- #1

Imagine

_{4}and O

_{3}are energy density vectors, and R

_{p}is momentum density value.

Could I write:

O

_{4}= ( O

_{3}, icR

_{p})

and therefore

(O

_{4})

^{2}= (O

_{3})

^{2}- (cR

_{p})

^{2}

where (O

_{4})

^{2}is invariant under Lorentz transformation.

The point here, from what I learned from preceding posts, is to write something like:

div4(O

_{4}) = div3(O

_{3}) +

^{dRp}/

_{dt}(partial)

Here,

R

_{p}has

^{(kg-m/s)}/

_{(m3)}

and

O

_{4}and O

_{3}have

^{(kg-m/s)}/

_{(m2-s)}

I would physically interpret this like:

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Considering a small volume, T.

The rate at which the momentum T*R

_{p}, enclosed in the volume T increase with time is T*

^{dRp}/

_{dt}(partial)

The rate at which the enclosed momentum decrease with time is T*div3(O

_{3}) since the energy density, O

_{3}, is the momentum flowing out per unit time and per unit area.

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