This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. (March 2011)

The invariant mass, rest mass, intrinsic mass, proper mass or just mass is a characteristic of the total energy and momentum of an object or a system of objects that is the same in all frames of reference related by Lorentz transformations. If the object is in motion, then the magnitude of invariant mass will differ from rest mass. Such distinction is particularly important when considering a two-body (or more) system of motion. For example, consider the simple case of two-body system, where object A is moving towards another object B which is initially at rest (in any particular frame of reference). The magnitude of invariant mass of this two-body system (see definition below) is different from the sum of rest mass A and B(i.e. their respective mass when stationary). Even if we consider the exact same system from center-of-momentum frame, where net momentum is zero, the magnitude of invariant mass are not equal to their sum of rest mass. Only when the system as a whole is at rest, then invariant mass is equivalent to the familiar concept of rest mass, which also equals to the total energy of the system divided by c². See mass-energy equivalence for a discussion of definitions of mass. Since the mass of systems must be measured with a weight or mass scale in a reference frame in which the system has zero momentum (the center of momentum frame), such a scale always measures the system's invariant mass.

Systems whose four-momentum is a null vector (for example a single photon or many photons moving in exactly the same direction) have zero invariant mass, and are referred to as massless. A physical object or particle moving faster than the speed of light would have space-like four-momenta (such as the theoretical tachyon), and these do not appear to exist.

For an isolated massive system, the four-momentum is a time-like vector and the center of mass moves in a straight line with a steady sub-luminal velocity. Thus, an observer can always be placed to move along with it. In this frame, which is the center of momentum frame, the total momentum is zero, and the system as a whole may be thought of as being "at rest" if it is a bound system (like a bottle of gas). In this frame, which always exists, the invariant mass of the system is equal to the total system energy (in the zero-momentum frame) divided by c². This total energy in the center of momentum frame, is the minimum energy which the system may be observed to have, when seen by various observers from various inertial frames.

Note that for reasons above, such a frame does not exist for single photons, or rays of light moving in one direction. When two or more photons move in different directions, however, a center of mass frame exists. Thus, the mass of a system of several photons moving in different directions is positive, which means that an invariant mass exists for this system.

The example above shows invariant mass of a system may be greater than sum of rest masses of its separate constituents. For example, rest mass and invariant mass are zero for individual photons even though they may add mass to the invariant mass of systems. For this reason, invariant mass is in general not an additive quantity (although there are a few rare situations where it may be, as is the case when massive particles in a system without potential or kinetic energy can be added to a total mass).

If a system consists of more than one particle moving in different directions, or the same direction in at different velocities, the particles will be moving relative to each other in the center of momentum frame. They will often also interact through one or more of the fundamental forces, giving them a potential energy of interaction, possibly negative. The kinetic energy of such particles and the potential energy of the force fields increase the total energy above the sum of the particle rest masses, and both terms contribute to the invariant mass of the system. The sum of the particle kinetic energies as calculated by an observer is smallest in the center of momentum frame (again, called the "rest frame" if the system is bound).

Possible 4-momenta of particles. One has zero invariant mass, the other is massive

Particle physics[link]

In particle physics, the invariant mass is a mathematical combination of a particle's energy E and its momentum p which is equal to the mass in the rest frame. This invariant mass is the same in all frames of reference (see Special Relativity).

Failed to parse (Missing texvc executable; please see math/README to configure.): m_0^2 c^2=\left(\frac{E}{c}\right)^2-\|\mathbf{p}\|^2\,

or in natural units where c = 1,

Failed to parse (Missing texvc executable; please see math/README to configure.): m_0^2 = E^2 - \|\mathbf{p}\|^2. \,

This equation says that the invariant mass is the pseudo-Euclidean length of the four-vector (E, p), calculated using the relativistic version of the pythagorean theorem which has a different sign for the space and time dimensions. This length is preserved under any Lorentz boost or rotation in four dimensions, just like the ordinary length of a vector is preserved under rotations. In quantum theory the invariant mass is a parameter in the relativistic Dirac equation for an elementary particle. The Dirac quantum operator corresponds to the particle four-momentum vector.

Since the invariant mass is determined from quantities which are conserved during a decay, the invariant mass calculated using the energy and momentum of the decay products of a single particle is equal to the mass of the particle that decayed. The mass of a system of particles can be calculated from the general formula:

Failed to parse (Missing texvc executable; please see math/README to configure.): \left(Wc^2\right)^2= \left(\sum E\right)^2-\left\|\sum \mathbf{p}c\right\|^2

where

Failed to parse (Missing texvc executable; please see math/README to configure.): W

is the invariant mass of the system of particles, equal to the mass of the decay particle.

Failed to parse (Missing texvc executable; please see math/README to configure.): \sum E

is the sum of the energies of the particles 

Failed to parse (Missing texvc executable; please see math/README to configure.): \sum \mathbf{p}

is the vector sum of the momentum of the particles (includes both magnitude and direction of the momenta)

The term invariant mass is also used in inelastic scattering experiments. Given an inelastic reaction with total incoming energy larger than the total detected energy (i.e. not all outgoing particles are detected in the experiment), the invariant mass (also known as the "missing mass") Failed to parse (Missing texvc executable; please see math/README to configure.): W

of the reaction is defined as follows:

Failed to parse (Missing texvc executable; please see math/README to configure.): W^2 = \left(\sum E_{in} - \sum E_{out}\right)^2 - \left(\sum \mathbf{p_{in}} - \sum \mathbf{p_{out}}\right)^2

If there is one dominant particle which was not detected during an experiment, a plot of the invariant mass will show a sharp peak at the mass of the missing particle.

In those cases when the momentum along one direction cannot be measured (i.e. in the case of a neutrino, whose presence is only inferred from the missing energy) the Transverse mass is used.

Example: two-particle collision[link]

In a two-particle collision (or a two-particle decay) the square of the invariant mass (in natural units) is

Failed to parse (Missing texvc executable; please see math/README to configure.): M^2 \,	Failed to parse (Missing texvc executable; please see math/README to configure.): = (E_1+E_2)^2-\|\textbf{p}_1 + \textbf{p}_2\|^2 \,
	Failed to parse (Missing texvc executable; please see math/README to configure.): = m_1^2 + m_2^2 + 2\left(E_1 E_2 - \textbf{p}_1 \cdot \textbf{p}_2 \right). \,

Massless particles[link]

The invariant mass of a system made of two massless particles whose momenta form an angle Failed to parse (Missing texvc executable; please see math/README to configure.): \theta

has a convenient expression:

Failed to parse (Missing texvc executable; please see math/README to configure.): M^2 \,	Failed to parse (Missing texvc executable; please see math/README to configure.): = (E_1+E_2)^2-\|\textbf{p}_1 + \textbf{p}_2\|^2 \,
	Failed to parse (Missing texvc executable; please see math/README to configure.): = [(p_1,0,0,p_1)+(p_2,0,p_2\sin\theta, p_2\cos\theta)]^2 = (p_1+p_2)^2 -p_2^2\sin^2\theta -(p_1 + p_2\cos\theta)^2 \,
	Failed to parse (Missing texvc executable; please see math/README to configure.): = 2 p_1p_2(1 - \cos\theta). \,

Collider Experiments[link]

In particle collider experiments, one often defines the angular position of a particle in terms of a azimuthal angle Failed to parse (Missing texvc executable; please see math/README to configure.): \phi

and pseudorapidity Failed to parse (Missing texvc executable; please see math/README to configure.):  \eta 

. Additionally the transverse momentum, Failed to parse (Missing texvc executable; please see math/README to configure.): p_{T} , is usually measured. In this case if the particles are massless, or highly relativistic ( Failed to parse (Missing texvc executable; please see math/README to configure.): E >> m ,) then the invariant mass becomes:

Failed to parse (Missing texvc executable; please see math/README to configure.): M^2 \,

Failed to parse (Missing texvc executable; please see math/README to configure.): = 2 p_{T 1} p_{T 2} ( \cosh(\eta_1 - \eta_2) - \cos (\phi_1 - \phi_2) ) .\,

Rest energy[link]

The rest energy Failed to parse (Missing texvc executable; please see math/README to configure.): E_0

of a particle is defined as:

Failed to parse (Missing texvc executable; please see math/README to configure.): \ E_0=m c^2

,

where Failed to parse (Missing texvc executable; please see math/README to configure.): c

is the speed of light in a vacuum.[1] In general, only differences in energy have physical significance.[2]  

The concept of rest energy follows from the Special theory of relativity that leads to Einstein's famous conclusion about equivalence of energy and mass. See background for mass-energy equivalence.

On the other hand, the concept of the equivalent Dirac invariant rest mass may be defined in terms of the self energy corresponding to the product of a geometric matter current and a generalized potential ^[3] as part of a single definition of mass in a geometric unified theory.

See also[link]

• Mass in special relativity
• Invariant (physics)
• Transverse mass

References[link]

• Landau, L.D., Lifshitz, E.M. (1975). The Classical Theory of Fields: 4-th revised English Edition: Course of Theoretical Physics Vol. 2. Butterworth Heinemann. ISBN 0-7506-2768-9. 
• Okun, L.B. (1989). The Concept of Mass. http://www.worldscibooks.com/etextbook/6833/6833_02.pdf. 
• Halzen, Francis; Martin, Alan (1984). Quarks & Leptons: An Introductory Course in Modern Particle Physics. John Wiley & Sons. ISBN 0-471-88741-2. 

Citations[link]

This article reads more like a story than an encyclopedia entry. To meet Wikipedia's quality standards and conform to the neutral point of view policy, please help to introduce a more formal style and remove any personally invested tone. (July 2011)

This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. (July 2011)

David Crowder Band
Background information
Origin	Waco, Texas, United States
Genres	Christian rock, electronic rock, worship, bluegrass, rap
Years active	1996–2012
Labels	Sixstepsrecords, EMI
Website	www.davidcrowderband.com
Past members
David Crowder Jack Parker Jeremy "B-Wack" Bush Mike D Hogan Mark Waldrop Jason Solley Taylor Johnson
Notable instruments
Banjo Turntable Electric violin Keytar Guitar Hero Controller Mandolin Theremin Ukulele Steve 3P0 (drumming robot)

David Crowder Band (stylized as David Crowder*Band and The David Crowder Band) was a six-piece Christian rock and modern worship band from Waco, Texas. Their final album debuted at No. 1 on the Billboard Christian and No. 2 on the Billboard 200 charts.^[1]

Name[link]

Prior to the album Church Music, the band preferred not to be referred to as "The David Crowder Band". They explained that they preferred to omit the article, and stated that they "may revisit this issue if other groups named 'David Crowder Band' begin performing," and may in fact, should that eventuality occur, insert "The Original" in front of the band's present appellation. As of the release of Church Music, however, the band has begun referring to themselves using the article, and explained "we’ve been at for a while now without incident, so we felt justified in its formal inclusion."^[2]

The band's name is sometimes rendered with an asterisk, as "David Crowder*Band". In a faux-documentary, while recording Church Music, Crowder joked that the asterisk meant, "David Crowder [is about to go insane because Jack Parker continually tries to sabotage the work of the rest of the] band."^[3]

Band history[link]

The band began when Crowder realized that almost half of the students at Baylor University, a Christian university, were not attending church. Finding this very surprising he and Chris Seay started University Baptist Church (Waco, Texas) in 1995, while he was still a student. Crowder became Pastor of worship at the church and led worship and continued to do so throughout the year. The church's congregation grew, as did the band's lineup.

Crowder began writing songs to incorporate into the worship times at the church and eventually the church released an independent CD, Pour Over Me, followed by All I Can Say in 1999.^{[citation needed]} These CDs brought the band to a wider audience and invitations to festivals and events followed. The band was signed to sixstepsrecords/Sparrow Records when Louie Giglio talked to Crowder about the music and how it could be used more than just at UBC and more world-wide. Although the band toured extensively, they made it a point to be back at their home church UBC in Waco Texas for most Sundays.^{[citation needed]}

Kyle Lake, University Baptist Church's former pastor and also longtime friend of the band, had a strong influence on the band's music in terms of content and inspiration both during his life and after Lake's death.^{[citation needed]}

With their September 2005 release, A Collision, David Crowder Band explored a new realm of musical diversity. The album houses a mix of bluegrass, folk, alternative, and worship, woven together with a touch of electronic ambience. This release landed them the No. 2 spot on the iTunes Music Store and the No. 39 spot on Billboard 200 the second day after its release. The same day as the release of A Collision, their song "Turkish Delight" was released on the Music Inspired by the Chronicles of Narnia compilation CD. This song, which is a reference to the magical Turkish Delight in C. S. Lewis's book The Lion, the Witch and the Wardrobe, has an old-school disco feel.

March 19, 2007, the band officially started recording Remedy; the band also revealed the album's website, http://www.remedyiscoming.com/, which allows fans to follow the band via live webcams, and discover more about the album. Famously controversial rock musician Ted Nugent made a special guest appearance on the album, on the song "We Won't Be Quiet". Remedy was released on September 25, 2007. The day after its release, it reached No. 4 on the iTunes Music Store. When Mark joined the band as the album Remedy was released, his sidekick Rupert came with him. Rupert is a gnome.^[4][5] During the Remedy Tour the band had up a live web feed on Crowder's Xanga account. The feed had a chat room where fans chatted live with the band and their tourmates. It showed more than half of the tour stops live which included their tour bus, live stage feeds of shows, places the band went, etc. Much of the time the video feed would be on Rupert at different stops. On the final night of the tour Phil Wickham and The Myriad came on stage for a hoe down for the song "I Saw the light". The camera for the feed was on the lid of a ball-cap and was wired into a laptop the band had in a backpack; this equipment was provided by Xanga. The band also used the feed for some time after their Remedy Tour. July 16, 2008, the band announced it would releasing a live album and DVD titled Remedy Club Tour - Live,^[6] The DVD was filmed In NYC and GA.

Crowder's Xanga entry from January 31, 2009, mentioned the preproduction of the band's next studio album. Also on Mike Hogan's MySpace entry from March 4, 2009, he confirmed that actual recording and production had commenced and provided directions for getting to the live webcam feed, which is in a page simply titled "Church Music".^[7] The album was titled "Church Music" and was released on September 22, 2009.^[8] The first single off the album was a cover of John Mark McMillan's song "How He Loves". Crowder received permission from McMillan to change the words "So heaven meets earth like a sloppy wet kiss" to "So heaven meets earth like an unforeseen kiss".

The band hosted Crowder's Fantastical Church Music Conference September 30 through October 2, 2010 at Baylor University in Waco, Texas.^[9] Other presenters at the conference included Louie Giglio, Rob Bell, Israel Houghton, Hillsong London, Matt Redman, Jars of Clay, Matt Maher, Leeland, David Dark, Gungor, Derek Webb and others. Mark recorded a Rap song for the band titled "Bwack Be Creepin'" for the band's YouTube channel.^[10]

February 5, 2011 the band announced the official start to recording of Give Us Rest (A Requiem Mass in C [The Happiest of All Keys]).^[11] On May 21, 2011, the band announced through their website that the band will end after the completion of the Fall 2011 "The 7 Tour" and the release of their sixth album. At the same time the band also announced that they planned to disband after the release of their sixth album.^[12]

Later, on July 21, 2011, the band announced that a Christmas album, Oh for Joy, would be released on October 4, 2011.^[13] The band stated that they began to record Give Us Rest and subsequently Oh for Joy came out. Some of the songs in the albums Give Us Rest and Oh for Joy were recorded in greenrooms and restrooms during the band's last tour.^[14]

The band played their final show at the Passion 2012 Conference on January 3, 2012 at the Georgia Dome.^[15]

Crowder has formed a new collective called "Crowder" that will be making its first performance at the Creation East Festival in June.^[16][17] Parker, Dodson, Bush, and Waldrop have formed a new band, called "The Digital Age",^[16] and are opening a recording studio in Waco, Texas.^[18] Many of the members have rejoined UBC's worship team leading worship.^[18]

Unusual instrumentation[link]

The band often incorporated unconventional instruments and elements into their music which were created by the band's drummer Jeremy Bush. He modified a Speak & Spell for the song "I Can Hear the Angels Sing", a guitar-shaped controller for the Guitar Hero game to be used in "...Neverending...", and a robot drummer, named Steve 3PO, for use in "Church Music", a silver box with blue lights and switches for "Can You Feel It?", and a MOTM modular synthesizer used by Hogan. He also manufactured a seven square-foot MPC style-MIDI controller for the band Family Force 5. Hogan often played turntables and played electric violin with guitar effects. A Smule "I Am T-Pain" iPhone app is used on "The Nearness".^{[citation needed]}

The band often recorded their albums in a barn behind Crowder's house.^{[citation needed]}

Members[link]

Current members[link]

David Crowder performing in Lincoln, Nebraska

• David Crowder – vocals, acoustic guitar, piano, programming, theremin, keytar, electric guitar
• Jack Parker – electric guitar, background vocals, Rhodes piano, mandolin, and banjo
• Mike Dodson – bass guitar, keyboard, cello,
• Mike Hogan – violin/strings, turntables, guitar, keyboard
• Jeremy "B-Wack" Bush - drums, percussion, bells, programming
• Mark Waldrop – electric guitar, mandolin, background vocals

Former members[link]

• Jason Solley – electric guitar, background vocals and mandolin (1996–2006)
• Taylor Johnson – electric guitar, mandolin (2006–2007)

Discography[link]

Albums

• Pour Over Me (1998)
• All I Can Say (1999)
• Can You Hear Us? (2002)
• Illuminate (2003) U.S. No. 84^[19]
• A Collision (2005) U.S. No. 39
• Remedy (2007) U.S. No. 22
• Remedy Limited Edition (2008)
• Remedy Club Tour – Live (2008) U.S. No. 88
• Church Music (2009) U.S. No. 11
• Give Us Rest or (A Requiem Mass in C [The Happiest of All Keys]) (2012) U.S. No. 2^[20]

EPs

• The Lime CD (2004)
• Sunsets & Sushi (2005)
• B Collision (2006) U.S. No. 118
• Summer Happiness (2010)^[21]
• Oh for Joy (2011)

Collaboration[link]

• Thoughts of You - Robbie Seay (2000)
• Passion: The Road to One Day - Passion Worship Band (2000)
• Our Love is Loud - Passion Worship Band (live, 2002)
• Sacred Revolution - Passion Worship Band (live, 2003)
• Passion: Hymns Ancient and Modern - Passion Worship Band (2004)
• How Great Is Our God - Passion Worship Band (live, 2005)
• Live from Austin Music Hall - Chris Tomlin (live, 2005)
• Everything Glorious - Passion Worship Band (live, 2006)
• Music Inspired by the Chronicles of Narnia (2005)
• Ultimate Music Makeover: Michael W. Smith (compilation, 2005)
• X Worship 2006 (compilation, 2005)
• X Worship 2007 (compilation, 2006)
• When the Storm Comes - Minister RMB (When the Storm Comes, 2006)
• WOW Christmas: Green (compilation, Christmas)
• Music Inspired By the Motion Picture Amazing Grace (compilation, 2007, Sparrow Records)
• Glory Revealed (compilation by Mac Powell, 2007)
• Passion: Live from Passion07, Part 2 - Passion Worship Band (2007)
• God of This City - Passion Worship Band (2008)
• Passion: Awakening - Passion Worship Band (2010)
• The Shelter - Jars of Clay (2010) – on song "Lay It Down"
• Passion: Here for You - Passion Worship Band (2011)
• Seven Swans Reimagined (compilation, 2011)^[22]
• Passion: White Flag - Passion Worship Band (2012)
• The band also created the theme music for Dr. James MacDonald's radio program Walk in the Word.
• Crowder also wrote the song "Rise Up" for Baylor University football team.
• Mark Waldrop recorded "Bwack Be Creepin'", the band's rap song.^[10]

Awards[link]

GMA Dove Awards

Grammy Awards

David Crowder Band is also featured in other compilation albums that were either nominated or won Dove Awards for Special Event Album of the Year:

• 2006: Special Event Album of the Year - Music Inspired by the Chronicles of Narnia
• 2007: Special Event Album of the Year - Passion: Everything Glorious
• 2009: Special Event Album of the Year - Passion: God of This City

Others[link]

The band was named MSN's Artist of the Month for July 2006, and later won Artist of the Year for 2006.^[24]

Books[link]

David Crowder has authored two books:

• David Crowder, Praise Habit: Finding God in Sunsets and Sushi, NavPress, 2005.
• David Crowder with Mike Hogan, Everybody Wants to Go to Heaven, but Nobody Wants to Die or (The Eschatology of Bluegrass), Relevant Books, 2006.

References[link]

External links[link]

• David Crowder Band official website
• Christian Music Today interview - 11/07
• Christian Music Today interview - 04/06
• Christian Music Today interview - 10/02
• Home.FM Radio interview with David Crowder by Adam & Ben on Mornings at Home
• Gospel Music Channel interview with David Crowder by Alicia Carson