Albedo One

3 – Olbers’ Paradox


A surface that reflects equally in all directions is known as a white body and has what’s known as Lambertian Reflectance. As always, I’ll strive to achieve this property today. This is Albedo One. I’m Paul Kogan.

Our universe has a center, and yet is without one. Everything is the center! “Well, how can that be,” you may ask. “There was the Big Bang after all, right? And everything is expanding from it, so where it happened must be the center.” The thing is, the Big Bang was an explosion of space, not in space. Now, in this space, for there to be a center, there has to be a special point, like a center of rotation, center of mass, center of charge, center of curvature, or center of expansion. Based on our current understandings and observations, the universe isn’t rotating, it has an infinite and uniform distribution of mass and charge, it’s flat, and it’s expanding equally in all directions, meaning there is no special point. The Big Bang created space; it’s not a point in space, and it’s all around us. What I’m talking about is the Surface of Last Scattering, otherwise known as the Cosmic Microwave Background, or CMB. The CMB is the flash of the Big Bang, and since the flash is everywhere, so was the Big Bang.

About a second after the Big Bang, weakly interacting neutrinos decoupled, and photons and neutrinos became the dominant sources of energy during the electron-positron annihilation. Then, after approximately 4 minutes, the temperature decreased enough to allow nucleosynthesis, the process of protons and neutrons combining to form atomic nuclei, mostly helium-4. Neutrinos weren’t affected by this; photons, however, were, since they interact with charged particles. Consequently, matter gained quite some importance. Furthermore, sufficiently rapid collisions tied photons, electrons, and nuclei into a system known as a photon-baryon fluid, which stopped the temperature of matter particles from dropping too rapidly; they were kept at the same temperature as the photons. The high frequency of electron-proton collisions resulted in a very short life for individual photons, for the first few days after the Big Bang, at least. After about five days, the universe entered what we call the time of thermal decoupling. This is when electrons and protons collide infrequently enough so as to neither emit nor destroy photons. This is when the photons that we see today, when we look at the CMB, were created. Meanwhile, photon-electron collisions were still very frequent and kept changing the energy of the photons by what’s known as Compton scattering. It took 40 years for these collisions to lose enough energy so as to conserve the energy of the photons and stop the CMB’s spectrum from being further affected by matter. For the next 60,000 years the temperature of the universe continued decreasing until it hit the matter era, the time of recombination, when electrons started to prefer to bind to nuclei, rather than fly solo in an ionized fluid. (This is the first known such combination, so the name is a slight misnomer.) Consequently, about 400,000 years later, photons were finally able to escape the primordial soup, to move without obstruction, to one day reach us. The universe became transparent and left behind a wall of light in time. And in 1965, billions of years later, it was discovered, after a rollercoaster of events, allowing us to look back to the cosmological horizon and witness gravitational instability, map anisotropies, measure spatial curvature, compute polarization, support Mach’s principle, and loads of other stuff.

Let’s rewind a bit, to 1926, three years prior to Hubble’s famous contribution, the year Erik Rotheim invented the spray can, and the year Arthur Stanley Eddington published The Internal Constitution of the Stars. In this book, Eddington computed the effective temperature of the cosmos, and the temperature he thought blackbodies should assume, to be just over 3 degrees Kelvin. This fit the optical data available at the time and completely missed the CMB (and interstellar dust, too). About a decade later, in 1939, Hans Bethe demonstrated how thermonuclear reactions power the stars and it was discovered that fusion of lighter elements could create heavier ones. From these deductions, the abundances of elements in the universe were predicted under the assumption they were created in stars. The observations told a different story, but I’ll get to that in a bit. In 1941, Walter Adams and Andrew McKellar were studying cyanogen, particularly its absorption in interstellar space. Following Adams’ spectrographic observation of a star that revealed new cyanogen lines, McKellar was able to deduce that cyanogen’s rotational temperature is just over 2 degrees Kelvin. He then connected this number to Eddington and blackbodies.

Wait, no, he didn’t. He didn’t do anything with it. That’s all that most everybody at the time thought that number was. The rotational temperature of an interstellar molecule. McKellar misinterpreted the results and everyone missed the connection to the CMB, again. Why? Because cosmology wasn’t a very popular topic. It was separated from the rest of astrophysics and there was a lack of communication between theorists and experimentalists. Consequently, anything related to the early universe was generally just disregarded. Cue the PR battle between Fred Hoyle and George Gamow. Of all the various cosmological models being thrown around in the mid-20th century, the ones led by these two, Hoyle’s Steady State model and Gamow’s dynamic evolving model, were, by far, the most popular. The rival models were rigorously researched, eloquently communicated using easily understandable language (which, I’m sure, helped with their popularity), and led to Nobel Prizes.

Gamow and his buddies, Robert Herman and Ralph Alpher, saw the primordial soup as a nuclear reactor that created all of the chemical elements, and called it ylem. They were trying to explain the graph of abundance versus atomic-number, why the observations didn’t line up with their calculations. They were trying to explain why hydrogen and helium are so common, why there are 10 hydrogen atoms for every helium atom, and why all the other elements are so rare. In 1948, Gamow and Alpher, his student, published an allegedly breakthrough paper, the so-called “alphabetical article,” on nucleosynthesis that allegedly explained the elements were created during the instantaneous creation of the universe in which density changes over time. (I should mention here that the modern view on nucleosynthesis incorporates both primordial and stellar processes.) Gamow predicted evidence, a fossil record, of such an event could be found in a residual radiation field. Hoyle didn’t want to accept an instantaneous creation; he had a philosophical objection to such a concept. And, like any adult would do, he made fun of Gamow’s Dynamic Evolving model and called it the Big Bang. Without the predicted fossil record anywhere in sight (or so they thought), Hoyle and his supporters had no choice but to find an alternative to Big Bang nucleosynthesis.

Perhaps the universe is static. Well, Isaac Newton considered this idea in 1667 and envisioned a space similar to the Stoic universe, a finite system in an infinite inane, itself a contradiction of Aristotle’s picture and a rival to the Epicurean universe. But by 1693, he, ahem, gravitated towards the Epicurean view, an infinite, uniform system, during some correspondence with a theologian by the name of Richard Bentley. Bentley, you see, was confuting atheism through logos rather than pathos, and was consulting Newton on the matter. In his letters, Newton opined that in a finite sidereal system, the rest state of all its matter would be at the center, and concluded the stars must be uniformly distributed in unstable equilibrium, ignoring the possibility of motion and raising the problem of normalizing infinite gravitational forces — the gravity paradox. It wasn’t until 1917 that it was figured out, by none other than Albert Einstein, that only finite systems and certain infinite nonuniform systems are compatible with Newton’s theory.

The year prior, Einstein visited Leiden and debated with his friends Henrik Lorentz, Paul Ehrenfest, and Willem de Sitter. Most of the discussions were about boundary conditions, and Einstein had a particularly fascinating exchange with de Sitter. The culmination of these deliberations was his manuscript, Cosmological Considerations on the General Theory of Relativity. In covering Newton, Einstein recalled that to avoid an infinitely large gravitational force acting on a material particle, the sidereal system should be a finite island in the infinite ocean of space, but even this model has problems. Such problems include gradual stellar evaporation and gravitational potential at infinity. After modifying Newtonian mechanics, Einstein postulated a solution to boundary conditions to be a self-contained continuum of finite spatial volume. He continued on to present his own static universe, the first such relativistic model, and avoided other possibilities because he thought they would lead to bottomless speculations. Reactions to the Einstein World were not all supportive. De Sitter, one of Einstein’s friends, offered an alternative solution, an empty four-dimensional universe of closed spacetime geometry, which Einstein dismissed on the grounds that it was non-static, something he deemed impossible.

The de Sitter model gained a great deal of attention and corroborated contemporary observations of redshift. Meanwhile, in 1922, Russian physicist Alexander Friedmann brought attention to the non-static solutions to Einstein’s field equations that were rejected like de Sitter’s universe. He was mostly ignored, and even (wrongly) criticized by Einstein. A few years later, Belgian physicist Georges Lemaître suggested that the recession of nebulae was a manifestation of the expansion of space from a pre-existing Einstein universe. Not many paid attention to him either; Einstein dismissed this idea, too. 1929 came rolling around, and with it, Edwin Hubble published the first evidence of a linear relation between the redshifts of the spiral nebulae and their radial distance. Various relativistic time-varying models of the cosmos followed, including one similar to Lemaître’s model, by Eddington. An emergent universe. Soon, Einstein also accepted Hubble’s redshift observations and proposed his own model of the expanding universe, abandoning the Einstein World on the grounds that it was unstable and in conflict with empirical observation. A few years more, and we’re back with Hans Bethe and the predicted abundances of elements in the universe.

So what alternative to Big Bang nucleosynthesis could Hoyle come up with? He didn’t like instant creation, which is why he didn’t support the Big Bang. The other extreme end — a static universe — had already been considered, as has an emergent universe. Two articles were written in 1948 about another possibility — one by Herman Bondi and Thomas Gold, the other by Hoyle — a Steady State universe. The first paper postulates translation invariance in space, as well as in time; in other words, the “Perfect Cosmological Principle.” To account for the observed redshift, their stationary universe has matter forming slowly inside. In the second paper, Hoyle built on this theory by modifying Einstein’s field equations and introducing the “creation field” C. He thus obtained a universe similar to the de Sitter model, but in which the matter density is non-zero. His solution, a universe that never changes, maintaining a constant density over time thanks to the spontaneous generation of matter, was seen as elegant and free of the issues that came with the Big Bang theory, such as the cosmic age problem.

That is, until 1965, four years after Martin Ryle and Randolph Clarke found that faint radio galaxies were substantially more abundant than expected in the Steady State model. This year, Arno Penzias and Robert Wilson were refurbishing a horn antenna for the AT&T-Bell telephone company and coming across a noise, while Dicke switching, that they (and the antenna’s previous project, Echo) couldn’t get rid of: an unaccounted temperature of 3.5 degrees Kelvin in excess of their error budget. They went as far as deporting resident pigeons and scraping their “white dielectric substance” off of the antenna. At the same time, Robert Dicke and Jim Peebles were searching for the remnant radiation from the Big Bang using a simple receiver they built. Dicke immediately suspected that Penzias and Wilson had serendipitously found the radiation he was looking for. After the two groups partook in some private correspondence, Dicke’s wrote up a paper, Cosmic Black-Body Radiation, that was published alongside Penzias’ and Wilson’s in The Astrophysical Journal. The latter group’s paper was entirely focused on convincing the reader that they had obtained a real detection, and pointed to the other paper for a possible explanation. This second paper asks if the “universe [could be] filled with black-body radiation from [the] possible high-temperature state [of the Big Bang]. After discussing the constraints on the matter density from the radiation temperature, it answered said question: yes, the black body radiation measurement of 3.5 degrees Kelvin is that of the fossil record that flew under everybody’s radar in the 1950s and the one Gamow predicted all those years ago.

Nevertheless, Hoyle continued to defend the Steady State universe to his death, going so far as to develop Quasi-Steady State Cosmology, and inadvertently helped resolve problems in the Big Bang theory by pointing them out. Indeed, there were quite a few questions that loomed over people’s heads after 1965. Are cosmic structures the result of small density fluctuations undergoing gravitational collapse? (Well, yes, and we call the mechanism the Sachs-Wolfe effect, but it wasn’t known at the time.) And then there was the horizon problem, the difficulty people had in explaining the thermal consistency of the CMB. It was not until 1981 that Mukhanov and Chibisov realized that an epoch of inflationary expansion solves the horizon problem and, if there were perturbations in it, also explains how large-scale structures could have been created. Except, there was this other pesky problem. The related temperature fluctuations, anisotropy, that were expected, were not observed. A possible solution was proposed the year after, by Jim Peebles; if most matter could not interact electromagnetically, it would not leave a direct imprint in the cosmic background radiation. He’s talking about the abundance of dark matter, an idea introduced by Fritz Zwicky in 1933, confirmed by Vera Rubin in the 1970s, and potentially covered by me in the next episode. More specifically, he was talking about warm dark matter. I won’t go into what that is now; all you have to know is that it was decided by the mid-1980s that actually cold dark matter is responsible for cosmological structure formation. But experimental confirmation of the corresponding anisotropy was still missing.

Not for much longer, though. The Cosmic Microwave Background Explorer, COBE, was launched in 1989, carrying a few instruments, including the Far Infrared Absolute Spectrometer and the Differential Microwave Radiometer. The former was built to measure the CMB’s spectrum and the latter the missing temperature fluctuations. Just the next year, John Mather published data confirming the CMB is the afterglow of the early universe. And two years later, George Smoot published an analysis revealing the ancestors of today’s cosmic structures; the long sought temperature fluctuations were finally found. The end. Well, not quite. The CMB continued, and continues to, reveal more information about the universe. The Balloon Observations Of Millimetric Extragalactic Radiation and Geophysics, or BOOMERanG, experiment, for instance, determined that space is flat. Such a universe, however, requires all energy-density contributions to add up to the critical density. After accounting for all baryonic — normal — and dark matter, about 70 percent of the cosmic energy budget was unaccounted for. The most likely solution was thought to be the cosmological constant, an extension to Einstein’s field equations of gravity. Adam Reiss and his team, in 1998, and Saul Perlmutter and his team, in 1999, found distant supernovae to be significantly fainter than they should have been in a universe without a cosmological constant. The puzzle was completed. But our curiosity was not satiated.

Following COBE, NASA launched the Wilkinson Microwave Anisotropy Probe in 2001 to study the CMB in much greater detail than before. Its team has accomplished many things, including determining the universe to be 13.77 billion years old, determining baryons make up less than 5 percent of the universe (while dark matter is at 24 percent), and confirming inflation. Although WMAP’s data stream ended in 2012, the ESA launched Planck — a space-based observatory with even greater sensitivity — in 2009. While WMAP’s results have helped to establish the Standard Model of Cosmology, Planck aims to either prove it beyond doubt or find deviations from it. Most of its results were published last year, 5 years after it was turned off. The last paper was made public recently, on July 30th, 2019. You can find these papers in the last page linked to in the Show Notes, which can also be found on this episode’s page at

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3 – Olbers’ Paradox