srinivasan

Facts About Stars

2009-06-11T06:33:00.000-07:00

Facts About Stars
1)There are more stars than all of the grains of sand on earth.
2)You can see stars from the bottom of a well even in day light.
3)Stars with really strong gravity cause themselves to become smaller and smaller and eventually turn into black holes.
4)Stars come in different colors; hot stars give off blue light, and the cooler stars give off red light.
5)In honor of the original thirteen states, the U.S. $1 bill has the following on the back: 13 steps on the pyramid. The motto above the pyramid has 13 letters (annuity coatis). E pluribus Unum, written on the ribbon in the eagle's beak, has 13 letters. 13 stars appear over the eagle's head. 13 stripes are on the shield. 13 war arrows are in the eagle's left talon.
6)All of the stars comprising the Milky Way galaxy revolve around the center of the galaxy once every 200 million years or so.
7)Until the mid sixteenth century, Comets were believed to be not astronomical phenomena, but burning vapors that had arisen from distant swamps and were propelled across the sky by fire and light.
8)Our galaxy has approximately 250 billion stars and it is estimated by astronomers that there are 100 billion other galaxies in the universe.
9)A galaxy of typical size, about 100 billion suns produces less energy than a single Quasar.
10)A Comet's tail always points away from the sun.
11)A Pulsar is a small star made up of neutrons so densely packed together that if 12)one the size of a silver dollar landed on earth, it would weigh approximately 100 million tons.
13)The Star Alpha Herculis is twenty five times larger than the circumference described by the earth's revolution around the sun. This means that twenty five diameters of our solar orbit would have to be placed end to end to equal the diameter of this Star.

Facts About Sun

2009-06-11T06:19:00.000-07:00

Facts About Sun
1)Our sun has an expected lifetime of about 11 billion years.
2) Our sun and the surrounding planets orbit around the center of the Milky Way galaxy once every 250 million years.
3)Only 55% of all Americans know that the sun is a star.
4) On its trip around the sun, the earth travels over a million and a half miles per day.
5) No solar eclipse can last longer than 7 minutes 58 seconds because of the speed at which the sun moves.
6)Lightning bolts can sometimes be hotter than the sun. (about 50 000º F)
7)It takes only 8 minutes for sunlight to travel from the sun to the earth, which also means, if you see the sun go out, it actually went out 8 minutes ago.
8)In Spit Bergen, Norway at one time of the year the sun shines continuously for three and a half months.
9)In Newport, Rhode Island it is illegal to smoke from a pipe after sunset.
10)In Devon, Connecticut, it is unlawful to walk backwards after sunset.
11)If the sun stopped shining suddenly, it would take eight minutes for people on earth to be aware of the fact.
12)For 186 days you can not see the sun in the North Pole.
13)Every eleven years the magnetic poles of the sun switch. This cycle is called"Solarmax".
14)Because of the speed at which the sun moves, it is impossible for a solar eclipse to last more than 7 minutes and 58 seconds.
15)Aztecs believed that the sun died every night and needed human blood to give it strength to rise the next day. So they sacrificed 15,000 men a year to appease their sun god, Huitzilopochtli. Most of the victims were prisoners taken in wars, which were sometimes started solely to round up sacrificial victims.
16)At the distance at which our sun is located from the center of the Milky Way galaxy, Earth and the rest of our solar system are moving at a speed of about 170 miles per second around the center.
17)At its center, the sun has a density of over a hundred times that of water, and a temperature of 10-20 million degrees Celsius.
18)All the coal, oil, gas, and wood on Earth would only keep the Sun burning for a few days.
19)An area of the Sun's surface the size of a postage stamp shines with the power of 1,500,000 candles.
20)Your fingernails can turn yellow from wearing nail polish and from the sun.
21)If the entire solar system were the size of a quarter, the sun would be visible only under a microscope, and the nearest star would be 300 feet away.
22)The Sun provides our planet with 126,000,000,000,000 horsepower of energy every day.
23)If the earth were the size of a quarter, the sun would be as large as a 9 foot ball and would be located a football field distance from the earth.
24)More than 1 million earths would fit inside the sun.
99% of our solar systems mass is concentrated in the sun.
25)The sun is 330,330 times larger than the earth!

Optical Density Determination

2009-06-11T04:44:00.001-07:00

Optical Density Determination

1/24/2005

Question -   Why does light pass through some pure substances, but not others (eg. diamond vs graphite ... both are Carbon)? On a molecular level, what exactly determines optical density (it is not the same as mass density)? Why does light slow down in optically dense media? ----------------- Theresa- There are at least two kinds of "optical density", maybe more like three: 1) absorbance (it is clear, but it is to some degree dark,  like smoky glass.   Light is diminishing as it travels through.) 2) refractive index    (it is clear, but light goes slower through   it.   So it changes direction at surfaces. for large index, some of the light bounces off each   surface.  Metallic reflection is an extreme case of this.) 3) scattering density  ( it is clear but messy with refractive index   surfaces, so it becomes cluttered or frosty or milky or white)  Any given substance has some amount of each of these three "densities".  Only refractive index has any connection with mass density. That being: heavy substances are made of high-atomic-number elements,   which have many electrons, which cause higher refractive index. High concentrations of bound electrons (bound in one place, but   elastically movable by a short distance) are the "water" that slows down   the flight of light.  Viscously-movable electrons absorb light (1) at all wavelengths.  This is  graphite black, and it enforces the opacity of metals. You can see through metals if they are less than 0.1 micrometer  thick.  One-way mirrors are this. But if thicker, the part of light which is not reflected at the front   surface will be completely absorbed.  Metallic opacity.  Light is also absorbed by bound electrons using the energy to climb out of  their trapped state, or at least climb to a higher trapped state. But it has to be the right amount of energy, so it is a more  color-selective absorption.   It creates most of the non-neutral colors of  objects.  Chemical purity helps a clear substance be clearer, but it cannot help an  inherently absorbing substance like graphite become clear. Perfect single crystals of graphite are a lighter silvery color than  typical poly-crystalline graphite. Certain impurities in graphite actually donate more mobile electrons,  which sometimes make it lighter still.  Chemically pure glass is silicon dioxide. Light can go for tens to  thousands of meters in this, depending on color, if it is pure. Give it unnecessary surfaces by grinding it up, and you have sand: more  white than clear. Chemically pure aluminum oxide can be white if it is many small  crystallites, or clear if it is one large crystal (colorless sapphire). Pure water is not a crystal, it is random inside, but it can be clear in a  uniform mass, or milky if dispersed as fog. Ice can be either clear or cloudy or fractured with flaws.  Diamond vs Graphite: The carbon atom  can make 4 chemical bonds (shared-electron-links) to  its neighbors. In diamond, each atom links to 4 different neighbors, and every electron  is bound (confined) within its own link. So there are no mobile electrons, and diamond is a dielectric not a  conductor, and  it is clear, not absorbing. In graphite, each atom links to only 3 neighbors, making a flat sheet, and  each has one link left over. All these leftover links are shared in common by the whole sheet. The electrons of this pool of links are mobile, so graphite conducts  electricity and absorbs light. There are not many elements which have a choice of whether or not to be  conductive.  Those are the classical optical properties. Iridescence and dichroism are a different story.  Jim Swenson ===================================================== If a substance has an unoccupied electronic state whose energy difference from initial state is the same as the energy of the incident radiation (light), and given certain other restriction, then the substance will absorb the incident radiation. The electronic structure of the substance determines whether or not such unoccupied but accessible electronic states exist; however, the details of determining such states is rather involved. The bonding in diamond and graphite is a good example. Both are carbon, but in diamond the carbon atoms are bonded to one another by single bonds and these electrons do not respond to visible light. The electronic structure of graphite on the other hand is stacks of sheets of carbon in which the electrons are highly delocalized in such a way that essentially all visible light is absorbed. As a result graphite is black.      The measure of the ratio of the transmitted power, Ptrans. (energy / sec) to the incident power, Pincid.:  Ptrans. / Pincid. = Tr is called the transmittance (or in the older literature the transmission). This ratio has a range: 0 < tr =" 10^-1" tr =" 10^-5" n =" 1">

The Reflection And The Refraction Of The LIght

2009-06-11T04:38:00.000-07:00

The reflection and refraction of light

Rays and wave fronts

Light is a very complex phenomenon, but in many situations its behavior can be understood with a simple model based on rays and wave fronts. A ray is a thin beam of light that travels in a straight line. A wave front is the line (not necessarily straight) or surface connecting all the light that left a source at the same time. For a source like the Sun, rays radiate out in all directions; the wave fronts are spheres centered on the Sun. If the source is a long way away, the wave fronts can be treated as parallel lines.

Rays and wave fronts can generally be used to represent light when the light is interacting with objects that are much larger than the wavelength of light, which is about 500 nm. In particular, we'll use rays and wave fronts to analyze how light interacts with mirrors and lenses.

The law of reflection

Objects can be seen by the light they emit, or, more often, by the light they reflect. Reflected light obeys the law of reflection, that the angle of reflection equals the angle of incidence.

For objects such as mirrors, with surfaces so smooth that any hills or valleys on the surface are smaller than the wavelength of light, the law of reflection applies on a large scale. All the light travelling in one direction and reflecting from the mirror is reflected in one direction; reflection from such objects is known as specular reflection.

Most objects exhibit diffuse reflection, with light being reflected in all directions. All objects obey the law of reflection on a microscopic level, but if the irregularities on the surface of an object are larger than the wavelength of light, which is usually the case, the light reflects off in all directions.

Plane mirrors

A plane mirror is simply a mirror with a flat surface; all of us use plane mirrors every day, so we've got plenty of experience with them. Images produced by plane mirrors have a number of properties, including:

the image produced is upright
the image is the same size as the object (i.e., the magnification is m = 1)
the image is the same distance from the mirror as the object appears to be (i.e., the image distance = the object distance)
the image is a virtual image, as opposed to a real image, because the light rays do not actually pass through the image. This also implies that an image could not be focused on a screen placed at the location where the image is.

A little geometry

Dealing with light in terms of rays is known as geometrical optics, for good reason: there is a lot of geometry involved. It's relatively straight-forward geometry, all based on similar triangles, but we should review that for a plane mirror.

Consider an object placed a certain distance in front of a mirror, as shown in the diagram. To figure out where the image of this object is located, a ray diagram can be used. In a ray diagram, rays of light are drawn from the object to the mirror, along with the rays that reflect off the mirror. The image will be found where the reflected rays intersect. Note that the reflected rays obey the law of reflection. What you notice is that the reflected rays diverge from the mirror; they must be extended back to find the place where they intersect, and that's where the image is.

Analyzing this a little further, it's easy to see that the height of the image is the same as the height of the object. Using the similar triangles ABC and EDC, it can also be seen that the distance from the object to the mirror is the same as the distance from the image to the mirror.

Spherical mirrors

Light reflecting off a flat mirror is one thing, but what happens when light reflects off a curved surface? We'll take a look at what happens when light reflects from a spherical mirror, because it turns out that, using reasonable approximations, this analysis is fairly straight-forward. The image you see is located either where the reflected light converges, or where the reflected light appears to diverge from.

A spherical mirror is simply a piece cut out of a reflective sphere. It has a center of curvature, C, which corresponds to the center of the sphere it was cut from; a radius of curvature, R, which corresponds to the radius of the sphere; and a focal point (the point where parallel light rays are focused to) which is located half the distance from the mirror to the center of curvature. The focal length, f, is therefore:

focal length of a spherical mirror : f = R / 2

This is actually an approximation. Parabolic mirrors are really the only mirrors that focus parallel rays to a single focal point, but as long as the rays don't get too far from the principal axis then the equation above applies for spherical mirrors. The diagram shows the principal axis, focal point (F), and center of curvature for both a concave and convex spherical mirror.

Spherical mirrors are either concave (converging) mirrors or convex (diverging) mirrors, depending on which side of the spherical surface is reflective. If the inside surface is reflective, the mirror is concave; if the outside is reflective, it's a convex mirror. Concave mirrors can form either real or virtual images, depending on where the object is relative to the focal point. A convex mirror can only form virtual images. A real image is an image that the light rays from the object actually pass through; a virtual image is formed because the light rays can be extended back to meet at the image position, but they don't actually go through the image position.

Ray diagrams

To determine where the image is, it is very helpful to draw a ray diagram. The image will be located at the place where the rays intersect. You could just draw random rays from the object to the mirror and follow the reflected rays, but there are three rays in particular that are very easy to draw.

Only two rays are necessary to locate the image on a ray diagram, but it's useful to add the third as a check. The first is the parallel ray; it is drawn from the tip of the object parallel to the principal axis. It then reflects off the mirror and either passes through the focal point, or can be extended back to pass through the focal point.

The second ray is the chief ray. This is drawn from the tip of the object to the mirror through the center of curvature. This ray will hit the mirror at a 90° angle, reflecting back the way it came. The chief and parallel rays meet at the tip of the image.

The third ray, the focal ray, is a mirror image of the parallel ray. The focal ray is drawn from the tip of the object through (or towards) the focal point, reflecting off the mirror parallel to the principal axis. All three rays should meet at the same point.

A ray diagram for a concave mirror is shown above. This shows a few different things. For this object, located beyond the center of curvature from the mirror, the image lies between the focal point (F) and the center of curvature. The image is inverted compared to the object, and it is also a real image, because the light rays actually pass through the point where the image is located.

With a concave mirror, any object beyond C will always have an image that is real, inverted compared to the object, and between F and C. You can always trade the object and image places (that just reverses all the arrows on the ray diagram), so any object placed between F and C will have an image that is real, inverted, and beyond C. What happens when the object is between F and the mirror? You should draw the ray diagram to convince yourself that the image will be behind the mirror, making it a virtual image, and it will be upright compared to the object.

A ray diagram for a convex mirror

What happens with a convex mirror? In this case the ray diagram looks like this:

As the ray diagram shows, the image for a convex mirror is virtual, and upright compared to the object. A convex mirror is the kind of mirror used for security in stores, and is also the kind of mirror used on the passenger side of many cars ("Objects in mirror are closer than they appear."). A convex mirror will reflect a set of parallel rays in all directions; conversely, it will also take light from all directions and reflect it in one direction, which is exactly how it's used in stores and cars.

The mirror equation

Drawing a ray diagram is a great way to get a rough idea of how big the image of an object is, and where the image is located. We can also calculate these things precisely, using something known as the mirror equation. The textbook does a nice job of deriving this equation in section 25.6, using the geometry of similar triangles.

Magnification

In most cases the height of the image differs from the height of the object, meaning that the mirror has done some magnifying (or reducing). The magnification, m, is defined as the ratio of the image height to the object height, which is closely related to the ratio of the image distance to the object distance:

A magnification of 1 (plus or minus) means that the image is the same size as the object. If m has a magnitude greater than 1 the image is larger than the object, and an m with a magnitude less than 1 means the image is smaller than the object. If the magnification is positive, the image is upright compared to the object; if m is negative, the image is inverted compared to the object.

Sign conventions

What does a positive or negative image height or image distance mean? To figure out what the signs mean, take the side of the mirror where the object is to be the positive side. Any distances measured on that side are positive. Distances measured on the other side are negative.

f, the focal length, is positive for a concave mirror, and negative for a convex mirror.

When the image distance is positive, the image is on the same side of the mirror as the object, and it is real and inverted. When the image distance is negative, the image is behind the mirror, so the image is virtual and upright.

A negative m means that the image is inverted. Positive means an upright image.

Steps for analyzing mirror problems

There are basically three steps to follow to analyze any mirror problem, which generally means determining where the image of an object is located, and determining what kind of image it is (real or virtual, upright or inverted).

Step 1 - Draw a ray diagram. The more careful you are in constructing this, the better idea you'll have of where the image is.
Step 2 - Apply the mirror equation to determine the image distance. (Or to find the object distance, or the focal length, depending on what is given.)
Step 3 - Make sure steps 1 and 2 are consistent with each other.

An example

A Star Wars action figure, 8.0 cm tall, is placed 23.0 cm in front of a concave mirror with a focal length of 10.0 cm. Where is the image? How tall is the image? What are the characteristics of the image?

The first step is to draw the ray diagram, which should tell you that the image is real, inverted, smaller than the object, and between the focal point and the center of curvature. The location of the image can be found from the mirror equation:

which can be rearranged to:

The image distance is positive, meaning that it is on the same side of the mirror as the object. This agrees with the ray diagram. Note that we don't need to worry about converting distances to meters; just make sure everything has the same units, and whatever unit goes into the equation is what comes out.

Calculating the magnification gives:

Solving for the image height gives:

The negative sign for the magnification, and the image height, tells us that the image is inverted compared to the object.

To summarize, the image is real, inverted, 6.2 cm high, and 17.7 cm in front of the mirror.

Example 2 - a convex mirror

The same Star Wars action figure, 8.0 cm tall, is placed 6.0 cm in front of a convex mirror with a focal length of -12.0 cm. Where is the image in this case, and what are the image characteristics?

Again, the first step is to draw a ray diagram. This should tell you that the image is located behind the mirror; that it is an upright, virtual image; that it is a little smaller than the object; and that the image is between the mirror and the focal point.

The second step is to confirm all those observations. The mirror equation, rearranged as in the first example, gives:

Solving for the magnification gives:

This gives an image height of 0.667 x 8 = 5.3 cm.

All of these results are consistent with the conclusions drawn from the ray diagram. The image is 5.3 cm high, virtual, upright compared to the object, and 4.0 cm behind the mirror.

Refraction

When we talk about the speed of light, we're usually talking about the speed of light in a vacuum, which is 3.00 x 10⁸ m/s. When light travels through something else, such as glass, diamond, or plastic, it travels at a different speed. The speed of light in a given material is related to a quantity called the index of refraction, n, which is defined as the ratio of the speed of light in vacuum to the speed of light in the medium:

index of refraction : n = c / v

When light travels from one medium to another, the speed changes, as does the wavelength. The index of refraction can also be stated in terms of wavelength:

Although the speed changes and wavelength changes, the frequency of the light will be constant. The frequency, wavelength, and speed are related by:

The change in speed that occurs when light passes from one medium to another is responsible for the bending of light, or refraction, that takes place at an interface. If light is travelling from medium 1 into medium 2, and angles are measured from the normal to the interface, the angle of transmission of the light into the second medium is related to the angle of incidence by Snell's law :

Bose-Einstein Condensate

2009-06-10T07:48:00.000-07:00

A Bose–Einstein condensate (BEC) is a state of matter of a dilute gas of weakly interacting bosons confined in an external potential and cooled to temperatures very near to absolute zero (0 K, −273.15 °C, or −459.67 °F). Under such conditions, a large fraction of the bosons collapse into the lowest quantum state of the external potential, and all wave functions overlap each other, at which point quantum effects become apparent on a macroscopic scale.

This state of matter was first predicted by Satyendra Nath Bose and Albert Einstein in 1924–25. Bose first sent a paper to Einstein on thequantum statistics of light quanta (now called photons). Einstein was impressed, translated the paper himself from English to German and submitted it for Bose to the Zeitschrift für Physik which published it. Einstein then extended Bose's ideas to material particles (or matter) in two other papers.^[1]

Seventy years later, the first gaseous condensate was produced by Eric Cornell and Carl Wieman in 1995 at the University of Colorado at Boulder NIST-JILA lab, using a gas of rubidium atoms cooled to 170 nanokelvin (nK) ^[2] (1.7×10⁻⁷ K). Cornell, Wieman, and Wolfgang Ketterleat MIT were awarded the 2001 Nobel Prize in Physics in Stockholm, Sweden for their achievements.^[3]

Introduction

"Condensates" are extremely low-temperature fluids which contain properties and exhibit behaviors that are currently not completely understood, such as spontaneously flowing out of their containers. The effect is the consequence of quantum mechanics, which states that since continuous spectral regions can typically be neglected, systems can almost always acquire energy only in discrete steps. If a system is at such a low temperature that it is in the lowest energy state, it is no longer possible for it to reduce its energy, not even by friction. Without friction, the fluid will easily overcome gravity because of adhesion between the fluid and the container wall, and it will take up the most favorable position (all around the container).^[4]

Bose-Einstein condensation is an exotic quantum phenomenon that was observed in dilute atomic gases for the first time in 1995, and is now the subject of intense theoretical and experimental study.^[5]

[edit]Theory

The slowing of atoms by use of cooling apparatuses produces a singular quantum state known as a Bose condensate or Bose–Einstein condensate. This phenomenon was predicted in 1925 by generalizing Satyendra Nath Bose's work on the statistical mechanics of (massless)photons to (massive) atoms. (The Einstein manuscript, believed to be lost, was found in a library at Leiden University in 2005.^[6]) The result of the efforts of Bose and Einstein is the concept of a Bose gas, governed by Bose–Einstein statistics, which describes the statistical distribution of identical particles with integer spin, now known as bosons. Bosonic particles, which include the photon as well as atoms such as helium-4, are allowed to share quantum states with each other. Einstein demonstrated that cooling bosonic atoms to a very low temperature would cause them to fall (or "condense") into the lowest accessible quantum state, resulting in a new form of matter.

This transition occurs below a critical temperature, which for a uniform three-dimensional gas consisting of non-interacting particles with no apparent internal degrees of freedom is given by:

where:

	is	the critical temperature,
	is	the particle density,
	is	the mass per boson,
	is	the reduced Planck constant,
	is	the Boltzmann constant, and
	is	the Riemann zeta function; (sequence A078434 in OEIS)

[edit]Einstein's Argument

Consider a collection of N noninteracting particles which can each be in one of two quantum states, and . If the two states are equal in energy, each different configuration is equally likely.

If we can tell which particle is which, there are $2 N$ different configurations, since each particle can be in or independently. In almost all the configurations, about half the particles are in and the other half in . The balance is a statistical effect, the number of configurations is largest when the particles are divided equally.

If the particles are indistinguishable, however, there are only N+1 different configurations. If there are K particles in state , there are N-K particles in state . Whether any particular particle is in state or in state cannot be determined, so each value of K determines a unique quantum state for the whole system. If all these states are equally likely, there is no statistical spreading out; it is just as likely for all the particles to sit in as for the particles to be split half and half.

Suppose now that the energy of state is slightly greater than the energy of state by an amount E. At temperature T, a particle will have a lesser probability to be in state by exp(-E/T). In the distinguishable case, the particle distribution will be biased slightly towards state and the distribution will be slightly different from half and half. But in the indistinguishable case, since there is no statistical pressure toward equal numbers, the most likely outcome is that most of the particles will collapse into state .

In the distinguishable case, for large N, the fraction in state can be computed. It is the same as coin flipping with a coin which has probability p = exp(-E/T) to land tails. The fraction of heads is 1/(1+p), which is a smooth function of p, of the energy.

In the indistinguishable case, each value of K is a single state, which has its own separate Boltzmann probability. So the probability distribution is exponential:

For large N, the normalization constant C is (1-p). The expected total number of particles which are not in the lowest energy state, in the limit that , is equal to 0} C n p^n=p/(1-p) " src="http://upload.wikimedia.org/math/d/d/e/dde8fb5801d339a6b6bd9b6ffac40e57.png" style="border-top-style: none; border-right-style: none; border-bottom-style: none; border-left-style: none; border-width: initial; border-color: initial; margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; vertical-align: middle; ">. It doesn't grow when N is large, it just approaches a constant. This will be a negligible fraction of the total number of particles. So a collection of enough bose particles in thermal equilibrium will mostly be in the ground state, with only a few in any excited state, no matter how small the energy difference.

Consider now a gas of particles, which can be in different momentum states labelled . If the number of particles is less than the number of thermally accessible states, for high temperatures and low densities, the particles will all be in different states. In this limit the gas is classical. As the density increases or the temperature decreases, the number of accessible states per particle becomes smaller, and at some point more particles will be forced into a single state than the maximum allowed for that state by statistical weighting. From this point on, any extra particle added will go into the ground state.

To calculate the transition temperature at any density, integrate over all momentum states the expression for maximum number of excited particles p/(1-p):

When the integral is evaluated with the factors of k_B and ℏ restored by dimensional analysis, it gives the critical temperature formula of the preceding section. Therefore, this integral defines the critical temperature and particle number corresponding to the conditions of zero chemical potential (μ = 0 in the Bose–Einstein statistics distribution).

[edit]The Gross-Pitaevskii equation

Main article: Gross-Pitaevskii equation

The state of the BEC can be described by the wavefunction of the condensate . For a system of this nature, is interpreted as the particle density, so the total number of atoms is

Provided essentially all atoms are in the condensate (that is, have condensed to the ground state), and treating the bosons using mean field theory, the energy (E) associated with the state is:

Minimising this energy with respect to infinitesimal variations in , and holding the number of atoms constant, yields the Gross-Pitaevski equation (GPE) (also a non-linear Schrödinger equation):

where:

	is the mass of the bosons,
	is the external potential,
	is representative of the inter-particle interactions.

The GPE provides a good description of the behavior of BEC's and is thus often applied for theoretical analysis.

[edit]Discovery

In 1938, Pyotr Kapitsa, John Allen and Don Misener discovered that helium-4 became a new kind of fluid, now known as a superfluid, at temperatures less than 2.17 K (the lambda point). Superfluid helium has many unusual properties, including zero viscosity (the ability to flow without dissipating energy) and the existence of quantized vortices. It was quickly realized that the superfluidity was due to Bose–Einstein condensation of quasiparticles – the elementary excitations in the low-energy spectrum of liquid helium. In fact, many of the properties of superfluid helium also appear in the gaseous Bose–Einstein condensates created by Cornell, Wieman and Ketterle (see below). Superfluid helium-4 is a liquid rather than a gas, which means that the interactions between the atoms are relatively strong; the original theory of Bose–Einstein condensation must be heavily modified in order to describe it. Bose–Einstein condensation remains, however, fundamental to the superfluid properties of helium-4.

The first "pure" Bose–Einstein condensate was created by Eric Cornell, Carl Wieman, and co-workers at JILA on June 5, 1995. They did this by cooling a dilute vapor consisting of approximately two thousand rubidium-87 atoms to below 170 nK using a combination of laser cooling (a technique that won its inventors Steven Chu, Claude Cohen-Tannoudji, and William D. Phillips the 1997 Nobel Prize in Physics) and magnetic evaporative cooling. About four months later, an independent effort led by Wolfgang Ketterle at MIT created a condensate made of sodium-23. Ketterle's condensate had about a hundred times more atoms, allowing him to obtain several important results such as the observation ofquantum mechanical interference between two different condensates. Cornell, Wieman and Ketterle won the 2001 Nobel Prize in Physics for their achievement.^[7]

The Bose–Einstein condensation also applies to quasiparticles in solids. A magnon in an antiferromagnet carries spin 1 and thus obeys Bose–Einstein statistics. The density of magnons is controlled by an external magnetic field, which plays the role of the magnon chemical potential. This technique provides access to a wide range of boson densities from the limit of a dilute Bose gas to that of a strongly interacting Bose liquid. A magnetic ordering observed at the point of condensation is the analog of superfluidity. In 1999 Bose condensation of magnons was demonstrated in the antiferromagnet TlCuCl₃.^[8] The condensation was observed at temperatures as large as 14 K. Such a high transition temperature (relative to that of atomic gases) is due to the greater density achievable with magnons and the smaller mass (roughly equal to the mass of an electron). In 2006, condensation of magnons in ferromagnets was even shown at room temperature,^[9] where the authors used pumping techniques.

[edit]Velocity-distribution data graph

Velocity-distribution data of a gas of rubidium atoms, confirming the discovery of a new phase of matter, the Bose–Einstein condensate. Left: just before the appearance of a Bose–Einstein condensate. Center: just after the appearance of the condensate. Right: after further evaporation, leaving a sample of nearly pure condensate.

In the image accompanying this article, the velocity-distribution data indicates the formation of a Bose–Einstein condensate out of a gas of rubidium atoms. The false colors indicate the number of atoms at each velocity, with red being the fewest and white being the most. The areas appearing white and light blue are at the lowest velocities. The peak is not infinitely narrow because of theHeisenberg uncertainty principle: since the atoms are trapped in a particular region of space, their velocity distribution necessarily possesses a certain minimum width. This width is given by the curvature of the magnetic trapping potential in the given direction. More tightly confined directions have bigger widths in the ballistic velocity distribution. This anisotropy of the peak on the right is a purely quantum-mechanical effect and does not exist in the thermal distribution on the left. This famous graph served as the cover-design for 1999 textbook Thermal Physics by Ralph Baierlein.^[10]

[edit]Vortices

As in many other systems, vortices can exist in BECs. These can be created, for example, by 'stirring' the condensate with lasers, or rotating the confining trap. The vortex created will be a quantum vortex. These phenomena are allowed for by the non-linear term in the GPE. As the vortices must have quantised angular momentum, the wavefunction will be of the form where $ρ, z$ and $θ$ are as in the cylindrical coordinate system, and is the angular number. To determine $φ(ρ, z)$ , the energy of must be minimised, according to the constraint . This is usually done computationally, however in a uniform medium the analytic form

where:

	is	density far from the vortex,

	is	healing length of the condensate.

demonstrates the correct behavior, and is a good approximation.

A singly-charged vortex () is in the ground state, with its energy $ε v$ given by

where:

the farthest distance from the vortex considered.

(To obtain an energy which is well defined it is necessary to include this boundary $b$ .)

For multiply-charged vortices (1" src="http://upload.wikimedia.org/math/b/f/f/bffb5674d87e89e6825e9ffe591338d9.png" style="border-top-style: none; border-right-style: none; border-bottom-style: none; border-left-style: none; border-width: initial; border-color: initial; margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; vertical-align: middle; ">) the energy is approximated by

which is greater than that of singly-charged vortices, indicating that these multiply-charged vortices are unstable to decay. Research has, however, indicated they are metastable states, so may have relatively long lifetimes.

Closely related to the creation of vortices in BECs is the generation of so-called dark solitons in one-dimensional BECs. These topological objects feature a phase gradient across their nodal plane, which stabilizes their shape even in propagation and interaction. Although solitons carry no charge and are thus prone to decay, relatively long-lived dark solitons have been produced and studied extensively.^[11]

[edit]Unusual characteristics

Further experimentation by the JILA team in 2000 uncovered a hitherto unknown property of Bose–Einstein condensates. Cornell, Wieman, and their coworkers originally used rubidium-87, an isotope whose atoms naturally repel each other, making a more stable condensate. The JILA team instrumentation now had better control over the condensate so experimentation was made on naturally attracting atoms of another rubidium isotope, rubidium-85 (having negative atom-atom scattering length). Through a process called Feshbach resonance involving a sweep of the magnetic field causing spin flip collisions, the JILA researchers lowered the characteristic, discrete energies at which the rubidium atoms bond into molecules, making their Rb-85 atoms repulsive and creating a stable condensate. The reversible flip from attraction to repulsion stems from quantum interference among condensate atoms which behave as waves.

When the scientists raised the magnetic field strength still further, the condensate suddenly reverted back to attraction, imploded and shrank beyond detection, and then exploded, blowing off about two-thirds of its 10,000 or so atoms. About half of the atoms in the condensate seemed to have disappeared from the experiment altogether, not being seen either in the cold remnant or the expanding gas cloud.^[12] Carl Wieman explained that under current atomic theory this characteristic of Bose–Einstein condensate could not be explained because the energy state of an atom near absolute zero should not be enough to cause an implosion; however, subsequent mean field theories have been proposed to explain it.

Because supernova explosions are also preceded by an implosion, the explosion of a collapsing Bose–Einstein condensate was named "bosenova", a pun on the musical style bossa nova.

The atoms that seem to have disappeared almost certainly still exist in some form, just not in a form that could be accounted for in that experiment. Most likely they formed molecules consisting of two bonded rubidium atoms. The energy gained by making this transition imparts a velocity sufficient for them to leave the trap without being detected.

[edit]Current research

Compared to more commonly encountered states of matter, Bose–Einstein condensates are extremely fragile. The slightest interaction with the outside world can be enough to warm them past the condensation threshold, eliminating their interesting properties and forming a normal gas. It is likely to be some time before any practical applications are developed.

Nevertheless, they have proven useful in exploring a wide range of questions in fundamental physics, and the years since the initial discoveries by the JILA and MIT groups have seen an explosion in experimental and theoretical activity. Examples include experiments that have demonstrated interference between condensates due to wave-particle duality,^[13] the study of superfluidity and quantized vortices,^[14] and theslowing of light pulses to very low speeds using electromagnetically induced transparency.^[15] Vortices in Bose-Einstein condensates are also currently the subject of analogue gravity research, studying the possibility of modeling black holes and their related phenomena in such environments in the lab. Experimentalists have also realized "optical lattices", where the interference pattern from overlapping lasers provides a periodic potential for the condensate. These have been used to explore the transition between a superfluid and a Mott insulator,^[16] and may be useful in studying Bose–Einstein condensation in fewer than three dimensions, for example the Tonks-Girardeau gas.

Bose–Einstein condensates composed of a wide range of isotopes have been produced.^[17]

Related experiments in cooling fermions rather than bosons to extremely low temperatures have created degenerate gases, where the atoms do not congregate in a single state due to the Pauli exclusion principle. To exhibit Bose–Einstein condensation, the fermions must "pair up" to form compound particles (e.g. molecules or Cooper pairs) that are bosons. The first molecular Bose–Einstein condensates were created in November 2003 by the groups of Rudolf Grimm at the University of Innsbruck, Deborah S. Jin at the University of Colorado at Boulder andWolfgang Ketterle at MIT. Jin quickly went on to create the first fermionic condensate composed of Cooper pairs.^[18]

In 1999, Danish physicist Lene Vestergaard Hau led a team from Harvard University which succeeded in slowing a beam of light to about 17 metres per second and, in 2001, was able to momentarily stop a beam. She was able to achieve this by using a superfluid. Hau and her associates at Harvard University have since successfully transformed light into matter and back into light using Bose-Einstein condensates: details of the experiment are discussed in an article in the journal Nature, 8 February 2007.^[19]

[edit]Some subtleties

One should not overlook that the effect involves subtleties which are not always mentioned. One may be already "used" to the prejudice that the effect really needs ultralow temperatures of 10^-7 K or below, and is mainly based on the nuclear properties of (typically) alkaline atoms, i.e. properties which fit to working with "traps". However, the situation is more complicated.

Up to 2004, using the above-mentioned "ultralow temperatures", Bose-Einstein condensates had been obtained for a multitude of isotopes involving mainly alkaline and alkaline earth atoms (⁷Li, ²³Na, ⁴¹K, ⁵²Cr, ⁸⁵Rb, ⁸⁷Rb, ¹³³Cs and ¹⁷⁴Yb). Not astonishingly, condensation research was finally successful even with hydrogen, although with the aid of special methods. In contrast, the superfluid state of the bosonic⁴He at temperatures below the temperature of 2.17 K is not a good example of Bose-Einstein condensation, because the interaction between the ⁴He bosons is simply too strong, so that at zero temperature, contrary to Bose-Einstein theory, only 8% rather than 100% of the atoms are in the ground state. Even the fact that the above-mentioned alkaline gases show bosonic, rather than fermionic behaviour, as solid state physicists or chemists would expect, is based on a subtle interplay of electronic and nuclear spins: at ultralow temperatures and corresponding excitation energies, the half-integer (in units of ) total spin of the electronic shell and the also half-integer total spin of the nucleus of the atom are coupled by the (very weak) hyperfine interaction to the integer (!) total spin of the atom. Only the fact that this last-mentioned total spin is integral causes the ultralow-temperature behaviour of the atom to be bosonic, whereas the "chemistry" of the systems at room temperature is determined by the electronic properties, i.e. is essentially fermionic, since at room temperature thermal excitations have typical energies which are much higher than the hyperfine values. (Here one should remember the spin-statistics theorem of Wolfgang Pauli, which states that half-integer spins lead to fermionic behaviour, e.g., the Pauli exclusion principle forbidding that more than two electrons possess the same energy, whereas integer spins lead to bosonic behaviour, e.g., condensation of identical bosonic particles in a common ground state.)

The ultralow temperature requirement of Bose-Einstein condensates of alkali metals does not generalize to all types of Bose-Einstein condensates. In 2006, physicists under S. Demokritov in Münster, Germany,^[20] found Bose-Einstein condensation of magnons (i.e. quantized spinwaves) at room temperature, admittedly by the application of pump processes.

Unified Field Theory

2009-06-10T07:47:00.000-07:00

Unified Field Theory

In physics, a unified field theory is a type of field theory that allows all of the fundamental forcesbetween elementary particles to be written in terms of a single field. There is no accepted unified field theory yet, and this remains an open line of research. The term was coined by Albert Einstein who attempted to unify the general theory of relativity with electromagnetism. A Theory of Everything is closely related to unified field theory, but differs by not requiring the basis of nature to be fields, and also attempts to explain all physical constants of nature.

This article describes unified field theory as it is currently understood in connection with quantum theory. Earlier attempts based on classical physics are described in the article on classical unified field theories.

There may be no a priori reason why the correct description of nature has to be a unified field theory; however, this goal has led to a great deal of progress in modern theoretical physics and continues to motivate research. Unified field theory is only one possible approach to unification of physics.

[edit]Introduction

According to the current understanding of physics, forces between objects (e.g. gravitation) are not transmitted directly between the two objects, but instead go through intermediary entities called fields. All four of the known fundamental forces are mediated by fields, which in theStandard Model of particle physics result from exchange of bosons (integral-spin particles). Specifically the four interactions to be unified are (from strongest to weakest):

Strong nuclear interaction: the interaction responsible for holding quarks together to form neutrons and protons, and holding neutrons and protons together to form nuclei. The exchange particle that mediates this force is the gluon.
Electromagnetic interaction: the familiar interaction that acts on electrically charged particles. The photon is the exchange particle for this force.
Weak nuclear interaction: a repulsive short-range interaction responsible for radioactivity, that acts on electrons, neutrinos and quarks. It is governed by the W and Z bosons.
Gravitational interaction: a long-range attractive interaction that acts on all particles with mass. The postulated exchange particle has been named the graviton.

Modern unified field theory attempts to bring these four force-mediating fields together into a single framework. Quantum theory seems to limit any deterministic theory's descriptive power (in simple terms, no theory can predict events more accurately than allowed by the Planck constant).

[edit]History

The first successful (classical) unified field theory was developed by James Clerk Maxwell. In 1820 Hans Christian Ørsted discovered thatelectric currents exerted forces on magnets, while in 1831, Michael Faraday made the observation that time-varying magnetic fields could induce electric currents. Until then, electricity and magnetism had been thought of as unrelated phenomena. In 1864, Maxwell published his famous paper on a dynamical theory of the electromagnetic field. This was the first example of a theory that was able to encompass previous separate field theories (namely electricity and magnetism) to provide a unifying theory of electromagnetism. Later, in his theory of special relativity Albert Einstein was able to explain the unity of electricity and magnetism as a consequence of the unification of space and time into an entity we now call spacetime.

In 1921 Theodor Kaluza extended General Relativity to five dimensions and in 1926 Oscar Klein proposed that the fourth spatial dimension be curled up (or compactified) into a small, unobserved circle. This was dubbed Kaluza-Klein theory. It was quickly noticed that this extra spatial direction gave rise to an additional force similar to electricity and magnetism. This was pursued as the basis for some of Albert Einstein's later unsuccessful attempts at a unified field theory. Einstein and others pursued various non-quantum approaches to unifying these forces; however as quantum theory became generally accepted as fundamental, most physicists came to view all such theories as doomed to failure.

[edit]Modern progress

In 1963 American physicist Sheldon Glashow proposed that the weak nuclear force and electricity and magnetism could arise from a partially unified electroweak theory. In 1967, Pakistani Abdus Salam and American Steven Weinberg independently revised Glashow's theory by having the masses for the W particle and Z particle arise through spontaneous symmetry breaking with the Higgs mechanism. This unified theory was governed by the exchange of four particles: the photon for electromagnetic interactions, a neutral Z particle and two charged W particles for weak interaction. As a result of the spontaneous symmetry breaking, the weak force becomes short range and the Z and W bosons acquire masses of 80.4 and 91.2 $G e V / c 2$ , respectively. Their theory was first given experimental support by the discovery of weak neutral currents in 1973. In 1983, the Z and W bosons were first produced at CERN by Carlo Rubbia's team. For their insights, Salam, Glashow and Weinberg were awarded the Nobel Prize in Physics in 1979. Carlo Rubbia and Simon van der Meer received the Prize in 1984.

After Gerardus 't Hooft showed the Glashow-Weinberg-Salam electroweak interactions was mathematically consistent, the electroweak theory became a template for further attempts at unifying forces. In 1974, Sheldon Glashow and Howard Georgi proposed unifying the strong and electroweak interactions into a Grand Unified Theory, which would have observable effects for energies much above 100 GeV.

Since then there have been several proposals for Grand Unified Theories, although none is currently universally accepted. A major problem for experimental tests of such theories is the energy scale involved, which is well beyond the reach of current accelerators. Grand Unified Theories make predictions for the relative strengths of the strong, weak, and electromagnetic forces, and in 1991 LEP determined that supersymmetrictheories have the correct ratio of couplings for a Georgi-Glashow Grand Unified Theory. Many Grand Unified Theories predict that the proton candecay, and if this were to be seen, details of the decay products could give hints at more aspects of the Grand Unified Theory. It is at present unknown if the proton can decay, although experiments have determined a lower bound of $1035$ years for its lifetime.

[edit]The current state of unified field theories

Gravity has yet to be successfully included in a theory of everything. Simply trying to combine the graviton with the strong and electroweak interactions runs into fundamental difficulties (the resulting theory is not renormalizable). Theoretical physicists have not yet formulated a widely accepted, consistent theory that combines general relativity and quantum mechanics. The incompatibility of the two theories remains an outstanding problem in the field of physics. Some theoretical physicists currently believe that a quantum theory of general relativity may require frameworks other than field theory itself, such as string theory or loop quantum gravity. One promising string theory is the heterotic string which can tie together gravity and the three other forces into a tight connection. Other candidate string theories do not have this feature of unifying the forces and gravity in a compelling manner. Loop quantum gravity does not appear to link the electroweak and strong forces to gravity, and if so, it would fail as a unified field theory. Ultimately, nature may not be best understood in terms of a unified field theory; this conceptualization may not be correct, although it has led to advances in physics.

[edit]Non-mainstream theories

Albert Einstein famously spent the last two decades of his life searching for a Unified Field Theory. This has led to a great deal of fascination with the subject and has drawn many people from outside the mainstream of the physics community to work on such a theory. Most of this work typically appears in non-peer reviewed sources, such as self-published books or personal websites. The work that appears outside of the standard scientific channels may or may not be considered pseudoscience by definition.

Examples of "non-mainstream" theories are Heim theory and Antony Garrett Lisi's "An Exceptionally Simple Theory of Everything".

Grand Unified Field Theory

2009-06-10T07:46:00.000-07:00

Grand Unification, grand unified theory, or GUT refers to any of several very similar unified field theories or models in physics that predicts that at extremely high energies (above 10¹⁴ GeV), the electromagnetic, weak nuclear, and strong nuclear forces are fused into a single unified field.^[1]

Thus far, physicists have been able to merge electromagnetism and the weak nuclear force into theelectroweak force, and work is being done to merge electroweak and quantum chromodynamics into a QCD-electroweak interaction sometimes called the electrostrong force. Beyond grand unification, there is also speculation that it may be possible to merge gravity with the other three gauge symmetries into a theory of everything

Motivation

There is a general aesthetic among high energy physicists that the more symmetrical a theory is, the more "beautiful" and "elegant" it is. According to this aesthetic, the Standard Model gauge group, which is the direct product of three groups (modulo some finite group), is "ugly". Also, reasoning in analogy with the 19th-century unification of electricity with magnetism into electromagnetism, and especially the success of the electroweak theory, which utilizes the idea of spontaneous symmetry breaking to unify electromagnetism with the weak interaction, people wondered if it might be possible to unify all three groups in a similar manner. Physicists feel that three independent gauge coupling constants and a huge number of Yukawa coupling coefficients require far too many free parameters, and that these coupling constants ought to be explained by a theory with fewer free parameters. A gauge theory where the gauge group is a simple group only has one gauge coupling constant, and since the fermions are now grouped together in larger representations, there are fewer Yukawa coupling coefficients as well. In addition, the chiral fermion fields of the Standard Model unify into three generations of two irreducible representations () in SU(5), and three generations of an irreducible representation (16) in SO(10). This is a significant observation, as a generic combination of chiral fermions which are free of gauge anomalies will not be unified in a representation of some larger Lie group without adding additional matter fields. SO(10) also predicts a right-handed neutrino.

GUT specifically predicts relations among the fermion masses, such as between the electron and the down quark, the muon and the strange quark, and the tau lepton and the bottom quark for SU(5) and SO(10). Some of these mass relations hold approximately, but most don't. SeeGeorgi-Jarlskog mass relation. If we look at the renormalization group running of the three-gauge couplings have been found to nearly, but not quite, meet at the same point if the hypercharge is normalized so that it is consistent with SU(5)/SO(10) GUTs, which are precisely the GUT groups which lead to a simple fermion unification. This is a significant result, as other Lie groups lead to different normalizations. However, if thesupersymmetric extension MSSM is used instead of the Standard Model, the match becomes much more accurate. It is commonly believed that this matching is unlikely to be a coincidence. Also, most model builders simply assume supersymmetry (SUSY) because it solves thehierarchy problem—i.e., it stabilizes the electroweak Higgs mass against radiative corrections. And the Majorana mass of the right-handed neutrino SO(10) theories with its mass set to the gauge unification scale is examined, values for the left-handed neutrino masses (see neutrino oscillation) are produced via the seesaw mechanism. These values are 10–100 times smaller than the GUT scale, but still relatively close.

(For a more elementary introduction to how Lie algebras are related to particle physics, see the article Particle physics and representation theory.)

[edit]Proposed theories

Several such theories have been proposed, but none is currently universally accepted. An even more ambitious theory that includes allfundamental forces, including gravitation, is termed a theory of everything. Some common mainstream GUT models are:

Not quite GUTs:

Note: These models refer to Lie algebras not to Lie groups. The Lie group could be [SU(4)×SU(2)×SU(2)]/Z₂, just to take a random example.

The most promising candidate is SO(10).^{[citation needed]} (Minimal) SO(10) does not contain any exotic fermions (i.e. additional fermions besides the Standard Model fermions and the right-handed neutrino), and it unifies each generation into a single irreducible representation. A number of other GUT models are based upon subgroups of SO(10). They are the minimal left-right model, SU(5), flipped SU(5) and the Pati-Salam model. The GUT group E₆ contains SO(10), but models based upon it are significantly more complicated. The primary reason for studying E₆ models comes from E₈ × E₈ heterotic string theory.

GUT models generically predict the existence of topological defects such as monopoles, cosmic strings, domain walls, and others. But none have been observed. Their absence is known as the monopole problem in cosmology. GUT models also generically predict proton decay, although current experiments still haven't detected proton decay. This experimental limit on the proton's lifetime pretty much rules out minimal SU(5).

Proton Decay. These graphics refer to the X bosons and Higgs bosons.
Dimension 6 proton decay mediated by the $X$ boson in $S U (5)$ GUT	Dimension 6 proton decay mediated by the $X$ boson in flipped $S U (5)$ GUT	Dimension 6 proton decay mediated by the triplet Higgs and the anti-triplet Higgs in $S U (5)$ GUT

Some GUT theories like SU(5) and SO(10) suffer from what is called the doublet-triplet problem. These theories predict that for each electroweak Higgs doublet, there is a corresponding colored Higgs triplet field with a very small mass (many orders of magnitude smaller than the GUT scale here). In theory, unifying quarks with leptons, the Higgs doublet would also be unified with a Higgs triplet. Such triplets have not been observed. They would also cause extremely rapid proton decay (far below current experimental limits) and prevent the gauge coupling strengths from running together in the renormalization group.

Most GUT models require a threefold replication of the matter fields. As such, they do not explain why there are three generations of fermions. Most GUT models also fail to explain the little hierarchy between the fermion masses for different generations.

[edit]Ingredients

A GUT model basically consists of a gauge group which is a compact Lie group, a connection form for that Lie group, a Yang-Mills action for that connection given by an invariant symmetric bilinear form over its Lie algebra (which is specified by a coupling constant for each factor), aHiggs sector consisting of a number of scalar fields taking on values within real/complex representations of the Lie group and chiral Weyl fermions taking on values within a complex rep of the Lie group. The Lie group contains the Standard Model group and the Higgs fields acquireVEVs leading to a spontaneous symmetry breaking to the Standard Model. The Weyl fermions represent matter.

[edit]Current status

As of 2009, there is still no hard evidence that nature is described by a Grand Unified Theory. Moreover, since the Higgs particle has not yet been observed, the smaller electroweak unification is still pending.^[2] The discovery of neutrino oscillations indicates that the Standard Model is incomplete and has led to renewed interest toward certain GUT such as $S O (10)$ . One of the few possible experimental tests of certain GUT isproton decay and also fermion masses. There are a few more special tests for supersymmetric GUT.

The gauge coupling strengths of QCD, the weak interaction and hypercharge seem to meet at a common length scale called the GUT scale and equal approximately to $1016$ GeV, which is slightly suggestive. This interesting numerical observation is called the gauge coupling unification, and it works particularly well if one assumes the existence of superpartners of the Standard Model particles. Still it is possible to achieve the same by postulating, for instance, that ordinary (non supersymmetric) $S O (10)$ models break with an intermediate gauge scale, such as the one of Pati-Salam group.

The coining of the widely-used acronym GUT has been attributed to a paper published in 1978 by Texas A&M University theorist Dimitri Nanopoulos (previously at Harvard University