User:Quondum/sandbox

Breakable gaps template

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subst

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GEM

Define

$\mu ={\frac {1}{c^{2}\varepsilon _{0}}}$ (EM)

$\mu _{\text{g}}=-{\frac {4\pi G}{c^{2}}}$ (GEM)

Lorenz gauge used for vector potentials

EM	Proposed	Mashhoon
$(\phi ,\mathbf {A} )$	$(\phi _{\text{g}},\mathbf {A} _{\text{g}})=(\phi _{\text{g}},4\mathbf {A} _{\text{g}}')$	$(\Phi _{\text{m}},\mathbf {A} _{\text{m}})=(-\phi _{\text{g}},-{\tfrac {c}{2}}\mathbf {A} _{\text{g}})$
$(\mathbf {E} ,\mathbf {B} )$	$(\mathbf {E} _{\text{g}},\mathbf {B} _{\text{g}})=(\mathbf {E} _{\text{g}},4\mathbf {B} _{\text{g}}')$	$(\mathbf {E} _{\text{m}},\mathbf {B} _{\text{m}})=(-\mathbf {E} _{\text{g}},-{\tfrac {c}{2}}\mathbf {B} _{\text{g}})$
$(\rho ,\mathbf {j} )$	$(\rho _{\text{g}},\mathbf {j} _{\text{g}})$	$(\rho _{\text{m}},\mathbf {j} _{\text{m}})=(\rho _{\text{g}},\mathbf {j} _{\text{g}})$
${\tfrac {1}{c^{2}}}\partial _{t}\phi +\nabla \cdot \mathbf {A} =0$	${\tfrac {1}{c^{2}}}\partial _{t}\phi _{\text{g}}+\nabla \cdot \mathbf {A} _{\text{g}}'=0$	(1.6) ${\tfrac {1}{c}}\partial _{t}\Phi _{\text{m}}+\nabla \cdot ({\tfrac {1}{2}}\mathbf {A} _{\text{m}})=0$
$\mathbf {E} =-\nabla \phi -\partial _{t}\mathbf {A}$	$\mathbf {E} _{\text{g}}=-\nabla \phi _{\text{g}}-\partial _{t}\mathbf {A} _{\text{g}}'$	(1.7) $\mathbf {E} _{\text{m}}=-\nabla \Phi _{\text{m}}-{\tfrac {1}{c}}\partial _{t}({\tfrac {1}{2}}\mathbf {A} _{\text{m}})$
$\mathbf {B} =\nabla \times \mathbf {A}$	$\mathbf {B} _{\text{g}}'=\nabla \times \mathbf {A} _{\text{g}}'$	(1.7) $\mathbf {B} _{\text{m}}=\nabla \times \mathbf {A} _{\text{m}}$
$\nabla \times \mathbf {E} +\partial _{t}\mathbf {B} =0$	$\nabla \times \mathbf {E} _{\text{g}}+\partial _{t}\mathbf {B} _{\text{g}}'=0$	(1.8) $\nabla \times \mathbf {E} _{\text{m}}+{\tfrac {1}{c}}\partial _{t}({\tfrac {1}{2}}\mathbf {B} _{\text{m}})=0$
$\nabla \cdot \mathbf {B} =0$	$\nabla \cdot \mathbf {B} _{\text{g}}'=0$	(1.8) $\nabla \cdot ({\tfrac {1}{2}}\mathbf {B} _{\text{m}})=0$
$\nabla \cdot \mathbf {E} =c^{2}\mu _{0}\rho$	$\nabla \cdot \mathbf {E} _{\text{g}}=c^{2}\mu _{\text{g}}\rho _{\text{g}}$	(1.9) $\nabla \cdot \mathbf {E} _{\text{m}}=-c^{2}\mu _{\text{g}}\rho _{\text{m}}$
$\nabla \times \mathbf {B} -{\tfrac {1}{c^{2}}}\partial _{t}\mathbf {E} =\mu _{0}\mathbf {j}$	$\nabla \times \mathbf {B} _{\text{g}}'-{\tfrac {1}{c^{2}}}\partial _{t}\mathbf {E} _{\text{g}}=\mu _{\text{g}}\mathbf {j} _{\text{g}}$	(1.9) $\nabla \times ({\tfrac {1}{2}}\mathbf {B} _{\text{m}})-{\tfrac {1}{c}}\partial _{t}\mathbf {E} _{\text{m}}=-c^{2}\mu _{\text{g}}{\tfrac {1}{c}}\mathbf {j} _{\text{m}}$
$\nabla \cdot \mathbf {j} +\partial _{t}\rho =0$	$\nabla \cdot \mathbf {j} _{\text{g}}+\partial _{t}\rho _{\text{g}}=0$	$\nabla \cdot \mathbf {j} _{\text{m}}+\partial _{t}\rho _{\text{m}}=0$
$\mathbf {F} =q(\mathbf {E} +\mathbf {v} \times \mathbf {B} )$	$\mathbf {F} =m(\mathbf {E} _{\text{g}}+\mathbf {v} \times \mathbf {B} _{\text{g}})$	(1.11) $\mathbf {F} =m(-\mathbf {E} _{\text{m}}-{\tfrac {2}{c}}\mathbf {v} \times \mathbf {B} _{\text{m}})$
$\mathbf {S} ={\frac {1}{\mu _{0}}}\mathbf {E} \times \mathbf {B}$	$\mathbf {S} ={\frac {1}{\mu _{\text{g}}}}\mathbf {E} _{\text{g}}\times \mathbf {B} _{\text{g}}$	(1.17) $\mathbf {S} ={\frac {2}{c\mu _{\text{g}}}}\mathbf {E} _{\text{m}}\times \mathbf {B} _{\text{m}}$

rounding

test of template:physconst (trailing zeros)

137.03600

M(¹²C) ≈ 12.00000×10⁻³ kg⋅mol⁻¹

line breaking

test of template:su/sandbox

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_{bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb}⁠XXXXXXXXXXXXXXXXXXXXXXXXXXXXXX

XXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX⁠^{bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb}
_{bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb}⁠XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX

XXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX⁠^{bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb}
_{bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb}⁠XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX

test of template:tmath

plainAAAAAAAAAAAAAAAAAAAAAA XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX$zzzzzzzzzzzzz$XXXXXXXXXXXXXXXXXXXXXXXX

NoBreakAAAAAAAAAAAAAAAAAAAA XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX⁠$zzzzzzzzzzzzz$⁠XXXXXXXXXXXXXXXXXXXXXXXX

zwjAAAAAAAAAAAAAAAAAAAAAAAA XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX‍$zzzzzzzzzzzzz$‍XXXXXXXXXXXXXXXXXXXXXXXX

tmathAAAAAAAAAAAAAAAAAAAAAA XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX⁠$zzzzzzzzzzzzz$⁠XXXXXXXXXXXXXXXXXXXXXXXX

reference combining

Variation 1

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Variation 2

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Variation 3

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Variation 4

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