Featured Comments: Week of 2013 April 21

There was one post that got a handful of comments this past week, so I'll repost most of those.

Review: Fuduntu 2013.2

Reader Tran Mere asked, "Was there ever really big community behind Fuduntu or was it mostly just one man show?"
Commenter Andrew Wyatt, who created Fuduntu and is soon to retire from the project, replied, "There is a team of 20 people working on Fuduntu from developers to support to marketing, and we estimated having close to 150K users until we announced the project being EOL in September."
An anonymous reader clarified, "New name to Fuduntu will be FuSE linux, based on openSUSE. We'll see, but openSUSE is a great base, better than Fedora IMO".

Thanks to all those who commented on that post. This coming week, I don't have anything particularly planned because I anticipate this week will be quite busy. After all, the semester is drawing to a close rather quickly. Anyway, if you like what I write, please continue subscribing and commenting!

Thoughts on Typesetting

In 2012 IAP, I taught myself how to use LaTeX by typesetting the 8.033 — Relativity lecture notes. I also did this so that the lecturer I had that semester and the lecturer for the following semester would both have these notes at their disposal; for the record, the former is on sabbatical this academic year, while the latter did indeed use it when he taught the class this past fall. I needed to teach myself LaTeX because I was going to be taking 8.13, which I did this past fall, and that requires LaTeX use for papers (and recommends Beamer for presentations as well). That said, recently I was hanging out with some friends and a couple of them suggested that LaTeX isn't really necessary as far as producing scientific papers goes, because Microsoft Office Word 2013 has an advanced enough equation editor that it can essentially replace LaTeX, especially as it now recognizes basic LaTeX syntax. At first, given how much I had used LaTeX (and also given some of my past negative feelings toward Microsoft), I felt a little defensive. But then I realized I should give the comparison a fairer shot, so I decided to see if I could try to replicate one of my PRL-formatted LaTeX-typeset papers in LibreOffice Writer. Follow the jump to see my findings.

Magnetic Field Tensor and Continuum Optical Modes

There is actually a third thing in this post, but I'm not going to list that in the title. Also, the two things in the title are separate and unrelated. Follow the jump to see it all.

Review: Fuduntu 2013.2

I haven't checked out Fuduntu in over a year. I wasn't particularly planning to do so either, because I wasn't exactly expecting huge changes. But then I saw some news that changed my mind.

Welcome Screen + Main Menu

Fuduntu, as regular readers know, is an independent distribution that maintains GNOME 2 essentially as-is and uses the RPM package format, so it can sometimes use third-party packages developed for Fedora. Recently, though, there was a discussion among Fuduntu developers that culminated in the developers announcing a feature freeze for Fuduntu along with support ending by this September, along with the lead developer Andrew Wyatt (also known as FEWT) announcing his official resignation (though he may still unofficially consult with the project from time to time) from the project after support ends. The main reasons for this were that maintaining GNOME 2, keeping Fuduntu independent from Fedora while maintaining support for RPM, and having Andrew Wyatt work way too hard on this were all unsustainable; the remaining developers may decide to turn Fuduntu into something else entirely, in which case it would be once again based on another distribution (a likely candidate is openSUSE, which is interesting because I am not aware of any major distributions based on openSUSE at all), and it would probably need a new DE (perhaps the Consort DE from SolusOS, though that is purely speculation on my part). In any case, I am reviewing Fuduntu because this will certainly be the last such review I can do of Fuduntu in its current incarnation, and may be my last review of it ever.

For this final review, I tested Fuduntu using a live USB made with MultiSystem. Follow the jump to see what it's like and how it will be remembered.

Featured Comments: Week of 2013 April 14

There were two posts this past week that got a couple comments between them, so I will repost comments from one of those.

Review: Manjaro Linux 0.8.5 Xfce

Reader crabdog said, "Thanks for the write up. I'm a long time Manjaro fan and have been using it since its early days. I previously always had a full install of it on my laptop alongside windows 7 and usually another linux distro but I had some problems with 0.8.4 and ended up with Netrunner and Zorin OS on the laptop. I'm waiting for one of those to break so I have an excuse to put Manjaro back on ^^".
Commenter smakked had this clarification: "Arch devs have never shipped Cinnamon it is in the AUR but never been done by the Devs themeselves, and yes you are right Cinnamon uses old libraries that are not compatible with 3.8".
Reader Ade Malsasa Akbar had this bit of support: "What I like about Arch is BIG+SKILLFUL COMMUNITY and its rolling release system (but I don't know yet what is it). But my problem is installing Arch via console, I can't. With GUI, now I can try Arch first. I am curious with pacman also. Thank you for posting this review. I save it."

Thanks to all those who commented on this past week's posts. This coming week, I will have a review out; a hint as to what it might be is that this might be the last such review I do of it (but certainly not the last review I will ever do, in case that sounded confusing). Anyway, if you like what I write, please continue subscribing and commenting!

Review: Manjaro Linux 0.8.5 Xfce

Main Screen + Xfce Menu

It has been a while since I have reviewed Manjaro Linux. It has also been a while since I have done a normal distribution review, and I have a long weekend now, so this seems like the ideal time.

Manjaro Linux used to basically be a dressed-up version of Arch. It has since matured a bit, in that now it depends only on its own repositories, though it does allow access to the Arch User Repository (AUR). One of the big new features is a graphical installer adapted from Debian-based Linux Mint. Other features include the usual round of application upgrades and such.

I tried Manjaro Linux on a live USB made with MultiSystem. Follow the jump to see what it's like.

Harmonic Oscillator from Fields not Potentials

I finally started writing my paper for 8.06 yesterday. Before that, though, I had asked a couple questions about the topic to my UROP supervisor, whose primary area of expertise is actually in QED and Casimir problems. I was asking him why the book The Quantum Vacuum by Peter Milonni uses the magnetic potential $\vec{A}$ instead of the electromagnetic fields $\vec{E}$ and $\vec{B}$ to expand in Fourier modes and derive the harmonic oscillator Hamiltonian. He said that is just a matter of choice, and in fact the same derivation can be done using the fields rather than the potential; moreover, he encouraged me to try this out for myself, and I did just that. Lo and behold, the right answer popped out by modifying the derivation in that book to use the fields and the restrictions of the Maxwell equations instead of the potential and the Coulomb gauge choice; follow the jump to see what it looks like. I'm going to basically write out the derivation in the book and show how at each point I modify it.

Featured Comments: Week of 2013 April 7

There was one post this past week that got one comment, so I will repost that.

Long-Term Review: Chakra 2013.02 "Benz"

An anonymous reader asked, "Is there any reason not to use pacman -Syyu instead of pacman -Syy followed by pacman -Syu (or even instead of pacman -Syy followed by pacman -Su)?"

Thanks to that person for posting that. This coming week, I have holidays on Monday and Tuesday, giving me time to relax and perhaps post a distribution review. Other than that, I will probably post another thing about physics as well. Anyway, if you like what I write, please continue subscribing and commenting!

Charge Conservation and Legendre Transformations

As a follow-up (sort of, but not exactly) to my previous post on the matter, I would like to post a few updates and new questions, using Einstein summation throughout for convenience. The first has to do with why $p^{\mu} = \int T^{(0, \mu)} d^3 x$ is a Lorentz-contravariant vector. Apparently Noether's theorem says that if some Noether current $J^{\mu}$ generates a symmetry and satisfies \[ \partial_{\mu} J^{\mu} = 0 \] then the quantity \[ q = \int J^{(0)} d^3 x \] called the Noether charge is Lorentz-invariant and conserved. The first is not easy to show, but apparently some E&M textbooks do it for the example of electric charge. The second is fairly easy to show: using the condition that $\int \partial_{j} J^{j} d^3 x = \int_{\partial \mathbb{R}^3} J^{j} d\mathcal{S}_{j} = 0$ (from the divergence theorem applied to all of Euclidean space) in conjunction with $\partial_{\mu} J^{\mu} = 0$, the result $\dot{q} = 0$ follows.

As an example, let us consider the generator of rotations and Lorentz boosts for a general energy distribution: that is the 3-index angular momentum tensor \[ M^{\mu \nu \sigma} = x^{\mu} T^{\nu \sigma} - x^{\nu} T^{\mu \sigma} .\] Given that $\partial_{\nu} T^{\mu \nu} = 0$ then $\partial_{\sigma} M^{\mu \nu \sigma} = (\partial_{\sigma} x^{\mu})T^{\nu \sigma} + x^{\mu} \partial_{\sigma} T^{\nu \sigma} - (\partial_{\sigma} x^{\nu})T^{\mu \sigma} - x^{\nu} \partial_{\sigma} T^{\mu \sigma}$ $= \delta_{\sigma}^{\; \mu} T^{\nu \sigma} - \delta_{\sigma}^{\; \nu} T^{\mu \sigma} = T^{\nu \mu} - T^{\mu \nu} = 0$. Therefore the 3-index angular momentum is a proper Noether current. Its corresponding conserved charge is the 2-index angular momentum integrated over spatial directions: \[ L^{\mu \nu} = \int M^{(\mu \nu, 0)} d^3 x \] (except for perhaps a sign because $M^{\mu \nu \sigma}$ is antisymmetric in its indices) and it should be easy now to show that $\dot{L}^{\mu \nu} = 0$, which is cool. The only remaining question I have is whether it is more correct to say $L^{\mu \nu} = x^{\mu} p^{\nu} - x^{\nu} p^{\mu}$ where $p^{\mu} = \int T^{(\mu, 0)} d^3 x$ as before or if the better definition is the one integrating $M^{(\mu \nu, 0)}$ over space.

Now I have an even bigger question looming ahead of me though. The Noether current generating spacetime translational symmetry is exactly the stress-energy tensor derivable as the Legendre transformation of the Lagrangian. The term involving the conjugate momenta is easy, but the term involving the Lagrangian is confusing. For a scalar field $\phi$ (and for a vector field this is easily replaced with $A^{\sigma}$), what I have seen is \[ T^{\mu \nu} = \frac{\partial \mathcal{L}}{\partial (\partial_{\mu} \phi)} \partial^{\nu} \phi - \mathcal{L} B^{\mu \nu} .\] The problem is that the tensor $B^{\mu \nu}$ seems to depend on either the field $\phi$ used or on the notation consistently used. Sometime $B^{\mu \nu} = \delta^{\mu \nu}$, while other times $B^{\mu \nu} = \eta^{\mu \nu}$. I'm not really sure which it is supposed to be, as sometimes for scalar fields $B = \delta$ is used, while for the electromagnetic field $B = \eta$ is used, and sometimes the notation isn't even that consistent. The issue is that either one would properly specify a Lorentz-contravariant 2-index tensor, but only one of them actually defines the translational symmetry Noether current properly. Which one is it? The issue appears to be akin to the problem of two grammatically correct sentences where one carries meaning and makes sense while the other makes no sense at all (e.g. "colorless green ideas sleep furiously").

Long-Term Review: Chakra 2013.02 "Benz"

I did this long-term review on my normal UROP desktop computer with the 64-bit edition of the OS. Follow the jump to see how it fared. Also do note that there are more days logged because I intend to use it for about 60-80 full hours of work, which is the equivalent of 7-10 full days in the summer, though now I am working on a part-time basis as classes have started.