• RSS
  • Facebook
  • Twitter
Abhijeet
Comments


The Maya calendar is a system of distinct calendars and almanacs used by the Maya civilization of pre-Columbian Mesoamerica, and by some modern Maya communities in highland Guatemala.

These calendars can be synchronized and interlocked in many ways, their combinations giving rise to further, more extensive cycles. The essentials of the Maya calendric system are based upon a system which had been in common use throughout the region, dating back to at least the 6th century BCE. It shares many aspects with calendars employed by other earlier Mesoamerican civilizations, such as the Zapotec and Olmec, and contemporary or later ones such as the Mixtec and Aztec calendars. Although the Mesoamerican calendar did not originate with the Maya, their subsequent extensions and refinements of it were the most sophisticated. Along with those of the Aztecs, the Maya calendars are the best-documented and most completely understood.

By the Maya mythological tradition, as documented in Colonial Yucatec accounts and reconstructed from Late Classic and Postclassic inscriptions, the deity Itzamna is frequently credited with bringing the knowledge of the calendar system to the ancestral Maya, along with writing in general and other foundational aspects of Maya culture.


General Overview

The most important of these calendars is one with a period of 260 days. This 260-day calendar was prevalent across all Mesoamerican societies, and is of great antiquity (almost certainly the oldest of the calendars). It is still used in some regions of Oaxaca, and by the Maya communities of the Guatemalan highlands. The Maya version is commonly known to scholars as the Tzolkin, or Tzolk'in in the revised orthography of the Academia de las Lenguas Mayas de Guatemala. The Tzolk'in is combined with another 365-day calendar (known as the Haab, or Haab' ), to form a synchronized cycle lasting for 52 Haabs, called the Calendar Round. Smaller cycles of 13 days (the trecena) and 20 days (the veintena) were important components of the Tzolk'in and Haab' cycles, respectively.

A different form of calendar was used to track longer periods of time, and for the inscription of calendar dates (i.e., identifying when one event occurred in relation to others). This form, known as the Long Count, is based upon the number of elapsed days since a mythological starting-point. According to the correlation between the Long Count and Western calendars accepted by the great majority of Maya researchers (known as the GMT correlation), this starting-point is equivalent to 11 August 3114 BCE in the proleptic Gregorian calendar or 6 September in the Julian calendar (−3113 astronomical). The Goodman-Martinez-Thompson correlation was chosen by Thompson in 1935 based on earlier correlations by Joseph Goodman in 1905 (11 August), Juan Martínez Hernández in 1926 (12 August), and John Eric Sydney Thompson in 1927 (13 August). By its linear nature, the Long Count was capable of being extended to refer to any date far into the future (or past). This calendar involved the use of a positional notation system, in which each position signified an increasing multiple of the number of days. The Maya numeral system was essentially vigesimal (i.e., base-20), and each unit of a given position represented 20 times the unit of the position which preceded it. An important exception was made for the second place value, which instead represented 18 × 20, or 360 days, more closely approximating the solar year than would 20 × 20 = 400 days. It should be noted however that the cycles of the Long Count are independent of the solar year.

Many Maya Long Count inscriptions are supplemented by what is known as the Lunar Series, another calendar form which provides information on the lunar phase and position of the Moon in a half-yearly cycle of lunations.

A 584-day Venus cycle was also maintained, which tracked the appearance and conjunctions of Venus as the morning and evening stars. Many events in this cycle were seen as being inauspicious and baleful, and occasionally warfare was timed to coincide with stages in this cycle.

Other, less-prevalent or poorly-understood cycles, combinations and calendar progressions were also tracked. An 819-day count is attested in a few inscriptions; repeating sets of 9- and 13-day intervals associated with different groups of deities, animals and other significant concepts are also known.

Maya concepts of time

With the development of the place-notational Long Count calendar (believed to have been inherited from other Mesoamerican cultures), the Maya had an elegant system with which events could be recorded in a linear relationship to one another, and also with respect to the calendar ("linear time") itself. In theory, this system could readily be extended to delineate any length of time desired, by simply adding to the number of higher-order place markers used (and thereby generating an ever-increasing sequence of day-multiples, each day in the sequence uniquely identified by its Long Count number). In practice, most Maya Long Count inscriptions confine themselves to noting only the first 5 coefficients in this system (a b'ak'tun-count), since this was more than adequate to express any historical or current date (with an equivalent span of approximately 5125 solar years). Even so, example inscriptions exist which noted or implied lengthier sequences, indicating that the Maya well understood a linear (past-present-future) conception of time.

However, and in common with other Mesoamerican societies, the repetition of the various calendric cycles, the natural cycles of observable phenomena, and the recurrence and renewal of death-rebirth imagery in their mythological traditions were important and pervasive influences upon Maya societies. This conceptual view, in which the "cyclical nature" of time is highlighted, was a pre-eminent one, and many rituals were concerned with the completion and re-occurrences of various cycles. As the particular calendaric configurations were once again repeated, so too were the "supernatural" influences with which they were associated. Thus it was held that particular calendar configurations had a specific "character" to them, which would influence events on days exhibiting that configuration. Divinations could then be made from the auguries associated with a certain configuration, since events taking place on some future date would be subject to the same influences as its corresponding previous cycle dates. Events and ceremonies would be timed to coincide with auspicious dates, and avoid inauspicious ones.

The completion of significant calendar cycles ("period endings"), such as a k'atun-cycle, were often marked by the erection and dedication of specific monuments such as twin-pyramid complexes such those in Tikal and Yaxha, but (mostly in stela inscriptions) commemorating the completion, accompanied by dedicatory ceremonies.

A cyclical interpretation is also noted in Maya creation accounts, in which the present world and the humans in it were preceded by other worlds (one to five others, depending on the tradition) which were fashioned in various forms by the gods, but subsequently destroyed. The present world also had a tenuous existence, requiring the supplication and offerings of periodic sacrifice to maintain the balance of continuing existence. Similar themes are found in the creation accounts of other Mesoamerican societies.


Tzolk'in

Main article: Tzolk'in

The Tzolk'in calendar combines twenty day names with the thirteen numbers of

Some Mayanists employ the name Tzolk'in (in modern Maya orthography; also and formerly commonly written tzolkin) for the Maya Sacred Round or 260-day calendar. Tzolk'in is a neologism coined in Yukatek Maya, to mean "count of days" (Coe 1992). The actual names of this calendar as used by Precolumbian Maya peoples are still debated by scholars. The Aztec calendar equivalent was called Tonalpohualli, in the Nahuatl language.

the trecena cycle to produce 260 unique days. It is used to determine the time of religious and ceremonial events and for divination. Each successive day is numbered from 1 up to 13 and then starting again at 1. Separately from this, each day is given a name in sequence from a list of 20 day names:

Tzolk'in calendar: named days and associated glyphs
Seq.
No. 1
Day
Name 2
Glyph
example 3
16th C.
Yucatec 4
reconstructed
Classic Maya 5
Seq.
No. 1
Day
Name 2
Glyph
example 3
16th C.
Yucatec 4
reconstructed
Classic Maya 5
01 Imix' Imix Imix (?) / Ha' (?) 11 Chuwen Chuen (unknown)
02 Ik' Ik Ik' 12 Eb' Eb (unknown)
03 Ak'b'al Akbal Ak'b'al (?) 13 B'en Ben (unknown)
04 K'an Kan K'an (?) 14 Ix Ix Hix (?)
05 Chikchan Chicchan (unknown) 15 Men Men (unknown)
06 Kimi Cimi Cham (?) 16 K'ib' Cib (unknown)
07 Manik' Manik Manich' (?) 17 Kab'an Caban Chab' (?)
08 Lamat Lamat Ek' (?) 18 Etz'nab' Etznab (unknown)
09 Muluk Muluc (unknown) 19 Kawak Cauac (unknown)
10 Ok Oc (unknown) 20 Ajaw Ahau Ajaw
NOTES:
  1. The sequence number of the named day in the Tzolk'in calendar
  2. Day name, in the standardised and revised orthography of the Guatemalan Academia de Lenguas Mayas[2]
  3. An example glyph (logogram) for the named day. Note that for most of these several different forms are recorded; the ones shown here are typical of carved monumental inscriptions (these are "cartouche" versions)
  4. Day name, as recorded from 16th century Yukatek Maya accounts, principally Diego de Landa; this orthography has (until recently) been widely used
  5. In most cases, the actual day name as spoken in the time of the Classic Period (ca. 200–900) when most inscriptions were made is not known. The versions given here (in Classic Maya, the main language of the inscriptions) are reconstructed based on phonological evidence, if available; a '?' symbol indicates the reconstruction is tentative.

Some systems started the count with 1 Imix', followed by 2 Ik', 3 Ak'b'al, etc. up to 13 B'en. The trecena day numbers then start again at 1 while the named-day sequence continues onwards, so the next days in the sequence are 1 Ix, 2 Men, 3 K'ib', 4 Kab'an, 5 Etz'nab', 6 Kawak, and 7 Ajaw. With all twenty named days used, these now began to repeat the cycle while the number sequence continues, so the next day after 7 Ajaw is 8 Imix'. The repetition of these interlocking 13- and 20-day cycles therefore takes 260 days to complete (that is, for every possible combination of number/named day to occur once).

Divination

Each day of the Tzolk'in has a Patron Spirit who influences events. Ah K'in, the Maya shaman-priest, whose title means "Day Keeper", read the Tzolk'in to determine the answers to yes/no questions as well as more complex questions involving health, wealth and family. The Sacred Calendar is also used to set the most auspicious dates for household, lineage, and community rituals.

When a child is born, the day keeper interprets the Tzolk'in cycle to identify the baby’s character (similarly done today with a natal chart). For example, a child born on the day of Ak'b'al is thought to be feminine, wealthy, and verbally skillful. The birthday of Ak'b'al (along with several other days) is also thought to give the child the ability to receive messages with the supernatural world through somatic twitches of "blood lightning", so he or she might become a Shaman-priest or a Marriage Spokesman.

There are several forms of Maya Calendar divination employing the sacred coral seeds which each Calendar diviner carries in a small bag with crystals and 'other small things' (Tozzer 1941).

The Precolumbian Maya practiced a form of Bibliomancy, in which they would cast the seeds upon a calendar to determine the good and bad days for the year.

Precolumbian Maya employed and Modern Maya Ah K'in employ Sortilage, in which piles of four or five beans are counted from the current calendar day of the Sacred Round to arrive at the result.

Modern Maya Ah K'in also employ Cartomancy, in which the fifty two cards of the poker deck represent the fifty two Year Bearers of the Maya Calendar Round.

Maya shamans also perform a wide variety of divinatory arts which do not specifically depend upon a mastery of the sacred calendar, including crystal, mirror, and water gazing; and spirit possession, among others.

Origin of the Tzolk'in

The exact origin of the Tzolk'in is not known, but there are several theories. One theory is that the calendar came from mathematical operations based on the numbers thirteen and twenty, which were important numbers to the Maya. The numbers multiplied together equal 260. Another theory is that the 260-day period came from the length of human pregnancy. This is close to the average number of days between the first missed menstrual period and birth, unlike Naegele's rule which is 40 weeks (280 days) between the last menstrual period and birth. It is postulated that midwives originally developed the calendar to predict babies' expected birth dates.

A third theory comes from understanding of astronomy, geography and paleontology. The mesoamerican calendar probably originated with the Olmecs, and a settlement existed at Izapa, in southeast Chiapas Mexico, before 1200 BCE. There, at a latitude of about 15° N, the Sun passes through zenith twice a year, and there are 260 days between zenithal passages, and gnomons (used generally for observing the path of the Sun and in particular zenithal passages), were found at this and other sites. The sacred almanac may well have been set in motion on August 13, 1359 BCE, in Izapa. Vincent H. Malmström, a geographer who suggested this location and date, outlines his reasons:

(1) Astronomically, it lay at the only latitude in North America where a 260-day interval (the length of the "strange" sacred almanac used throughout the region in pre-Columbian times) can be measured between vertical sun positions -- an interval which happens to begin on the 13th of August -- the day the peoples of the Mesoamerica believed that the present world was created; (2) Historically, it was the only site at this latitude which was old enough to have been the cradle of the sacred almanac, which at that time (1973) was thought to date to the 4th or 5th centuries B.C.; and (3) Geographically, it was the only site along the required parallel of latitude that lay in a tropical lowland ecological niche where such creatures as alligators, monkeys, and iguanas were native -- all of which were used as day-names in the sacred almanac.

Malmström also offers strong arguments against both of the former explanations.

A fourth theory is that the calendar is based on the crops. From planting to harvest is approximately 260 days.

Haab'

Haab' Months
Name Meaning
Pop mat
Wo black conjunction
Sip red conjunction
Sotz' bat
Sek ?
Xul dog
Yaxk'in new sun
Mol water
Ch'en black storm
Yax green storm
Sac white storm
Keh red storm
Mak enclosed
K'ank'in yellow sun
Muwan owl
Pax planting time
K'ayab' turtle
Kumk'u granary
Wayeb' five unlucky days
Jones 1984
Main article: Haab'

The Haab' was the Maya solar calendar made up of eighteen months of twenty days each plus a period of five days ("nameless days") at the end of the year known as Wayeb' (or Uayeb in 16th C. orthography). Bricker (1982) estimates that the Haab' was first used around 550 BCE with the starting point of the winter solstice.

The Haab' month names are known today by their corresponding names in colonial-era Yukatek Maya, as transcribed by 16th century sources (in particular, Diego de Landa and books such as the Chilam Balam of Chumayel). Phonemic analyses of Haab' glyph names in pre-Columbian Maya inscriptions have demonstrated that the names for these twenty-day periods varied considerably from region to region and from period to period, reflecting differences in the base language(s) and usage in the Classic and Postclassic eras predating their recording by Spanish sources.

Each day in the Haab' calendar was identified by a day number in the month followed by the name of the month. Day numbers began with a glyph translated as the "seating of" a named month, which is usually regarded as day 0 of that month, although a minority treat it as day 20 of the month preceding the named month. In the latter case, the seating of Pop is day 5 of Wayeb'. For the majority, the first day of the year was 0 Pop (the seating of Pop). This was followed by 1 Pop, 2 Pop as far as 19 Pop then 0 Wo, 1 Wo and so on.

As a calendar for keeping track of the seasons, the Haab' was crude and inaccurate, since it treated the year as having 365 days, and ignored the extra quarter day (approximately) in the actual tropical year. This meant that the seasons moved with respect to the calendar year by a quarter day each year, so that the calendar months named after particular seasons no longer corresponded to these seasons after a few centuries. The Haab' is equivalent to the wandering 365-day year of the ancient Egyptians. Some argue that the Maya knew about and compensated for the quarter day error, even though their calendar did not include anything comparable to a leap year, a method first implemented by the Romans.

Wayeb'

The five nameless days at the end of the calendar called Wayeb' were thought to be a dangerous time. Foster (2002) writes "During Wayeb, portals between the mortal realm and the Underworld dissolved. No boundaries prevented the ill-intending deities from causing disasters." To ward off these evil spirits, the Maya had customs and rituals they practiced during Wayeb'. For example, people avoided leaving their houses or washing or combing their hair.

Calendar Round

Neither the Tzolk'in nor the Haab' system numbered the years. The combination of a Tzolk'in date and a Haab' date was enough to identify a date to most people's satisfaction, as such a combination did not occur again for another 52 years, above general life expectancy.

Because the two calendars were based on 260 days and 365 days respectively, the whole cycle would repeat itself every 52 Haab' years exactly. This period was known as a Calendar Round. The end of the Calendar Round was a period of unrest and bad luck among the Maya, as they waited in expectation to see if the gods would grant them another cycle of 52 years.

Long Count

Detail showing three columns of glyphs from 2nd century CE La Mojarra Stela 1.  The left column gives a Long Count date of 8.5.16.9.9, or 156 CE. The two right columns are glyphs from the Epi-Olmec script.

Detail showing three columns of glyphs from 2nd century CE La Mojarra Stela 1. The left column gives a Long Count date of 8.5.16.9.9, or 156 CE. The two right columns are glyphs from the Epi-Olmec script.

Since Calendar Round dates can only distinguish in 18,980 days, equivalent to around 52 solar years, the cycle repeats roughly once each lifetime, and thus, a more refined method of dating was needed if history was to be recorded accurately. To measure dates, therefore, over periods longer than 52 years, Mesoamericans devised the Long Count calendar.

The Maya name for a day was k'in. Twenty of these k'ins are known as a winal or uinal. Eighteen winals make one tun. Twenty tuns are known as a k'atun. Twenty k'atuns make a b'ak'tun.

The Long Count calendar identifies a date by counting the number of days from August 11, 3114 BCE. But instead of using a base-10 (decimal) scheme like Western numbering, the Long Count days were tallied in a modified base-20 scheme. Thus 0.0.0.1.5 is equal to 25, and 0.0.0.2.0 is equal to 40. As the winal unit resets after only counting to 18, the Long Count consistently uses base-20 only if the tun is considered the primary unit of measurement, not the k'in; with the k'in and winal units being the number of days in the tun. The Long Count 0.0.1.0.0 represents 360 days, rather than the 400 in a purely base-20 (vigesimal) count.

Table of Long Count units
Days Long Count period Long Count period Approx solar years
1 = 1 K'in

20 = 20 K'in = 1 Winal 1/18th
360 = 18 Winal = 1 Tun 1
7,200 = 20 Tun = 1 K'atun 20
144,000 = 20 K'atun = 1 B'ak'tun 395

There are also four rarely-used higher-order cycles: piktun, kalabtun, k'inchiltun, and alautun.

Since the Long Count dates are unambiguous, the Long Count was particularly well suited to use on monuments. The monumental inscriptions would not only include the 5 digits of the Long Count, but would also include the two tzolk'in characters followed by the two haab' characters.

The Mesoamerican Long Count calendar forms the basis for a New Age belief, first forecast by José Argüelles, that a cataclysm will take place on or about 21 December 2012, a forecast that mainstream Mayanist scholars consider a misinterpretation.

Venus Cycle

Main article: Transits of Venus

Another important calendar for the Maya was the Venus cycle. The Maya were skilled astronomers, and could calculate the Venus cycle with extreme accuracy. There are six pages in the Dresden Codex (one of the Maya codices) devoted to the accurate calculation of the location of Venus. The Maya were able to achieve such accuracy by careful observation over many years. There are various theories as to why Venus cycle was especially important for the Maya, including the belief that it was associated with war and used it to divine good times (called electional astrology) for coronations and war. Maya rulers planned for wars to begin when Venus rose. The Maya also possibly tracked other planets’ movements, including those of Mars, Mercury, and Jupiter.



Source : Wikipedia

[...]

Categories:
Abhijeet
Comments

There is little purpose to listing theories simply for the sake of it. A real search for an answer must follow the path upon which the evidence leads one. For the Triangle, this path takes us on an unnerving odyssey through fascinating concepts, from deep below the ocean to far out in space, from high in the atmosphere to the very zero-point of existence, from the complex makeup of this huge planet to the smallest particles of existence. The paradoxes do not cease—the outback nature of the Triangle leads us to the prehistoric past and the rise of the civilization of mankind. And to answer what happened to very tangible ships and planes, we must even consider the opposite: the science behind “clairvoyance” and if the predictions about the Bermuda Triangle long before it became a concept have any merits. No matter which theory one decides to tackle, the path weaves many of them together in a cunning way. In the end, one can truly wonder, are these theories really the cause, or are they only the symptoms of something that lies deeper down?

These are some of the theories taken from
Gian Quasar’s new book'Into The Bermuda Triangle'

Magnetic North vs.True North


Magnetic Variation: possibly the most bogus theory of them all. When the Coast Guard put their name on this theory they neutered a lot of their credibility. No one had heard about this theory until the Coast Guard put out a little hastily written chit about 30 years ago, stating their position on the subject of the Bermuda Triangle.
It reads, in part:

Countless theories attempting to explain the many disappearances have been offered throughout the history of the area. The most practical seem to be environmental and those citing human error. The majority of disappearances can be attributed to the area's unique environmental features. First, the "Devil's Triangle" is one of the two places on earth that a magnetic compass does point towards true north. Normally it points toward magnetic north. The difference between the two is known as compass variation. The amount of variation changes by as much as 20 degrees as one circumnavigates the earth. If this compass variation or error is not compensated for, a navigator could find himself far off course and in deep trouble.
This is a very misleading statement. For one, the area of no compass variation is a very narrow corridor, tantamount to a fraction of the overall Triangle. It also overlooks the fact that one cannot even plot a course without having a navigational chart, and all navigational charts have the amount of variation written on them for every degree of longitude. Before a navigator could even chart a course he would have to know the amount of variation. This also overlooks the large number of disappearances of pilots and skippers who were old hands in this part of the world, being charter pilots and the like. They were very familiar with local variation.
It also presupposes that the navigator was stupid enough not to compensate. Yet compensation in navigating is second nature to any navigator.

But lets expand on compass variation, since many do not understand it. Compass variation does not mean that the compass needle points somewhere else. The compass always points to Magnetic North. The problem with this is Magnetic North is not at the North Pole, the absolute geographic northern spot on this planet; it is 1,500 miles away. As far as the compass is concerned, the absolute north of this planet is at Prince of Wales Island in the Northwest Territories of Canada.
The magnetic field of the earth can be likened to a bar magnet running through the earth from north to south. Both ends of the bar would be the north and south magnetic poles. The bar itself would be the axis or, as it is called in geophysics, the Agonic Line.
This would not pose any problem to the navigator were it not for the fact that Magnetic North is located 1,500 miles away from the North Pole. Therefore, geographic north on the earth, the area we mentally consider absolute north, is not where the compass points. Following the N on your compass is not going to
The area of the Agonic Line marked in red, as it was when the Coast Guard drew up their statement 30 years ago. Along this line there is no need to adjust one’s heading because Magnetic North and True North coincide. Already at Bimini island there is a 2 degree westerly variation. That means if a pilot wanted to head True West here, he would not steer 270o by his compass but 272o. It seems infinitesimal, but over time 2 degrees can lead to dozens of miles off course. In the short distances between the coast and the Bahama Islands, it doesn’t amount to much here.
lead you to the North Pole; it will lead you to Prince of Wales Island. See illustration.











The red dots indicate True North, that is, the absolute geographic north of this planet (North Pole); and Magnetic North, 1,500 miles in a southerly direction from it. The central axis (Agonic Line) of the magnetic field extends through the planet to the South Magnetic Pole at Antarctica. When off Florida, both the North Pole and the Magnetic Pole are in line. The Compass truly points to the North Pole here but only briefly. It is merely incidental because Magnetic North is directly due south of the North Pole here.
To compensate for this, the navigator must know the number of degrees of difference between Magnetic North and True North in his longitude. This changes according to one’s longitude around the earth. For instance, at the Azores Islands there is a 20 degree difference between True North and Magnetic North. Off the east coast of Florida, there is none. The compass is still pointing to Magnetic North. It just so happens that True North is directly north of here. See illustration.
Right: as the Compass sees the four cardinal points. See what happens if you blindly follow your magnetic compass. Everything is tilted because it believes North is 1,500 miles south of the North Pole. West is slightly southwest; East is slightly northeast; North is slightly northwest; South: southeast. Wherever a navigator is, he must adjust his heading to maintain a true course. . . except at the Agonic Line.
Except for this narrow corridor, there is always some form of compensation the navigator must go through.* For example, at the Azores, if a navigator wanted to go straight north, he could not follow the N on his compass. If he did, he would end up in Canada and not in Greenland. So he heads 020 degrees and now he is heading True north. That is what Compass Variation means: the amount of difference between the North Pole and the Magnetic North Pole at a given location. The result is a simple navigational adjustment to stay on course.
Right, what we imagine the Compass to reflect: the true North, East, West, and South of this geographic sphere. Far left, the Compass’ concept of where North, West, East, and South are located, if viewed from the Azores. True North is actually 020o.
This amount of variation will decrease the further one travels West until one reaches the Agonic Line. Soon after, the amount of variation will increase again, with the compass pointing Easterly of True North.
There is little reason to suppose that this has contributed to any loss. Failure to compensate the amount of variation correctly can cause a pilot to get lost anywhere in the world, whether there is no degree variation to compensate for or 15 degrees. One degree off can, over time, result in many miles in error, making a pilot miss his intended destination.
But as I said this can happen anywhere in the world. The Triangle does not stand out as unique because there is no variation in degrees to calculate for a brief period in a very narrow corridor of it.
I try and list theories objectively. But in this case a dead horse is a dead horse. There is no merit to this theory at all.
A further factor contributing to this deduction is that the Agonic Line moves as the magnetic pole shifts, due to many factors in the rotation of the earth. Over time the Agonic Line can be miles from where it was. Actually every 2 months or so a flight is manned and sent to find the magnetic pole. The upshot is that the Agonic Line is not in the Triangle anymore. It is located in the Gulf of Mexico beyond Key West— to those who demand adherence to a strict shape to the “Triangle,” completely outside of it.
The artwork and maps above show the Agonic Line where it was when the Coast Guard made up their little chit about 30 years ago. Magnetic Variation was not a satisfactory explanation before. It is even more passé now. Disappearances still occur in the same places as before, even though the Line is on the other side of Florida now.


*Yes I know it happens on the exact other side of the world; but that is not relevant here so we can dispense with it in this article.
[...]

Categories:
Abhijeet
Comments


Raman scattering or the Raman effect (pronounced: [rə.mən] —) is the inelastic scattering of a photon.Discovered By "Dr. C.V. Raman".

When light is scattered from an atom or molecule, most photons are elastically scattered (Rayleigh scattering). The scattered photons have the same energy (frequency) and wavelength as the incident photons. However, a small fraction of the scattered light (approximately 1 in 10 million photons) is scattered by an excitation, with the scattered photons having a frequency different from, and usually lower than, the frequency of the incident photons. In a gas, Raman scattering can occur with a change in vibrational, rotational or electronic energy of a molecule (see energy level). Chemists are concerned primarily with the vibrational Raman effect.

In 1922, Indian physicist Chandrasekhara Venkata Raman published his work on the "Molecular Diffraction of Light," the first of a series of investigations with his collaborators which ultimately led to his discovery (on 28 February 1928) of the radiation effect which bears his name. The Raman effect was first reported by C. V. Raman and K. S. Krishnan, and independently by Grigory Landsberg and Leonid Mandelstam, in 1928. Raman received the Nobel Prize in 1930 for his work on the scattering of light. In 1998 the Raman Effect was designated an ACS National Historical Chemical Landmark in recognition of its significance as a tool for analyzing the composition of liquids, gases, and solids.

Raman scattering: Stokes and anti-Stokes

The different possibilities of visual light scattering: Rayleigh scattering (no Raman effect), Stokes scattering (molecule absorbs energy) and anti-Stokes scattering (molecule loses energy)

The different possibilities of visual light scattering: Rayleigh scattering (no Raman effect), Stokes scattering (molecule absorbs energy) and anti-Stokes scattering (molecule loses energy)

The interaction of light with matter in a linear regime allows the absorption or simultaneous emission of light precisely matching the difference in energy levels of the interacting electrons.

The Raman effect corresponds, in perturbation theory, to the absorption and subsequent emission of a photon via an intermediate electron state, having a virtual energy level (see also: Feynman diagram). There are three possibilities:

  • no energy exchange between the incident photons and the molecules (and hence no Raman effect)
  • energy exchanges occur between the incident photons and the molecules. The energy differences are equal to the differences of the vibrational and rotational energy-levels of the molecule. In crystals only specific photons are allowed (solutions of the wave equations which do not cancel themselves) by the periodic structure, so Raman scattering can only appear at certain frequencies. In amorphous materials like glasses, more photons are allowed and thereby the discrete spectral lines become broad.
  • molecule absorbs energy: Stokes scattering. The resulting photon of lower energy generates a Stokes line on the red side of the incident spectrum.
  • molecule loses energy: anti-Stokes scattering. Incident photons are shifted to the blue side of the spectrum, thus generating an anti-Stokes line.

These differences in energy are measured by subtracting the energy of the mono-energetic laser light from the energy of the scattered photons. The absolute value, however, doesn't depend on the process (Stokes or anti-Stokes scattering), because only the energy of the different vibrational levels is of importance. Therefore, the Raman spectrum is symmetric relative to the Rayleigh band. In addition, the intensities of the Raman bands are only dependent on the number of molecules occupying the different vibrational states, when the process began. If the sample is in thermal equilibrium, the relative numbers of molecules in states of different energy will be given by the Boltzmann distribution:

\frac{\ N_1}{N_0} = \frac{\ g_1}{g_0} e^{-\frac{\Delta E_v}{kT}}
with:

N0: amount of atoms in the lower vibrational state
N1: amount of atoms in the higher vibrational state
g0: degeneracy of the lower vibrational state (number of orbitals of the same energy)
g1: degeneracy of the higher vibrational state (number of orbitals of the same energy)
ΔEv: energy difference between these two vibrational states
k: Boltzmann's constant
T: temperature in kelvin

Thus lower energy states will have more molecules in them than will higher (excited) energy states. Therefore, the Stokes spectrum will be more intense than the anti-Stokes spectrum.

Distinction with fluorescence

The Raman effect differs from the process of fluorescence. For the latter, the incident light is completely absorbed and the system is transferred to an excited state from which it can go to various lower states only after a certain resonance lifetime. The result of both processes is essentially the same: A photon with the frequency different from that of the incident photon is produced and the molecule is brought to a higher or lower energy level. But the major difference is that the Raman effect can take place for any frequency of the incident light. In contrast to the fluorescence effect, the Raman effect is therefore not a resonant effect.

Selection rules

The distortion of a molecule in an electric field, and therefore the vibrational Raman cross section, is determined by its polarizability.

A Raman transition from one state to another, and therefore a Raman shift, can be activated optically only in the presence of non-zero polarizability derivative with respect to the normal coordinate (that is, the vibration or rotation):

0" src="http://upload.wikimedia.org/math/b/b/9/bb9afc2a8e70ade1230dd91fd1507026.png">

Raman-active vibrations/rotations can be identified by using almost any textbook that treats quantum mechanics or group theory for chemistry. Then, Raman-active modes can be found for molecules or crystals that show symmetry by using the appropriate character table for that symmetry group.

Stimulated Raman scattering and Raman amplification

Raman amplification can be obtained by using Stimulated Raman Scattering (SRS), which actually is a combination between a Raman process with stimulated emission. It is interesting for application in telecommunication fibers to amplify inside the standard material with low noise for the amplification process. However, the process requires significant power and thus imposes more stringent limits on the material. The amplification band can be up to 100 nm broad, depending on the availability of allowed photon states.

Raman spectrum generation

For high intensity CW (continuous wave) lasers, SRS can be used to produce broad bandwidth spectra. This process can also be seen as a special case of four wave mixing, where the frequencies of the two incident photons are equal and the emitted spectra are found in two bands separated from the incident light by the phonon energies. The initial Raman spectrum is built up with spontaneous emission and is amplified later on. At high pumping levels in long fibers, higher order Raman spectra can be generated by using the Raman spectrum as a new starting point, thereby building a chain of new spectra with decreasing amplitude. The disadvantage of intrinsic noise due to the initial spontaneous process can be overcome by seeding a spectrum at the beginning, or even using a feedback loop like in a resonator to stabilize the process. Since this technology easily fits into the fast evolving fiber laser field and there is demand for transversal coherent high intensity light sources (i.e. broadband telecommunication, imaging applications), Raman amplification and spectrum generation might be widely used in the near future.

Applications

Raman spectroscopy employs the Raman effect for materials analysis. The frequency of light scattered from a molecule may be changed based on the structural characteristics of the molecular bonds. A monochromatic light source (laser) is required for illumination, and a spectrogram of the scattered light then shows the deviations caused by state changes in the molecule.

Raman spectroscopy is also used in combustion diagnostics. Being a completely non-intrusive technique, it permits the detection of the major species and temperature distribution inside combustors and in flames without any perturbation of the (mainly fluid dynamic and reactive) processes examined.

Stimulated Raman transitions are also widely used for manipulating a trapped ion's energy levels, and thus basis qubit states.


source : WikiPedia

[...]

Categories: