Maxwell's equations in tensor form

we know that the action
S=ba(mcdsecAμdxμ)

and since δS=0$\delta S = 0$, we can rewrite the above equation as
δS=ba(mcδdsecδ(Aμdxμ))

δS=ba(mcdδsec(dxμδAμ+Aμδ(dxμ))

δS=ba(mcdδsec(dxμδAμ+Aμdδxμ)

using ds=(dxμdxμ)12$ds = (dx_{\mu}dx^{\mu})^{\frac{1}{2}}$, we can calculate that δds=vμδ(dxμ)$\delta ds = v_{\mu}\delta(dx_{\mu})$ i.e
\ dδs=vμdδxμ$d \delta s = v_{\mu}d \delta x_{\mu}$. We can substitute this term in the previous equation which therefore becomes
δS=ba(mcvμdδxμec(dxμδAμ+Aμdδxμ)

We can rewrite vμdδxμ=d(vμδxμ)δxμdvμ$v_{\mu}d \delta x_{\mu} = d (v_{\mu} \delta x_{\mu}) - \delta x_{\mu}dv_{\mu}$
\ similarly Aμdδxμ=d(Aμδxμ)δxμdAμ$A_{\mu} d \delta x^{\mu} = d(A_{\mu}\delta x^{\mu}) - \delta x^{\mu}dA_{\mu}$
substituting the above results in the previous equation leads to
δS=ba(mc(d(vμδxμ)δxμdvμ)ec(dxμδAμ+d(Aμδxμ)δxμdAμ)

δS=ba(mcd(vμδxμ)ecd(Aμδxμ))+ba(mcδxμdvμ)ec(dxμδAμδxμdAμ)

let us rewrite δAμ$\delta A_{\mu}$ as dAμdxνδxν$\frac{dA_{\mu}}{dx^{\nu}}\delta x^{\nu}$
and similarly dAμ$dA_{\mu}$ as dAμdxνdxν$\frac{dA_{\mu}}{dx^{\nu}}dx^{\nu}$
correcting for the above changes in the equation above gives
δS=ba(mcδxμdvμ)ec(dxμdAμdxνδxνδxμdAμdxνdxν)

δS=ba(mcδxμdvμ)ec(dxνdAνdxμδxμδxμdAμdxνdxν)

δS=baδxμ((mcdvμ)ec(dxνdAνdxμdAμdxνdxν))

and since δS=0$\delta S = 0$
baδxμ((mcdvμ)ec(dxνdAνdxμdAμdxνdxν))=0

mcdvμec(dxνdAνdxμdAμdxνdxν)=0

mcdvμ=ec(dxνdAνdxμdAμdxνdxν)

mcdvμ=ec(dAνdxμdAμdxν)dxν

dividing the whole equation by ds$ds$ and remembering that dxμds=vμ$\frac{dx_{\mu}}{ds} = v_{\mu}$, we can rewrite the above equation as
mcdvμds=ec(dAνdxμdAμdxν)dxνds

mcdvμds=ec(dAνdxμdAμdxν)vν

we now define
Fμν=dAνdxμdAμdxν

mcdvμds=Fμνvν

We can understand from the construction of Fμν$F_{\mu \nu}$ that it is an antisymmetric matrix i.e Fνμ=Fμν$F_{\nu \mu} = -F_{\mu \nu}$

S=ba(mcdsecAμdxμ)

specifically, let’s look at Aμdxμ$A_{\mu}dx^{\mu}$. we know that Aμ=(ϕ/c,A⃗ )$A_{\mu} = (\phi /c,\vec{A})$ and that dxμ=(cdt,dr⃗ )$dx_{\mu} = (cdt,-d\vec{r})$
therefore Aμdxμ=ϕdtA⃗ dr⃗ $A_{\mu}dx^{\mu} = \phi dt - \vec{A}\cdot d\vec{r}$
S=ba(mcdsec(ϕdtA⃗ dr⃗ ))

S=ba(mcdsecϕdt+ecA⃗ dr⃗ ))

we know that ds=cdτ$ds = cd\tau$ and that dτ=dtγ$d\tau = \frac{dt}{\gamma}$ substituting these changes changes the above equation to
S=ba(mc2dtγecϕdt+ecA⃗ dr⃗ ))

S=ba(mc2dtγecϕdt+ecA⃗ dr⃗ dtdt))

where
L=mc21γecϕ+ecA⃗ dr⃗ dt

L=mc21γecϕ+ecA⃗ V⃗

we can get the equations of motion from
LrddtLr˙=0

Lr=ecϕ+ec⃗ (A⃗ V⃗ )

⃗ (A⃗ V⃗ )=V⃗ ×(⃗ ×A⃗ )A⃗ (⃗ V⃗ )

since A⃗ (⃗ V⃗ )=0$\vec{A}(\vec{\nabla}\cdot\vec{V}) = 0$, we can rewrite the earlier equation as
Lr=ecϕ+ecV⃗ ×(⃗ ×A⃗ )

similarly
Lr˙=r˙(mc21γecA⃗ V⃗ )

Lr˙=r˙(mc21v2c2ecA⃗ V⃗ )

Lr˙=γmV⃗ +ecA⃗

going back to
LrddtLr˙=0

ecϕ+ecV⃗ ×(⃗ ×A⃗ )ddt(γmV⃗ +ecA⃗ )=0

ecϕ+ecV⃗ ×(⃗ ×A⃗ )dp⃗ dt+ecdA⃗ dt=0

where p⃗ =γmV⃗ $\vec{p}=\gamma m\vec{V}$
dp⃗ dt=ecϕ+ecdA⃗ dt+ecV⃗ ×(⃗ ×A⃗ )

dp⃗ dt=e(1cϕ+1cdA⃗ dt)+ecV⃗ ×(⃗ ×A⃗ )

we’re defining
E⃗ =1cϕ1cdA⃗ dt
and
B⃗ =⃗ ×A⃗

dp⃗ dt=eE⃗ +ecV⃗ ×B⃗

if we assume Aμ=(ϕ,A⃗ )$A_{\mu} = (\phi,\vec{A})$,
E⃗ =ϕ1cdA⃗ dt

Animation using GNUPlot

Animation using GNUPlotI've been trying to create an animation depicting a quasar spectrum moving across the 5 SDSS pass bands with respect to redshift. It is important to visualise what emission lines are moving in and out of bands to be able to understand the color-redshift plots and the changes in it.
I've tried doing this using the animate function in matplotlib, python but i wasn't able to make it work - meaning i worked on it for a couple of days and then i gave up, not having found solutions for my problems on the internet.
And then i came across this site, where the gunn-peterson trough and the lyman alpha forest have been depicted - in a beautiful manner. And this got me interested in using js and d3 to do the animations and make it dynamic - using sliders etc.
In the meanwhile, i thought i'd look up and see if there was a way to create animations in gnuplot and whoopdedoo, what do i find but nirvana!

In the image, you see 5 static curves and one dynam…

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I'm talking about MOOCs because one of my new year resolutions is to take online courses, atleast 2 per semester (6 months). And I've chosen the following two courses on edX - Analyzing Big Data with Microsoft R Server and Data Science Essentials for now. I looked at courses on Coursera but I couldn't find any which was worthy and free. There are a lot more MOOC providers out there but let's start here. And I feel like the two courses are relevant to where I …

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I am not going to give you a tl;dr version of the talk because it is a talk that I believe everyone should watch, that everyone should learn from. Instead, I am going to give my own parallel-ish views on programmers and programming.
As pointed out in the talk, there are mythical creatures in the software development industry who are revered as gods. Guido Van Rossum, the creator of Python, was given the title Benevolent Dictator For Life (BDFL). People flock around the creators of popular languages or libraries. They are god-like to most programmers and are treated like gods. By which, I mean to say, we assume they don't have flaws. That they are infallible. That they are perfect.
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