46
THE MEANING OF RELATIVITY
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(34)
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If there exists with respect to
only a magnetic field,
, but no electric field,
, then with respect to
there exists an electric field
as well, which would act upon an electric particle at rest relatively to
. An observer at rest relatively to
would designate this force as the Biot-Savart force, or the Lorentz electromotive force. It therefore appears as if this electromotive force had become fused with the electric field intensity into a single entity.
In order to view this relation formally, let us consider the expression for the force acting upon unit volume of electricity,
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(35)
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in which
is the vector velocity of electricity, with the velocity of light as the unit. If we introduce
and
according to (30a) and (31), we obtain for the first component the expression
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Observing that
vanishes on account of the skew-symmetry of the tensor (
), the components of
are given by the first three components of the four-dimensional vector
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(36)
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and the fourth component is given by
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(37)
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