We are used to thinking about space as a smooth continuum, which can, in principle at least, be probed to infinitely small dimensions.  For instance, in Euclidean geometry, a point is defined as “that which has no part.”  In other words, points have no volume, area, or length, and yet they are fundamental objects in Euclidean geometry (Figure 1 shows part of one of the oldest surviving copies of Euclid’s The Elements).

Figure 1. One of the oldest surviving copies of a part of Euclid’s book on the elements of geometry, from circa 100 CE. (Image in the public domain: https:// en.wikipedia.org/wiki/File:P._Oxy._I_29.jpg)

Figure 2. The German theoretical physicist Max Planck (1858-1947). (Image in the public domain: https://en.wikipedia.org/wiki/File:Max_Planck_1933.jpg)

It may therefore come as a surprise that in modern physics, there exists a scale below which the very notions of length and space cease to exist.  This is known as the Planck length, named after the German physicist Max Planck (Figure 2).  The Planck length is defined using three so-called “constants of nature”:  Newton’s gravitational constant G (which determines the strength of gravity), the speed of light c, and the constant characterizing all subatomic quantum phenomena $\mathbf{\hbar}$ (pronounced “h-bar”). The Planck length is given by

$\mathbf{ \ell_p=\sqrt{\frac{\hbar G}{c^3}}}$

and its value is about 1.616 × 10-33 cm [0.000 … 1 at the thirty-third decimal place].

To get an approximate appreciation for the value of this tiny length, consider the following.  With the unaided human eye we can see dots that are a bit smaller than one-tenth of a millimeter in size.  Such dots are larger than the Planck scale by the same factor that the entire observable universe is larger than the dots themselves.

You may think: If the Planck scale is so tiny, why should we even discuss it?  The reason is that in attempts to unify the theory of gravity—General Relativity—with the theory of the subatomic world and light—Quantum Mechanics—the Planck length may be the shortest measurable length.  That is, irrespective of how much we would improve our measurement instruments, we would not be able to measure shorter dimensions.  Since the way we probe tiny distances in the subatomic regime is through high-energy collisions, this limitation translated into the statement that no matter what energies we would use, we would not split spacetime into finer pieces.  In fact, while no precise prediction can be made in quantum gravity (since no self-consistent theory has been formulated so far), some physicists guess that spacetime may behave like a discrete type of “foam” at the Planck scale.  In string theory, still the leading candidate for a theory of all the fundamental particles and forces, the Planck length represents the size of the oscillating loops whose vibrations form the elementary particles.  To paraphrase William Blake, who wrote:  “To see a World in a Grain of Sand,” we can perhaps say: “To see a World in a Grain of Planck Length.”

The original inflationary model of the universe proposed that when our universe was only a tiny fraction of a second old, it underwent a brief, but stupendously accelerated expansion.  The expansion took quantum fluctuations (on subatomic scales) and enlarged them to astronomically relevant dimensions.  This idea (put forward by physicist Alan Guth) explained in one blow a number of otherwise perplexing features of our universe.  For instance, observations of the cosmic microwave background show that our universe is geometrically flat.  This is easy to understand in the context of the inflationary model.  To a tiny ant on the surface of an enormous balloon, any local region would seem flat.  Similarly, the cosmic microwave background is the same in all directions (isotropic) to within one part in a hundred thousand, because our entire observable universe expanded during inflation from a tiny region that had sufficient time to be smoothed out in the early universe.

Soon after the inflationary model was proposed, however, physicists Alex Vilenkin and Andrei Linde discovered that the model also has some unexpected consequences.  In particular, the model seems to produce not just one universe, but rather an infinite ensemble of universes—a multiverse!  While our own universe seems to have had a starting point—a Big Bang—and it seems to be heading towards a cold death, this collection of “pocket” universes has no end, and indeed needs no beginning, with new “bubbles” continuing to pop up eternally.

The picture of “eternal inflation,” if true, provides a new perspective on our place within the cosmic landscape.  Not only do we live on a small planet, around a mediocre star, in one galaxy out of hundreds of billions of similar ones.  Even our entire universe may be just one bubble (one that nonetheless allowed for complexity and life to emerge), out of an infinite ensemble.

Figure 1. “Kandinsky Universe,” a simulation of eternal inflation by Andrei Linde. Credit: Andrei Linde (http://www.stanford.edu/~alinde/).

Figure 2. Wassily Kandinsky’s “Composition VII.” The Tretyakov Gallery, Moscow (image in the public domain;  https://en.wikipedia.org/wiki/File:Kandinsky_WWI.jpg).

Andrei Linde carried out some numerical simulations of this ever self-reproducing inflation.  In two dimensions, one of his simulations is represented in Figure 1, which Linde entitled a “Kandinsky Universe,” because it reminded him of the abstract works of painter Wassily Kandinsky (e.g., Figure 2).  Linde also produced simulations of an eternal inflation represented as a three-dimensional landscape (Figure 3), and those look extraordinarily similar to works of another artist, Sol Lewitt (Figure 4 shows the work “Splotch 15”).  The correspondence between simulations of the cosmos and art brings to mind a witty quote from (who else?) Oscar Wilde:  “Paradoxically though it may seem, it is none the less true that life imitates art far more than art imitates life!”

Figure 3. The fractal “landscape” resulting from eternal inflation. Credit: Andrei Linde (http://www.stanford.edu/~alinde/).

Figure 4. Sol Lewitt’s “Splotch 15.” Credit: Spencer T. Tucker.

Here are five science stories that I found intriguing during 2013.  I don’t mean to imply that these necessarily represent the most important discoveries, rather, these are simply stories that, for one reason or another, caught my attention more than others.

1.  Great Ball of Fire

On the morning of February 15, an asteroid that penetrated the Earth’s atmosphere unnoticed (Figure 1), exploded above the Siberian town of Chelyabinsk.  The resulting shockwave shattered windows, destroyed buildings, and injured more than 1,500 people.  This was a relatively gentle reminder of the dangers posed by asteroid impacts.  For this reason, NASA has an Automatic Near-Earth Asteroid Collision Monitoring System called SENTRY in place.

Figure 1. Chelyabinsk meteor explosion. Credit: Wikimedia Commons (http://en.wikipedia.org/wiki/File: Взрыв_метеорита_над_Челябинском_15_02_2013_avi-iCawTYPtehk.ogv).

Figure 2. The skeletal remains of King Richard III.

2.  My Kingdom for a Horse!

While excavating in a parking lot in Leicester, England, archaeologists hit the jackpot.  They uncovered what has by now been confirmed to be the skeleton of one of Shakespeare’s most memorable characters—King Richard III (1452–1485; Figure 2).  The conclusive proof (following radiocarbon dating) that this was indeed the correct identification came from comparing the DNA extracted from a tooth to that of two living known matrilineal descendants of the king’s eldest sister.  I am sure that this news excited anyone who has ever seen Sir Lawrence Olivier’s portrayal of this apparently ruthless king.

3.  Yes, Prime Minister

The “Goldbach conjecture” is one of those famous problems in mathematics that has already awaited its solution for more than a quarter of a millennium (since 1742).  The conjecture states that every even integer greater than 2 can be written as the sum of two primes (integers divisible only by 1 and themselves; Figure 3).  For instance, 18 = 7 + 11.  The conjecture has been shown to be true for numbers up to four million trillion, but a general proof remains elusive.  On May 13, 2013, a Peruvian mathematician working in France, Harald Helfgott, took an important step towards a proof.  He released two papers in which he appears to have proved what is known as “Goldbach’s weak conjecture”—that every odd integer greater than 7 can be expressed as the sum of three primes.  While the road from this proof to a complete proof of Goldbach’s conjecture is still long, Helfgott’s work (if fully confirmed) does represent major progress.

Figure 3. The even integers from 4 to 28 expressed as a sum of two primes. Goldbach’s conjecture states that every even integer greater than 2 can be expressed in this way. Credit: Wikimedia Commons (http://en.wikipedia.org/wiki/File: Goldbach_partitions_of_the_even_integers_from_4_to_50_rev4b.svg).

Figure 4. Iron melting at high pressure between two diamonds. A thin beam of synchrotron X-rays is used to detect whether solid iron has started to melt. This changes the crystalline structure, in turn modifying the “diffraction pattern” of deflected X-rays behind the sample. Credit: ESRF/Denis Andrault.

4.  Some Like It Hot

In his pioneering attempts to calculate the age of the Earth (in 1862) Lord Kelvin had to estimate the temperature in the Earth’s deep interior.  He took that to be in the range of 7,000–10,000° Fahrenheit.  Today we know that understanding phenomena such as the Earth’s magnetic field and processes related to geothermal activity require knowledge of the Earth’s core temperature.  The Earth has a solid inner core, composed mainly of iron, and a liquid outer core that is also iron rich.  The temperature at the boundary between the two is expected to be the melting temperature of iron at enormously high pressure.  In 2013, a French research team studied the melting of a piece of iron held between two diamonds at a pressure of 200 gigapascals (Figure 4).  They found a melting temperature of 10,754° Fahrenheit, almost 2,000° hotter than previous estimates!

Figure 5. Artist’s impression of the cloud of gas and dust G2, falling onto the black hole at the center of our Galaxy. Credit: ESO.

5.  Feeding the Monster

A cloud of gas and dust, called G2, is falling onto the central supermassive black hole at the center of our Milky Way galaxy.  The black hole, called Sagittarius A*, has a mass of 4.3 million times the mass of our Sun.  In April 2013, astronomers already started to see the effects of stretching that the cloud is experiencing, due to the black hole’s intense gravity.  Figure 5 shows an artist’s impression of those effects.  Astronomers will continue to closely monitor the Galactic center in 2014, since we rarely get a ringside seat for such close encounters.

Figure 1. Albert Einstein (1879–1955). Credit: The Leo Baek Institute, New York.

Figure 2. The French mathematician Évariste Galois (1811–1832), as drawn by a classmate. Credit: Wikimedia Commons (http://en.wikipedia.org/ wiki/File:Evariste_galois.jpg).

Albert Einstein (Figure 1) died on April 18, 1955 at Princeton Hospital in New Jersey.  Évariste Galois (Figure 2) died on May 31, 1832 at the Cochin Hospital in Paris.  The two men had something in common.  They were both geniuses who formulated game-changing mathematical theories.  Einstein formulated General Relativity—the theory that describes and predicts the behavior of the universe on its largest scales.  Galois formulated Group Theory—the mathematical language of the symmetries of the world.  Even though Galois had no application to physics in mind, his theory has become the tool of choice when discussing all the subatomic particles.

Through two bizarre sequences of events, Galois and Einstein had something else in common—the brains of both were subjected to a detailed investigation after their death!

Galois died of peritonitis at age twenty, after having been shot in the stomach in a duel.  Yet, the pathologist opened his skull, and more than half of the autopsy report was devoted to the brain.  Among other details, the pathologist wrote:  “The brain is heavy, its convolutions large, its crevices deep, especially on the lateral parts… the weight of the brain and the cerebellum together is three pounds, two ounces less one eighth of an ounce.”

Why did the pathologist examine Galois’s brain so thoroughly when the cause of death was obvious?  The first sentence of the autopsy report may provide a clue:  “Young Galois Évariste, 21 years of age, a good mathematician, known primarily for his ardent imagination, has just succumbed in 12 hours to acute peritonitis, caused by a bullet shot from 25 paces.”  The impression one gets, therefore, is that aware of Galois’s reputation as a mathematician, the pathologist felt compelled to examine the brain for potential clues as to the origin of the young man’s unusual attributes.

The story of Einstein’s brain is even more astonishing.  The pathologist, Thomas S. Harvey, dissected the brain into 240 pieces, which he then embedded in a plastic-like substance called celoidin.  For more than two decades, no one, not even Einstein’s family, knew that Einstein’s brain was being kept in jars at Harvey’s home.  This fact was only brought to light in 1978 by investigative journalist Steven Levy.  Since then, Harvey has allowed three teams to examine parts of the brain.  Although each team published some findings hailed at the time (in 1985, 1996, and 1999, respectively) as potential keys to Einstein’s genius, none could be regarded as conclusive.  Perhaps the most meaningful characteristic was the wider-than-normal (by about 15%) inferior parietal region (which is thought to be responsible for mathematical reasoning), and the absence of a groove (sulcus) in that region.

When asked why he took the brain, Harvey explained that he felt obligated to salvage the precious gray matter for posterity.  As a side note, let me comment that indeed having scientific data that are inaccessible (as in the case of Einstein’s brain), can impede progress. This is precisely why modern astronomical observatories have easily accessible archives, and all the data are routinely made public (typically after a short proprietary period).

While the pathologists did not discover any clear explanation for either man’s genius, we can understand their fascination with the brains of two individuals who were far ahead of their time.

As I indicated in the previous blog pieces in this series, while extraterrestrial life almost certainly exists in our Milky Way galaxy, even the nearest life-harboring planet may be tens of light-years away.  This means that our best shot at detecting such life is through remote observations by large telescopes.  In particular, future telescopes will be examining exoplanet atmospheres for biosignatures—characteristics that are produced (ideally uniquely) by life processes.

You may wonder what another civilization might regard as relatively reliable biosignatures of Earth, were this civilization to observe Earth from a distance of tens of light-years.  One of the telltales could be the relatively high abundance of oxygen (about 21% by volume) and the presence of ozone (a byproduct of oxygen; composed of three oxygen atoms).  While small amounts of oxygen were initially released into the Earth’s atmosphere through the dissociation of water by the Sun’s radiation, the vast majority was contributed photosynthetically by plants and bacteria.  The ozone layer probably played a crucial role in blocking ultraviolet radiation, thereby allowing more complex molecules to form.  Water vapor in the Earth’s atmosphere (and the associated inference of liquid water on the surface) would have been another positive indicator for the potential existence of life on Earth for a remote observer.  Most importantly, however, the most telling biosignature for life is an atmosphere that is out of equilibrium.  In other words, astrobiologists observing exoplanet atmospheres would be looking for gases whose abundances are absolutely discrepant when considering expectations from equilibrium chemical processes alone.

Two of the most promising telescopes for this type of quest for the near future are the Transiting Exoplanet Survey Satellite (TESS), scheduled for launch in 2017 (Figure 1), and the James Webb Space Telescope (JWST), scheduled for launch in 2018 (Figure 2).  While TESS will not be able to detect Earth-size planets around Sun-like stars, it will most probably find at least a few Earth-size planets orbiting (and transiting) smaller M-dwarf stars, in the Habitable Zone (that allows for liquid water) around those stars.  JWST will be able to study in detail the composition of the atmospheres of those candidates for life-bearing planets.

Figure 1. The TESS telescope. Credit: TESS team.

Figure 2. The James Webb Space Telescope. Credit: Wikimedia Commons (http://en.wikipedia.org/wiki/File: James_Webb_Telescope_Design.jpg).

Figure 3. Artist’s concept of a potential design of a 16-meter ATLAST. Credit: Northrop Grumman Aerospace Systems & NASA/STScI.

I do not want to give the impression that even the powerful pairing of TESS and JWST working in tandem (TESS leading to detections and JWST to atmospheric follow-up characterizations) is likely to find biosignatures.  Nevertheless, the probability of finding life is not zero, either.  In particular, if given the right conditions, life always emerges, then JWST could perhaps find life on suitable TESS candidates.  Future optical-ultraviolet telescopes, such as the proposed Advanced Technology Large-Aperture Space Telescope (ATLAST; Figure 3), would be needed to take us to the next step—finding an Earth analog with life on its surface.  What a huge step that would be!

Astrobiology is a rapidly evolving, interdisciplinary field of research that concerns the origin, frequency, and evolution of life in the universe. Given, however, that so far we only know of one example of life—the one on Earth—astrobiology generally proceeds with the assumption that, in terms of its basic requirements, extraterrestrial life should resemble the terrestrial template.

Ingredients that appear to have been crucial for life on Earth to emerge were: a certain level of environmental stability (e.g., not too many impacts by asteroids); the presence of liquid water; temperatures and levels of radiation that are not too extreme; a reliable energy source (the Sun); and the availability of certain elements such as oxygen, carbon, and phosphorus.  It is not unreasonable to assume as a first guess that many or maybe even all of these ingredients are essential for life anywhere (after all, carbon, for instance, is quite unique in its ability to form complex molecules), but until we find alien life we wouldn’t know for sure which of these are absolutely necessary.

All life on Earth, for instance, relies on DNA and RNA for replication, the issuing of instructions at the molecular level, and heredity.  Does that mean that our Earthly DNA (Figure 1) is universal throughout the cosmos?  That’s actually hard to believe, since studies show that even our DNA could continue to function after the insertion of laboratory-created bases into its molecular structure.  Similarly, different genetic codes can be used to create amino acids, which are the building blocks of proteins.  Furthermore, one of the pillars of Darwin’s theory of evolution by means of natural selection is the concept of a common ancestor—in his words, “all the organic beings which have ever lived on Earth have descended from some one primordial form.”  This means that the fact that all life forms on Earth use the same DNA is not that surprising, and it certainly does not necessarily imply that this is the only way for life to evolve.  The biochemistry involved in the emergence of life may not be unique either.  While we normally discuss processes based on carbon and oxygen, some researchers have suggested sulfur and iron as potential alternatives (e.g., in the environments of ocean floor hydrothermal vents; Figure 2).  The existence of extremophiles—life forms that survive and even multiply in conditions that to us appear extreme (such as very cold or very hot temperatures; high degree of salinity)—also suggests that life can surprise us.  The bottom line is simple.  With only one known form of life, our conception of what it takes for life to emerge is necessarily biased, and no definitive conclusions can be reached.  The lesson is also clear:  seek, and ye shall find.

Figure 1. The structure of DNA. The pairs of bases, A-T, and G-C form the rungs of the Double-helix “ladder.” Credit: Wikimedia Commons (http://en.wikipedia.org/wiki/ File:DNA_Structure%2BKey%2BLabelled.pn_NoBB.png).

Figure 2. Black Smoker at deep ocean hydrothermal vent. Credit: Wikimedia Commons (http://en.wikipedia.org/wiki/ File:Blacksmoker_in_Atlantic_Ocean.jpg).

In the third part of this series, I shall briefly discuss the near-future steps that astrobiologists are taking to discover biosignatures in extrasolar planets.

Figure 1. The Kepler Spacecraft. Credit: Ball Aerospace.

Figure 2. The Hubble Space Telescope.

Arguably, the questions of whether extraterrestrial life in general, and intelligent life in particular exist, are two of the most intriguing questions in science today.  The discovery (if and when it happens) of extraterrestrial complex life will undoubtedly usher in a revolution that will rival the Copernican and Darwinian revolutions combined.  At the most basic level one could wonder what the probability is that the Earth is unique in harboring life.  Recent observations with the Kepler spacecraft (Figure 1) and the Hubble Space Telescope (Figure 2) allow us to make at least a rough estimate of this probability.  Astronomers using Kepler found that about one in five (22%) Sun-like stars in the Milky Way has an Earth-sized planet in the so-called Habitable Zone around that star.  The Habitable Zone is that circular band around the star that is neither too hot nor too cold, so that liquid water can exist on the planet’s surface (Figure 3).  This, of course, doesn’t mean that life would actually emerge on such a planet, but a planet in the habitable zone satisfies at least some of the necessary conditions for life.  How many such planets exist in the Milky Way?  There are about 100 billion Sun-like stars in our Galaxy, which puts the number of “habitable” planets around these stars at about 20 billion.  Now, how many galaxies are there in the cosmos?  Estimates from the Hubble Ultra Deep Field put that number at about 200 billion in the observable universe.  Not all of these galaxies are as large as the Milky Way, but some are much larger.  Assuming that on the average about one in ten galaxies is similar to the Milky Way in its contents, we obtain for the number of potentially habitable planets the staggering number of 4 × 1020—that is, four hundred million trillion. If we now use the law of large numbers, for there to be (on average) only one planet (Earth) with life on it, the probability for a planet to harbor life must be as small as one in four hundred million trillion, or 2.5 × 10-21.  Furthermore, any deviation from this probability (say, by a factor of one thousand, which could easily be possible), would result in there either being no planets with life on them at all, or in there being one thousand such planets.  This makes it highly unlikely that we are the only game in the universe.

Figure 4. The James Webb Space Telescope. Credit: Wikimedia Commons (http://en.wikipedia.org/wiki/File:James_Webb_Space_ Telescope_ 2009_top.jpg).

Figure 3. The “Habitable Zone” around a star corresponds to the region that allows for liquid water to exist on the planet’s surface. Credit: Petigura/UC Berkeley, Howard/UH-Manoa, Marcy/UC Berkeley.

The best news that emerges from the Kepler findings is that the abundance of habitable planets puts the nearest one (to Earth) at about 12 light-years away.  This makes such planets superb targets for the James Webb Space Telescope (Figure 4) and for future optical-ultraviolet telescopes to search for biosignatures—signs for life—in their atmospheres.  Still, intelligent civilizations may be rare, which would make the average distance among such civilizations in the Milky Way quite large.  In my next blog I shall explore what we might expect for the characteristics of alien life.

Figure 1. A schematic structure of the double helix of DNA. Credit: Pam Jeffreys.

Figure 2. A schematic of the alpha helix, that characterizes the structure of many proteins. Credit: Pam Jeffreys.

Ask anyone to name the most important molecule and the answer will undoubtedly be DNA—the molecule of life.  Most people are also familiar with the general structure of DNA (Figure 1).  They know that it is a double helix.  In other words, it looks a bit like a twisted ladder, in which the sides are composed of sugars and phosphates, while each rung is formed by a pair of two bases.  The base adenine is always attached to thymine, and guanine to cytosine.  The molecules of many proteins also contain a helical substructure known as the alpha helix (Figure 2).  But helices appear not only on the tiny scales of molecules.  Amazingly, some astrophysical jets—streams of charged particles collimated and accelerated over astronomical distances—also exhibit a helical structure.  One such jet emanates from the Vela pulsar.  The Vela pulsar resulted from the collapse of the core of a massive star more than 10,000 years ago.  The collapsed core formed a neutron star, an extremely compact and highly magnetized object with roughly the mass of the Sun, but with a radius of only about six miles.  The pulsar spins around its axis, making more than 11 complete rotations every second.  Acting like a high-voltage generator, it powers a jet that is more than half a light-year long, along which charged particles race at about 70 percent of the speed of light.  The intriguing feature is that the jet appears to be whipping around like a loose fire hose, creating the helical structure (Figure 3).

Figure 3. The Vela Pulsar’s jet. Credit: G. Pavlov, M. Teter, O. Kargaltsev, D. Sanwal (PSU), CXC, NASA.

The Vela pulsar is not the only astronomical object exhibiting a helical jet.  Evidence for such jets has been observed in other pulsars and in active galactic nuclei.  The latter represent supermassive black holes at the centers of galaxies.  The black holes accrete mass from their vicinity, and the energy that is being released in the accretion disks that surround the black holes powers the spectacular jets.  It is believed that the helical structure is one of the important pieces of evidence pointing to the major role played by magnetic fields in the formation of these jets.  In fact, elementary electrodynamics shows that charged particles move along a helical path in a uniform magnetic field.

Helices thus provide one more manifestation of the remarkable fact that geometrical shapes that can be described by simple mathematics lie at the core of phenomena ranging from molecular to cosmic scales.

The most common encounter with the concept of infinity is associated with the positive whole numbers 1, 2, 3, 4, 5, 6… , which go on without end. In ancient Greece, the celebrated mathematician Euclid famously proved (around 300 BCE) that there is even an infinite number of primes (numbers divisible only by 1 and themselves, such as 3, 7, 17, or 541).  Not until the nineteenth century, however, did anyone find a way to actually rank infinities, and manipulate them in ways one would normally do with ordinary numbers.  The person who in some sense “tamed” infinities, by demonstrating that they can be properly defined and arranged in a hierarchy in which each infinity is manifestly larger than the one below it, was Georg Cantor (1845–1918; Figure 1).  Cantor first found a clever way to show that even though it seems that there are many more fractions, quantities such as 3/5, 9/11, or 241/509, than whole numbers, their infinities are actually of the same size!  This sounds surprising, since clearly even just between 1 and 2 there are infinitely many fractions of the form p/q (where p and q are whole numbers).  Yet, Cantor found a way to show that there is a one-to-one correspondence between the whole numbers and the fractions.  In other words, the fractions (known as rational numbers) are definitely countable.  Cantor’s recipe for how to do the counting is shown in Figure 2.   First count all those fractions in which the nominator and denominator add up to 2, then those that add to 3, then to 4, and so on.  Since this procedure clearly counts all the fractions, and each one is only counted once, you discover that the infinity of the fractions and of the whole numbers are of the same size.  Cantor then proceeded to show that all the non-ending decimals are uncountable,  meaning that the size of that infinity is larger than that of the whole numbers.  In this way he constructed an endless hierarchy of infinities. For any given infinity size, one can construct an infinity of a bigger size.  Cantor labeled the smallest infinity—that of the whole numbers—by the Hebrew letter aleph, to which he added the subscript zero, ℵ0.  He then labeled all the larger infinities by increasing subscripts, ℵ0, ℵ1, ℵ2, ℵ3

Figure 1. The mathematician Georg Cantor. Credit: Wikimedia Commons.

Figure 2. A schematic demonstrating Cantor’s recipe for counting fractions. Cantor used this procedure to show that the size of the infinity represented by the fractions is equal to the size of the infinity represented by the whole numbers.

An intriguing question that arises is whether infinities are only a mathematical concept, or whether they can occur in physical reality.  Interestingly, cosmology—the study of the universe as a whole—provides quite a few examples where in principle one could encounter infinity.  First, there is the Big Bang itself—the singular event believed to have brought space, time, and our universe into existence.  If the Big Bang (which we believe occurred some 13.8 billion years ago) should indeed be associated with a mathematical “singularity” (where one is essentially driven to divide by a size approaching zero), then quantities such as density (defined as mass per unit volume) would have had to be infinite.

Similarly, one could ask whether our universe is infinite in size, or whether it would exist for an infinite time into the future.  Most physicists see singularities merely as an indication of the breakdown of the theory.  In the case of the Big Bang, they point to the fact that we don’t yet have a quantum theory of gravity.  Such a theory would unify our ideas about the largest cosmic scales (as expressed by Einstein’s General Relativity) with those on the subatomic scales (the quantum realm) and it may eliminate singularities and infinities.

We don’t actually know if our universe is infinite in size or not, but since our universe has a finite age, the (in principle) observable universe is definitely finite, with a radius of about 46 billion light-years.  (One light year is the distance light travels in one year—about 6 trillion miles).  Telescopes such as Hubble, and the upcoming James Webb Space Telescope have certainly expanded and will continue to expand our horizons far beyond what had been possible a century ago.  The practical horizon of an optical or infrared telescope, no matter how powerful, is going to be limited by the fact that the universe was opaque to such radiation when it was younger than about 380,000 years.  To probe the universe before that time, we would need different techniques such as gravitational waves or neutrinos.

Will our universe continue to exist for an infinite amount of time?  We are not sure of that either.  The mass of the recently discovered Higgs boson (Figure 3) suggests that the vacuum of our universe may be inherently unstable, meaning that at some point (tens of billions of years from now), our universe could be destroyed by a bubble “alternate” universe.

Figure 3. Representation of an event recorded at the Large Hadron Collider. Events like this led to the discovery of the Higgs boson. Credit: Wikimedia Commons.

To conclude, infinities do occur in a variety of physical theories.  In some cases they may simply indicate that the existing theory is too naïve.  In others, they may signal the existence of new physics.  To some questions we may never know if the answer is infinity or not.

The Hubble Space Telescope has arguably been one of the most successful scientific experiments in history.  It has produced (among many other things) images of galaxies when the universe was only about half a billion years old (it is now 13.8 billion years old), and has given us a glimpse into the actual composition of the atmospheres of extrasolar planets.  Hubble’s scientific successor, the James Webb Space Telescope (JWST), will literally infuse new meaning into the phrase “the search for our origins.”  It will show us the very first galaxies to have formed in our universe, and will identify those extrasolar planets likely to have liquid water (and therefore origin-of-life ingredients) on their surface.

Figure 1. Artist conception of the James Webb Space Telescope. Credit: NASA.

Figure 2. Technicians and scientists check out one of the Webb telescope’s first two flight mirrors in the clean room at NASA’s Goddard Space Flight Center in Greenbelt, Md. Credit: NASA/Chris Gunn.

The James Webb Space Telescope (Figure 1) represents an ambitious international collaboration led by NASA, with the important participation of the European and Canadian space agencies.  The machine itself is nothing short of a marvel, with a gold-coated beryllium mirror 6.5 meters in diameter (Figure 2).  The mirror itself is composed of 18 hexagonal segments, which will unfold, origami-like, after the telescope is launched.  Since the light from objects in the distant, early universe is significantly redshifted, JWST will observe in infrared light.  In addition, the ability of infrared radiation to penetrate through dust and gas (which are opaque to visible light), will allow JWST to peek into regions where new stars and planets are born.  The telescope will be equipped with a tennis-court-sized sunshield that will unfurl and protect it from radiation coming from the Sun, Earth, and Moon (Figure 3).

Figure 3. One-third scale Sunshield showing one of the five layers being installed at Northrop Grumman. Credit: Nexolve.

Unlike Hubble, which is in a low-Earth orbit at a distance of just over 300 miles above the surface of the Earth, JWST will be about a million miles from Earth—about four times the distance between the Earth and the Moon.

As amazing as the telescope itself is from a technological perspective, to me personally and to many other astronomers, JWST’s chief appeal is in its immense scientific promise.  And even in that, two goals stand head and shoulders (or should I say light-years?) above the rest.  One is understanding the formation of planetary systems and of the conditions that led to the origin of life.  By observing both objects in the outer parts of our own solar system, and the atmospheres of extrasolar planets, JWST will take us one step closer in our quest to find extraterrestrial life.

The second, extremely fascinating topic is that of the so-called “first light”—the very first objects in the universe to have illuminated their surroundings and reionized the cosmic intergalactic gas.  JWST could detect the earliest progenitors of today’s galaxies, and even the massive explosions (known as pair-instability supernovae) that the first generation of stars is predicted to have produced.

Perhaps even more importantly, however, we have to expect the unexpected.  More than half of the major discoveries by the Hubble Space Telescope were not anticipated.  I expect nothing less from the James Webb Space Telescope!  I cannot wait for its launch in 2018.