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mass,in physics, the quantity of matter in a body regardless of its volume or of any forces acting on it. The term should not be confused with weightweight,
measure of the force of gravity on a body (see gravitation). Since the weights of different bodies at the same location are proportional to their masses, weight is often used as a measure of mass.
..... Click the link for more information. , which is the measure of the force of gravity (see gravitationgravitation,
the attractive force existing between any two particles of matter. The Law of Universal Gravitation
Since the gravitational force is experienced by all matter in the universe, from the largest galaxies down to the smallest particles, it is often called
..... Click the link for more information. ) acting on a body. Under ordinary conditions the mass of a body can be considered to be constant; its weight, however, is not constant, since the force of gravity varies from place to place. There are two ways of referring to mass, depending on the law of physics defining it: gravitational mass and inertial mass. The gravitational mass of a body may be determined by comparing the body on a beam balance with a set of standard masses; in this way the gravitational factor is eliminated. The inertial mass of a body is a measure of the body's resistance to acceleration by some external force. One body has twice as much inertial mass as another body if it offers twice as much force in opposition to the same acceleration. All evidence seems to indicate that the gravitational and inertial masses of a body are equal, as demanded by Einstein's equivalence principle of relativityrelativity,
physical theory, introduced by Albert Einstein, that discards the concept of absolute motion and instead treats only relative motion between two systems or frames of reference.
..... Click the link for more information. ; so that at the same location equal (inertial) masses have equal weights. Because the numerical value for the mass of a body is the same anywhere in the world, it is used as a basis of reference for many physical measurements, such as density and heat capacity. According to the special theory of relativity, mass is not strictly constant but increases with the speed according to the formula m=m0/√1−v2/c2, where m0 is the rest mass of the body, v is its speed, and c is the speed of light in vacuum. This increase in mass, however, does not become appreciable until very great speeds are reached. The rest mass of a body is its mass at zero velocity. The special theory of relativity also leads to the Einstein mass-energy relation, E=mc2, where E is the energy, and m and c are the (relativistic) mass and the speed of light, respectively. Because of this equivalence of mass and energyenergy,
in physics, the ability or capacity to do work or to produce change. Forms of energy include heat, light, sound, electricity, and chemical energy. Energy and work are measured in the same units—foot-pounds, joules, ergs, or some other, depending on the system of
..... Click the link for more information. , the law of conservation of energy was extended to include mass as a form of energy.
Mass,religious service of the Roman Catholic Church, which has as its central act the performance of the sacrament of the EucharistEucharist
[Gr.,=thanksgiving], Christian sacrament that repeats the action of Jesus at his last supper with his disciples, when he gave them bread, saying, "This is my body," and wine, saying, "This is my blood." (Mat. 26; Mark 14; Luke 22; 1 Cor. 11.
..... Click the link for more information. . It is based on the ancient Latin liturgy of the city of Rome, now used in most, but not all, Roman Catholic churches. The term Mass [Lat. missa,=dismissed] probably derives from the practice of dismissing the catechumens—those not yet initiated into the mystery of the Eucharist—before the offertory and from the words Ite, missa est [Go, you are dismissed] spoken to the faithful at the end of the Mass. The term is also used among Anglo-Catholics; in the Eastern churches the Mass is generally called the Holy Liturgy or the Offering. For non-Roman liturgies, see liturgyliturgy, Christian
[Gr. leitourgia = public duty or worship] form of public worship, particularly the form of rite or services prescribed by the various Christian churches.
..... Click the link for more information. .
The Role of the Catholic Mass
In the Roman Catholic Church, except for the altogether distinct Ambrosian rite (see Ambrose, SaintAmbrose, Saint
, 340?–397, bishop of Milan, Doctor of the Church, b. Trier, of Christian parents. Educated at Rome, he became (c.372) governor of Liguria and Aemilia—with the capital at Milan.
..... Click the link for more information. ) and for some variant forms among religious orders, especially that of the Dominicans, the service is the same everywhere, under regulation of the Holy See. The language of the liturgy is typically terse. The celebrant, who must be a priest, follows a prescribed missal and wears certain vestments. Mass is said at an altar containing relics; two candles must be burning. A congregation is not essential, but solitary Mass is discouraged. A High (solemn) Mass requires a priest, deacon, and choir. Low Mass, much more common, is the same service said by one priest. Normally at Low Mass a server or acolyte, traditionally called an altar boy but now often a girl, helps the celebrant. Most of the text is invariable, or "ordinary," but certain parts, called "proper," change with the occasion or day. Mass may be offered with a special intention, as in thanksgiving or for peace. A requiemrequiem
[Lat.,=rest], proper Mass for the souls of the dead, performed on All Souls' Day and at funerals. The reformation of Roman Catholic liturgy following the Second Vatican Council (see Vatican Council, Second) has modified the traditional requiem, and it is now called the
..... Click the link for more information. is a proper Mass for the dead. Most priests say Mass daily. Sunday Mass is an important sociocultural factor in Roman Catholic life. All members are required to attend Mass on Sunday as a minimum participation in public worship.
The Mass begins with an entrance hymn, a greeting, and a brief penetential rite that includes the Kyrie eleison, the Gloria in excelsis (not always), a collectcollect
[Late Lat.,=meeting], in Western liturgies, short prayer proper to an occasion, often asking a particular favor. In the Roman Catholic Church the collect is said, typically, at Mass just before the epistle and at vespers.
..... Click the link for more information. or collects, the proper epistleepistle
, in the Bible, a letter of the New Testament. The Pauline Epistles (ascribed to St. Paul) are Romans, First and Second Corinthians, Galatians, Ephesians, Philippians, Colossians, First and Second Thessalonians, First and Second Timothy, Titus, Philemon, and Hebrews.
..... Click the link for more information. , an anthem and the proper GospelGospel
[M.E.,=good news; evangel from Gr.,= good news], a written account of the life of Jesus. Though the Gospels of the New Testament are all anonymous, since the 2d cent. they have been named Matthew, Mark, Luke, and John.
..... Click the link for more information. (usually chanted and with all standing), and a homily on the texts. This ends the part of the Mass known in earlier times as the Mass of the Catechumens.
Mass continues with the creed (sometimes), the offertoryoffertory
[Lat.,=offering], in the Roman Catholic Mass and in derived liturgical forms, the preparation of bread and wine on the altar and their formal offering to God. It takes place after the gospel and the creed and before the preface.
..... Click the link for more information. (anthem with offering of bread and wine), offering of incense (sometimes), washing of the celebrant's hands, and proper prayers called "secrets." Then there is a chanted or spoken dialogue and proper preface of thanksgiving, ending in the Sanctus. That opens the long eucharistic prayer, or canon. It begins with prayers for the living. The consecration of the bread and wine follows; then the celebrant raises Host and chalice above his head for all to see and adore. The canon ends with prayers for the dead and a doxology, which is the solemn climax of the eucharistic prayer.
After the canon the Mass consists of the Lord's PrayerLord's Prayer
or Our Father,
the principal Christian prayer that Jesus in the New Testament (Mat. 6.9–13; Luke 11.2–4) taught his followers, beginning, "Our Father in heaven, hallowed be your name.
..... Click the link for more information. , a prayer amplifying the supplication "Deliver us from evil," the symbolic breaking of the Host and putting a piece into the cup, the kiss of peace (shared by the members of the congregation), the Agnus Dei, the communion, the ablution of vessels, the communion anthem, postcommunion prayers, the dismissal, and the blessing. There are ceremonial adjuncts such as processions, blessings, censings, and in some places, the ringing of a handbell at the consecration.
Music in the Mass
Of the portions of the Mass that may be sung, some are chanted solo at the altar with choral response; there are also nine hymns for the choir. Four of these are proper and related in theme, with texts usually from the Psalms: introit, anthem after the epistle (alleluia, gradual, tract, or sequence), offertory, and communion. The five ordinary choral pieces are Kyrie eleisonKyrie eleison
[Gr.,=Lord, have mercy], in the Roman Catholic Church, prayer of the Mass coming after the introit, the only ordinary part of the traditional liturgy said not in Latin but in Greek.
..... Click the link for more information. , Gloria in excelsisGloria in excelsis
[Lat.,=glory in the highest], the Angelic Hymn or greater doxology, ancient Christian hymn beginning, according to the Authorized Version, "Glory be to God on high, and on earth, peace, goodwill towards men." An amplification of Luke 2.
..... Click the link for more information. , Credo (see creedcreed
[Lat. credo=I believe], summary of basic doctrines of faith. The following are historically important Christian creeds.
1 The Nicene Creed, beginning, "I believe in one God the Father Almighty, maker of heaven and earth, and of all things visible and
..... Click the link for more information. ), SanctusSanctus
[Lat.,=holy], hymn of the Roman Catholic Mass, beginning, "Holy, holy, holy," from Isa. 6.3; Mat. 21.9. It is the solemn choral ending of the preface. In the old liturgy the second part of the hymn, called Benedictus, was sometimes sung after the elevation.
..... Click the link for more information. , and Agnus DeiAgnus Dei
[Lat.], the Lamb of God, i.e., Jesus. The lamb of the Passover sacrifice is said to prefigure the crucifixion. Isaiah calls the expected Messiah the Lamb of God, and Jesus is met by John the Baptist with the words, "Behold, the Lamb of God, who takes away the sins of
..... Click the link for more information. . Plainsongplainsong
the unharmonized chant of the medieval Christian liturgies in Europe and the Middle East; usually synonymous with Gregorian chant, the liturgical music of the Roman Catholic Church.
..... Click the link for more information. is prescribed for all texts, but latitude is permitted the choir. A musical setting for the five ordinary hymns, called a Mass, has been a major musical form. The principal period of Mass composition lasted from 1400 to 1700. It came to an end with shift of interest to instrumental music, although later composers did use the form. Among the many composers who produced Masses are Josquin des Prés, Palestrina, Monteverdi, Bach, Haydn, Mozart, Beethoven, Verdi, and Stravinsky.
Changes in the Mass
The basic structure of the Mass is largely unchanged since the 6th cent. In the Counter Reformation the forms were restricted and local variants eliminated. As a result of the Constitution on the Sacred Liturgy of the Second Vatican Council, the Roman Mass liturgy has undergone extensive reformation. The revisions include the use of the vernacular languages in the place of Latin, an emphasis on congregational singing, latitude for modifications that may be introduced by local bishops, additional eucharistic prayers, and communion in both bread and wine. In 2011, however, a new English translation of the Mass was put into effect. The changes were designed to align the English text more literally with the Latin, and revised much of the wording adopted after Vatican II.
See J. A. Jungmann, The Mass of the Roman Rite (rev. ed. 1959); F. Amiot, History of the Mass (tr. 1959); H. Daniel-Rops, This Is the Mass (rev. ed. 1965); P. Loret, The Story of the Mass (1983).
The quantitative or numerical measure of a body's inertia, that is, of its resistance to being accelerated.
Because it is often necessary to compare masses of such dissimilar bodies as a sample of sugar, a sample of air, an electron, and the Moon, it is necessary to define mass in terms of a property that not only is inherent and permanent but is also universal in that it is possessed by all known forms of matter. All matter possesses two properties, gravitation and inertia. The property of gravitation is that every material body attracts every other material body. The property of inertia is that every material body resists any attempt to change its motion. A body's motion is said to change if the body is accelerated, that is, if it increases or decreases its speed or changes the direction of its motion. Because of its inertia a body cannot be accelerated unless a force is exerted on it. The greater the inertia of a body, the less will be the acceleration produced by a given force. See Gravitation, Inertia
The present definition of mass is in terms of inertia. The masses of two bodies are compared by applying equal forces to the bodies and measuring their accelerations. For example, the two bodies may be allowed to collide. According to Newton's third law, each body will then experience an equally strong force. If there are no external forces, and if a1 and a2 are the measured accelerations of the two bodies, the ratio of the masses of the two bodies is by definition given by the equation
This equation gives only ratios of masses; it is therefore necessary to designate the mass of some one body as the standard mass to which the masses of all other bodies can be compared. The body that has been chosen for this purpose is a cylinder of platinum-iridium alloy. It is known as the international standard of mass; its mass is called 1 kilogram (kg), and it is kept at the International Bureau of Weights and Measures near Paris, France. Replicas of the standard mass, kept at various national laboratories, are periodically compared with this standard.
Einstein's special theory of relativity predicts that the inertia of a body should increase if the energy of the body increases. This prediction has been conclusively verified experimentally. It follows that the mass of a body will increase if, for example, the body gains speed (addition of kinetic energy), or its temperature rises (addition of heat energy), or the body is compressed (addition of elastic energy). See Conservation of mass
massA measure of the quantity of matter in a body. The SI unit of mass is the kilogram. The astronomical unit of mass is the solar mass, i.e. 2 × 1030 kg. Mass is a property of matter that determines both the inertia of an object, i.e. its resistance to any change in its motion or state of rest, and the gravitational field that it can produce. The former is called inertial mass, defined by Newton's laws of motion, and the latter is gravitational mass. Inertial and gravitational mass have been found to be equivalent. This led to Einstein's principle of equivalence between inertial and gravitational forces. See also relativity, special theory; stellar mass; weight.
masssee MASS SOCIETY, ÉLITE THEORY.
Three of the four Gospel accounts of Jesus' death state that on the night before he died he shared a ceremonial meal with his followers. Christians call this meal the Last Supper and honor it with religious observances that take place on Maundy Thursday. This meal is also commemorated each Sunday in churches throughout the world in a ceremony called the Eucharist. The Eucharist serves as the central and most important ritual in Christian communal worship. As this ceremony recalls the events surrounding Jesus' death and resurrection, it may be thought of as an Easter symbol and custom which millions of Christians participate in every Sunday.
The Last Supper and Passover
Jesus himself founded the ceremony of the Eucharist at the Last Supper (for more on the Last Supper, see Maundy Thursday). Christian scripture asserts that at this meal Jesus gave thanks to God for bread and wine, identified them as his body and blood, and passed them to his disciples to eat and drink (Matthew 26:26-29, Mark 14:22-25, Luke 22:16-19). These words and actions form the basis of the contemporary celebration of the Eucharist. A closer examination of their historical and cultural context illuminates their significance to Jesus'followers and to the first Christians.
The Gospels of Mark, Matthew, and Luke assert that the Last Supper was a Passover meal. (The Gospel according to John implies that the Passover supper would take place on the evening of the following day.) The yearly Passover festival originated in biblical times as a means for Jews to express their gratitude to God for leading their ancestors out of slavery in Egypt over a thousand years before Christ was born (see also Salvation). Through participation in the religious ceremonies associated with Passover, Jews also reaffirmed their relationship with God.
The Book of Exodus tells that the Jews enslaved in Egypt sacrificed a lamb to God and smeared its blood over their doorways as a sign of their faithfulness to the Lord. Afterwards they consumed the sanctified flesh of the lamb, waiting in readiness for God to deliver them.
In Jesus' time religious custom required those celebrating Passover to make a pilgrimage to Jerusalem. Once there they brought a lamb to the Temple, where the animal was killed as an offering to God. The sacrificial lamb recalled the original offering their ancestors made while slaves in Egypt. In Jesus' day worshipers took the lamb home after it had been offered to God by the Temple priests. Then it was roasted and eaten by a gathering of family and friends. This ceremonial meal also included unleavened bread and wine.
Scriptural accounts of the Last Supper describe a meal that resembles a traditional Passover supper in some ways and diverges from Jewish custom in others. As in a traditional Jewish Passover meal, Jesus gave thanks to God for the bread and wine before passing them to his disciples. But in a sharp break from Jewish religious teaching he proclaimed that the bread was his body and the wine his blood. In Matthew's account Jesus adds that his blood is "my blood of the covenant, which is poured out for many for the forgiveness of sins" (Matthew 26:28). Here Jesus is painting himself as a new kind of sacrificial lamb, one whose death will rescue his followers from the consequences of sin, and pave the way to a new relationship with God.
Origins of the Eucharist
The first Christians quickly interpreted Jesus' words and deeds at the Last Supper in terms of the Passover themes of sacrifice, redemption, and salvation. Jesus' death on the cross on Good Friday became the sacrifice which reunited a straying humanity with God. By accepting Jesus' body and blood as represented in bread and wine at the Last Supper, Jesus' original followers accepted both his act of sacrifice and the spiritual renewal that sprang from it. The early Christians developed a ceremony called the Eucharist in order that Jesus' growing numbers of followers could also share in this new relationship with God and one another through Christ. Just as religious Jews consumed the flesh of the Passover lamb, the new ceremony required Christians to consume the body and blood of the Savior who had died for their sakes. The body and blood were represented, as they had been at the Last Supper, by bread and wine.
The word "Eucharist" is an English pronunciation of the ancient Greek word eucharistia, which means "thanksgiving" or "gratitude." This name, given to the ceremony by the early Christians, reflects their attitude towards it. The ceremony and the prayers that accompanied it expressed their gratitude to Christ for rescuing them from sin, opening the door to a new relationship with the Divine, and promising them eternal life. At first, groups of Christians shared bread and wine together informally, as part of an everyday meal. As time went by this sharing of bread and wine grew increasingly ceremonial. By the fourth century Christians were celebrating the Eucharist in public buildings under the supervision of robed clergy, accompanied by Bible readings, prayers, chants, homilies, and the prayer of thanksgiving, which retold Jesus'words and deeds at the Last Supper.
Interpreting the Eucharist
Over the centuries many controversies have erupted over differing interpretations of the Eucharist. One of the most significant debates took place during the sixteenth-century western European Reformation. This period of religious strife gave birth to Protestant Christianity. Among other things, Protestants disagreed with the Roman Catholic doctrine concerning the Eucharist. This doctrine states that although neither the bread nor the wine of the Eucharist seems to change in appearance, they change in actual substance, becoming the real body and blood of Christ. Roman Catholic theologians explained the mechanics of this transformation in a doctrine known as transubstantiation. Protestant reformers disagreed with the idea that the bread and wine change into the actual body and blood of Christ. Today's many Protestant denominations attribute varying shades of meaning to the ceremony, but most tend to view the bread and wine as symbols that represent the body and blood of the Savior. They would also affirm, however, that Christ, through the power of the Holy Spirit, is indeed present with those who participate in the ceremony.
Other differences distinguish Protestant and Roman Catholic views of the Eucharist. Whereas Roman Catholic theology views the ceremony as an invitation to worshipers to partake of Jesus'sacrifice, many Protestant theologians instead see it as a memorial, or reminder, of Jesus' sacrifice.
The Orthodox Christians of eastern Europe, the Middle East, and north Africa offer yet another perspective on the ceremony. Like Roman Catholics they tend to view the ceremony as Jesus' renewed offering of himself to the assembled worshipers. They also agree that worshipers partake of the actual body and blood of Christ. Yet unlike Roman Catholic theologians, Orthodox theologians offer no definite explanation for how this miracle takes place. Instead they view Christ's presence in the bread and wine of the Eucharist as a mystery. By "mystery" they mean one of the hidden and unfathomable ways that God works in the world, sometimes perceived by those who look through the eyes of faith. Therefore the best way to "understand" the Eucharist is to participate in it with reverence, prayer, and meditation. In sum, Orthodox Christian authorities approach the ceremony as a spiritual experience to be savored rather than an intellectual problem to be solved.
Contemporary Ceremonies and Services
Today many different versions of the ceremony exist. Nevertheless, the heart of the ritual consists of the identification of bread and wine as Jesus' body and blood and the invitation to worshipers to partake of them. In doing so Christians remember Jesus' sacrificial death and resurrection and commit themselves again to the new covenant, or relationship with God, that these events brought about. They ask to draw nearer to God through Christ, and accept the spiritual healing, or salvation, that comes from this relationship. Participation in the ceremony helps to create a feeling of fellowship between worshipers as they together share in God's hospitality, expressed in spiritual food and drink. At some contemporary Protestant services grape juice substitutes for wine (for more on this issue, see also Wine).
In many churches, including those of the Roman Catholic, Orthodox, and Anglican traditions, the Eucharist stands at the heart of the Sunday worship service. Protestants, in general, celebrate the Eucharist less frequently. In some denominations the ceremony is known as the Eucharist, while in others it may be called the Lord's Supper or Holy Communion. Various Christian denominations have assigned different names to the worship service centered around the celebration of the Eucharist. Roman Catholics and some Anglicans call it a "Mass" and Orthodox Christians know it as the "Divine Liturgy." Protestants refer to the service by a variety of names, including the Eucharist, the Lord's Supper, or Holy Communion.
Ferguson, Everett, ed. "Eucharist." In his Encyclopedia of Early Christianity. Volume 1. New York: Garland, 1997. Hellwig, Monica K. "Eucharist." In Mircea Eliade, ed. The Encyclopedia of Religion. Volume 5. New York: Macmillan, 1987. "Hospitality." In Leland Ryken, James C. Wilhoit, and Tremper Longman III, eds. Dictionary of Biblical Imagery. Downers Grove, IL: InterVarsity Press, 1998. McNicol, Allan J. "Lord's Supper." In David Noel Freedman, ed. Eerdmans Dictionary of the Bible. Grand Rapids, MI: William B. Eerdmans Publishing, 2000. Peifer, C. J. "Passover Lamb" and "Passover Meal." In New Catholic Ency- clopedia. Volume 10. New York: McGraw-Hill, 1967. "Redemption." In Leland Ryken, James C. Wilhoit, and Tremper Longman III, eds. Dictionary of Biblical Imagery. Downers Grove, IL: InterVarsity Press, 1998. Reumann, John. The Supper of the Lord. Philadelphia, PA: Fortress Press, 1985. "Supper." In Leland Ryken, James C. Wilhoit, and Tremper Longman III, eds. Dictionary of Biblical Imagery. Downers Grove, IL: InterVarsity Press, 1998. Williams, Sam K. "The Lord's Supper." In Paul J. Achtemeier, ed. The Harper- Collins Bible Dictionary. New York: HarperCollins, 1996.
An explanation of the Orthodox understanding of the Eucharist, posted by the Orthodox Church in America web site: chri/Orthodox-Faith/Worship/Holy-Eucharist.html
An article entitled "The Holy Eucharist," by the Rev. Thomas Fitzgerald, posted at the Greek Orthodox Archdiocese of America in New York, NY, web site:
a physical quantity; a fundamental characteristic of matter that defines its inertial and gravitational properties. A corresponding distinction is made between inertial and gravitational mass.
The concept of mass was introduced in mechanics by I. Newton. In Newtonian classical mechanics, mass is part of the definition of the momentum of a body: the momentum P is proportional to the velocity of motion v of the body,
(1) p = mv
The proportionality factor—the quantity m, which is constant for a given body—is the mass of the body. An equivalent definition of mass can be obtained from the equation of motion of classical mechanics:
(2) f = ma
Here the mass is the proportionality factor between the force f acting on a body and the acceleration of the body a that it causes. The mass defined by equations (1) and (2) is called the inertial mass, or inert mass; it characterizes the dynamic properties of a body and is a measure of the body’s inertia. The greater the mass of a body, the smaller the acceleration it acquires upon application of a constant force—that is, the more slowly its state of motion changes (the greater its inertia).
The mass ratio of various bodies may be determined by applying a given force to them and measuring their acceleration: m1 : m2 : m3,… = a1 : a2 : a3.… If one of the masses is taken as the unit of measurement, then the masses of the other bodies can be found.
In the Newtonian theory of gravitation, mass assumes a different form—it is the source of the gravitational field. Each body creates a gravitational field proportional to its mass and experiences the effect of the gravitational field generated by other bodies, whose force is also proportional to the masses of the bodies. This field causes the attraction of any other body to the given body with a force that is defined by Newton’s law of gravitation:
where r is the distance between the bodies, G is the universal constant of gravitation, and m1 and m2 are the masses of the attracting bodies. A formula for the weight P of a body of mass m in the earth’s gravitational field may be easily obtained from formula (3):
(4) P = m · g
Here g = G·M/r2 is the free-fall acceleration in the earth’s gravitational field and r ≈ R is the radius of the earth. The mass defined by equations (3) and (4) is called the gravitational mass of the body.
In principle it does not follow that a mass that creates a gravitational field also defines the inertia of the same body. However, experiment has shown that inertial and gravitational mass are proportional to each other (and, with the choice of ordinary units of measurement, are numerically equal). This fundamental natural law is called the principle of equivalence. Its discovery is associated with Galileo, who established that all bodies on earth fall with identical acceleration. Einstein, who was the first to formulate this principle, made it the basis for the general theory of relativity. The principle of equivalence has been established experimentally with very high accuracy. A precise test of the equality of inertial and gravitational masses was first made (1890-1906) by L. Eötvös, who found that the masses coincide with an error of ˜ 10’8. The error was reduced to 10-11 by the American physicists R. Dicke, R. Krotkov, and P. Roll in 1959-64 and to 10-12 by the Soviet physicists V. B. Braginskii and V. I. Panov in 1971.
The principle of equivalence makes possible the most natural determination of the mass of a body, by weighing.
Mass was originally considered (by Newton, for example) to be a measure of the quantity of matter. This definition has clear meaning only for comparison of homogeneous bodies that are constructed of the same material. It emphasizes the additivity of mass—the mass of a body is equal to the sum of the mass of its parts. The mass of a homogeneous body is proportional to its volume; therefore, the concept of density—the mass per unit volume of a body—may be introduced.
In classical physics it was believed that the mass of a body does not change in any processes. The law of conservation of mass (matter), which was discovered by M. V. Lomonosov and A. L. Lavoisier, corresponded to this. In particular, the law asserted that in any chemical reaction the sum of the masses of the initial components is equal to the sum of the masses of the final components.
The concept of mass acquired deeper meaning in the mechanics of Einstein’s special theory of relativity, which considers the motion of bodies (or particles) with very great velocity to be comparable to the speed of light, c ≈ 3 × 1010 cm/sec. In the new mechanics, which is called relativistic mechanics, the relation between the momentum and velocity of a particle is given by the equation
For low velocities (v « c) this equation becomes the Newtonian relation p = mv. Therefore, the quantity mo is called the rest mass, and the mass m of a moving particle is defined as the proportionality factor between p and v, which is dependent on the velocity:
Keeping in mind this formula in particular, we say that the mass of a particle (body) increases as its velocity. This relativistic increase in the mass of a particle with increased velocity must be taken into account in the design of high-energy particle accelerators. The rest mass m0 (the mass in a frame of reference that is connected with the particle) is the most important intrinsic characteristic of a particle. All elementary particles have strictly defined values of m0 that are inherent in the given type of particle.
It should be noted that in relativistic mechanics the definition of mass from equation of motion (2) is not equivalent to the definition of mass as the proportionality factor between the momentum and velocity of a particle, since its acceleration ceases to be parallel to the force that causes it, and the mass is found to be dependent on the direction of the particle’s velocity.
According to the theory of relativity, the mass m of a particle is related to its energy E by the equation
The rest mass determines the internal energy of a particle—its rest energy, E0 ×m0c2. Thus, energy is always related to mass (and vice versa). Therefore, the laws of conservation of mass and energy do not exist separately (in contrast to classical physics) but are fused into the unified law of conservation of total energy (that is, including the rest energy of the particles). Its approximate division into the law of conservation of energy and the law of conservation of mass is possible only in classical physics, when the particle velocities are low (v « c) and processes of conversion of particles do not take place.
In relativistic mechanics, mass is not an additive characteristic of a body. When two particles are combined, forming a composite stable state, an energy excess ΔE (equal to the binding energy), which corresponds to the mass Δm = ΔE/c2, is released in the process. Therefore, the mass of a composite particle is less by the quantity ΔE/c2 than the sum of the masses of the particles that form it (the mass defect). This effect is particularly strongly manifested in nuclear reactions. For example, the mass of a deuteron (d) is less than the sum of the mass of a proton (p) and a neutron (n); the mass defect Δm is related to the energy Eγ of the gamma quantum (y) that is produced during the formation of a deuteron: p + n → d + γ, Ey + Δm·c2. The mass defect that arises during the formation of a composite particle reflects the natural relation between mass and energy.
The gram is the unit of mass in the cgs system of units and the kilogram in the International System of Units. The mass of atoms and molecules is usually measured in atomic mass units. The mass of elementary particles is commonly expressed either in units of mass of the electron me or in energy units, by indicating the rest energy of the corresponding particles. For example, the mass of the electron is 0.511 mega electron volt (MeV); the mass of the proton is 1,836.1 me, or 938.2 MeV.
The nature of mass is one of the most important unsolved problems of modern physics. It is commonly assumed that the mass of an elementary particle is determined by the fields associated with it (such as electromagnetic and nuclear fields). However, a quantitative theory of mass has not been developed, nor are there theories that would explain why the masses of elementary particles form a discrete spectrum of values or possible determination of the spectrum.
In astrophysics, the mass of a body that generates a gravitational field determines the gravitational radius of the body, Rg = 2GM/c2. Because of gravitational attraction no radiation, including light, can emerge from the surface of a body having a radius R≦Rg. Stars of such dimensions would be invisible; therefore, they are called black holes. Such celestial bodies should play an important role in the universe.
REFERENCESJammer, M. Poniatie massy v klassicheskoi i sovremennoifizike. Moscow, 1967. (Translated from English.)
Khaikin, S. E. Fizicheskie osnovy mekhaniki. Moscow, 1963.
Elementarnyi uchebnik fiziki, 7th ed., vol. 1. Edited by G. S. Landsberg. Moscow, 1971.
the name of the liturgy used by the Catholic Church.
The components and the order of conducting the mass took shape over the course of many centuries. They became essentially fixed at the Council of Trent (1545–63). The Second Vatican Council (1962–65) made changes in the mass (for example, permitting the service to be conducted in local languages as well as in Latin). The liturgical songs forming an invariable part of a given service make up what is called the ordinary of the mass. They are named after the initial word of each text: Kyrie, Gloria, Credo, Sanctus and Benedictus, and Agnus Dei. Originally, the liturgical songs of the mass were monophonic, based on the Gregorian chant. Later, with the development of polyphony, there appeared polyphonic arrangements of the liturgical music of the mass as well as entire ordinaries of the mass written for the traditional text by just one composer. There was also a distinction made between the high mass (missa solemnis) and the low mass (missa brevis), which consisted as a rule of the first two or three liturgical parts of the ordinary of the mass.
In the Renaissance era the mass was the most monumental of musical genres. Masses were written by J. Dunstable (England), G. Dufay, J. Ockeghem, J. Obrecht, Josquin Depres, and O. de Lassus (the Netherlands), Palestrina, A. Willaert, and G. Gabrieli (Italy), and T. L. de Victoria (Spain). At a later period, classical versions of the mass were composed by J. S. Bach (Mass in B minor), Mozart, Beethoven (two masses, including the Missa Solemnis), L. Cherubini, F. Schubert, F. Liszt, and A. Bruckner. The funeral mass is known as a requiem.
REFERENCESBobrovnitskii, I. O proiskhozhdenii i sostave rimsko-katolicheskoi liturgii i otlichii ee ot pravoslavnoi, 4th ed. Kiev, 1873.
Ivanov-Boretskii, M. V. Ocherk istorii messy. Moscow, 1910.
Wagner, P. Geschichte der Messe. Leipzig, 1913.
B. V. LEVIK