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Relational Quantum Gravity : IntroductionToVectorSpace

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Revision [465]

Last edited on 2012-04-13 05:14:12 by CharlesFrancis
Additions:
The Lorentz transform is simply a ""coordinate transformation "", and is represented by a matrix. Coordinate transformations do not affect the inner product. As a result they are represented by ""unitary"" matrices. Real unitary matrices are symmetrical. For a boost in the ""1""-direction the matrix representation is found by acting on ""4-velocity"" ""(γ, γv)"" such that 3-velocity, ""v"", becomes zero:
Deletions:
The Lorentz transform is simply a ""coordinate transformation "", and is represented by a matrix. Coordinate transformations do not affect the inner product. As a result they are represented by ""unitary"" matrices. Real unitary matrices are symmetrical. For a boost in the ""1""-direction the matrix representation is found by acting on ""4-velocity"" such that 3-velocity becomes zero:


Revision [464]

Edited on 2012-04-13 05:09:40 by CharlesFrancis
Additions:
The Lorentz transform is simply a ""coordinate transformation "", and is represented by a matrix. Coordinate transformations do not affect the inner product. As a result they are represented by ""unitary"" matrices. Real unitary matrices are symmetrical. For a boost in the ""1""-direction the matrix representation is found by acting on ""4-velocity"" such that 3-velocity becomes zero:
Deletions:
The Lorentz transform is simply a ""coordinate transformation , and is represented by a matrix. Coordinate transformations do not affect the inner product. As a result they are represented by ""unitary"" matrices. Real unitary matrices are symmetrical. For a boost in the ""1""-direction the matrix representation is found by acting on ""4-velocity"" such that 3-velocity becomes zero:


Revision [448]

Edited on 2012-04-05 06:13:22 by CharlesFrancis
Additions:
In ""Minkowski Coordinates"", as used in ""special relativity"", the momentum 4-vector, or 4-momentum, ""pi = (p0p1p2p3)"" is given by:
The Lorentz transform is simply a ""coordinate transformation , and is represented by a matrix. Coordinate transformations do not affect the inner product. As a result they are represented by ""unitary"" matrices. Real unitary matrices are symmetrical. For a boost in the ""1""-direction the matrix representation is found by acting on ""4-velocity"" such that 3-velocity becomes zero:
Deletions:
In Minkowski Coordinates, as used in ""special relativity"", the momentum 4-vector, or 4-momentum, ""pi = (p0p1p2p3)"" is given by:
The Lorentz transform is simply a coordinate transformation, and is represented by a matrix. Coordinate transformations do not affect the inner product. As a result they are represented by ""unitary"" matrices. Real unitary matrices are symmetrical. For a boost in the ""1""-direction the matrix representation is found by acting on ""4-velocity"" such that 3-velocity becomes zero:


Revision [308]

Edited on 2010-07-09 02:16:28 by CharlesFrancis
Additions:
""Scalars""
""Vector Space""
""Coordinates ""
""The Dot Product ""
""Ket Notation""
""Hilbert Space""
""Dirac’s Joke""
""The Cauchy-Schwarz Inequality""
""The Dot Product as an Inner Product""
""Orthonormal Bases""
""Contravariant and Covariant Vectors""
""Einstein Summation Convention""
""The Metric""
""3 Dimensions plus Time""
""The Light Cone""
""Coordinate Transformation ""
""Lorentz Transformation ""
""Spherical Coordinates ""
""Scalars""
""Vector Space""
""Coordinates ""
""The Dot Product ""
""Ket Notation""
""Hilbert Space""
""Dirac’s Joke""
""The Cauchy-Schwarz Inequality""
""The Dot Product as an Inner Product""
""Orthonormal Bases""
""Contravariant and Covariant Vectors""
""Einstein Summation Convention""
""The Metric""
""3 Dimensions plus Time""
""The Light Cone""
""Coordinate Transformation ""
""Lorentz Transformation ""
""Spherical Coordinates ""


Revision [58]

The oldest known version of this page was created on 2009-04-25 06:47:24 by CharlesFrancis
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