Page:AbrahamMinkowski1.djvu/13

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Though, Lorentz's vectors and have an illustrative meaning. Namely, the excitations and can be split into two parts according to eq. (29), (30):

(31)

The first contribution of the electric and magnetic excitation, which is represented by and , is interpreted by Lorentz as electric and magnetic excitation of the aether, and the second contribution, which is represented by the vectors and (electric and magnetic polarization), is interpreted as the electric and magnetic excitation of matter; the latter is set proportional to the electric and magnetic force and , which acts upon the unit charges which is co-moving with matter.

We want to consider and in this paragraph as being (for a certain material point) dependent on velocity and time, although we reserve us the right to remove these confinements later.

To find the momentum density on the basis of relation (18), we calculate the quantities

(31a)

From (30) it follows

Since the two other terms in (31) are vanishing according to (31), then relation (18) gives

(32)

as the value of the electromagnetic momentum density.

Now the question arises, whether this value at the same time satisfies the condition (18a)

According to (29), it is

From (30) it also follows

Due to the known identity

it will be seen, that expression (32) for the momentum density really satisfies condition (18a).

Now from (19), the value of the energy density follows

(33)

which one can also write

(33a)