Atomic Mass Unit

Faraday's Constant

Believe it or not, there are actually several atomic mass units … however, the one that’s standard – throughout chemistry, physics, biology, etc – is the unified atomic mass unit (symbol u). It is defined as 1/12 (one-twelfth) of the mass of an isolated carbon-12 atom, in its ground state, at rest. You’ll still sometime see the symbol amu – which stands for atomic mass unit – but that’s actually two, slightly different, units (and each is different from the unified atomic mass unit!) … these older units are defined in terms of oxygen (1/16th of an isolated oxygen-16 atom, and 1/16th of an ‘average’ oxygen atom).

As it’s a unit of mass, the atomic mass unit (u) should also have a value, in kilograms, right? It does … 1.660 538 782(83) x 10-27 kg. How was this conversion worked out? After all, the kilogram is defined in terms of a bar of platinum-iridium alloy, sitting in a vault in Paris! First, it is important to recognize that the unified atomic mass unit is not an SI unit, but one that is accepted for use with the SI. Second, the kilogram and unified atomic mass unit are related via a primary SI unit, the mole, which is defined as “the amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kilogram of carbon 12“. Do you remember how many atoms there are in a mole of an element? Avogadro’s number! So, work out the Avogadro constant, and the conversion factor follows by a simple calculation …

The Dalton (symbol D, or Da) is the same as the unified atomic mass unit … why have two units then?!? In microbiology and biochemistry, many molecules have hundreds, or thousands, of constituent atoms, so it’s convenient to state their masses in terms of ‘thousands of unified atomic mass units’. That’s far too big a mouthful, so convention is to use kDa (kilodaltons).

Find out more on the (unified) atomic mass unit, from the Argonne National Laboratory, from the International Union of Pure and Applied Chemistry, and from the National Institute of Standards and Technology (NIST).

Learning to Breathe Mars Air and Mini-Detector Could Find Life on Mars or Anthrax at the Airport are two Universe Today articles relevant to the atomic mass unit.

Energy Levels and Spectra and Inside the Atom are two Astronomy Cast episodes related to the atomic mass unit.

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Physicists Tie Beam of Light into Knots

Imagine taking a beam of light and tying it in knots like a piece of string. Hard to fathom? Well, a group of physicists from the UK have achieved this remarkable feat, and they say understanding how to control light in this way has important implications for laser technology used in wide a range of industries.

“In a light beam, the flow of light through space is similar to water flowing in a river,” said Dr. Mark Dennis from the University of Bristol and lead author of a paper published in Nature Physics this week. “Although it often flows in a straight line – out of a torch, laser pointer, etc – light can also flow in whirls and eddies, forming lines in space called ‘optical vortices.’ Along these lines, or optical vortices, the intensity of the light is zero (black). The light all around us is filled with these dark lines, even though we can’t see them.”

Optical vortices can be created with holograms which direct the flow of light. In this work, the team designed holograms using knot theory – a branch of abstract mathematics inspired by knots that occur in shoelaces and rope. Using these specially designed holograms they were able to create knots in optical vortices.

This new research demonstrates a physical application for a branch of mathematics previously considered completely abstract.

“The sophisticated hologram design required for the experimental demonstration of the knotted light shows advanced optical control, which undoubtedly can be used in future laser devices,” said Miles Padgett from Glasgow University, who led the experiments

“The study of knotted vortices was initiated by Lord Kelvin back in 1867 in his quest for an explanation of atoms,” addeds Dennis, who began to study knotted optical vortices with Professor Sir Michael Berry at Bristol University in 2000. “This work opens a new chapter in that history.”

Paper: Isolated optical vortex knots by Mark R. Dennis, Robert P. King, Barry Jack, Kevin O’Holleran and Miles J. Padgett. Nature Physics, published online 17 January 2010.

Source: University of Bristol

What is Absolute Temperature?

If you measure temperature relative to absolute zero, the temperature is an absolute temperature; absolute zero is 0.

The most widely used absolute temperature scale is the Kelvin, symbolized with a capital K, which uses Celsius-scaled degrees (there’s another one, the Rankine, which is related to the Fahrenheit scale). We write temperatures in kelvins without the degree symbol; absolute zero is 0 K.

Another name for absolute temperature is thermodynamic temperature. Why? Because absolute temperate is directly related to thermodynamics; in fact it is the Zeroth Law of Thermodynamics that leads to a (formal) definition of (thermodynamic) temperature.

Roughly speaking, the temperature of an object (or similar, like the gas in a balloon) measures the kinetic energy of the particles (atoms, molecules, etc) of the matter it’s made up of … in an average sense, and macroscopically. Note that blobs of matter have far more energy than just the kinetic energy of the atoms in the blob – there’s the energy that holds the atoms together in molecules (if there are any), the binding energy of the nuclei (unless the blog is pure hydrogen, with no deuterium), and so on; none of these energies are counted in the blob’s temperature.

You might think that at absolute zero a substance would be in its lowest possible energy state, especially if it is a pure compound (or isotopically pure element). Well, it isn’t quite that simple … leaving aside zero point energy (something quite counter-intuitive, from quantum mechanics), there’s the fact that many solids have several different, stable crystal structures (even at 0 K), but only one with minimal energy. Then there’s helium, which is a liquid at 0 K (the solid phase of a substance has a lower energy than the corresponding liquid phase), unless under pressure.

The Kelvin is one of the International System of Units (SI) base units (there are seven of these), and is defined with reference to the triple point of water (“The kelvin, unit of thermodynamic temperature, is the fraction 1/273.16 of the thermodynamic temperature of the triple point of water” is the 1967/8 definition; the current one – adopted in 2005 – expands on this to take account of isotropic variations).

Why is it called the Kelvin? Because William Thompson – Lord Kelvin – was the first to describe an absolute temperature scale, in a paper he wrote in 1848; he also estimated absolute zero was -273o C.

Project Skymath has a nice introduction to absolute temperature.

Some Universe Today material you may find interesting: Absolute Zero, Coldest Temperature Ever Created, and Planck First Light.

Sources: Wikipedia, Hyperphysics


Quintessence is one idea – hypothesis – of what dark energy is (remember that dark energy is the shorthand expression of the apparent acceleration of the expansion of the universe … or the form of mass-energy which causes this observed acceleration, in cosmological models built with Einstein’s theory of general relativity).

The word quintessence means fifth essence, and is kinda cute … remember Earth, Water, Fire, and Air, the ‘four essences’ of the Ancient Greeks? Well, in modern cosmology, there are also four essences: normal matter, radiation (photons), cold dark matter, and neutrinos (which are hot dark matter!).

Quintessence covers a range of hypotheses (or models); the main difference between quintessence as a (possible) explanation for dark energy and the cosmological constant Λ (which harks back to Einstein and the early years of the 20th century) is that quintessence varies with time (albeit slooowly), and can also vary with location (space). One version of quintessence is phantom energy, in which the energy density increases with time, and leads to a Big Rip end of the universe.

Quintessence, as a scalar field, is not the least bit unusual in physics (the Newtonian gravitational potential field is one example, of a real scalar field; the Higgs field of the Standard Model of particle physics is an example of a complex scalar field); however, it has some difficulties in common with the cosmological constant (in a nutshell, how can it be so small).

Can quintessence be observed; or, rather, can quintessence be distinguished from a cosmological constant? In astronomy, yes … by finding a way to observed (and measure) the acceleration of the universe at widely different times (quintessence and Λ predict different results). Another way might be to observe variations in the fundamental constants (e.g. the fine structure constant) or violations of Einstein’s equivalence principle.

One project seeking to measure the acceleration of the universe more accurately was ESSENCE (“Equation of State: SupErNovae trace Cosmic Expansion”).

In 1999, CERN Courier published a nice summary of cosmology as it was understood then, a year after the discovery of dark energy The quintessence of cosmology (it’s well worth a read, though a lot has happened in the past decade).

Universe Today articles? Yep! For example Will the Universe Expand Forever?, More Evidence for Dark Energy, and Hubble Helps Measure the Pace of Dark Energy.

Astronomy Cast episodes relevant to quintessence include What is the universe expanding into?, and A Universe of Dark Energy.

Source: NASA

Electron Mass

The mass of the electron, or the electron’s mass, written as me, is 9.109 382 15(45) x 10-31 kg. This is the “CODATA recommended value”. It was published in March 2007, and is referred to as the 2006 CODATA recommended value.

Some background: CODATA stands for Committee on Data for Science and Technology. Per NIST (the US National Institute for Standards and Technology), “CODATA was established in 1966 as an interdisciplinary committee of the International Council of Science (ICSU), formerly the International Council of Scientific Unions. It seeks to improve the compilation, critical evaluation, storage, and retrieval of data of importance to science and technology. The CODATA Task Group on Fundamental Constants was established in 1969. Its purpose is to periodically provide the international scientific and technological communities with an internationally accepted set of values of the fundamental physical constants and closely related conversion factors for use worldwide. The first such CODATA set was dated 1973, the second 1986, the third 1998, the fourth 2002, and the fifth (the current set) 2006.

The mass of the electron is one of the fundamental physical constants, so called because they are widespread in theories of physics, and because they are widely used in the application of those theories to other branches of science and to practical uses (such as engineering). Four of the other fundamental physical constants are c (speed of light in a vacuum), e (the charge of the electron), h (Plank’s constant), and α (fine structure constant).

The method used for measuring me is to measure the Rydberg constant (R) and calculate me from it ( me = 2Rh/(cα2 ); the Rydberg constant is, in the words of the paper (by Peter J. Mohr, Barry N. Taylor, David B. Newell) in which the 2006 CODATA recommended values were published “can be accurately determined by comparing measured resonant frequencies of transitions in hydrogen (H) and deuterium (D) to the theoretical expressions for the energy level differences in which it is a multiplicative factor.For more details, refer to the paper itself.

Given that it is a fundamental physical constant, no surprise that Universe Today has some articles on it! For example Are the Laws of Nature the Same Everywhere in the Universe, and Fermilab putting the Squeeze on Higgs Boson.

Here are two Astronomy Cast episodes in which the electron mass figures prominently Electromagnetism, and Energy Levels and Spectra.

Wikipedia – Electron Rest Mass
Wikipedia – Rydberg constant


Particle Collider

Particles made up of three quarks are called baryons; the two best known baryons are the proton (made up of two up quarks and one down) and the neutron (two down quarks and one up). Together with the mesons – particles comprised of a quark and an antiquark – baryons form the hadrons (you’ve heard of hadrons, they’re part of the name of the world’s most powerful particle collider, the Large Hadron Collider, the LHC).

Because they’re made up of quarks, baryons ‘feel’ the strong force (or strong nuclear force as it is also called), which is mediated by gluons. The other kind of particle which makes up ordinary matter is leptons, which are not – as far as we know – made up of anything (and as they do not contain quarks, they do not participate in the strong interaction … which is another way of saying they do not experience the strong force); the electron is one kind of lepton. Baryons and leptons are fermions, so obey the Pauli exclusion principle (which, among other things, says that there can be no more than one fermion in a particular quantum state at any time … and ultimately why you do not fall through your chair).

In the kinds of environments we are familiar with in everyday life, the only stable baryon is the proton; in the environment of the nuclei of most atoms, the neutron is also stable (and in the extreme environment of a neutron star too); there are, however, hundreds of different kinds of unstable baryons.

One big, open question in cosmology is how baryons were formed – baryogenesis – and why are there essentially no anti-baryons in the universe. For every baryon, there is a corresponding anti-baryon … there is, for example, the anti-proton, the anti-baryon counterpart to the proton, made up of two up anti-quarks and one down anti-quark. So if there were equal numbers of baryons and anti-baryons to start with, how come there are almost none of the latter today?

Astronomers often use the term ‘baryonic matter’, to refer to ordinary matter; it’s a bit of a misnomer, because it includes electrons (which are leptons) … and it generally excludes neutrinos (and anti-neutrinos), which are also leptons! Perhaps a better term might be matter which interacts via electromagnetism (i.e. feels the electromagnetic force), but that’s a bit of a mouthful. Non-baryonic matter is what (cold) dark matter (CDM) is composed of; CDM does not interact electromagnetically.

The Particle Data Group maintains summary tables of the properties of all known baryons. A relatively new area of research in astrophysics (and cosmology) is baryon acoustic oscillations (BAO); read more about it at this Los Alamos National Laboratory website …

… and in the Universe Today article New Search for Dark Energy Goes Back in Time. Other Universe Today stories featuring baryons explicitly include Is Dark Matter Made Up of Sterile Neutrinos?, and Astronomers on Supernova High Alert.


Parallel Universe

To some extent, ‘parallel universe’ is self-referential … there are parallel meanings of the very term! The two most often found in science-based websites (like Universe Today) are multi-verse, or multiverse (the universe we can see is but one of many universes), and the many-worlds interpretation of quantum physics (most often associated with Hugh Everett).

Cosmologist Max Tegmark (currently at MIT) has a neat classification scheme for pigeon-holing most parallel universe ideas that have at least some relationship to physics (as we know it today).

The most straight-forward kind of parallel universe(s) is one(s) just like the one we can see, but beyond the (cosmic) horizon … space is flat, and infinite, and the laws of physics (as we know them today) are the same, everywhere.

Similar, but different in some key ways, are parallel universes which developed out of inflation bubbles; these have the same (or very similar) physics to what applies in the universe we can see, except that the initial values (e.g. fine-structure constant) and perhaps number of dimensions may differ. The Inflationary Multiverse ideas of Standford University’s Andrei Linde are perhaps the best known example of this type. Parallel universes at this level tie in naturally to the (strong) anthropic principle.

Tegmark’s third class (he calls them Levels; this is Level 3) is the many-worlds of quantum physics. I’m sure you, dear reader, are familiar with poor old Schrödinger’s cat, whose half-alive and half-dead status is … troubling. In the many-worlds interpretation, the universe splits into two equal – and parallel – parts; in one, the radioactive material decays, and the cat dies; in the other, it does not, and the cat lives.

Level 4 contains truly weird parallel universes, ones which differ from the others by having fundamentally different laws of physics.

Operating somewhat in parallel are two other parallel universe concepts, cyclic universes (the parallelism is in time), and brane cosmology (a fallout from M-theory, in which the universe we can see is confined to just one brane, but interacts with other universes via gravity, which is not restricted to ‘our’ brane).

As you might expect, much, if not most, of this has been attacked for not being science (for example, how could you ever falsify any of these ideas?), but at least for some parallel universe ideas, observational tests may be possible. Perhaps the best known such test is the WMAP cold spot … one claim is that this is the imprint on ‘our’ universe of a parallel universe, via quantum entanglement (the most recent analyses, however, suggest that the cold spot is not qualitatively different from others, which have more prosaic explanations What! No Parallel Universe? Cosmic Cold Spot Just Data Artifact is a Universe Today story on just this).

Other Universe Today stories on parallel universes include If We Live in a Multiverse, How Many Are There?, Warp Drives Probably Impossible After All, and Book Review: Parallel Worlds.

Astronomy Cast has several episodes which include mention of parallel universes, but the best two are Multiple Big Bangs, and Entanglement.

Sources: MIT, Stanford University

Parabolic Mirror

Sometimes, in astronomy, the name of a thing describes it well; a parabolic mirror is, indeed, a mirror which has the shape of a parabola (an example of a name that does not describe itself well? How about Mare Nectaris, “Sea of Nectar”!). Actually, it’s a circular paraboloid, the 3D shape you get by rotating a parabola (which is 2D) around its axis.

The main part of the standard astronomical reflecting telescope – the primary mirror – is a parabolic mirror. So too is the dish of most radio telescopes, from the Lovell telescope at Jodrell Bank, to the telescopes in the Very Large Array; note that the dish in the Arecibo Observatory is not a parabolic mirror (it’s a spherical one). Focusing x-ray telescopes, such as Chandra and XMM-Newton, also use nested parabolic mirrors … followed by nested hyperbolic mirrors.

Why a parabolic shape? Because mirrors of this shape reflect the light (UV, IR, microwaves, radio) from distant objects onto a point, the focus of the parabola. This was known in ancient Greece, but the first telescope to incorporate a parabolic mirror wasn’t made until 1673 (by Robert Hooke, based on a design by James Gregory; the reflecting telescope Newton built used a spherical mirror). Parabolic mirrors do not suffer from spherical aberration (spherical mirrors cannot focus all incoming, on-axis, light onto a point), nor chromatic aberration (single lens refracting telescopes focus light of different colors at different points), so are the best kind of primary mirror for a simple telescope (however, off-axis sources will suffer from coma).

The Metropolitan State College of Denver has a cool animation of how a parabolic mirror focuses a plane wave train onto a point (the focus).

Universe Today has many articles on the use of parabolic mirrors in telescopes; for example Kid’s Telescope, Cassegrain Telescope, Where Did the Modern Telescope Come From?, Nano-Engineered Liquid Mirror Telescopes, A Pristine View of the Universe … from the Moon, Largest Mirror in Space Under Development, and 8.4 Metre Mirror Installed on Huge Binoculars.

Telescopes, the Next Level is an excellent Astronomy Cast episode, containing material on parabolic mirrors.

Physicist Vitaly Ginzburg Dies at age 93

Vitaly Ginzburg, a Russian physicist and Nobel laureate, died yesterday of cardiac arrest. He was 93 years old. Ginzburg shared the 2003 Nobel Prize in physics for his work on superconductors, but contributed to many other fields of study, including quantum theory, astrophysics, radio-astronomy and diffusion of cosmic radiation in the Earth’s atmosphere. In addition, he is known for his contributions to the development of the Russian hydrogen bomb in the 1950s, for which he received the Stalin Prize.

Ginzburg was born in 1916, before the Bolshevik Revolution, to a Jewish family in Moscow. He lived through the hardships of his childhood to enter Moscow State University in 1933, where he took up the study of physics, he wrote in his autobiography for the 2003 Nobel Prize.

Ginzburg went on to work on the hydrogen bomb during the 1950s, for which he credits his escape from Stalinist purges and anti-Semitism of the period. He became a member of the Soviet Academy of Sciences in 1953. Ginzburg later bcame editor of a leading scientific magazine on theoretical physics, Uspekhi Fizicheskikh Nauk and the head of the P.N. Lebedev Physical Institute, Moscow, Russia.

Ginzburg shared the 2003 Nobel Prize in physics with Alexei A. Abrikosov and Anthony J. Leggett for their work in the field of superconductivity, the ability of materials to conduct electricity with little or no resistance. Ginzburg also authored a book on the subject, titled On Superconductivity and Superfluidity.

His position on his role of the development of the H-bomb for Stalinist Russia is best left in his own words. Ginzburg said just last week in an interview with Physics World :

We thought at the time that we were working to prevent a monopoly on the atomic bomb – Hitler’s monopoly if he got the bomb before Stalin. The thought of what would happen if Stalin had a monopoly on atomic weapons somehow never entered my head. Scary thought. Stalin would seek to subjugate the entire world. I admit this may betray stupidity, but this stupidity was, back then, a common way of thinking in the Soviet Union.

Ginzburg will be buried Wednesday in the Novodevichye Cemetery in Moscow. To read more about Ginzburg and his long life and incredible list of achievements, see this video interview on the Nobel Prize site, and read his autobiography.

Source: AP, Nobel Prize site, Physics World

Angular Motion

You watch something (some distance from you) move … its direction changes … that’s angular motion. In other words, as measured from a fixed point (or axis), the angular motion of an object is the change in direction of the line (of sight) to the object; the angle swept by the line. Notice that if the distance to the object changes but the direction doesn’t, then there is no angular motion (though there is radial motion).

Standing on the surface of the Earth (and not moving, relative to the hills, valleys, etc), you see the Sun rise, move across the sky, and set. Ditto the Moon … and the stars, and the planets, and satellites like the ISS, and … “moving across the sky” simply means the direction of the Sun (the line from you to the Sun) changes, so that motion is angular motion.

Because it involves changes in angle, angular motion is measured in terms of degrees per second (or hour) … or radians per minute, or arcseconds per year, or … i.e. an angle per a unit of time.

Well, that’s one particular kind of angular motion, angular velocity (strictly we need to add a direction, to make it a velocity; in which way is the angle changing, due East perhaps?). There’s also angular acceleration, which is just like linear acceleration except that what the “per second per second” (or, perhaps, “per year per year”) refers to is an angle, not a length (or distance).

As the Earth turns on its axis once a day, and as a circle has 2π radians, the angular motion of the stars and the Sun is 2π rads/day, right? Well, close, but no cigar … the Earth also revolves around the Sun, so from one day to the next it has moved approximately 1/365-th of a complete circle, and as the Earth’s rotation is in the same direction as its orbit, the angular motion of the stars is a little bit less than 2π rads/day (it’s actually 2π radians per sidereal day!).

Many kinds of angular motion, in astronomy, have special names; for example, the angular motion of stars with respect to distant quasars (actually the fixed celestial coordinate system) is proper motion; the tiny ellipses (relatively) nearby stars seem to complete every year is parallax; and there’s precession, nutation, … and even the anomalous advance of the perihelion (of Mercury)! This last one is actually one component of a precession, but it played an important role in the history of physics (the first test the then new theory of general relativity passed); by the way, it’s only about 43″ (” = arcseconds) per century.

Wellesley College’s Phyllis Fleming has a 100-level concise intro to angular motion.

Some of the many Universe Today stories which involve angular motion are Globular Clusters Sort their Stars, and Does a Boomerang Work in Space?