
are almost infinite suns as you say, doesn’t the night have to be pretty
much lighted?”
Apparently simple and naive, my friends had posed a very hard question.
Were the Universe filled with infinitely many stars for an also infinite
time, it sounded reasonable that no night could exist, as heavens would
be bright enough per se even though the Sun were below the horizon. I
had not the slightest idea about the proper answer. A long silence
followed up. I still vividly remember my next words: “Waiter, please,
the check!”
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Olbers’ paradox
The question about
the night’s darkness involves not only a difficult topic by itself, but
a truly essential one, as it is intimately connected with the structure
and evolution of the universe as a whole. Assuming an infinite old
universe with stars scattered more or less randomly throughout infinite
space -the usual model since the end of medieval times- the night sky
should not be dark as it obviously has ever been.
This evident
contradiction between theory and reality became generically known as
“Olbers’ paradox”, after the German amateur astronomer who took out his fountain pen and wrote about
it in 1823. Being his own explanation neither the first, nor the last,
and even wrong, Heinrich Olbers’ objective merits look quite
disproportionate for such a tribute, thus seeming like the scientific
community actually got two paradoxes for the price of one.
Under clear skies, the starry night appears wearing its very best party
dress. Having the chance to ever observe it, urban citizens usually get
immediately captured by its majestic beauty and begin wondering about
its endless mysteries. Any kind of deep questions could consequently
arise … Newton thought that
the universe had to be a static, infinitely old, unlimited expanse of
stars homogeneously distributed. This model effectively resolved the
otherwise problematic appearance of a privilege centre of gravity -in a
non homogenous universe large gravitational forces would not be
compensated at all-
but failed to solve the riddle of the sky darkness (which consequently
became posed).
We
now know that space and time are no longer independent entities as
previously thought, but integrate a single reality called spacetime.
According to Einstein’s Theory of General Relativity, spacetime has the
property to grip mass, telling it how to move, while at the same time
mass grips spacetime, telling it how to curve. The geometry and history
of our universe are currently described firmly buttressed on those
foundations.
By
joining together theoretical solutions derived from General Relativity,
with practical compelling evidence obtained from our best observational
instruments, most cosmologists agree that our universe (that is, all the
space, matter, time, and energy) was “created” in a singular episode
called the Big Bang, some 13.7 billion years ago, and it has been
expanding ever since.
Regarding this widely accepted model, Olbers’ paradox has now become
resolved. However, the long and winding road actually travelled towards
its definite solution is still worthily to be known, not only for being
very instructive by itself, but at least as a deserved tribute to all
other unreferenced road-makers.
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Analysis of the
proposed solutions
Since first serious attempts to explain the cause of the night darkness,
elaborated more than 400 years ago, many alternative solutions have been
candidated to justify why the sky is not seen as fully covered by stars.
Most of them have proved to be wrong, as they were based on incorrect
models about the universe’s structure and/or its evolution.
A
succinct presentation of each one of the more plausible proposed
solutions is next discussed, including the author(s) and date(s), an
explanation about its main argument and a conclusion evaluating its
definite pertinence. The order of the following presentation actually
corresponds to the chronological order of appearance (Harrison 2000).
“Starlight is too feeble”:
Originally proposed by Englishman Thomas Digges in 1576, it was based in
the simple assumption that distant stars, although infinite in number,
could be just too faint to be observed. This argument is clearly false,
as the combined light of “invisible” stars should itself be visible
anyway, which is not the case.
“Dark cosmic wall”:
Originally proposed by the great German Johannes Kepler in 1610, it was
based in the concept that the universe is not infinite at all, abruptly
ending towards a dark boundary that completely surrounds the starry
space. Obviously this is not true.
“Stoic finite cosmos”:
Originally proposed by the Prussian Otto von Guericke in 1672, by the
Irish Agnes Mary Clerke in 1890, and even by the famous American
astronomer Harlow Shapley as late as 1917, it was based on the idea that
the whole Universe was just a “one-island universe” floating in an
infinite void of empty space, that is, the star-populated region
supposedly only extents up to a finite size, although the beyond
remaining space spans endless. This solution is basically the same as
the previous one, just that the “dark cosmic wall” has been replaced by
a much more “scientifically-correct” infinite void. Anyway, this model
of universe is wrong.
“Geometric effect”:
Originally proposed by English scientist Edmund Halley in 1720, it also
was the first solution derived after a mathematical analysis of the
question. By considering imaginary concentric spheres of increasing
radius, forming a series of shells of constant thickness, Halley found
that the respective starlight contribution of each shell does not depend
on the given radius of the shell.
As this reasoning should have concluded that infinite shells would give
a bright sky, the proposed solution was to assume that the combined
light from distant shells actually resulted obstructed by nearby stars.
Wrong argument, as despite the claimed obstruction every line of sight
would still end at a star’s surface, and the sky should be very bright
anyway.
“Interstellar obscuration”:
Originally proposed by Swiss astronomer Jean-Philippe Loys de Chéseaux
in 1744, and also subscribed by German Heinrich Olbers in 1823. Realizing
that even the furthest stars would anyway contribute with some light to
the sky, the darkness was attributed to the non-transparency of the
space. This argument is false because any absorbed radiation will
gradually heat the blocking material, which in time would end up by
radiating light as stars themselves.
“Hierarchical structure”:
Originally proposed by British astronomers John Herschel in 1848, and
Richard Proctor in 1870, it was based on the idea that matter in the
universe tends to become progressively clustered around increasingly
larger sizes, thus making that the minimum requested radius for assuring
that every line of sight eventually ends at a star’s surface accordingly
increases up to become indefinitely large. This argument is at least
compatible with our current cosmological believes, although its direct
effect on the final night darkness is of relative secondary importance.
“Cosmic age too short”:
Originally proposed by American poet Edgar Allan Poe in 1848, and by
German astronomer Johann Mädler in 1861. The basic idea was simply that
light from distant stars still hasn’t reached us, since light has a
finite speed, and the universe a finite age. In 1901, the Scottish
mathematician and physicist Lord Kelvin analysed quantitatively the
connection between the sky-cover fraction by stars and its relative
brightness, concluding that in order to obtain a sky continuously bright
as the Sun’s surface, it would be necessary to include all starlight up
to a distance of 3,000 trillion light years. As we can not receive any
light that has travelled from longer than 13.7 billion years (the
present cosmic particle horizon), this proposed solution is
really on the right track.
“Static steady state”:
Originally proposed by the American astronomer William MacMillan in
1922. It was based in the assumption that the universe, although
infinite in size and time, was in a perpetual state of evolution as
matter slowly evolve into radiation, and viceversa (conserving the total
energy), thus preventing “autotransforming” starlight from reaching
distant locations. This model is incorrect, as shown by the irrefutable
evidence of an expanding universe obtained after the 1930s.
“Redshift”:
Originally proposed by the American cosmologist Hermann Bondi in 1955.
It was based in the fact that starlight from distant regions of the
expanding universe becomes affected by the cosmological redshift, so
that the arriving carried energy results increasingly weakened as the
distance from stellar sources enlarges. This redshift effect effectively
accounts for a barely darker sky, but is not one of its principal
causes.
“Too little energy”:
Originally proposed by American cosmologist Edward Harrison in 1964. It
was derived after computing the amount of energy required to create a
bright sky, and finding out that it implies an overwhelming large
number: the observable universe would need 10 trillion times more energy
than it currently shows. This means that even if all matter in the
universe were transformed into energy according to Einstein’s famous
formula, the night sky would be barely brighter than it really is. This
argument is truly one of the few heavy weight solutions to the riddle.
The
following table summarizes all major alternatives so far presented:
Proposed solution |
Author & Date |
Viability |
Starlight is too feeble |
Digges (1576) |
wrong |
Dark cosmic wall |
Kepler (1610) |
wrong |
Stoic finite cosmos |
Guericke
(1672),
Clerke
(1890), Shapley
(1917) |
wrong |
Geometric effect |
Halley (1720) |
wrong |
Interstellar obscuration |
Chéseaux (1744), Olbers (1823) |
wrong |
Hierarchical structure |
Herschel (1848), Proctor (1870) |
barely applies |
Cosmic age too short |
Poe (1848), Mädler (1861), Kelvin (1901)
|
truly important |
Static steady state |
MacMillan (1922) |
wrong |
Redshift |
Bondi (1955) |
barely applies |
Too little energy |
Harrison (1964) |
truly important |
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The final
explanation
As
seen, just a few proposed solutions to Olbers’ paradox are compatible
with our current cosmological model derived from General
Relativity' solutions and its description of the evolution of the
universe from its main flagship: the Big Bang.
This
definite beginning imposes a finite age for the universe. If it is 13.7
billion years old, then light from stars further away than 13.7 billion
light years just has not had enough time to get here. This is true even
if the universe is infinite. And we did not even consider the fact that
the luminous age of stars is certainly limited, which actually makes
“things even worse”.
The
scarcity of the contained energy and matter in the whole universe also
becomes an independent valid reason to justify its darkness. As the
contained amount of energy and matter are intimately related to the way
that the universe has actually evolved according to General Relativity
(Freedman & Turner 2003), it is the particular developed evolution of
the universe which synthesizes at last the final explanation for the
Olbers’ paradox.
The
darkness effect attributed to the cosmological redshift has been
quantitative compared to the darkness effect just originated by the
finiteness of the age of the universe in the aforementioned cosmological
context (Wesson 1989), resulting that the latter argument is far more
important. However, not all scientists agree with that model, and the
redshift solution is still the accepted one for those defenders of the
“expanding steady- state” theory (Vicino 2003).
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Conclusions
The subject of the
night darkness is an essential cosmological question, as it is
intimately related to the actual architecture of the universe. In fact,
the “easy” model of an endless spatial and perpetual universe
immediately becomes controversial with our real night.
Many solutions have
been proposed to solve the so called Olbers’s paradox, almost each one
based on a different explanation for the whole universe. The majority of
those models have been proved to be wrong, as they collide to our
current cosmological believes.
Nowadays we
confidently can assure that there are just two principal factors that
separately concur to produce a dark night sky: the universe is too
young, and it also contains far less matter than it would be required
to. Two other reasons (redshift and hierarchical structure) only
contribute to just darken an already dark sky.
Finally, the author
now feels self-confident again to resume answering astronomical layman
questions from relatives and friends.
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References
Croswell, Ken 2001,
“Wondering in the Dark”, Sky & Telescope magazine, December 2001,
pages 44-50
Freedman, Wendy L. and
Turner, Michael S. 2003, “Cosmology in the New Millennium”, Sky &
Telescope magazine, October 2003, pages 31-41
Harrison, Edward 2000,
“Cosmology, The Science of the Universe”, 2nd Ed,
Cambridge University Press, Chapter 24: Darkness at night, pages
491-514
Vicino, Gonzalo 2003, “Relatividad
y Cosmología”, A. Monteverde y Cía. S.A., Chapter 12: Estado
actual de la cosmología: Afirmaciones, disidencias y opiniones,
pages 161-184
Wesson, Paul S. 1989,
“The real reason the night sky is dark: Correcting a myth in astronomy
teaching”, Journal of the British Astronomical Association, vol. 99,
no. 1, p. 10-13
The
image included on page 2 (“The magnificent Milky Way at Sagitarius”)
was taken by the author on September 14th, 2004 (piggyback,
Kodak Ultra ISO 400, 135-mm, f/2.8, 4 min exp.)
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