Discrepancy on the value of $\phi(v)$ in Einstein's 'On the Electrodynamics of moving bodies'?
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On Einstein's derivation of the Lorentz Transformation he obtains the differential equation
∂τ
∂
x
′
+
v
c
2
−
v
2
∂τ
∂t
=0
∂τ∂x′+vc2−v2∂τ∂t=0
From this is obtained
τ=a(t−
v
c
2
−
v
2
x
′
)
τ=a(t−vc2−v2x′)
Where a is described as being an unknown function of
v
v
ϕ(v)
ϕ(v)
. As one derives this, it is pretty clear that
a=
∂τ
∂t
a=∂τ∂t
. Einstein then proceeds to derive the Lorentz transformations as
τ
ξ
η
ζ
=ϕ(v)β(t−
vx
c
2
)
=ϕ(v)β(x−vt)
=ϕ(v)y
=ϕ(v)z
∂τ
∂
x
′
+
v
c
2
−
v
2
∂τ
∂t
=0
∂τ∂x′+vc2−v2∂τ∂t=0
From this is obtained
τ=a(t−
v
c
2
−
v
2
x
′
)
τ=a(t−vc2−v2x′)
Where a is described as being an unknown function of
v
v
ϕ(v)
ϕ(v)
. As one derives this, it is pretty clear that
a=
∂τ
∂t
a=∂τ∂t
. Einstein then proceeds to derive the Lorentz transformations as
τ
ξ
η
ζ
=ϕ(v)β(t−
vx
c
2
)
=ϕ(v)β(x−vt)
=ϕ(v)y
=ϕ(v)z
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Disperancy on the value of Einstein on electrodynamics of moving bodies
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Disperancy on the value of Einstein on electrodynamics of moving bodies
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