Electromagnetism Basics in 1 or 2 Dimensions

This was a post that I had been thinking of doing for a while, but I couldn't get around to it until now. A lot of introductory electricity & magnetism problems constrain charges to only move in 1 or 2 dimensions, but in reality the constraint existed within a 3-dimensional space. I thought that would cover the bases for electrodynamics in 1 or 2 dimensions, but then I saw that in cylindrical coordinates, the order-0 multipole moment outside a line charge is $\phi \propto \ln(r)$ as opposed to $\phi \propto \frac{1}{r}$. That made me realize that there is in fact a distinction among 1 or 2 or 3 dimensions. In all of the following, I will make use of the conventions and relations \[ x^{\mu} = (ct, x, y, z) \\ \partial_{\mu} = \left(\frac{1}{c} \frac{\partial}{\partial t}, \frac{\partial}{\partial x}, \frac{\partial}{\partial y}, \frac{\partial}{\partial z}\right) \\ \eta_{\mu \nu} = \begin{bmatrix} -1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{bmatrix} \\ F^{\mu \nu} = \begin{bmatrix} 0 & E_x & E_y & E_z \\ -E_x & 0 & B_z & -B_y \\ -E_y & -B_z & 0 & B_x \\ -E_z & B_y & -B_x & 0 \end{bmatrix} \\ \partial_{\nu} F^{\mu \nu} = \frac{4\pi}{c} J^{\mu} \\ \epsilon_{\mu \nu \zeta \xi} \partial^{\nu} F^{\zeta \xi} = 0 \\ \mathbf{F} = q\left(\mathbf{E} + \frac{\mathbf{v}}{c} \times \mathbf{B}\right) \] in 3 dimensions, with Einstein summation and CGS implied (with more on that last point nearer to the end), with Latin indices representing only spatial components, and with Greek indices representing spacetime components. Also note that the fully antisymmetric tensor $\epsilon$ has $n$ Latin indices in $n$ spatial dimensions and $n+1$ Greek indices in $n+1$ spacetime dimensions; for example, in 2 spatial dimensions, the antisymmetric tensor over only space looks like $\epsilon_{ij}$, while over spacetime it looks like $\epsilon_{\mu \nu \xi}$, and I will frequently switch between the two as needed. Follow the jump to see what happens.


Gibbs Entropy and Two-Level Systems

Today, I was browsing through the MIT news page when I saw this article about how two mathematicians claim to have disproved the notion of negative temperature. My heart sank, because one of the coolest things I remembered learning in 8.044 — Statistical Physics I was the notion of negative temperature existing, being hotter than hot, and being experimentally realizable. I also became confused when the article referred to Gibbs entropy, because the definition I thought was being used for Gibbs entropy was \[ S = -\sum_j p_j \ln(p_j) \] which is exactly equivalent to the Boltzmann entropy \[ S = \ln(\Omega) \] where \[ p_j = \frac{1}{\Omega} \] in the microcanonical ensemble. I figured this would mean that the Gibbs entropy would exactly reproduce negative temperature results in systems with bounded energies such as two-level systems. I wasn't able to read the most recent paper as discussed in the news article, because it is behind a paywall, but I was able to read this article by the same authors, which appears to lay the foundational ideas behind the most recent paper. It seems like on my end, the misconception appears to hinge on what one would call the Gibbs entropy. The formula \[ S = \ln(\Phi) \] appears to be the correct one for the Gibbs entropy, where $\Phi$ is the total number of states with energy not greater than $E$ and $\Omega = \frac{d\Phi}{dE}$ is the number of states with energy exactly equal to $E$ quantum mechanically (or the number of states with energy within a sufficiently small neighborhood of $E$ in the classical limit). With this in mind, follow the jump to see how this might work for a two-level system and explore the other implications of this new definition of statistical entropy. (UPDATE: Note that in all of this, $k_B = 1$.)


Featured Comments: Week of 2013 December 15

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

Review: Linux Mint 16 "Petra" Cinnamon + MATE

Reader Michael Freeman said, "Compiz doesn't work in Petra? It works fine in Maya LTS with MATE 1.6. What version of Compiz comes with Petra? Do you have all the needed packages installed?"
An anonymous commenter had this to say: "I must say that I am surprised by your assessment of Cinnamon 2.0. I have Petra installed and have been using it as my daily driver since the day it was released. I find it to be incredibly stable and not at all laggy, but rather snappy. Of course, everyone's hardware is different. Give it a go in a VM if you have the resources, you may find you like it. Cheers!"
Another anonymous reader followed up on the first comment: "Compiz worked fine for me on petra 32bit. First of all u have to install all the packages needed. Then you have to set an autostart entry like 'cinnamon --replace' and change the default desktop manager from 'marco' to 'compiz' using the dconf editor. If you're using live session without a persistance file to save settings, you have to install and run it manually every time you boot. check here - http://community.linuxmint.com/tutorial/view/1298".

Thanks to all those who commented on that post. I'm at home for break now, but I don't have any posts particularly planned. Anyway, if you like what I write, please continue subscribing and commenting!


Review: Linux Mint 16 "Petra" Cinnamon + MATE

Cinnamon: Main Menu
This is the second review that I'm doing at the moment. Linux Mint 16 "Petra" came out in MATE and Cinnamon guises recently, so as a fan of Linux Mint, I'll be reviewing those now. I tried each edition separately on a live USB made with UnetBootin. Follow the jump to see what each is like.


Done with 7th Semester!

It finally happened! The end of the semester rushed in and washed over just as quickly. My classes — 8.07 — Electromagnetism II, 8.09 — Classical Mechanics III, 8.333 — Statistical Mechanics I, and 14.12 — Economic Applications of Game Theory — were all together a bit more challenging than I anticipated. On top of that, I worked a lot on my UROP, and of course I had to submit graduate school applications by last weekend. Thankfully, my classes and graduate school applications are done. Now I can go home, relax, enjoy the company of family and friends...and probably work on my UROP. Of course, I'll be continuing my UROP over IAP, but I hope to be transitioning into a new project then, so I hope to get a fair amount of my current project done during the break. Happy holidays everyone!


Featured Comments: Week of 2013 December 8

There was one post that got a couple of comments, so I'll repost both of those.
Review: openSUSE 13.1 GNOME
Reader Kaf Shiel said, "Thanks for the excellent review. I tried the live usb openSUSE 13.1 RC with the Gnome desktop but it wouldn't boot to the desktop. Then I found out online that it was a bug affecting more users. After reading your review I'll give it another go. I have a friend that uses openSUSE and he swears by it so I'm curious, although I think that it's not for distro hoppers. It's more like a full install commitment. I use Ubuntu Studio (I'm an amateur musician) and Voyager (both have the Xubuntu engine) in both my workstation and netbook because I really love the Xfce desktop but I like to test other distros for fun (tested Tails 0.22 today). I love your blog and understand that your academic life won't give you enough time to write every week but when you post something new I always come here to read. Merry Christmas!"
Commenter alcalde had this to say: "I wish reviewers would stop reviewing the live CDs. That's Ubuntu thinking, and OpenSUSE is not Ubuntu. The Live CDs are not the default or preferred installation medium and are not tested to the same degree as the DVD installer, nor are they even close to being the most downloaded versions of OpenSUSE. They're presented for convenience only. When you use these live CDs you do not get the full OpenSUSE install experience. Unlike the CDs, the DVD offers many more options, including the ability to customize the install by choosing which packages to (not) install. Calc is included in a normal install of OpenSUSE; this is another artifact of trying to squeeze OpenSUSE onto a live disk. There are some other differences, including the DVD installing Flash during the update process, being able to update before being dropped into the desktop, etc. Why would one want to recommend GNOME for newbies? Far and away KDE is going to most resemble what they're used to already."

Thanks to both of those people for commenting on that post. I have another review written up that will be out this week. In addition, this week is my week of final exams, so I'll be writing a reflection on the semester at the end of that. Anyway, if you like what I write, please continue subscribing and commenting!


Review: openSUSE 13.1 GNOME

GNOME Activities Overview
I haven't been able to write up any reviews recently because of the confluence of classes, UROP, and graduate school applications. Now my classes are sort of wrapping up, in that my last problem sets were due yesterday (the publication date is after the date of writing), so I have a little time to relax and do some reviews. The first is openSUSE 13.1 GNOME. I've reviewed openSUSE before a number of times, so I won't try to introduce it again. I tried the live version of the GNOME edition on a live USB made with MultiSystem. Follow the jump to see what it's like.


Classes, UROP, and Applications Galore

I know I haven't posted here in a while. That's because this is around the time that a lot of graduate school applications are due, so I've been busy getting those done. At the same time, my UROP has been getting busier as I'm trying to wind down my current project, and classes are of course ever-present in the background. Anyway, my applications and classes will be done in about 3 weeks, so at that time I should have more time to write here. Meanwhile, happy Thanksgiving!


Business Insider and Women in Physics

I wasn't planning on posting anything else in particular this week, but a friend of mine shared this, and it really got my goat. I'd actually ask you not to click on it, because this article appears to be more like clickbait than anything else (and thats the shameful part for a site as well respected as Business Insider); essentially its premise is that women will be more welcome on Wall Street if some really "sexy" female physicists were to stop doing physics and enter finance.
Why? Do you really need to trash the self-confidence of a woman wanting to enter male-dominated fields like physics or finance by telling her that she needs to be "sexy" to be well-respected? Do you really need to make women who want to get into physics insecure about their career choices by saying that they're "pretty" so they should leave physics and get into finance? While I'm generally OK (more specifically, I have mixed feelings) with finance organizations trying to convince up-and-coming physicists to enter finance, these are clearly not up-and-coming physicists but are very well-established in their fields, so they likely aren't going to leave anytime soon. It takes some chutzpah to try to draw these women into finance, and it is doubly insulting to suggest they do so because they are "sexy". The first sentence of the article says, "Lately, there has been a lot of talk about the lack of high ranking women at top firms." Hmm...I wonder why that is...oh wait, maybe groups like Business Insider are part of the problem.


Economics and Empiricism

I know it has been a while since I've posted anything here. That's because I had been busy until the end of last month with studying for the Physics GRE. Since then, my life has been dominated by a combination of classes, my UROP, and graduate school applications. That also means that for the next several weeks, posts here will once again be fairly infrequent. That said, I read an article today in the New York Times by economist Raj Chetty, who would like to convince readers that economics is a science like any of the natural sciences. Having seen such arguments poorly presented in my economics textbooks, I figured this would make for a nice quick rant. But then as I thought about it more, I realized that this issue is actually a lot more subtle than I originally imagined.

As a physics student, I don't know if I can ever shake the gut feeling that economics somehow will always be "mushier" in some way compared to the natural sciences. But I need to make sure that there is solid grounding for that feeling, or else I should be casting away that feeling as well. So why do I feel that economics is "mushier"?

Let's take the following sentence: "I’m troubled by the sense among skeptics that disagreements about the answers to certain questions suggest that economics is a confused discipline, a fake science whose findings cannot be a useful basis for making policy decisions." I'm sure there are people who believe that having multiple opinions and interpretations of even raw empirical data alone makes economics untrustworthy. I'm sure this thought may have crossed my mind at various points as well, but I realize this isn't why I feel economics is mushy. As I think about, I realize for example that after electroweak symmetry breaking (i.e. the reason why electromagnetic and weak interactions become identical at certain energy scales, but why at the scales we usually observe the photon is massless while the W and Z bosons are massive) was discovered, a few different explanations were posited for the underlying cause. One was the Higgs boson, and the other was technicolor. After the discoveries of the past two years, of course, it is safe to say the Higgs boson is a much more likely candidate than technicolor, but there was a decades-long gap between the theory and experiment. Clearly this is an instance in physics where before further experiments could be performed, two competing explanations were jockeying for attention in the physics community. So I can't say that economics is mushy because there are disagreements among economists in their interpretations and explanations of the same sets of data. So why do I feel that it is mushy?

It's likely because of what happened with Reinhart/Rogoff. From what I understand, Reinhart and Rogoff published an influential paper which posited that a country whose debt-to-GDP ratio pushes above 90% will quickly be plunged from economic growth into a recession (or worse if the starting conditions are worse). As it turns out, a graduate student found an error in the calculations that led to this conclusion and showed that in fact no such debt-to-GDP threshold ratio causing a sharp reversal of macroeconomic fortunes exists. As far as I can tell, rather than backing down, Reinhart and Rogoff have been pushing their findings harder than ever. So I may think economics is mushy because there seems to be little drive at the upper echelons to maintain scientific skepticism and admit errors as they happen, especially when it comes to macroeconomics. Granted, it took a long time after the first cosmic microwave background measurements came in for the steady-state theory to be cast out of cosmology, but it seems like especially in macroeconomics, this is a more prevalent problem than in the natural sciences.

In fact, the author of the article briefly touches on this, but proceeds to pretend that this is not the reason why people don't believe that economics is a science. Yes, the article does go through in pretty good detail what advances have been made in empirical microeconomics and econometrics that should earn economics the respect given to other sciences. And after having taken the class 14.03 — Microeconomic Theory and Public Policy and having learned there a little about empirical microeconomics and econometrics, I'm actually rather inclined to agree (as I actually learned some of the details of some of the examples in this article).

The issue is that when most news articles quote economists, it's usually in the context of macroeconomics, as macroeconomic activity will by definition affect the largest segment of the readership, as opposed to microeconomic moves taken by certain firms, labor groups, or municipalities. Macroeconomics is a very young field with not a whole lot of data as yet. Additionally, there is a lot of disagreement among macroeconomic theorists about how to interpret macroeconomic events/trends, and too many of them are acting more for political gain than for the sake of advancing the field (see: Reinhart/Rogoff). It's really cool when the LHC performs experiments to further probe the Higgs boson (i.e. science), but honestly, people will care a lot more if their federal income taxes change (i.e. macroeconomics), and such a change cannot be effected in a controlled environment (in relative contrast to the Higgs boson experiments). Regarding that last point, macroeconomic models are too unreliable compared to scientific models of macroscopic systems that economists would love to emulate, because they very frequently fail to predict the outcomes of certain economic events or enacted policies. So it's the combination of the fact that macroeconomics is unreliable and that its scholars have the very real power to personally gain from their models being correct potentially at the expense of other people's livelihoods (where I've emphasized that last point in contrast to natural sciences) that makes myself want to push economics away from the natural sciences.

But this isn't fair to microeconomics. So what's the solution? I would personally split microeconomics and macroeconomics much more. In any case, the author says that more and more research that even affects macroeconomic decisions is coming from empirical microeconomics. In that case, I would say that news outlets should devote more space to highlighting empirical research done in microeconomics that clearly affects people's lives, such as those highlighted in the article. And maybe farther in the future, all economics will basically be microeconomics, and macroeconomics will become what classical thermodynamics has become in relation to statistical mechanics: a bulk limit that is only obtainable under very specific conditions.


Featured Comments: Week of 2013 September 8

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

Featured Comments: Week of 2013 September 1

Reader Kaf Shiel said, "I tried Luna 2 last night but the desktop is dead (no point in clicking it at all) and the configuration of everything is not available (unless you really want to waste a few hours) also Planck is of no use at all as it is, since is just too basic and you can't configure anything on this OS without resorting to dConf and tons of work that don't really pay off... As for the comment that 'spend less time making it look and feel like i want to' i'm sorry but i like to do that, i like it personal... Distraction free? Nope! A dead desktop and a flintstones dock are bound to distract you a lot... It kinda gets in your nerves! Sorry but this one i have to "86" (cuisine chefs code). Best regards, Kaf".

Thanks to that commenter for that comment. This coming week, as with last week, I don't have any particular posts planned because of the business of the semester. Anyway, if you like what I write, please continue subscribing and commenting!


Featured Comments: Week of 2013 September 1

There was one post this week that got two comments, so I'll repost both of those.

Review: Elementary OS 2 "Luna"

Reader sgreen said, "and we need Elementary for ??. I know the developer just wants to keep busy. If there's anything that will ruin Linux it's this kind of crap. How many are in its user-base??"
An anonymous commenter disagreed: "I think the Elementary team are doing a great job. I find eOS to be very distraction-free. I spend less time in making it look and feel like I want to, because the developers have done that for me. Keep it up, guys! =)"

Thanks to both of those people for commenting on that post. As the semester has started and as I start to worry about graduate school applications, my frequency of writing new posts will generally go down, but I hope to have something written here from time to time. Anyway, if you like what I write, please continue subscribing and commenting!


Seventh Semester at College

How did I become a senior? It doesn't feel like orientation and freshman year happened that long ago.
Tomorrow is the first day of class for the 2013 fall semester. I'll be taking 8.07 — Electromagnetism II, 8.09 — Classical Mechanics III, 8.333 — Statistical Mechanics I (a graduate class), and 14.12 — Economic Applications of Game Theory. I'm looking forward to all of these classes along with continuing my UROP (which may transition sooner or later into a new project as I wrap up my current one). The bigger things I have to deal with though are graduate school applications and the Physics GRE. The latter will be over in a few weeks. The former will be going on until around the beginning of December, but I hope to be done a while before that. Hopefully this semester goes well. Good luck to everyone else for the start of their school year/job/whatever else!


Review: Elementary OS 2 "Luna"

Main Screen + Slingshot Menu
About 9 months ago, I checked out the first beta release of Elementary OS 2 "Luna". Since then, the final release has been put out for everyone to see and try, so I am trying it now. I tested this as a live USB made with UnetBootin. Follow the jump to see what it's like. Also note that I will not go over all the same things as I did last time, but I will take note of any changes.


Particles in the Continuous Quantum Field

The last thing I discussed in the last post was about the energy eigenstates of the continuous field. The ground state $|0\rangle$ classically corresponds to there being no displacement in the chain at any spatial index $x$ and quantum mechanically corresponds to each oscillator for each normal mode index $k$ being in its ground state, while the first excited state $|k\rangle = a^{\dagger} (k)|0\rangle$ for a given $k$ classically corresponds to a traveling plane wave normal mode of wavevector $k$ and quantum mechanically corresponds to only the oscillator at the given normal mode index $k$ being in its first excited state (and all others being in their ground states). The excited state $|k\rangle$ has energy $E = \hbar v|k|$ above the ground state and overall momentum $p = \hbar k$ above the ground state. This post will discuss what the second and higher excited states are. Follow the jump to see more.


Operators and States of the Continuous Quantum Field

In my last post about intuiting and visualizing quantum field theory, I discussed the diagonalization of the Hamiltonian and overall momentum and how they become operators. In this post I'm going to discuss more the meanings of the operators and associated quantum states of this field. Follow the jump to see more.


Featured Comments: Week of 2013 August 18

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

Cap and Trade and Soda

After an odd irritable initial pair of ranting comments, an anonymous reader followed up with this: "i apologize for my snide remarks before. i was just irritated. okay, so maybe there are a few other ingredients (like oils). it might be worth your while to check out OpenCola, which (or so i've heard online) tastes pretty close to Coke. http://en.wikipedia.org/wiki/OpenCola_(drink)".

Thanks to that commenter for that (and especially also for apologizing about the previous comments). This coming week I will have a few more posts about quantum field theory out, but no reviews as I had promised, as that will likely have to wait until after I get back to campus next week. In the meantime, if you like what I write, please continue subscribing and commenting!


Diagonalizing and Quantizing the Continuous Field Hamiltonian

In my previous post I discussed the intuition behind the classical acoustic field in one dimension. Now I'm going to talk about diagonalizing the Hamiltonian and making the step into quantum field theory. Follow the jump to see what it's like.


Classical Discrete and Continuum Fields

I've been reading various documents about quantum field theory over the last several weeks, specifically about the canonical quantization of quantum fields. In doing so, I've come to realize that quantum mechanics has a lot of crazy math and even crazier physical interpretations, and I just took that for granted, but now those things are coming back to haunt me in quantum field theory. It is very hard for me to wrap my head around, and I feel like I could use a lot more help in visualizing and intuiting what certain concepts in canonical quantization mean. This will be the first of a few posts which are outlets for me to gather my thoughts and put them out there for you all to see and correct; this one will be about classical fields.

I feel like the easiest quantum field system to study is the phonon. It is a spin-0 bosonic system, so it can be described by a scalar field. Furthermore, said field can be restricted to one dimension, which simplifies the math even further. This means that taking the continuum limit becomes a bit easier than in three dimensions. Follow the jump to see how it goes.


Cap and Trade and Soda

A few days ago, my family and I went on vacation. On the way back, my family and I were discussing various things including some matters of politics. One thing that came up was some of New York City mayor Michael Bloomberg's recent actions. I expressed the view that the ban on soft drinks larger than 16 ounces seemed rather heavy-handed. (After reading a little more about the exceptions for fruit drinks along with sales at grocery stores, I'm a little more happy to see that, but I still feel the ban was heavy-handed.) I then heard the argument that even if it is heavy-handed, it does help combat the obesity crisis by reducing access to drinking 16 ounces of soda at a time, because even if it is still technically possible for someone to fill up an 8-ounce cup twice, human psychology is such that said person would only fill up once, because for many people the convenience of filling up once trumps the desire to have as much as possible. I then wondered what other alternatives could be considered. The simplest alternative would seem to be a tax akin to taxes on cigarettes; if the large sodas are taxed heavily at such venues, people would naturally be discouraged from drinking as much. I have taken the class 14.03 — Microeconomic Theory and Public Policy, though, so I have seen that in many cases a Pigovian tax scheme like that may not achieve the most efficient outcome because it is difficult to adjust tax rates to control quantities precisely. Then I also remembered learning about cap and trade schemes to control quantities. Would that work? Let's take a look after the jump.


Reflection: 2013 Summer UROP

Wow. This summer has been incredibly busy, productive, and fun all at once. I can't believe it's already over!

So what did I do this summer?
My primary concern this summer was my UROP. I have been able to bring it very close to an end point; I wasn't able to finish it up completely, but I guess that was an unrealistic expectation because that's just not how science works. It doesn't wrap up cleanly; it's an ongoing process. I learned a whole lot more about Scheme and MEEP in the process, though, which was great.
On a related note, another UROP project fell by the wayside (as I wrote about earlier this summer) once I realized it was based on flawed calculations. To be honest, I'm not really sure if I want to pick up that project again and try to bring it to some sort of conclusion or if that's really worth my time.
My secondary concern was preparing for graduate school. I took the GRE this past Tuesday, and I am happy to say that went quite well. I have also been studying for the Physics GRE, along with making my list of graduate schools/programs/professors that I want to further investigate and send applications.
My tertiary concern was making another video for the MIT-K12 project. That went off successfully as well.

Apart from that, not being around my usual set of friends for the summer had a silver lining. While I would have certainly liked to have been able to hang out with them more, I was able to become a lot closer to a few people who usually live on my floor during the semester and hang out with them a lot more. Compared to the end of last semester, where I would basically just say "hi" to them but not a whole lot more, I now intend to hang out with them significantly more during this coming semester.

What didn't I do? These things didn't happen because I didn't have the time or energy to carry them out.
I wasn't able to edit and publish all the videos I took of 8.033 lectures from 2 years ago. In fact, I couldn't really look at those at all.
I wasn't able to do much work for OCW as I had planned.
(Actually, that's mostly it.)

I'm excited for the coming semester. My classes all look quite exciting, and I'm still deciding what I want to do regarding my UROP once my current project can truly said to be concluded. That said, I feel a bit sad that this has been my last summer at MIT, and it is already over. After that, I only have 9 more months at this place. I hope I can make those 9 months really special. Before that, though, I'll be going on a vacation with my family for a few days and then spending the remaining 1.5 weeks of August at home. Yay!


Featured Comments: Week of 2013 August 4

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

Review: Linux Mint 15 "Olivia" KDE + Xfce

An anonymous reader said, "Looking at your screenshots from the KDE spin I don´t see them looking different from oxygen. Did you change them before taking the screenshots? Also a general thank you for reviewing distros."

Thanks to that person for leaving that comment. This coming week, I'm going to be taking the GRE, so I definitely can't post anything until after Tuesday. After that, I may really only have time to put out my planned post reflecting on the past summer. After that, I'm going to be relaxing at home for two weeks, so my posts may become somewhat sporadic until September, which is when I get back to campus. Anyway, if you like what I write, please continue subscribing and commenting!


Review: Linux Mint 15 "Olivia" KDE + Xfce

I realize that I haven't posted anything in the last 2.5 weeks. That's because in that time I got quite busy with a combination of UROP work, video making for the MIT-K12 project, and studying for the General and Physics GREs. Given that I will be taking the General GRE in just over a week, and given that I will be going home for vacation shortly thereafter, I won't be able to post much after this for this month aside from a probable post reflecting on the summer. That said, it is a Sunday as I write this, and I figured I could use a break from the studying. So to do that, I'm reviewing Linux Mint 15 "Olivia" KDE and Xfce.

Main Screen + KDE Kickoff Menu
Why am I doing this if I have already reviewed the MATE and Cinnamon editions? Well, if you remember those reviews, I felt a little let down by both; granted, I could still recommend the MATE edition to newbies, but it wasn't with the same confidence as in the past. I want to see if the latest version of Linux Mint can redeem itself through the KDE or Xfce editions.

I tried each separately through a live USB system made with UnetBootin. Follow the jump to see what each is like.


Skepticism in My Photonics UROP

I've mentioned here on several occasions that I've been doing a UROP regarding nanophotonics/photonic crystals. Specifically, my first project was in determining whether particular types of photonic structures might enhance absorptivity of light, which would help solar cells that convert that light into electricity. The goal is that the absorptivity enhancement (versus no texturing over the solar cell) should be over as broad of a frequency band as possible, because it is difficult to manufacture many different kinds of photonic structures just to satisfy performance demands over many narrow frequency bands. I worked on this project for about 4 months, because that was the time that my postdoctoral UROP supervisor was around (he moved after that). I was able to get some really nice-looking results in that time, and I figured there wasn't much more I needed to do to wrap it up, so I felt comfortable generally moving on to a new project (which I have been working on since 2012 February or so). The enhancement results looked great compared to existing designs, so I thought we might be on to something here. Recently, things started gearing up for a publication submission.

Today, it all came crashing down. Why? Another postdoctoral UROP supervisor (who I have worked with since last year primarily on my more current project but recently joined in to help progress of the older project, which is the subject of this post) asked me some hard questions about what I was really doing. Because of this, I realized that one of the parameter choices in my calculations that were giving such nice results was fatally flawed. When I fixed that issue, the results I was getting suddenly looked significantly less compelling; with that, any dreams of publication were dashed.

Why did this happen? It boils down to me not being skeptical enough about what was going on. A large part of this has to do with the fact that because this was my first UROP, I didn't have a great idea of what was going on in terms of details. And because that time I spent was only about 4 months and was followed immediately by a new project, I didn't spend much more time on that project after that. Ultimately I got complacent in more ways than one. Because the code I was using was based on existing code for similar calculations, I figured it must have been written to work even with the modifications I was making. I also figured that because I had been getting consistently good results from what I had done over those 4 months, I just needed to worry about those results on the surface and not the fundamentals operation of the code. Those two assumptions combined such that even though I had seen the results of not being careful in my second UROP project and had become much more careful about checking that code as a result, I didn't think I needed to apply the same level of care in checking the code used for the first project.

After realizing the implications of this, I did a few more calculations in a significantly more mopey mood. But then I thought about this and I realize that I shouldn't feel so bad about this. Why is that? Here are a few reasons in no particular order.

1. I've made similar mistakes before, and I've really come to learn from them. One example of something that I thought was going great but turned out badly has to do with email. People who know me may have heard this story, and people who have known me for a while may have actually been there to see me do this, but I won't share the story now; I believe it is sufficient to say that I am now a lot more careful when sending emails especially to large groups of people. A reverse example actually comes from my second UROP project: for a while I was making a mistake in my code that was giving garbage, but after many months of trying various fixes, one particular fix solved all the other issues. Since then I have been a lot more careful about checking my code for that project (though I guess I was confident enough about the code used in the first project that I thought such a high level of care might be unnecessary).

2. I didn't think I would be in the position of having my work for both projects on paper until very recently. Now I can go back to thinking that in any case my second project work would be more likely to go on paper (especially as I know that I have taken a lot more care in checking my code for that project).

3. Several months ago, when my second project was stalling, I was asking myself why it wasn't going as smoothly or quickly as my first project. Now I know that the first project should have in fact gone as slowly as the second project for the work to become as solid and carefully checked. The other part of this issue is that I have been working on the second project continuously, so I have been able to make continuous adjustments to the code and work progressively higher levels of care in checking the code in a smooth manner. Because I essentially stopped working on the first project after those first four months, if I adopt more careful code-checking now, it'll feel more like I'm starting over from scratch, which makes the process feel a lot more frustrating.

4. With all this, I feel like I have already learned a lot more from this lesson than I would have if everything was fine and dandy and this work did get submitted for publication.

5. If nothing else, I hold out hope that I may be able to salvage some good results with the fixes I have made to the code of the first project.

There are two morals to this story. The first is that I shouldn't just check the code I run; I should check it in an actively skeptical manner, always questioning each and every line. The second is that C++ is way more painful to read and (to a lesser extent) write than Scheme is for the kinds of calculations I run.


Featured Comments: Week of 2013 July 7

I didn't post anything in the two weeks before this past one because I didn't really have much to post (not because I was particularly busy). This past week, there was one post that got a handful of comments, so I'll repost some of those.

Review: Korora 19 "Bruce" GNOME

Reader Barnaby said, "Skype works fine with Debian and Slackware 32-bit systems, probably Redhat based ones as well. I wouldn't blame errors with software installation in a live session on the distribution though, some things need a proper install, like the force switch to ignore the architecture."
Commenter arindam sen had this to say: "I agree with Kevin, 64 bit skype is required for Linux. It takes a bit to install the 32-bit Skype in a 64 bit OS and if you are not using Ubuntu/Debian, life becomes a bit tougher actually. There are some quick fixes suggested for Fedora/Kororaa but at times they worked for me and many times they didn't. So, it may not be the fault of the OS. Also, Gnome 3.8 is quite buggy compared to KDE. I reviewed Fedora 19 Gnome 3.8 (32-bit) and it is no where close to the performance offered by Fedora 19 KDE (4.10.4). Plus, I found GNOME a bit counter-intuitive to use. I really loved GNOME2 :(."
Reader dnlcerqueira had this to share: "I use Fedora 19 x64 and just installed the 32bit rpm without any problems , skype works perfectly on my pc."
Commenter crabdog countered, "I've tried the last few versions of Korora but only in VirtualBox. It looks fantastic and I really want to like it but it always seems very sluggish although my system has nice specs. Perhaps it would run better from a live boot and most likely better again on a proper install but for me if something doesn't run well in a virtual machine it doesn't get another chance."

Thanks to all those who commented on that post. This coming week, I may have another review out (or I may wait a bit). Anyway, if you like what I write, please continue subscribing and commenting!


Review: Korora 19 "Bruce" GNOME

Activities screen
In the comments of my review of Korora 18 "Flo" KDE, a bunch of people asked me to review Korora 19 "Bruce" GNOME. Now that this new version is out, I'm going to review it. It hasn't been too long since my last review of Korora, so I'll skip the introduction and get right to the main stuff. I reviewed the 64-bit edition (usually I review the 32-bit versions of distributions essentially by default, but this time the 32-bit edition seemed rather delayed to the point when I first downloaded the ISO file, I was under the impression that Korora might have dropped 32-bit support) on a live USB made with MultiSystem. Follow the jump to see what it's like.


Featured Comments: Week of 2013 June 16

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

Review: Zorin OS 7 Core

Reader arindam sen said, "Thanks for the good review. I agree with you - it is sad the Ubuntu 13.04 derivatives are only supported till Oct'13. Like what Fuduntu did with Fedora, some Ubuntu derivative should target of creating a rolling release distro. Anyway, Ubuntu developers were also debating over a rolling release distro last year. I am not sure what is the present status now."
Commenter Eddie had this to say: "Zorin does look interesting and I also have a problem with the new release schedule that Ubuntu has now, even tho I know and understand why they are doing it. I don't think that a rolling release would work well and that is just because of some bad experiences I've had with several rolling release distros in the past. The distribution upgrade path for Ubuntu has worked well for me the last several releases but I'm not sure how well a derivative would do. The last time I checked the AWN project had mostly been abandoned. I feel that this could lead to problems with Zorin. Maybe they should take it over. Everything seems to be moving so much faster with distributions now than 10 years ago. It makes me miss the CP/M days. Anyway thanks for a nice review."

Thanks to both of those people for those comments. This week, I may have a review out (along with possibly other posts). Anyway, if you like what I write, please continue subscribing and commenting!


Review: Zorin OS 7 Core

It has been almost exactly a year since I reviewed Zorin OS 6 Core, which was based on Ubuntu 12.04 LTS "Precise Pangolin". The new version is based on Ubuntu 13.04 "Raring Ringtail", so I'm reviewing that now.

Main Screen + Zorin OS Menu
What is Zorin OS? It is based on Ubuntu, uses a heavily customized GNOME 3 environment with Compiz as the WM and AWN as a panel. It also aims to look as close to Microsoft Windows as possible; at the moment, the target is specifically Microsoft Windows 8. There haven't been a huge number of changes from version 6 to version 7 of Zorin OS, aside from some theme and branding updates along with the usual package updates.

I tried this as a live USB made with UnetBootin; the Zorin OS website warns that the live system may be less stable than the installed system, so I'll see how that plays out. Follow the jump to see what it's like.


Featured Comments: Week of 2013 June 9

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

Review: Linux Mint 15 "Olivia" Cinnamon + MATE

Reader Mechatotoro said, "Thank you for the time to write about Mint; your review is very useful and enlightening. I really appreciate your objective observations! Again, thank you and good luck with your studies."
An anonymous commenter had a different experience: "I have been using Mint 15 since the RC release and it has been rock solid for me as well."
Reader Bernard Victor had a similar counter: "I am using Mint with Cinnamon desktop. I have found it very stable and responsive. Desktop effects work well. I think it is the best all round distro that I have tried. I also have PClinuxOS loaded which is not half as responsive though seems pretty stable. Could be that some of your problems result from only usinga live USB system."
Commenter on4aa supported, "I am happy to read a rather objective Linux Mint review, pinpointing the same desktop environment issues that made me leave Linux Mint Debian Edition. [...]"

Thanks to all those who commented on that post. This coming week I will have another review along with maybe one other post coming out. Anyway, if you like what I write, please continue subscribing and commenting!


Review: Linux Mint 15 "Olivia" Cinnamon + MATE

It's that time of the year again. Linux Mint has just released the latest version of its distribution, and I'm going to review it.

Cinnamon: Main Screen + Cinnamon Menu
What has changed since the previous version? Cinnamon has gotten more bug fixes as usual. More importantly, its settings have been consolidated into one program, and it has become less immediately dependent on GNOME than before. Meanwhile, MATE has also been moving away from old libraries toward newer ones used in GNOME 3 as well, allowing for things like Caja to look a little more like Nautilus. There are other changes in store for Linux Mint itself, like new separate tools to manage software repositories and drivers, respectively (in opposition to how Ubuntu is doing it now).

I tested both of these as live USB systems made with UnetBootin. Follow the jump to see what they are like.


Featured Comments: Week of 2013 June 2

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

How-To: Make Xfce Like Unity

Reader Mike Frett shared, "That's why I use XFCE, very customizable. I don't particularly like Unity, but I enjoyed the article. Incidentally, you could have turned the Opacity down a bit on your Dock to match Unity's. I use Xubuntu, when I do I always delete the Dock on the bottom and drag the top bar down to the bottom. I add some spacers and launchers and such till it looks like *that* classic OS from around '98. It's just my preference because it's simple and stays out of my way. I use the Shiki-Brave and Classic Ambiance themes. Nothing in my System Tray on the right except the clock, weather update and Network Monitor (Bars only). And Dots style separators. I like it =p Point is, it's very customizable to anyone’s liking. But it annoys me they still call XFCE a 'light' WM when it's resource usage is the same as Gnome 3 and KDE; and they STILL don't have even basic effect's like fade-in and out or Min-Max animations."
Commenter Morten Juhl-Johansen Zőlde-Fejér had this bit of support: "This is an excellent documentation of the level of customization that is possible. I seem to recall another site where they did a Vista and MacOS X redesign - it was quite impressive."
An anonymous reader said, "Unity's screen layout is actually OK. But if Unity was just a reorganization of an on-screen dock and panel, then it wouldn't have generated so much controversy. Canonical eliminated the start menu, replacing it with a cumbersome search function; they also adopted the Mac's one-menubar-for-all-programs style, took away many customization options, and put all of that in a package that requires high-end graphics capability to even run. I don't know why anyone would want to emulate any of that. With Xfce, you can put a launcher in the dock that opens the "application finder", which is a nicely laid out menu of installed programs, organized by program type (graphics, internet, etc.). Alternatively, the launcher could run "thunar /usr/share/applications", which would produce a very Mac-like display of clickable icons of all installed applications. I imagine one could do this with Unity, in effect restoring the start menu (but I haven't tried - Xfce works just fine). And I still haven't found a simpler way to switch desktops than Xfce's trick of just moving the mouse off the right or left screen edge. No mouse clicks at all! Gnome 2.x had the same thing, I think; gone the way of the Dodo bird..."
Another anonymous commenter countered, "I'm with Innocent Bystander. I switched to Xfce 3 years mainly to get away from what I saw coming down the pike with GNOME 3 and Unity. While it's interesting to know that this can be done with Xfce, this article begs the question: WHY would anyone in his/her right mind WANT to do this? As someone who likes Xfce the way it is due to the Xfce team sticking to tried and true intuitive GUI design that has stood the test of time, I consider this article to be completely and utterly pointless."

Thanks to all those who commented on that post. I'm back on campus, but because my UROP (and graduate school preparations) are a bit less hectic than the normal semester, I'll probably be able to put out a review this week. Anyway, if you like what I write, please continue subscribing and commenting!


How-To: Make Xfce Like Unity

This is more or less the sequel to this post. It came about because I wanted to see if it would be easy to make Xfce look like Apple's Mac OS X; I figured that Unity looks similar enough, so I might as well write about that. Follow the jump to see how to do it. I would have added more pictures if I had more time, but I'm heading back to campus tomorrow, so I can only make this a quick post in the meantime.


Review: Semplice 4 "Atom Heart Mother"

A couple of people have asked in comments (especially of my review of #! 11 "Waldorf") that I review Semplice. I took a look at its website and was pretty intrigued, so here is the review.

Main Screen + Openbox Menu
What is Semplice? Much like #! (which I may end up referencing frequently whether I want to or not), it is based on Debian and uses Openbox as its default WM. Unlike #!, which is based on Debian Stable (and issues preview releases based on the future Debian Stable release), Semplice is based on Debian Unstable "Sid", which allows it to be maintained as a rolling-release distribution.

I reviewed Semplice 4 "Atom Heart Mother" (I found out the code name from the release notes) using a live USB made with UnetBootin. Follow the jump to see what it's like.


FOLLOW-UP: Rebutting the New York Times Review of "A Universe From Nothing"

Somehow a few months ago, my family discovered the existence of this blog, and the first post they read was this one, for which this post is a follow-up. They then bought the aforementioned book for me so that I could read it and perhaps understand the criticisms laid out in the New York Times article that I rebutted.

Well, I read the book. It was a fairly interesting read. Having taken the class 8.033 — Relativity, I would say that everything up to around the middle of the book is stuff I've seen before in the context of general relativity. After that comes some stuff that is new to me, like the ideas behind inflation, virtual particles, and how multiverses can be explained within the framework of quantum field theory. They were all new and fairly strange ideas, but I accepted them fairly easily because it was clear how they fit into the framework of quantum field theory. After finishing the book, I went back to read the book review as well as my rebuttal of it, and I have to say that in many ways, the book review looks even slightly more ridiculous than before, and I'm actually quite happy with the assessment I laid out about a year ago.


Featured Comments: Week of 2013 May 26

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

Review: SolydXK 2013.04.06

Reader Mechatotoro said, "Thanks for the useful review. I had not heard about SolydXK, so I will give it a try. Have you tried Mint Olivia yet? I'd like to hear your opinion since you are a Mint user and can therefore assess the system's general performance as compared to other versions of Mint... I'm also curious about the new themable login screen."

Thanks to him for leaving that comment. This coming week, I will have at least one review out along with at least one other post, as this is my last week at home before I go back to campus for the summer. Anyway, if you like what I write, please continue subscribing and commenting!


Review: SolydXK 2013.04.06

I originally wanted to do this one before final exams, but other hiccups in this review pushed that to now. Anyway, here it is.

Main Screen + KDE Kickoff Menu
What is SolydXK? Debian-based Linux Mint never had a KDE edition, so SolydK was born out of the unofficial project featuring KDE in Debian-based Linux Mint. Then, Linux Mint pushed its Xfce edition back to an Ubuntu base, necessitating the emergence of SolydX. Together they form SolydXK, based on Debian Testing but with update packs, just as Debian-based Linux Mint is.

I tried SolydXK on separate partitions of a live USB with UnetBootin, as MultiSystem did not recognize SolydXK (and that's why I was having trouble doing this review before final exams). Follow the jump to see what they are like.


Featured Comments: Week of 2013 May 26

I was out of town over the long weekend, so I couldn't post this yesterday. There was one post that got a couple of comments last week, so I will repost both of those.

Review: Korora 18 "Flo" KDE

An anonymous reader asked, "do you have a review for gnome edition"?
Another anonymous commenter shared, "I've been running Korora 18 for a few weeks now. It's extremely polished and I had none of the errors you encountered setting it up. Everything just works for me."

Thanks to both of those people for commenting on that post. This coming week, I will have at least one review coming up, as I am at home now and will have some time to do this again. Anyway, if you like what I write, please continue subscribing and commenting!


Done with 6th Semester!

I'm done with junior year! The spring semester was a bit more manageable than the fall semester, but was still challenging nevertheless. I intentionally chose to take only 3 classes: 8.06 — Quantum Physics III, 8.14 — Experimental Physics II, and 14.03 — Microeconomic Theory and Public Policy. I did this so that I could spend more time on each of those classes (especially 8.14 — Experimental Physics II) as well as on my UROP. Speaking of my UROP, things were progressing rather slowly in the beginning of the semester and only slowed further from there, until just after spring break, at which point progress went extremely quickly. I'm really looking forward to being able to make more such progress in the summer; plus, I may even be able to start on a new project about the Casimir effect, about which I wrote a paper for 8.06 — Quantum Physics III. Before that, I'm spending two weeks at home. For these next few days, I'm just going to relax and spend time and travel with family. After that, I'll probably be able to start work again on my UROP; a few weeks into the summer, I intend to start looking seriously into graduate programs in physics. Anyway, at last, it is summer!


Review: Korora 18 "Flo" KDE

Main Screen + Kickoff Menu
In the last week of classes, since finished all of my assignments, I have had a little time to do some distribution reviews before starting to prepare for final exams. The second such review is of the KDE edition of Korora 18 "Flo".

I have reviewed Korora before. Back then it was called Kororaa (with an extra 'a'), so I guess the name was shortened in a manner similar to that of Facebook (from "TheFacebook"). It's a distribution that essentially offers a bunch of niceties on top of Fedora with GNOME or KDE. This time I tried just the KDE version.

I tried this as a live USB system made with UnetBootin, as making it with MultiSystem gave problems on several occasions. Follow the jump to see what it's like.


Featured Comments: Week of 2013 May 12

There was one post this past week that got a handful of comments, so I will repost most of those. Also, I should mention that despite that post being a very short review-esque update, it somehow managed to get several thousands of views more quickly than any other post. I'd be curious to know where a lot of those views came from.

Review: CrunchBang ("#!") Linux 11 "Waldorf"

Reader DarkDuck shared, "I would not recommend #! to newbies. It's still to rough. But as soon as you become comfortable with the Linux system architecture and approach, #! maybe a good alternative. My own review of #!: http://linuxblog.darkduck.com/2012/03/crunchbang-linux-good-system-for.html".
Commenter krpalospo had the following question: "I really like debian, it was my first distro, but i have a question this distribution has support for apt-repository like ubuntu's distros the main reason for no using debian right now it's that this ubuntu tools help a lot in configuration of package system".
Reader Wolf had this to say: "Nice small delta review. I might try it someday, although I'm usually happy with Ubuntu LTS releases. One small thing: you may find even with error bars that 148 MB steady state RAM used is significantly different than the 150 MB steady state of before, but I question the practicality of this difference. 2 megabytes shaved off of steady state seems, practically, insignificant. I mean we are regularly seeing 32 and 64 GB RAM machines now, with 128 GB, 256 GB and higher on the high end. 2 MB steady state saved is miniscule."
An anonymous commenter asked, "Why isn't Semplice getting the attention it deserves. Imho it is better than #!, Been running it for a couple of weeks now and it a lot more polished than Crunchbang. Give Semplice a try."

Thanks to all those who commented on that post. This coming week, I have final exams and then I will be traveling home. My final exams go until (and include) Wednesday, so I won't really be able to write anything new for the week. However, I do have an already-written review on hold to publish this week. Also, I'll probably put out a post concerning the semester that is almost completed. Anyway, if you like what I write, please keep on subscribing and commenting!


Review: CrunchBang ("#!") Linux 11 "Waldorf"

Main Screen + Openbox Menu
This is the last week of classes for me. I have turned in all my assignments and a handful of days until finals, so I can take today and tomorrow to write a couple of reviews at my leisure. The first will be #!.

#! should be familiar to many readers here. It is a lightweight Debian-based distribution that uses Openbox. While it is not technically a rolling-release distribution because it is pinned to the stable release, there were tons of preview releases for this version. Now that Debian 7 "Wheezy" is finally stable, so is #! 11 "Waldorf". Since version 10 "Statler", the Xfce edition has been dropped, so #! is back to using Openbox exclusively.

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


Expected Utility in Quantum States

Last semester, 14.04 — Intermediate Microeconomic Theory covered choice theory under uncertainty; at the same time, I was taking 8.05 — Quantum Physics II, where we had talked about 2-state systems and the formalism of quantum states being complex vectors in a Hilbert space, and as choice under uncertainty discusses how consumers make choices based on states of the world, I thought it would be cool to extend it to quantum states, but I wasn't sure how to do that at that time. Now that 14.03 — Microeconomic Theory and Public Policy is talking about choice under uncertainty as well this semester, and now that I have had some time for the stuff about 2-state systems to simmer in my head, I think I have a slightly better idea of how to think about extended the states of the world to include the superpositions as allowed by quantum mechanics.

One of the simplest examples would be the 2-state system. In the class I am taking now, a typical 2-state system would be a fair coin which can either take on values of heads or tails (each with probability $\frac{1}{2}$). What might this look like in quantum mechanics? We could replace the coin with the spin $S_z$ of an electron. A state of the electron corresponding to being measured as $|\uparrow_z \rangle$ or $|\downarrow_z \rangle$ each with equal probability could be labeled as $|\psi \rangle = \frac{1}{\sqrt{2}} \left(|\uparrow_z \rangle + |\downarrow_z \rangle\right)$. This indeed gives equal probabilities of being measured as spin-up or spin-down in the $z$-direction. The problem is that this state is exactly $|\psi \rangle = |\uparrow_x \rangle$, so the probability of the state being measured in the $x$-direction as spin-up is unity. This leads to issues in trying to reconcile the interpretation of payoffs for different states of the world; this particular state would pay $w(|\uparrow_z \rangle)$ or $w(|\downarrow_z \rangle)$ with equal probabilities until $S_z$ is measured, but would pay $w(|\uparrow_x \rangle)$ with certainty as $S_x$ has essentially already been measured, collapsing a previously unknown state into this one. So there seems to be an issue with trying to stuff the interpretation of probabilistic measurement of a state of the world into the idea of superposing quantum states, as certain measurable states of the world do not commute ($[S_i, S_j] = i\hbar \epsilon_{ijk} S_k$ for instance). So what can be done now?

Recall that each state of the world $j$ has an associated probability $\mathbb{P}_j$. Yet, once a state is measured, those probabilities are meaningless, because a state becomes observed or not observed; it cannot be "observed in fraction $\mathbb{P}_j$" or anything like that. Taking the frequentist view, these probabilities are only meaningful in the large ensemble limit; after a large number of observations, the fraction of those observations corresponding to the state $j$ converges to $\mathbb{P}_j$. This is exactly the same rationale behind the density matrix, which describes the state of an ensemble of systems which are usually not all prepared in the same quantum state, but in the large number limit, the fraction of those prepared in the state $|\psi_j \rangle$ is $\mathbb{P}_j$ such that $\sum_j \mathbb{P}_j = 1$. It is then defined as \[ \rho = \sum_j \mathbb{P}_j |\psi_j \rangle \langle \psi_j | . \] Note that in general $\langle \psi_j | \psi_{j'} \rangle \neq \delta_{jj'}$ because the states do not in general need to be orthogonal. Furthermore, different state preparations can have the same density matrix, in which case the "different" state preparations are actually physically indistinguishable if a quantum mechanical measurement is made.

So what does this have to do with the states of the world? If the example of a fair coin flip is again translated into measuring each eigenvalue of $S_z$ with equal probability, then the density matrix becomes $\rho = \frac{1}{2} \left(|\uparrow_z \rangle \langle \uparrow_z | + |\downarrow_z \rangle \langle \downarrow_z |\right)$. Now it is much more plausible to define a wealth $w(|\psi_j \rangle)$ dependent on the state of the world.

For example, let us now consider an unfair "coin" represented by the density matrix $\rho = \frac{1}{3} \left(|\uparrow_z \rangle \langle \uparrow_z | + 2|\downarrow_z \rangle \langle \downarrow_z |\right)$. What is the probability of measuring this system in the state $|\uparrow_x \rangle$? That would be $\langle \uparrow_x | \rho | \uparrow_x \rangle = \frac{1}{2}$. Similarly, $\langle \downarrow_x | \rho | \downarrow_x \rangle = \frac{1}{2}$. It is interesting to note that equal probabilities are achieved for spin-up and spin-down in the $x$-direction (and $y$-direction as well) for this system; the difference is that now there are off-diagonal terms in the density matrix describing the degree of interference between the states of $S_x$ in the two populations of spins.

What can we do with this? Payoffs now need to be defined over every plausible noncommuting observable in the Hilbert space (because commuting observables yield the same state, and the payoff is really defined for the state). Thankfully this is fairly simple for spins, as the noncommuting observables in question are the components of $\vec{S}$.

Let us return to the previous unfair "coin". Classically (so it would be a coin), the result of the coin flip would be the end of the story. Let us suppose that the consumer had a risk-neutral utility $V(w) = w$. Let us also suppose that there was a game which payed off 20 if heads and 0 if tails and cost 10 to enter. The expected payoff, accounting for the cost of entering, would be $\mathbb{E}(w) = -\frac{10}{3}$, so the consumer would prefer to not play.
Classically that would be the whole story. Quantum mechanically, though, there is more to the story. If the owner of the game decided to measure $S_z$, then the result would be the same as the classical result. If the owner decided instead to measure $S_x$ or $S_y$, then $\mathbb{E}(w) = 0$ so the consumer would be indifferent between playing and not playing, which is certainly a different outcome from preferring not to play. In fact, if the consumer does not know for sure what the owner decides to measure, then probabilities could be assigned to the measurement choice itself, and these could then be used to find the expectation value of payoff or utility over all possible choices, where each of those choices will have an expected payoff or utility as well.

One thing to look further at is how to extend this to include continuous ensembles. The example in class was how a state of the world might be the outdoor temperature measured in some range. The quantum mechanical equivalent might be having a continuum of systems, each infinitesimal one having a position inside a given range of allowed positions; the only issue with this is that matter is not continuous, so I don't think it is possible to have a density matrix in the form of $\rho = \int |\psi(s) \rangle \langle \psi(s)| \, ds$ for some continuous index $s$. However, that can certainly be further investigated, and maybe I'll do that next time. The point is that states of the world in analyzing expected utility can easily be generalized to include quantum states through density matrices, and the question of which observable to measure in a noncommuting set brings out some interesting behavior not seen in classical states.


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.