- #1
Imagine
Posing that O4 and O3 are energy density vectors, and Rp is momentum density value.
Could I write:
O4 = ( O3, icRp )
and therefore
(O4)2 = (O3)2 - (cRp)2
where (O4)2 is invariant under Lorentz transformation.
The point here, from what I learned from preceding posts, is to write something like:
div4(O4) = div3(O3) + dRp/dt (partial)
Here,
Rp has (kg-m/s)/(m3)
and
O4 and O3 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*Rp, 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(O3) since the energy density, O3, is the momentum flowing out per unit time and per unit area.
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Could I write:
O4 = ( O3, icRp )
and therefore
(O4)2 = (O3)2 - (cRp)2
where (O4)2 is invariant under Lorentz transformation.
The point here, from what I learned from preceding posts, is to write something like:
div4(O4) = div3(O3) + dRp/dt (partial)
Here,
Rp has (kg-m/s)/(m3)
and
O4 and O3 have (kg-m/s)/(m2-s)
I would physically interpret this like:
---------------------------------------
Considering a small volume, T.
The rate at which the momentum T*Rp, 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(O3) since the energy density, O3, is the momentum flowing out per unit time and per unit area.
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