ψ=12μoB2=−12εoE2
∂ψ∂t=12μo∂B2∂t=−εo2∂E2∂t
If ψ=eiwt, just the time component to represent time itself.
∂ψ∂t=iωeiωt=12μo∂B2∂t=−εo2∂E2∂t
ωeiωt=−i12μo∂B2∂t=iεo2∂E2∂t
ωeiωt=−iii12μo∂B2∂t=iiiεo2∂E2∂t
ωeiωt=12μo∂B2∂it=−εo2∂E2∂it
where it is the orthogonal charge-time component postulated in the post "Temperature, Space Density And Gravity".
∵ω=2πf=2πcλt
eiωt=λt4πμoc∂B2∂it=−λtεo4πc∂E2∂it
c=1√μoεoZo=√μoεo
eiωt=λt4πμoc∂B2∂it=−λtεo4πc∂E2∂it
eiωt=λt4π1Zo∂B2∂it=−λt4πZo∂E2∂it
Let it=tc,
eiωt=λt4π1Zo∂B2∂tc=−λt4πZo∂E2∂tc
or,
eiωt=λt2πc∂ψ∂tc
which requires,
1=λt2πc.ω
that is always true.
→t2=→t2c+→t2g
This implies,
eiωctc=1√2eiωt.e−iπ/4=1√2ei(ωt−π/4)
eiωgtg=1√2eiωt.eiπ/4=1√2ei(ωt+π/4)
and of course,
eiwgtg=ieiwctc
There is no reason not be believe that,
ωg=ωc=ω by symmetry.
And so,
∂∂ω{eiωctc}=∂∂ω{eiωtc}=∂∂ω{1√2eiωt.e−iπ/4}
which implies,
tc=1√2t.e−iπ/4
Generalizing, we have
tg=1√2t.e+iπ/4
1√2|t|=|tc|=|tg|
Which makes us behind tc and tg in the absolute sense. tc lag t by π4 and tg leads t by π4 in phase. Time as a wave is a natural vector.