Nov 192013
Figure 1.  A schematic structure of the double helix of DNA. Credit: Pam Jeffreys.

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.

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.

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.

Nov 052013

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 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.

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.

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.

Oct 232013

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 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.

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.

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.

Oct 082013

Leonardo da Vinci (Figure 1) is not usually known for his astrophysics. Yet this remarkable individual – the quintessential “Renaissance Man” – made quite a few pronouncements related to astronomy and astrophysics.

Figure 1. Portrait of Leonardo da Vinci by the painter Francesco Melzi. From: Wikimedia Commons

Figure 1. Portrait of Leonardo da Vinci by the painter Francesco Melzi.
From: Wikimedia Commons

While many of Leonardo’s statements proved eventually to be wrong, some of them do demonstrate his immense intellectual curiosity, his unusually keen power of observation, and his ability to distill simple conclusions even from complex data.
     Take, for instance, his crisp description of the Sun: “The Sun has substance, shape,  movement, radiance, heat and generative power; and these qualities all emanate from itself without its diminution.” Indeed, the timescale on which the Sun evolves (about ten billion years) is so long, that it would appear unchanged during a human lifetime. Similarly, Leonardo addressed the question of whether the Sun is hot: “Some say that the Sun is not hot because it is not the color of fire is much paler and clearer. To these we may reply that when liquified bronze is at its maximum of heat it most resembles the Sun in color, and when it is less hot it has more the color of fire.”
     Generally, Leonardo’s interest in astronomy stemmed primarily from his attentiveness to vision and to optics. Still, he owned a copy of Ptolemy’s “Cosmography”, as well as a book by the medieval Persian astronomer Abu Mashar.
     One area in which Leonardo anticipated the later findings by Galileo, and clearly departed from the Aristotelian views of his time, concerned the nature of the Moon. Unlike Aristotle, who made a clear distinction between the “terrestrial” and the “celestial”, Leonardo concluded that there is no real difference between the Earth and the Moon: “If you were on the Moon…, our Earth would appear to you to make the same effect as does the Moon.” He further stated that: “The Moon is not luminous in itself. It does not shine without the Sun.”
     Leonardo also pointed out contradictions in the many erroneous ideas that existed about the spots seen on the lunar surface. Thus he declared, for instance, “some have said that vapors are given off from the Moon after the manner of clouds, and are interposed between the Moon and our eyes. If this were the case these spots would never be fixed either as to position or shape; and when the Moon was seen from different points, even although these spots did not alter their position, they would change their shape.”
Figure 2. A page from Leonardo's notebook, showing a sketch and accompanying text that may be related to the design of a telescope.

Figure 2. A page from Leonardo’s notebook, showing a sketch and accompanying text that may be related to the design of a telescope.

     A question that has intrigued many Leonardo scholars was whether or not he had ever attempted
to design a telescope. After examining much of the evidence, my personal (non-professional) conclusion is that while Leonardo certainly explored some of the theoretical aspects involved in the construction of telescopes (and he even made such statements as: “Construct glasses to see the Moon magnified”), he never actually built one. Figure 2 presents a sketch from Leonardo’s notebook, accompanied by text part of which reads: “eyeglass of crystal thick at the sizes at ounce of an ounce.” Leonardo researcher Domenico Argentieri found the full text to be suggestive of a design of a telescope.
     To conclude, Leonardo was definitely not an astronomer, but he was fascinated by nature, and he did not hesitate to attempt to provide explanations for natural phenomena, or to suggest tools that could help
decipher nature’s secrets.
Oct 012013
Figure 1. Image of the radio signal from Voyager 1, taken by the Very Long Baseline Array.  Credit: NRAO/AUI/NSF.

Figure 1. Image of the radio signal from Voyager 1, taken by the Very Long Baseline Array. Credit: NRAO/AUI/NSF.

You may have heard that NASA recently determined that the space probe Voyager 1 crossed the heliopause and entered interstellar space on August 25, 2012.  Figure 1 shows an image of the radio signal from the probe.  The heliopause marks the boundary beyond which charged particles from interstellar space (ejected by previous generations of stars) are no longer deflected by particles from the solar wind.  At about 12 billion miles from Earth, Voyager 1 became the first human-made spacecraft to have formally left the solar system.

Voyager 1 was launched on September 5, 1977, primarily to explore the planets Jupiter, Saturn, and their satellites.  It continues to communicate with the Deep Space Network and to return data.

You may wonder why the fact that it has left the solar system (though not the influence of the Sun’s gravity) is significant.  Indeed, from a purely scientific perspective, there isn’t much to expect from Voyager 1 in the future.  The probe is not heading towards any particular star.  The closest it will come to the first star it encounters will be about 1.6 light-years—and that will not happen for another 40,000 years.  So it is hard to believe that the gold-plated audio-visual record on board the spacecraft will ever be found by an intelligent alien civilization.  That record contains photos of lifeforms of Earth, a variety of scientific information, and various sounds.  Nevertheless, there is something truly symbolic and inspiring in being first in any adventure in space exploration.  Recall the commotion caused by the first artificial satellite, Sputnik 1, launched by the Soviet Union on October 4, 1957, or the excitement that accompanied the first person in space, Yuri Gagarin, in April 1961.

Figure 2.  Neil Armstrong on the Moon. Credit: NASA.

Figure 2. Neil Armstrong on the Moon. Credit: NASA.

Figure 3.  Sir Edmund Hillary on the summit of Mount Everest. From

Figure 3. Sir Edmund Hillary on the summit of Mount Everest. From

Of course, to date, nothing beats the landing on the Moon by the Apollo 11 astronauts on July 20, 1969, in terms of the emotions it evoked.  Figure 2 shows the late astronaut Neil Armstrong on the Moon.  I know of an entire generation of scientists who still cite the landing on the Moon as the single event that inspired them to choose a scientific career.  Historical milestones are important.  When Edmund Hillary and Tenzing Norgay finally conquered Everest on May 29, 1953 (Figure 3), there was clearly no immediate benefit to humankind.  But these types of accomplishments demonstrate what humans can achieve when they put their mind and determination into the task.

Voyager 1 will probably not discover new worlds, but it has already taken the first step in interstellar travel for us.

Sep 172013

In October 1604, the famous astronomer Johannes Kepler saw with his naked eye (and later observed in detail) what he thought to be a new star. In fact, what he saw was the explosion of an old star—a supernova. Over a period of centuries, there was no further historical record of a naked-eye supernova. Some jokingly said that this was because there hasn’t been a truly great astronomer since Kepler.

On February 23, 1987, however, something dramatic happened. Canadian astronomer Ian Shelton discovered a new supernova in our neighboring galaxy, the Large Magellanic Cloud, and that supernova was visible to the naked eye. According to tradition, since that was the first supernova (SN) observed in 1987, it was dubbed SN1987A (the second in any given year is denoted by the letter B, and so on).  I personally remember the tremendous excitement that this supernova, a mere 167,000 light-years away (very near, by cosmic standards), caused. Soon, every telescope on the face of the Earth’s southern hemisphere (where it was visible) and in space was directed to it.

The initial observations delivered an immediate surprise. Based on the theory of supernova explosions, the expectation was that the exploding star should have been a red supergiant. Instead, previous observations of the precise location of the explosion revealed that the exploding star was a blue supergiant. Eventually, astronomers understood that the star had suffered severe mass loss during its evolution, making it more compact and hotter (and therefore blue).

Figure 1.  Credit: Dr. Christopher Burrows, ESA/STScI and NASA.

Figure 1. Credit: Dr. Christopher Burrows, ESA/STScI and NASA.

Remarkably, one of the key predictions of supernova theory was readily confirmed. Supernova explosions occur when the dense core of a massive star collapses to form a neutron star (a very compact object, only about 12 miles in diameter), producing copious amounts of neutrinos in the process. Detectors, located deep underground in Ohio and Japan, indeed identified about a dozen of these elusive neutrinos as they passed through the Earth. This constituted an immense theoretical and experimental success.

After its launch, the Hubble Space Telescope also viewed SN1987A, and those observations revealed a mysterious structure of three rings (Figure 1). It took astrophysicists quite a while to understand their origin. Basically, mass loss from the star prior to the explosion formed an equatorial ring of material. An hourglass shape—in which the equatorial ring formed its “waist”— accompanied this, and fast-moving material expanding in a perpendicular direction formed the lobes. The outer rings mark the rim of the two lobes. The ultraviolet flash from the explosion heated all the rings, which consequently began to emit radiation.

Figure 2.  NASA, P. Challis, R. Kirshner (Harvard-Smithsonian Center for Astrophysics) and B. Sugerman (STScI).

Figure 2. Credit: NASA, P. Challis, R. Kirshner (Harvard-Smithsonian Center for Astrophysics) and B. Sugerman (STScI).

In 2001, ejecta from the supernova eventually began colliding with the inner ring. The collisions still continue today, causing that ring to shine like a bracelet of pearls (Figure 2).

Supernova 1987A has given astronomers an unprecedented look at what can happen to a massive star before and after it explodes, though why we have not observed the radio pulses expected from a spinning neutron star is still a mystery. There are three potential explanations: (1) The pulsar is obscured by heavy dust. (2) The Earth is not in the line of sight of the beam of this radio “lighthouse.” (3) The collapsing core has, in fact, formed a black hole rather than a neutron star. Hubble, the Chandra X-Ray Observatory, and the Herschel Space Observatory continue to monitor the evolution of this supernova remnant, and there is no doubt that it will also be a target for the upcoming James Webb Space Telescope.

Supernovae eject into space elements needed for life, such as oxygen, phosphorus, and iron. SN1987A therefore provided us with a glimpse of our own beginnings.

Sep 032013

If you’ll examine any list of the greatest mathematicians of all time, you’ll find that many of them were also interested in astronomy.  More generally, quite a few were passionate about understanding the workings of the cosmos. For instance, it goes without saying that Newton and Archimedes (considered by many to occupy the top two spots on the list) contributed significantly to astronomy.  Carl Friedrich Gauss (the third on most lists), developed (among other things) an elaborate method to calculate the orbit of the dwarf planet Ceres.

Henri Brocard (1845–1922) was not quite at the level of Archimedes, Newton, and Gauss (nobody was!), but he was nevertheless an accomplished mathematician and meteorologist, who spent the last years of his life in Bar-le-Duc, France, making extensive astronomical observations with a small telescope.

Figure 1. The Brocard point in a triangle, where the marked angles are equal. From Wikimedia Commons: Brocard_point.svg

It appears, somehow, that those infatuated with the abstract, so-called “Platonic world of mathematical forms,” also frequently were bewitched by the heavens.  Here, however, I want to concentrate neither on Brocard’s main, purely mathematical contributions (which were in the area of the geometry of the triangle; e.g., Figure 1), nor on his (more modest) contributions to meteorology and astronomy, but on a small, fascinating problem that he posed in articles written in 1876 and 1885.

For any whole number n, mathematicians denote by n! (called “n factorial”) the product of all the numbers up to and including n.  That is:

 n! = 1 × 2 × 3 × 4 … × n .

As it turns out, the different ways to arrange n objects in order is n!.  For instance, you can arrange the three letters a, b, c, in 3! = 1 × 2 × 3 = 6 ways:  abc; cab; bca; acb; cba; bac.

If you wonder in how many ways it is possible to arrange all 26 letters in the English alphabet, the answer is: 26! = 403, 291, 461, 126, 605, 635, 584, 000, 000.

What Brocard noticed was that in three cases, adding 1 to a factorial gave a perfect square:

4! + 1 = 24 + 1 = 25 = 52
5! + 1 = 120 + 1 = 121 = 112
7! + 1 = 5040 + 1 = 5041 = 712 .

He therefore asked the intriguing question of whether the same was true for any other numbers. That is, whether other whole numbers n and m exist, such that n! + 1 = m2.  Pairs of numbers (n, m) that satisfy Brocard’s problem are known (for reasons that I must admit I don’t know) as Brown numbers.

Figure 2. Mathematician Paul Erdös. From Wikimedia Commons: http:// wiki/File:Erdos_ budapest_fall_1992.jpg

Being unaware of Brocard’s query, in 1913 the famous Indian genius Srinivasa Ramanujan formulated the same question:  “The number 1 + n! is a perfect square for the values 4, 5, 7 of n.  Find other values.”  In 1935, H. Gupta claimed that calculations of n! up to n = 63 gave no further solutions.  It was only natural then for one of the most prolific authors of mathematical papers, Paul Erdös (Figure 2), to weigh in on this problem.  Erdös is known for having collaborated with more than 500 mathematicians on a variety of joint papers.  This productivity has led to the concept of the “Erdös number”—a measure of the number of steps needed to connect an author with Erdös.  For instance, his direct co-authors have an Erdös number of 1, their co-authors on other papers have number 2, and so on.  Incidentally, my own Erdös number is 4.  Erdös conjectured that no solutions other than the above pairs (4,5), (5,11), and (7,71) exist.  In 1993, Mathematician M. Overholt showed that if a weak form of another mathematical conjecture known as the “abc conjecture” holds true, then there is only a finite number of solutions to Brocard’s problem.  In August 2012, mathematician Shinichi Mochizuki claimed to have proved the abc conjecture. However, Vesselin Dimitrov and Akshay Venkatesh pointed out an error in his proof in October 2012.  Since then Mochizuki has posted a series of papers (the latest one just last month!) claiming to have corrected the mistake, but the jury is still out on those.  Finally, in 2000 mathematicians Bruce Berndt and William Galway showed that no other solutions exist up to n equals one billion.

The ancient Pythagoreans believed that the entire universe could be explained by whole numbers.  To their dismay, this turned out not to be correct.  But whole numbers continue to intrigue many people (not just professional matheticians) even today, and to date, no mathematically rigorous answer to Brocard’s problem exists.

Aug 202013

Figure 1.

What did we know about the size and contents of our universe a hundred years ago?  Very little.  Even the proton, the nucleus of the simplest atom (hydrogen), was only discovered by Rutherford in 1917–1919.  The neutron, the other occupant of the atomic nucleus, had to wait for its discovery until 1932, and the neutrino, the elusive particle that barely interacts with matter, was only discovered in 1956!

The size and structure of the cosmos were also a complete mystery to the astronomers and physicists of the beginning of the twentieth century.  In fact, it was only in 1924 when astronomer Edwin Hubble unambiguously confirmed that there are other galaxies beyond our own Milky Way.  Figure 1 shows a recent image of the Andromeda galaxy, M31, which was the first galaxy identified as being outside the Milky Way.

Figure 2. Standard Model of Elementary Particles. From: File:Standard_Model_of_Elementary_Particles.svg

What do we know today about our universe’s dimensions and composition?  Quite a bit, although much remains to be explored.  Here is a concise inventory.  While we don’t know the precise size of the universe, and it definitely may be infinite, the radius of the observable universe is about 46 billion light-years.  One light-year is the distance that light travels in one year—approximately six trillion miles.  For comparison, the distance to the Andromeda galaxy is “only” about 2.5 million light-years.  The universe is about 13.8 billion years old.  As far as we can tell, the universe is homogeneous (the same everywhere) and isotropic (the same in every direction) on its large scales.  It is also geometrically flat.  The average energy density in the universe is the equivalent of about 10-29 grams per cubic centimeter.  About 73 percent of this energy density appears to be in the form of a rather mysterious, smooth, “dark energy,” which may represent the energy of the physical vacuum.  About 23 percent appears to be “dark matter”—matter that does not shine light, but which can be detected through its gravitational influence.  Ordinary (“baryonic”) matter constitutes only about 4 percent of the cosmic energy budget.  According to the Standard Model of particle physics, there are 12 elementary particles (the most basic constituents of ordinary matter) that have a quantum mechanical spin of half a unit.  These include six quarks (that are called: up, down, charm, strange, top, and bottom) and six leptons (electron, electron neutrino, muon, muon neutrino, tau, and tau neutrino).  All of these are commonly grouped into three generations, the first of which includes, for instance, the up and down quarks, the electron, and the electron neutrino.  In addition to the matter particles, there are force-carrying gauge bosons that include the photon (carrier of electromagnetism) the gluons (carriers of the strong nuclear force), and the W± and Z bosons (the carriers of the weak nuclear force).  The latest addition to the list of elementary particles is the Higgs boson (discovered in 2012 and tentatively confirmed in 2013), which plays the crucial role of endowing all the other elementary particles (other than the photon and the gluons) with mass.  Figure 2 presents the elementary particles of the Standard Model.

Intriguingly, there are theories that predict the existence of additional components to the above inventory, both in terms of contents (on the smallest scales) and structure (on the largest).

In one suggested extension to the Standard Model known as supersymmetry, every particle is supposed to have a yet-undiscovered partner.  The leptons and quarks, for instance, would have sleptons and squarks, while the gluons would have gluinos.  So far the Large Hadron Collider has not discovered supersymmetric particles, but it might still do so when it returns to operation at full energy.

On the cosmic scale, a more speculative idea is that of the multiverse—the proposal that our universe is but one member of a huge ensemble of universes. This speculation is based on insights gained from the concept of inflation—the brief phase of explosive expansion early on in the universe’s evolution, and from string theory. Certain otherwise perplexing properties of our universe (such as the value of the density of “dark energy”) may find an explanation if such a multiverse exists.  String theory also suggests that in addition to the familiar three dimensions of space and one of time, our universe may have six or seven extra spatial dimensions.

To conclude, the last century has been absolutely phenomenal in terms of how much we have learned about our universe, but all signs are that the next one hundred years will be at least as exciting.

Aug 132013

Figure 1. “The Adoration of the Magi” by Giotto di Bondone. From:

The heavens have always been a source of inspiration for poetry, music and the visual arts.  The first chapter of the biblical book of Genesis already talks about the creation of the Sun, Moon and the stars.  The ancient Babylonian, Chinese, North European and Central American cultures all left records and artifacts related to various astronomical observations.  It was only natural then, that at the end of Medieval times, with the first signs of the Renaissance (in the fourteenth and early fifteenth centuries), the heavens would start making an appearance in important works of art.  One impressive demonstration of the interest in astronomy was in the great Italian painter Giotto di Bondone’s fresco “the Adoration of the Magi” (Figure 1).  The fresco was painted around 1305–06, and it features a very realistic depiction of a comet, representing the “Star of Bethlehem.”  It is thought that the comet’s image was inspired by Giotto’s observations of Halley’s comet in 1301.

Figure 2. “Très Riches Heures du Duc de Berry” by the Limburg brothers. From:ès_Riches_ Heures_du_duc_de_Berry_ Janvier.jpg

A second beautiful example of astronomy in art is provided by a famous illuminated manuscript.  The three Dutch miniature painters known as the Limburg brothers created the Très Riches Heures du Duc de Berry book of prayers (Book of Hours), and it is currently considered to be one of the most valuable books in the world.  The book was unfinished at the time of the death of the three brothers in 1416, and the work on it was completed by the painters Barthélemy van Eyck (possibly) and Jean Colombe (certainly).  As Figure 2 shows, an attempt was clearly made to give an accurate representation of the night’s sky, even including meteors.

Figure 3. “The Battle of Issus” by Albrecht Altdorfer. From:

A third magnificent painting, the “Battle of Issus,” by the German painter Albrecht Altdorfer (Figure 3), may be the first painting in which the curvature of the Earth is shown as seen from above, from a great height.

Finally, I find the illustration of the Ptolemaic geocentric model by the Portugese cosmographer Bartolomeo Velho (Figure 4) extremely attractive.  The illuminated illustration, “Figure of the Heavenly Bodies,” was created in France in 1568.

All of these works of art were being created shortly before or at a time when the Copernican revolution was about to forever change the view humans had of the cosmos and on their place within it.  Far from being perfect and immutable, the heavens turned out to be part of an ever-evolving universe.

Figure 4. “Figure of the Heavenly Bodies” by Bartolomeo Velho. From:


Aug 062013

Figure 1. Neptune as seen with the Hubble Space Telescope (from: newscenter/archive/releases/2005/22/image/ a/format/web_print/).

The tale of the discovery of Neptune, the eighth planet in the solar system (Figure 1) reads like a detective story.

The planet Uranus was discovered by astronomer William Herschel in 1781.  Almost immediately, astronomers started to see deviations of its orbit from predictions made by Newton’s theory of gravitation.  By the early 1840s, these deviations became substantial, leading a few astronomers to speculate that Uranus’s orbit might be perturbed by the presence of an unseen planet (alternatively, Newtonian gravity would have to be modified at large separations).  In some sense, this was the first suggestion for “dark matter”—mass not detected through its light, but rather through its gravitational effects.

On June 1, 1846, the French mathematician Urbain Le Verrier published a calculation that explained the discrepancies by predicting the existence of a transuranian planet, and its expected location in the sky.  Based on his prediction, the German astronomer Johann Galle and his student, Heinrich Louis d’Arrest, discovered Neptune just after midnight on the night of September 23, 1846.  The new planet’s celestial longitude was just about one degree away from Le Verrier’s prediction!  The excited Galle informed Le Verrier:  “the planet whose place you have really exists.”

If the story would have ended here, this would have simply been a fascinating story of how sciences progress through theoretical predictions and observational verifications.  This is, however, where the conventional plot started to thicken.  According to the commonly told version, as soon as news of the discovery reached England, George Biddell Airy, the British Astronomer Royal at the time, realized that he had seen a similar prediction in the fall of 1845 on a note left at his house by a little-known English mathematician named John Couch Adams.

Adams had indeed been doing calculations for several years concerning the potential location of a new planet, and he briefly communicated his results to Airy and to James Challis, director of the Cambridge Observatory.  However, the fact is, that the materials Adams provided to Challis and Airy were insufficient to convince the two to initiate an aggressive observational search.  Only after Le Verrier’s prediction became known in England did Challis make an unsuccessful attempt to search for the planet suggested by Adams’ calculations.  Nevertheless, following the announcement of the discovery of Neptune, a controversy arose between the English and French astronomical communities, with the English astronomers claiming that Le Verrier and Adams should share the credit for the prediction.  The French initially reacted with suspicion, and the magazine L’Illustration even published a cartoon depicting Adams “discovering” Neptune in Le Verrier’s manuscript (Figure 2).  The controversy eventually subsided after Airy presented certain documents which supposedly demonstrated that Adams had indeed produced predictions deviating from those of Le Verrier by only about one degree.  The emerging consensus was, therefore, that Le Verrier and Adams should both be credited with predicting Neptune.

Figure 2. A cartoon that appeared in the November 7, 1846 issue of L’Illustration, showing Adams looking for Neptune in vain, and then “discovering” it in Le Verrier’s notebook. From:

Amazingly, the story did not end there.  Modern science historians, such as Neptune scholar Dennis Rawlins and astronomy historian Robert Smith, discovered that it was difficult to examine the details of the discovery of Neptune since the “Neptune file” containing Adams’ correspondence with Airy had gone missing from the library in the 1960s.  In 1999, following the death of astronomer Olin Eggen, the file was discovered in his office in Chile, even though Eggen had previously denied having it.  Eggen had served as chief assistant to the Astronomer Royal in Britain in the early 1960s, and apparently he was given the file—or he “borrowed” it (as well as other rare books)—for some research he was doing on Airy’s work.  He then took the file with him to Australia and eventually to Chile.

Historian of science Nicholas Kollerstrom and his colleagues William Sheehan and Craig Woff have examined the file in detail, and in their view “the achievement [of predicting Neptune] was Le Verrier’s alone.”  They based their conclusion on two main points.  First, in successive calculations, Adams kept changing his prediction for the location of the putative new planet, once by as much as twenty degrees.  Second, even though there is no doubt that Adams’ calculations were similar in nature, and at some level even in accuracy, to those of Le Verrier (both miscalculated Neptune’s distance from the Sun), Adams failed to convince his contemporaries to engage in an extensive search.  Did, therefore, (in Kollerstrom’s words) “the Brits steal Neptune”?  Maybe this is too strong a statement, but they certainly presented the evidence in a way that boosted Adams’ (and thereby Britain’s) claim for credit.

Scientists are only human after all.