PHY3063
R. D. Field
Department of Physics
Chapter1_7.doc
University of Florida
Lorentz Transformation (derivation)
Look for a transformation of the form
z
z
y
y
Ect
Dx
x
Bx
Act
t
c
=
′
=
′
+
=
′
+
=
′
where A, B, D, and E are to be
determined.
The inverse
transformation is given by
z
z
y
y
BE
AD
t
Ec
x
A
x
BE
AD
x
B
t
Dc
ct
′
=
′
=
−
′
−
′
=
−
′
−
′
=
)
/(
)
(
)
/(
)
(
Also we know that for x’ = 0 dx/dt = V and for x = 0
dx’/dt’ = V thus
c
D
E
dt
dx
V
−
=
=
and
c
A
E
t
d
x
d
V
−
=
′
′
−
=
and hence D = A and E = AV/c = A
β
with
β
= V/c.
We now require that
2
2
2
2
2
2
)
(
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 Spring '07
 Field
 Physics, Special Relativity, dx, Lorentz, Lorentz Transformation, Department of Physics

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