Quantum Crops is dead! Long live Quantum Crops!

After fiddling with Blogger and Wordpress for a while I have decided to stop using Blogger and import this blog to Wordpress. I believe that Wordpress is sexier since it has LaTeX support. So this blog will remain like this forever.

The new home of QC is here: http://melvineloy.wordpress.com .

End of the first part of the summer

In this post I will try to convince myself that I have a lot of stuff to do and that I should start working ASAP.

Merideth left today. This brings an end to four weeks of rest and relaxation. I should not feel bad about anything since I am able to say I have done a lot of stuff, including

• Going to NYC many times,
• Eating a lot of bagels,
• Eating a lot of pizza slices,
• Meeting some friends from PR at NYC,
• Visiting many museums,
• Watching a lot of movies and TV boxed sets,
• Eating a lot of dessert.

And maybe more... But sometimes I felt guilty, like if I should have been doing something more productive related to me learning some physics during the summer.

It was not all fun, since I spent some time discussing some physics with my girlfriend. She was thinking about (as she calls it) the "rain drop problem". The idea is to calculate the optimal speed a person should have in order to minimize wetness under falling rain. My girlfriend argues that running causes some sort of effective cross section and one calculate the amount of drops one encounters while running a specific distance. I am trying to convince her to post her result here so stay tuned.

I have the rest of the week and next week to work on stuff. That stuff includes reading some of Srednicki's QFT and trying to go through some section of Carroll's relativity book. I kind of want to read the appendices on non-coordinate basis and sub-manifolds and hypersurfaces. Hopefully some of this will happen.

Another thing on my mind are next semester's courses. I am currently registered in field theory, relativity and group theory. This might be to much to bite on, but I need to take something touching on breadth, so I also registered on graduate laboratory. But I have been thinking that this lab course might be REALLY to much. So an option would be to take a course on atomic physics that will count for breadth and then take the lab class during the spring term.

Yet one more thing on mind is the comprehensive examination. I have the opportunity to take that exam this coming September. The thing is, I AM NOT PREPARED FOR THAT. So I could try reading a lot of stuff during the remaining days, but I really do not think that is going to take me anywhere. There is a lot of stuff to cover in those exams, most of the stuff that I do not have any idea.

So I believe that the best course of action would be to take that atomic physics course, and really try the comprehensive exam during the January offering and take the graduate laboratory during the spring term, along with field theory 2, another breadth course and maybe Warren Siegel's advanced field theory.

A minor concern is getting a new computer, and the money for it. The question would be, another Dell or a new Apple? 

Particle Physics

Yesterday I went through some of the comprehensive examinations. In total I had three exams, which meant 36 questions. Out of those, I only had a good idea about one of them:  a question about covariant derivatives and the curvature tensor. In fact, I do not think I can work out that problem...

Since I've noticed there were so many questions about particle physics, and I do not know much about particles in general, so I tried reading some of Huang's Quarks, Leptons and Gauge Fields. It is a bit full of jargon, so I have a feeling I need another good source.

Besides particles, I have not being up to much. Just watching lots of ALIAS and Netflix. Oh well...

Done with Deathly Hallows

Today I finished reading the last book of the Harry Potter series. I am happy to say that none of my predictions turned out to happen. It was a good book. The epilogue was kind of disappointing, but anyways. I guess now my amusement will come from Netflix...

The wait is almost over...

I cannot wait anymore to read the last book of the Harry Potter series. Almost 2 hours and 25 minutes! I guess I will not blog now for a while. Tomorrow I will go to Central Park for some outside reading. Should be fun!

In the meantime I have been reading an article on torsion gravity. It is kind of interesting, since the article claims that torsion might be important to understand spin angular momentum in general relativity theory. More on this later.

Closure

I feel like summarizing my thoughts, yet again.

Maybe it is because tomorrow I will formally start working. Or maybe it is that I feel like I am done with relativity for the summer.

Well, concerning relativity. I have not gotten yet to Einstein's Equation! I guess that I am not done with relativity until I discuss this part. So maybe I will stop reading Sean Carroll's book after the 4 chapter. I feel like I will be learning most of the physics during this coming semester, so I want to cover more mathematics during the summer. That is why I have been concerning more with topics about manifolds and geometry than with specific metrics like the example of the flat, expanding metric in the book.

So in the end I clear most of chapter 1, chapter 2 and most of chapter 3 from Spacetime and Geometry. I have on my queue to read the appendices on other mathematical topics (including non-coordinated basis, which are important for spinors, and hypersurfaces and induced metrics). Before I started I had read the first part of the chapter on manifolds in Nakahara's book. I think now I will turn to the second part of that chapter on Lie groups.

Additional topics I want to read about include more Yang-Mills theory, and spinor stuff. I am thinking of reading some of Siegel's book. I just cannot concentrate with my computer on, so sadly I might have to print some of the chapters. I guess it is not that sad, since the trees have already been used; the paper is ready for printing. As long as I put it in the recycling bin it is OK. If somebody wants to save some trees, he/she has to prevent them from being cut down. I guess not using paper will send some sort of message, but it might not be a effective.

Anyway, I guess I will start my second part of the summer term tomorrow.

Chief TA

Yesterday I had my first meeting regarding my summer TAing. It was funny since the professor appointed me as what I like calling "chief TA". This means that I will not TA per-se. Instead of grading reports and the usual, I will be in charge of the TA meetings and other stuff. I its good for me, since I will not be actually teaching but in charge of overseeing other TAs. But I think that will not be as much work as what the rest of the TAs do. Oh well, I am not really complaining.

I also bought my plane ticket for flying to CA at the end of the summer. That will be awesome, as usual.   

So far so good... (I)

During the end of last week I turned towards Sean Carroll's book Spacetime and Geometry: An Introduction to General Relativity. This is not the first time I go through some of it. I started on the first chapter, going through the mathematical details and skipping the part on energy and momentum and classical field theory. I will go through this two sections once I reach the chapter on gravitation. When I finished the first chapter I carried on to the second chapter on manifolds.

The second chapter formalizes ideas familiar ideas and puts them in the context of a manifold. These ideas include vectors, tensors, differentiation and integration. I am currently finishing the third section of the third chapter on curvature. Right now I am exploring the concept of parallel transport and geodesics.

So what have I learned so far? Here is an outline with the basics idea behind the mathematical construction of a nontrivial spacetime (not flat). It also serves as a nice summary of what I got so far...

The motivation behind General Relativity is the matter and energy curve spacetime and this curvature is what we call gravitation. (I have not reach the chapter on gravitation, hopefully by the end of this week, so that line that you just read might be very wrong...). We would like to construct a spacetime that can be curved, and we would like to describe this curvature mathematically. Another motivation behind relativity is the fact that the laws of physics should remain invariant under coordinate transformations. This tells us that we should use objects that have the same form in any coordinate system. We call this objects abstract vectors, dual vectors and higher-rank tensors. We also would like to describe things locally, since relativity tells us that the speed of light is an universal upper bound to the magnitude of the velocity of any object that carries information. From special relativity we know that this means that simultaneity looses validity between different observers. For a given physical object (a tensor, a vector, etc.) different observers will have different components but this components should be related by a coordinate transformation.

Most of the construction comes from making analogies with flat spacetime (a Cartesian product of many real lines R.) The first thing that we want is that given a region of curved spacetime, common sense tells us that locally (a very small patch) will look like flat space. We can imagine then a chunk of curved spacetime that is made up of flat patches of space, all sewn together. This is along the lines of the entity known in mathematics as a manifold. We need to also demand that this patches can communicate through continuous maps. I am not going into the formal details, but the basic idea is this: One construct a generalization of a Cartesian system by connecting neighborhoods of Cartesian systems with continuous and differentiable functions. The manifold is a collection of points, and this point in turn are mapped locally into a flat spacetime.

The next step is to set up the notion of a vector. In Euclidean space (which is the formal name of a space formed by taking a finite number of Cartesian products of real lines R ) a vector is an object that obeys a set of rules that constitute a vector space. This idea works well in Euclidean space, but when one considers the notion of moving a vector along a spacetime that is curved, it is not clear whether the vector changes or not. This is necessary for adding or taking products of vectors. Since each point on a manifold is locally flat, one can define a vector space on each point, this is called the tangent space. The tangent space is formed of all the vectors that originate at the point. A natural  choice for basis vectors are the set of partial derivatives.

Other objects that are generalized to curved spacetime include tensors and dual vectors. More on that later.

A terrible idea...

Since I am so excited about this fall's courses and have been thinking (to much) about them. I want to blog about them, but I am not happy with Blogger's LaTeX support, and am kind of jealous about Wordpress. I had some blogs over there, but lack of time forced me to forget about them. It is a time consuming task... but I want to do it! So I have been thinking of starting (or restarting) one of my Wordpress blogs. I thought of moving Quantum Crops there, but I like Blogger.

So I will try to keep some notes over here. Hopefully this blog will last more than my previous attempts.

Relativity, fall 2007!

I just checked the course's website and professor Siegel has updated it for this fall's Relativity course (formally know and Modern General Relativity). This website can be found here.

I am so excited! It definitely does not look like a traditional course in the sense of not having a first part on the mathematical formalisms like manifolds and curvature, among other topics from differential geometry. That will be good, I mean if the class is driven by the physics instead of some mindlessly index manipulation. The list of topics to be cover includes lots of quantum stuff like spinors, supersymmetry and supergravity, not to mention strings at the end. That would be awesome! I am also looking forward to learning about Yang-Mills theory. And the best part is that the textbook is free!

Also Warren has a link to what looks like a course on Advanced Field Theory for the 2008 spring term. This also looks pretty sweet, I hope I can take it. It is funny how he brags about the course having material like "stuff you may have missed if you didn’t take field theory (PHY 610 & 611) from me" :-).

I will try to blog about his lectures and my frustrations with the homework problems. Or maybe I should not blog to much and use my time on something else, like studying...

Predictions for book Harry Potter #7

For this year's Valentine's Day I got as a gift Harry Potter and the Sorcerer's Stone. It took me about two months to read, mainly because I was busy with homeworks and partial examinations (not to mention the weekly grading...). I finished it around the week before Holy Week. Since I enjoyed so much, I ordered books 2 and 3. They arrived on time for me to start #2 right after I finish with #1.

It took me less than 5 days to read the second book, since I was on my spring break. For book #3 I took more time, so I finished it after maybe two weeks. But then it went downhill (or uphill?) with books #4 and #5 over a few weekends, reading them on my way to Wellesley and back to Stony Brook. Finally book #6 had to wait after finals, but the truth is I did not finished it after finals... Instead of studying for that quantum final, I learn who was the Half-blood Prince. Oh well!

These books are good. I think this is the best point in my life to read them. I mean, when you are a student. I am pretty much grown up. But Harry Potter is just awesome.

I first considered reading the HP books when John Denker at NIST talked about them. John Denker is a physicist I met while working at NIST on the summer of 2005. He is pretty cool and I had the opportunity to eat some lunch meals with him. He used to work at Bell Labs and he told us some stories from his time there, including the lunch discussions about Buffy the Vampire Slayer (the TV show) between scientist and researchers. I still had this mental picture that scientist were usually pretty boring people and that I was the cool one. I was so wrong. In fact, at that time I hadn't saw any episode of Buffy, besides the old movie. After Buffy John says he started reading the HP books. At this point I kind of looked down upon him. I guess he noticed this, since he went on to explain why Harry Potter was important with magic.

Besides all the drama about a young boy growing up in a dangerous world with friends, family and foes, the book is about a magical world. This magical aspect is not traditionally magical, but somewhat understood and studied academically, just like science in real life. In the book magic can be seeing as a metaphor for science (mostly the physical and life sciences), but of course it is really portrait as an alternative to science. As John Denker argued, to most people what scientist do is like magic. Well for once what Feynman did was magical ;-).

But anyways, I would like to have a record of what I believe is going to happen on book #7. I believe this is the worst thing to do, and also wrong for many reasons:

1. I am not the writer of the book. When you are reading a story, you should sit back and let the story take you along for a ride on the invisible hands of the author. Stories are great ways of learning how other people see the world.
2. I am not thinking hard enough so my predictions are going to be obviously wrong.

Anyways, here are some possible scenarios that could happen or maybe I want them to happen.

• The nice and happy ending. Harry beats the Dark Lord and everyone is happy. In the future he marries Ginny and then is offer unanimously the position of Minister of Magic but turns it down to become the defense against the Dark Arts professor at Hogwarts where he then later becomes Headmaster. Hermione and Ron also get together and maybe Neville and Luna. Snape and Hagrid die.
• The more realistic ending. Harry and the Dark Lord both die during the last battle. This would prevent writing another book in the future and would give the series a definite ending. Harry will realize that dying for the sake of others is sort of a good thing, so I can see his sacrifice being completely justified.
  
• The nice and sad ending. Harry lives, but Hermione and/or Ron die. This does not make much sense, since then Harry will be alive but with no friends. At this year's Nathan's Hot Dog Eating Contest at Conney Island, NYC one of the contestants was holding a sign that read "Hermione Dies" on one of its side. Maybe it was just a prank or joke, or maybe...

I really do not know about Snape. I have a gut feeling (and I just had dinner...) that Snape is going to turn out to be good, in a not-so-usual way. Who knows, maybe he will be the one who finishes off the Dark Lord. Lupin and Moody are also two possible characters that could die (along with other professors from Hogwarts), but they are not main characters.

I just want July 20th, midnight, to come now. I will read some at that moment, then the next morning after breakfast and hopefully finish it by Monday morning.

Thank you J. K. Rowling for such a great story.

On a Manifold you can...

Well I am happy to say that there has been some learning going on at my desk. During the past few days I have been going through the sections three sections of the second chapter of Nakahara's book. That would be basics of maps, vector spaces, equivalence relations and topological spaces.

In theory I should know must of it since I took classes on Topology, Linear and Abstract Algebra, and Set Theory. The truth is that I have forgotten must of it, which is a shame. But reading it has been easy. At least I have been able to work out the exercises. Then I turned my attention to chapter five on manifolds. I choose to "ignore" the chapters on homology and homotopy groups. I technically read the first part on homology groups (on simplexes and simplicial complexes) but that was on an airplane heading to Puerto Rico and later back to NYC.

The first task is to define what a manifold actually is. Once this is done you go on and define what a vector is on a manifold. With vectors one can define the dual space of linear functions and then you can construct higher tensors.

I got kinda stuck while discussing differential forms. It was kind of sad, since I know that this exercises is easy. Basically one has to prove that given an r-form and a q-form the exterior product between them will be the same as that with reverse order multiply by a minus one to the power of the products of r and p. And also one has to show that for r an odd number, the exterior product of an r-form with it self vanishes. Both of this identities follow from the definitions of a differential form and the exterior product, it just include a counting part. Sadly I suck at counting things.

That was my least favorite part in statistical mechanics: counting micro-states or configurations. It is very sad that I have been always so stubborn and skeptic about counting and number theory in general. I am adding it to the list of things I should learn right before I die.

Pattern on my tea

I got this pattern once on my tea. Ever since I took the statistical mechanics course I pay more attention to all the fluids in my life. The cup of tea is particularly interesting.

I used to drink coffee. Most of the grown-ups around me were drinking coffee when I was young, so I tagged alone. I was drinking two cups during the morning. As long as I took those two cups I was a happy person. One time I did not had any coffee. It was horrible, my head wanted to implode.

Last winter I visited my girlfriend at Wellesley College. She did not had a coffee maker, so I just started drinking tea. I guess the transition was smooth, since I do not remember having that much of an ache. Tea is suppose to be healthy too.

I like making my tea on a clear, see-through cup. That way I can follow the trail of particles diffusing on the water. The growing arms of the spirals is awesome. I cannot help but think of the particles approaching each other and then separating when I use my spoon. The sugar dissolves, sometimes yes and sometimes no.

But the fun lies at the surface of the cup. Here there is an ongoing exchange of particles with the air. If you blow on it you can see the lines of particles separating from the surface. The streams of vapor pulling more and more molecules into liberation.

OK. I am done with the poetry. Just wanted to appreciate a bit the beauty of a cup of tea.

Cold feet?

I believe I am getting cold feet about my summer readings. I really need the dicipline to read on my own. I have been reading snippets of many texts. I have the tools for this. If I really put the effort, I know I can get a lot from this.

But really. I do not have the dicipline to sit down in front of a book and read and read and then solve some problems to see if I actually learned something. I should have the dicipline, or whatever it is that you need, to learn by myself. If I could talk to somebody else. But most of the people I know are more advanced than me.

So I am going to see if this works: I am going to check my email in the morning, then turn off my computer and concentrate my attention on reading the first 5 chapters on Nakahara

Amherst

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Been off...

I have been off the books all this time with the visit from Meri and Ann. Even today that I was by myself. I woke up around 10:12 AM and took a shower, made some oatmeal and checked my feeds on Google's Reader. Then I headed to my office where I bought the bus tickets for the trip to Amherst online and then went to the post office to get boxes to ship some stuff for Meri's parents in California. When I got back to my office I decided to recycle all the used paper in the lab notebooks of my past class. I got a nice set of empty sheets of paper that I can use for calculations.

Most of the blogging online now is about Strings 2007, the annual conference about new developments in the field of string theory and related topics. I just want to say something about this: I was keeping an eye on the Strings 07 poster at the department's board and I guess someone took it. I wanted that poster! Oh well... The main buzz is about Ed Witten's latest paper on 2 + 1 gravity. Clifford writes that he not attending the conference might be a sign of some exciting new development being announce this year. Let us cross our fingers.

I should stop blogging about something I do not even understand and try to read something that could at least put me on the track to some day reach this understanding. With the trip to Amherst this week, and with friends visiting next weekend all seems a bit hopeless. I am going to try to finish the chapter on manifolds and see if I can cover the one on Riemannian geometry.

Some NYC exploring, finally

Finally I can say I have explore (a bit of) NYC. My loving girlfriend and her sister came on last Thursday and stayed with me at Stony Brook.

On Friday we took the LIRR train to Penn Station. We started by heading out of Penn Station looking for the Empire State Building. After mistakenly pointing to the wrong antenna, we "came across" the tallest building in the city. It was pretty impressive. I had been here before, probably like ten years ago, so I had forgotten how tall it looks. Then we headed toward Grand Central and the Chrysler Building. We walked by the New York Public Library, which looked pretty nice so I might return there by myself to read some mathematics or physics. On fifth avenue we looked for a bagel place, but instead settled down for a cafe that was close to the Museum of Modern Art, which was our main target. At the cafe I had a croissant sandwich with imported ham and Swiss cheese with some pesto pasta salad on the side. It was better than I expected.

The MoMa was pretty nice. The first thing that we saw was a very tall wall full of cartoon-ish drawings with a political attitude. We wandered around the different floors. The most boring was the floor on Design and Architecture. It was annoying that The Persistence of Memory by Dalí was out on tour. It will not be back until mid 2008. The Picasso paintings were nice at least. I really like Picasso since he explore the concept of viewing something from all points of view at the same time. I think that in his book Hyperspace, Michio Kaku discusses that just like a three-dimensional being can observe all of "space" on a two-dimensional piece of paper, a hyper-being living on a four-dimensional world would be able to see all perspective of a three-dimensional world.

Anyways, after the MoMa we walked to the toy store F.A.O. Schwartz and then through Central Park. The park was pretty nice, we walked through the south-east corner towards the mid-west part, catching the train on 72nd street to finally returned to Penn Station and catch the train back to Stony Brook.

On Saturday we started by heading to 79th street to get some bagels at the nearby H&H. The service was a bit rude, since I had to repeat the lady the list of bagels I wanted many times and to top it all they did not accepted debit cards. Nevertheless, the bagels were good. H&H is not a sit-down place, so we headed outside with no napkins or even a knife for our bagels. I had an everything bagel, same as my girlfriend's sister Ann. Merideth had a plain bagel. For home I bought two poppy seed (which are becoming my favorite bagel now...), two everything, two plain and one pumpernickel. After bagels we headed to a Starbucks for drinks. After all that w hoped on the 3 line of the subway downtown to South Ferry. We realized that we needed to be on the 1 line so we got off at Time Square and took the 1 that came behind us. It turned out that because of constructions the 1 is not going down to the South Ferry so we had to change at 4th street for a 2/3 train down to Chamber street and there we took a bus to the ferry. It was all annoying because of the sense of slow moving. By the time we got to the ferry for the Statute of Liberty all the boats for that day were sold and they were selling tickets for the next day trips. That was also depressing, but my company reacted well and instead we wandered around Battery Park and watch the street performers The Positive Brothers. They were pretty good, besides some technical problems with their audio and some out-of-the-hand jokes like expressing the desire for making an Oreo with one person from the crowd. Still they got one dollar from my wallet.

After this we had a fruit break where I had an orange, and literally came across the insides of a very nice looking building when I suggested to visit the bathrooms of the National Museum of the American Indian which was previously the U.S. Customs House. This museum is not part of the Smithsonian system, and it looked a lot like the ones in D.C. The small bit we saw was very empty, but the security guards at the entrance were really nice. We checked out Wall street, where we saw the New York Stock Exchange and the building where George Washington took the oath as the first president of the U.S. I wanted to find this place since it appears during the end sequence of Metal Gear Solid 2: Sons of Liberty. After Wall street we took the subway to Spring street, where we had a few slices of pizza from nearby Lombardi's. This place claims to be the first pizzeria in the U.S. It was truly great pizza, we had the traditional Margherita. Very yummy and tasty!

We headed to the Empire State Building after the pizza. The line was OK, but it was annoying all the stuff they are trying to sell you while you wait for the elevator. They even take a picture of you. The view from the top was spectacular, of course. This is the highest point in the city, since September 11th, 2001. After the view we sat down in front of the public library and then headed across Time Square to for the train to Penn Station.

It was all fun. I might go by myself at some point. Maybe next week since I have booked a trip to Amherst, MA on this Wednesday returning on Saturday to visit my friend Michael. Should be fun. Meri and her sister left on Sunday afternoon to London where they will start a trip along Europe for a three weeks. My girlfriend called around noon to tell me she made it fine to the hostel and that it was a bit cold. I told her that envy-green was my favorite color.

So far into the summer

Yesterday I just got back from two weeks worth of vacation visiting my family and friends in Puerto Rico. After procrastinating during the first week, I am happy to say that during the second week I was able to go out and do stuff. I went to Playa El Combate, a beach in Cabo Rojo, close to my hometown Lajas. The water was so nice. I wanted to just float all day. After this past winter I was really looking forward to the Puertorrican beaches. With my siblings I went to see Pirates 3 and with a friend I saw Rise of the Silver Surfer. I guess it is the summer of sequels. I did not had high expectations regarding any of these two movies, but I am please with both in the sense that they entertained me. [With a small exception in FF2 when Mr. Fantastic mentions the Tachyon Pulse... but that was not that bad...] I also attended the wedding of one of my friends, José Emilio, who married his long time girlfriend Miriel.

I found that some relatives where having more health-related issues. My cousin had a baby boy on last October and since then baby Edwin has grown a lot. Combined with the wedding, all this made me feel really old. I mean, serious stuff is going on around me now, deaths, births, and even weddings of friends. I must confess that watching my friend and his (now) wife in their wedding attires made me feel weird. To me their still two young persons who just finished high school. Well, the truth is that I finished high school 5 years ago. A lot of things have happen since then.

Before leaving to Puerto Rico I spent one week with my girlfriend in Wellesley. She finished her undergraduate education in physics this past spring at Wellesley College. I am really proud of her :-) she got a physics prize and was offer membership to two honor societies. I always said she is the smart one in the family. Which family? This is another sign of my age, I am thinking of marrying her and leaving together! There are some details that have to be figured out before, but we are working on that.

I stopped reading Srednicki's book on QFT and started Ryder's version. On my way to Puerto Rico I started reading Nakahara's book on geometry and topology. I tried reading it before, but now it makes more sense. So far I skimmed through the first two chapters and read a bit on chapter 3 on homology groups and also read a bit on chapter 5 on manifolds.

While at PR I also finished reading the biography/memoir of John Archibald Wheller. It was a nice read; a combination of personal stories about meetings with great physicist such as Bohr and Einstein, and how Wheller developed important concepts such as geons and black holes. The first thing I did when I came back was to download the article on geons from the APS website, using the university's account.

Speaking of the university, Stony Brook is like a ghost place this days. Today I walked to the mail room to pick up some packages. I had to walked through one of the quads. Maybe there is really nobody there, since it looks like they are refurnishing the rooms. But really, it is kind of eerie walking through the plaza. It reminded me of last summer when I visited the student union looking for the ATM and found the building completely desolated. Summer classes have already started, so I guess there are not that much people around. Or maybe they are staying elsewhere. Or maybe I just do not go out to often. I suspect the latter to be more correct than the former...

LaTeX on Blogger?

Testing Blogger's LaTeX capabilities...

Not bad...

Tis a bit sad

I think it is best for me to stop trying to blog on that one Wordpress blog. I should not spent so much time blogging, and besides what I wanted to do might had been a good idea but I need more time now to expand it properly...

In the heat... for a while

The weather here in Puerto Rico is pretty hot! I have been reading John Archibald Wheeler's biography. It has been a fun read, with some geometry on the side...

Equation of the week

Instead of concentrating hard on my summer readings, I have been thinking instead about my other blog. Mainly I have been re-evaluating my original purposes for starting The problemsheet. It has been fun so far. All the problems I have typed have been nice and typing has helped me understand them more. But honeslty it is very time consuming. And I can see this not being as fun all the time.

So I have been thinking, maybe it would be nice instead to post about a random equation every day. That way I can mention some of my favorite equations and at the same time post about other not-so-familiar equations. Now this seems more of a realistic goal! So I guess I am going to get the crane and start demolishing the blog, so I can reconstruct. It is a pity that Blogger does not have any LaTeX support.

Stay tuned for EOW.

A random prime

Here is a random 300-digit prime number. Enjoy!

2039568783564019774057658669290345772801939
9331434826309477264645328306272270127763293
6616063144088173312372882677123879538709400
1583065673383282791544996983660719067664400
3707421711780569087279284814911202228633214
4876183376326512083574821647933992961249917
319836219304274280243803104015000563790123

Oh, the mysteries of number theory!

Problem-solving

First I would like to discuss some quotes from Feynman. Here is the first:

Know how to solve every problem that has been solved.

What is Feynman trying to say? He means understand the solution to every problem that has be solved so far. Well, to most problems that have been solved. The way I see things so far, physics can be seen in some ways as a collection of canonical problems in different disguises. For example, the linearisation of non-linear equations of motion. Some of them admit solutions that involve harmonic oscillations about a certain point. In this case, the harmonic oscillator is the canonical problem. Even though this approach does not gives us the complete equations of motion, it still gives us some information about this small oscillations. And of course, the importance of the (classical and quantum) harmonic oscillator cannot be overstressed.

I do not think I have the capabilities of ever learning how to solve every problem that has ever been solved. But I guess it is a nice goal to set in life, unrealistic as it is. Is it worth learning all that stuff? Well, one can imagine that if we adopt this task, it will be eternal; new problems are solved everyday. In fact, in mathematics it is customary to re-solve problems with different approaches until the most elegant and simple way of getting the results have been reach. But life is all about learning. One will never know enough. In my opinion this is true, only arrogant will believe that they will know enough one day that they will simply stop learning.

Another quote from Feynman goes like:

The worthwhile problems are the ones you can really solve or help solve, the ones you can really contribute something to.

Now Feynman is trying to tell us that some problems are more worthwhile than others, based on their resolvability. I think this is a comment address to individuals. In my opinion it says something like "Know when you have more than you can bite". That is, everybody has their talents and it does not make much sense to approach problems where you will just stare at it silently for long hours with no idea at all. Now I am not talking about classroom-type problems, but in general physical questions. For example it could refer to some sort of experiment that cannot be carried out for some particular reason, or simply a calculation that is really out of ones league.

I am not saying that one should not try something hard and just comfort on the easy problems, whatever those are. The thing is this too is individual. Some people find some problems easy and others hard and some other people do the opposite, so in the end it also depends on interest. What I am trying to say can be explain better through an example. Say I am a theorist, and I want to calculate something that involves an application of a branch of mathematics I really do not know much about. In this case learning the new math will come as part of the knowledge package that comes during the process of solving the problem. But if I am really bad with that particular branch of mathematics, then depending on the degree of badness one can try and try and someday solve the problem or just be stuck forever on something that simply is not your stuff.

Maybe, just maybe, that quote was also referring to Feynman's view on string theory or quantum gravity in general. Maybe Feynman wants to tell us that there are some questions that really do not matter. Personally I do not think that the problem of quantum gravity does not matter just because it might not be pertinent in life. The truth is that there are also other open questions in modern physics that are more "basic", like understanding turbulence. It is "basic" in the sense that the problem is of classical origin, and has been around for a long time. I recall reading something along the lines of "There are other exiting problems in physics other then quantum gravity, like understanding the flow of water through a pipe". This is true. But I believe that turbulence is not an easy problem so in my case it is not worthwhile ;-).

In the end there are no such things as easy or hard problems; all problems require a consideration of certain ideas and situation that sometimes happen to be the most familiar to the person trying to solve them. For example, in my Quantum Mechanics final exam I could not answer one question about eigenfunctions of the quantum harmonic oscillator. Of course as an undergraduate student I went through all the derivation of the solutions (which apparently I forgot). Was the problem hard? No, I just happened to forgot a particular set of information, namely a set of symbols that represent the energy eigenfunctions for the quantum harmonic oscillator in an arbitrary energy level. It was not just a set of symbols, but I am still bitter about it ;-).

Some time ago I started another blog, The problemsheet. My intentions to start that blog were (1) to share with others solutions to some of the problems I encountered as a graduate student, and (2) to practice my typesetting with LaTeX.

In the back of my head I had some other intentions, like pursuing my own version of Feynman's goal and trying to show "someone" that I can solve problems. Maybe I wanted to be a smart ass like the people who display the solution to famous textbook problems online. I guess most of them do not want to show-off, they are just trying to help other students. That is particularly my first intention, but I know that in the back of my head I also want to show-off the grandness that I sincerely do not have. Nevertheless I comfort myself by thinking that by typing this solutions I am actually going through the problem again from the start, following it and looking for mistakes.

Another point that is also related to teaching is the fact that sometimes it is not easy to present one's results in a clear way without omitting some important steps. When I write down my solutions to assigned problem sets I try to be as clear and explicit as possible. Maybe it is the mathematician in me (who does not help me that much, that bastard...), or maybe it was the product of my undergraduate professors. I notice that fellow graduate students are not as explicit as I am in their solutions. I guess I want to be as clear as possible that (I think) I know the stuff I am talking about and am not fooling anybody. Nevertheless, I have been able to fool myself a couple of times.

Do people really expect students to solve every problem that is thrown at them? Now that I look back, I think my professors did. And I wonder why I was not able to solve every problem from the problem sets. Most of them were easy, in the sense that they involve some application of the stuff that was discussed in class. I do not think I encountered any evil problem during this two semesters, evil in the way that it requires some amount of genius to realize some not-so-obvious pattern or what-have-you. But as a professional, am I supposed to solve all the problems I encounter in life? I am afraid that a negative answer might imply some relying on others or something like that to avoid responsibilities. But after all, are we not working on a community? Well, I guess I tried being independent during this past semesters... but I suppose most people discuss their problems with somebody else.

I would like to mention something attributed to Gell-mann about Feynman's problem-solving algorithm:

1. write down the problem;
2. think very hard;
3. write down the answer.

I am going to adopt this mantra from now on.

One last thing I would like to address. Solving textbook problems does not make me great. After all, their purpose is to teach and get some ideas across. All this problems have been solved countless times by many others. So me and my little blog about problems does not makes me any better than anybody else. I am eager to start working on research problems, the type of problems that nobody has solved yet. This is what science is about in the first place, to understand the unknown.

Where is the quanta in this blog?

I have been reading the first few chapters of Srednicki's QFT. I feel like I have been moving slowly, I am still struggling with chapter 2 on Lorentz Invariance. I just want to make sure I understand how to work out all the derivations that are part of the end-of-the-chapter problems. Most of the problems are finding the commutator of a scalar field with the Lorentz generators and other stuff. More progress has been made in the next chapter on canonical quantization. I think I was successful in quantizing the complex (non-hermitian) scalar field. I was able to show that the field and its hermitian conjugate ( h.c.) obey the Klein-Gordon equation, I found that the conjugate momenta of a field are really the time-derivative of the h.c. field (i.e. for the field the conjugate momenta is the h.c. of the field-dotted) and wrote everything in terms of a mode expansion. Then I tried my hand at writing the commutators for the coefficients and their h.c., but I had a bit of a hard time understanding the motivation behind some of these commutators. Anyways, I think I wrote down the Hamiltonian density and integrated to obtain the Hamiltonian. I am going to try my hand now at the LSZ reduction formula for the complex scalar field.

I also found some nice material on Ryder's book on QFT about Lorentz invariance and the generators. Might take a look at that later in the evening.

Lorentz generators

Today I spent the day reading about the Lorentz generators. Just like spatial rotations, one can find generators that describe boosts. These have the same form as rotations, with the "angle" being the rapidity and instead of having trigonometric functions one has hyperbolic ones.

Basically I just went through some of the steps that Srednicki skips in deriving the commutation relations for the Lorentz generators. I have been slow, if I want to cover a lot of material during the summer I must move faster through the book. At least I am able to reproduce the calculations, which makes me feel not so stupid.

Where to start?

I want to do a lot of readings during the summer. My list includes Srednicki's Quantum Field Theory, Zwiebach's A first course in String Theory and Nakahara's Geometry, Topology and Physics.

The thing is, I do not know where to start... I was reading the first few chapters of Zwiebach's. It is alright, but I kind of want something more pertinent. The first few chapters are just building up to the relativistic quantum open and close string on chapters 12 and 13. I do not want to skip anything, but at the same time I feel a bit desperate. Anyways, I think I am going to try now Srednicki's book. Maybe I will be able to get through the first part on spin 0. I have to start with the math at some point too...

Spring grades are up!

I am sad to inform that I got B+ in most of my classes on this spring semester, compare to last semester's two B+ and one A-. I even got an A- in seminar, last semester I got an A!

I have mixed feelings about this. On one side I am still thinking like an undergrad, saying to myself that I could have done better, that I need to be on the top of my class, that nobody would like to work with a mediocre students with all B+s. On the other side I just do not care, and I feel like grades are not important. I have learned a lot, and sometimes I have been a bastard (like with Quantum Mechanics, which ironically was my favorite topic). I did a bit poorly on some homeworks because I did not had an idea on how to start some of the problems. The only thing that makes me feel better was that I did not copy solutions from websites or other students.

So I guess in the end all this grades make me feel more human. I am not a "perfect, know-it-all" student. I cannot solve every problem that is aimed at me. I will try them, and maybe I did not tried hard enough sometimes... but I did tried. Hopefully somebody will still want to work with me next year...

Pi time!

Quantum crops like to celebrate pi time, instead of the British tradition of tea time.

[Edit: I have just realized that pi time should be taken to be 3:14 AM not PM... Oh well!]

One year down...

... and so many to go. Today I had my last final examination of the spring semester, on Quantum Mechanics.

Overall it was a fair examination. I think some of the problems involved a significant amount of tedious algebra. I finished 15 minutes early, but I did not worked on the last problem, and I deserved it. The first problem was a harmonic potential along the z- axis define on a square region of the x-y plane, outside this region an infinite potential in the x and y directions. We were asked to find the energy eigenvalues and normalized eigenfunctions, but I could not recall the functional form of the harmonic oscillator eigenfunctions. I learned them at some point and I got used to reading them from textbooks, so I could not remember from the top of my head. Oh well. This makes me a tad annoyed, since the professor did not allowed a formula sheet. If I were stranded on a deserted island with no books or any food, I think the first thing on my mind will be to get something to eat, not doing any physics. But maybe that would be the fundamental difference between me and "the good students"; they choose physics above personal satisfaction.

Anyways, the second problem was about time-dependent perturbation theory. We had a potential that was turned on and was cubic in x and decayed exponentially in time. The system was a harmonic oscillator. We were asked to find the probability to have transitions to any state starting in the ground state. It took me a while to remember the expression for the first order correction, but at the end I think I got it. I was happy with my self, since I was able to write the cubic x term in terms of the creation and annihilation operators and the number operators and this time I got something that was really easy to finish. I remember one homework we had a cubic term and I did not simplified it enough. But thankfully I had the idea to write everything in terms of the number operator and the made it easy to realized only two terms survived. The third problem was two identical fermions in an infinite well potential and we were asked to consider the spatial wavefunction for the triplet and singlet spin states. Finally, the last problems were about a constant potential radial barrier, and we had to answer some questions about phase shifts. I knew this question was coming and guess what? I did not study for it. The last week of classes were really hard on my sleeping, so I was half awake during class; and I just thought it was a complicated topic for an exam. Wrong! None of those is a real reason not to studied. I never learn my lesson, it is a good thing that I could not answer that last question, because I did not deserved to done well.

All is done, I passed Statistical Mechanics with a B+. I finished my finals. I can relax. Meri is coming tomorrow and we might go to New Haven for some exploring. Today I will try to start with my summer self study: Quantum Field Theory, basic String Theory and a big load of Mathematics!

Graduate Food

Now that I am finishing with my first year of graduate school, I think I should start writing about my impressions and experiences. I decided to comment first on the food ;-). You see, when you are so busy sometimes you can forget that you need to eat food at least twice a day. I tried having three meals a day. Since there is so little time to cook, I thought of sharing my usual meals and some recipes.

Breakfast

The easiest breakfast by far is cereal. I fluctuated between Frosted Flakes, Honey Nut Cheerios and regular Cheerios; most of the time buying the generic brand. I know, all this are not very healthy. In fact I do not eat that healthy. But I try! Anyway, some mornings I had late classes (10:40 AM), and since I tried waking up everyday at 8 AM, I had some extra time. These days I made scramble eggs with toast, or pancakes.

I am particularly fond of pancakes, they were the cheer-up meal. Usually I just followed the recipe in the box. But of course, one gets pretty tired of things, so I started experimenting. I remember that my father use to add cinnamon to the batter. I also had some oatmeal pancakes during last summer. Combining these with bananas and some vanilla, I came up with banana-oatmeal pancakes. Just prepare the usual pancake batter. Then add two drops of vanilla, a sprinkle of ground cinnamon, and a mashed banana. These were mostly prepared during the weekends, to my loving girlfriend who also loves them ;-).

My girlfriend and I are also very fond of French toast, but again this is a slightly complicated meal that takes a bit of time. So I guess my final advice for breakfast is cereal. If you really are on a hurry, there is always a bagel or a pair of toasts.

Lunch

My lunch is also not that healthy, but I found it very popular among graduate students. In order to force myself to eat some fiber, I have been eating peanut butter and grape jelly sandwiches on whole wheat bread. This is money friendly, since with less than $10 you can buy lunch for the whole week. In fact, the jelly and butter will last for a few weeks. Sides include a fruit, mostly a banana, apple or an orange; and sometimes white corn chips. All this drown under a litter of water, all important.

Maybe I will try to experiment with salads during the summer...

Dinners

Dinners are also sometimes rushed. I found that it is best to pack something and heat it on the microwave, than to walk back to the apartment or buy something at the student center. I am pretty sure pasta is the most popular food for graduate students, since it is easy to cook. Well, I am convinced now that pasta with marinara sauce does not saves well. Once you save it in the fridge, the next time you heat it it is very dry and nasty. But pesto saves the pasta, maybe because I love pesto. I had never heard of pesto before I came to the US. Two years ago I had my first basil pesto pasta. I liked it, and I am happy to say it saves well, after a couple of days it still tastes fresh. Just buy a big box of pasta and a jar of traditional basil pesto, boil the pasta, then just add the pesto. You will have three days worth of dinner. I found that helpful, cooking on Sunday night and then not bothering until Thursday night.

Another popular thing is the Mexican tortilla. You can make burritos, quesadillas, etc. Quesadillas are easy to make and are a quick meal. But my favorite are the spinach enchiladas. I learned about these two summers ago, but finally tried them last summer while at Stanford. This is the only dish that has any type of vegetable, I feel bad about that... but they are really good! I guess I add lots of cheese, which is not good for your veins... Anyways, here is the recipe:

Spinach Enchiladas

1/3 of a package of frozen chopped spinach, defrosted of course
ricotta cheese
sour cream
Mexican cheese blend
one can of enchilada sauce
flour tortillas

In a big bowl add the spinach, three spoons of ricotta, one small spoon of sour cream, half of the Mexican cheese blend and a drip of sauce. Mix well. Spread over tortillas and roll. Place enchiladas on a baking pan, maybe you want to add a layer of sauce at the bottom. Cover the enchiladas with a layer of sauce and the rest of the cheese blend. Cover with aluminum foil and bake in the oven at 435.927778 Kelvin for about 25 minutes or until the cheese is melted; you might want to uncovered them so they can get a bit golden. This makes about 4 servings.

You can make enchiladas on a Sunday night and have dinner through Thursday! Other things I tried were rice with frozen vegetables, but that never came out fine. There is always delivery. Here in the Stony Brook area so far I have tried Lan Wo, Chinese food that is cheap and they have SUNY student dinner deals. There is always Domino's and I also tried once a nearby Greek place, but that was a visit. There is an Irish pub, but I asked for a Parmesan sandwich and they brought me a chicken Parmesan pasta, which was not bad, but i was sick of pasta. When I visit Merideth in Boston, we always stop by Anna's Taqueria in the MIT campus. Their chicken quesadillas are just amazing.

Another favorite dish is the pita-bread-pizza. Just take a pita bread slice, spread some tomato sauce and add some mozzarella cheese, then bake in the oven for about 15 minutes or you can also try the microwave oven for about 2 minutes. I just love these!

I am not going to say it is very original, but after some time I decided to sprinkle some Italian garlic seasoning to the top layers of a grilled cheese. The result now is pretty tasty, you might want to try it.

There is not much meat in my usual meals. I found that meat takes longer to prepare, and I have grown comfortable with the simplistic attitude in the kitchen. I love my pork, sometimes I made some pork chops with mashed potatoes. But these were very rare.

Desserts!

This might be a surprised, but desserts might be the thing that can keep you happy through a week of exams, homeworks and grading. Mostly I made brownies. Just follow the recipe on the back of any mix box. I also rediscovered pumpkin pie. Again just follow the recipe in the pumpkin can. Pumpkin pie will also be my holiday dish for March 14th (3/14).

All this made me feel hungry...

Happy Birthday, Mr. Feynman

On this very day, 89 years ago (according to Wikipedia) Richard Phillips Feynman was born. Feynman was natural of Far Rockaway, which is located to the west of Stony Brook, here in Long Island.

Most physicist will tell you that Feynman was one of the best scientist of all time. He was part of the Manhattan Project, where the first atomic bomb was developed. Independent of the final purpose of this weapon, the Manhattan Project was an important and unorthodox scientific project. As a physicist, Feynman contributed to the development of the theory behind Quantum Electrodynamics and developed a diagrammatic approach to calculation that now bears his name. He also had important insights into areas such as elementary particles, computation, nanotechnology and statistical physics.

Last summer I read Feynman's biography by James Gleick. It was a wonderful read. The first thing I did after I finished reading it was to buy the Feynman Lectures. I really admire Feynman, he was really special. But sometimes I wonder whether he was really like that or whether most of his doings were exaggerations by people. In the end I do not care. Once I met somebody that actually had met Feynman. I asked this person how Feynman really was. The person just look to the sky, smiled and said "Oh he really was something...". That was the only thing he said.

Sometimes I feel like it is a bit silly to admire somebody that much. I guess (in general) people think they could be like them, they could attain all the fame and glory that a given famous have had. Well the truth is that there was only one Feynman. Nobody else can be him. And sometimes it is a bit hard to even try to be like them. What I am trying to say is that the best thing that can be done is to be honest with yourself and say: "Hey, Feynman was awesome, but I am not Feynman and should not even pretend to accomplish what he did". I want to say this, because I feel like I tried to accomplish many things that people around me where doing for some time. Maybe I am still doing some of that.

When I was in high school I remember everybody wanted to be an engineer or a doctor or a lawyer or a psychologist. I did not had an idea what an engineer did, I only knew that it had to do with NASA and space travel. When I was younger I wanted to be an astronaut too, but I think that is more common. Anyways, I remember hearing about the subject "physics", I had to take it during my 11th grade but there was some problem in my school and my class ended up taking biology as the science class. Along that same time line, I remember that I had one of those test about professions and interest. I do not remember what was my result, by I remember reading about all the descriptions for different areas. I had liked the chemistry class, but for some reason I enjoyed more the atoms and electrons part than the whole chemical balance and solutions, etc. Physics was described as something along the lines of "the study of matter and energy and their interactions". For some reason this reminded me of Albert Einstein, I guess because of his most famous equation. So I read on my encyclopedia about Einstein work, and about physics in general and found everything very interesting. And above all nobody else was interested in doing physics. So I felt good about it.

On my 12th grade I finally took my first course in physics, which was a bit disappointing. Around that same time the news of a child prodigy from a nearby town started appearing. At the time he was eleven years old, just finished high school and was going to start college to pursue a degree in physics. I remember that the first thing that came to my mind was hate, I hated him for being ahead of my and for being all smart. Then I realized that there was no real reason for me feeling this way, so I change my attitudes. Still, I continued with my interest in physics and now I wanted to attend the same university the prodigy was attending so I could meet him. It was not until my second year of college that I finally met him. To my surprise I was taking a course with him. And as it turned out, I took mostly all my physics courses with him. During the first few days it was very bad. He was quick and answered most of the professor's questions. Most of the times I did not even had time to consider the question at hand and think of how to answer it. I remember that I concentrated on getting better, just for the sole purpose of beating him. Thankfully it was not to late before I realized I was doing the wrong thing.

Pushing yourself hard just to be better than somebody else is the worst think that one can do. Along the way it makes you act in ways you never thought of behaving. In the end I realized that there was a fundamental difference between the prodigy and I, and that I should not care about his progress but care about my own. It worked well most of the time. We became good friends, just as life should be. I think life should not be about who is the best, but about what individual people accomplish and the importance of everybody's contribution.

In graduate school I found myself monitoring others still. Haven't I learned my lesson? Why is it so hard to disregard other people's progress, and just concentrate on yourself? I guess in the end one wants to success in life, and the fear of not doing so takes over everything else. My ideal state of mind is to fully concentrate on my own progress and flaws, and disregard others. It is not about ignoring, no. I want to have friends and celebrate their own success. But I do not want to compare myself with others. It is just a waste of time and energy (to conjugate variables).

Well, I wanted to talked about Feynman. At the same time I mentioned a bit bout idols and comparing yourself with others. Maybe later I will write some more on this topic.

Two final exams, two silly mistake

Well I feel accomplished! Yesterday night I did my last chunk of grading of the spring semester. I had my Statistical Mechanics final exam yesterday morning too. It went better than I expected, considering the fact that I had been doing pretty bad on the partial exams and on some of the homeworks.

There were three problems. The first problem was to consider an ideal spin-0 boson gas. We were asked to find an expression for the chemical potential, and then decided whether you can achieve Bose-Einstein condensation with that system. It was a straight-forward calculation. In the end I found that there could not be any condensation. The second problem was a two-cite Ising model. We were asked to find the susceptibility and the energy variance. At first I started to freak about about the susceptibility, since I had to calculate the average spin. But then I found an expression for the average spin; it was just the derivative of the free energy, which can be found easily with the partition function. Then I completely forgot that I wanted the susceptibility and carried on to the next part. This was my first silly mistake. I had to provided low and high-temperature behavior of the susceptibility and instead provided the analysis for the average spin. Oh well! The last problem was to consider a weakly damped one-dimensional harmonic oscillator. We had to find the spectral densities for the spatial coordinate and the momentum coordinate. I tried something, but to be honest I never fully understood this last part of the course. Partly because I did not cared (and I should have cared), and partly because It was something new and I felt it was a bit rushed (I know, that is a very lame excuse). Overall, I hope to pass the course, at least with the minimum. I have worst things to think about next semester...

But it was not until today early morning, around 2:12 AM, that I realized my second silly mistake. The Electrodynamics final exam had been on the day before yesterday. Again, three problems. The first was an easy question. My professor is an experimentalist, he works with x-rays at the National Synchrotron Light Source. In day during class he asked us what was the wavelength of one photon with an electronvolt of energy. It turns out that this is related to an expression that involves three  fundamental constants: Planck's constant h, the speed of light c , and the elementary charge e. The answer is 1239.8 nm. The second problem was to reproduce the calculation of the electromagnetic fields of a charge particle in motion. The idea was to consider a charge moving with constant velocity along the x-axis and to calculate the field at a fixed point along the y axis by considering the fields in the rest frame of the particle and then Lorentz- transforming to the lab frame. It was straight forward. Finally the last problem was about an electric dipole that was rotating along the x-y plane with a given angular frequency and we were asked to calculate the radiation fields and the angular distribution of the radiated power. This expressions involve a unit vector from the source to the observer. Usually this unit vector is a position vector divided by its magnitude. But no sir, the gentlemen writing to you on this cloudy afternoon decided that the unit vector was just the sum of three unit coordinate vectors. For starters that is not even a unit vector! Everything depended on that unit-vector, so of course everything came out wrong; my power distribution was uniform... I did not realized what my mistake was until after a day. What makes me most angry is the fact that I knew it had to be wrong. But I continued on, lying to myself. It all sucks. Oh well, I had been doing better at E&M, so I expect to pass this class too.

Next Tuesday I have my last final, Quantum Mechanics. I hope I do not have to writ about my third silly mistake.

Undergraduate orientation

When I was a freshman (not so long ago... well 4 years) I had a class that was suppose to be an orientation for freshmen. What I recall the most from this class was the professor (who was the head of the department at that time) saying a lot "physics is the science, the rest are details" and claiming that this quote was from Einstein. Anyways, now that I look back, I see all that could have been covered on that class.

Something that needed to be covered was to present physics as the interesting and exciting field that it is. I would have talked about all the interesting work going on at the many national laboratories in the US and around the world. I guess from my point of view, physics sounds interesting. After all it might be a matter of whether the students are not to stubborn. In my year most of the students wanted to change to engineering. They all regarded physics as "hard". To this very day, I still get from people that physics is hard when I tell them about me being a physics graduate student.

I would have mentioned some historical background of important discoveries and advances in physics. For example, the Manhattan project provides a very interesting theme to discuss topics like ethics and working conditions. Other examples would include a small survey of Nobel prizes. The history of Quantum Mechanics would have also been a nice interesting topic, mentioning names like Bohr, Schroedinger, Dirac, Heisemberg and Feynman. Biographical talks would be nice too.

At the freshman level, physics is not that fun. I know some people will disagree with me, but I believe that with no calculus it is hard to go into much details. Still, maybe a survey of the many branches of physics and its topics. An example would be Statistical Mechanics and different species of particles (fermions versus bosons), interacting particles, mention of BECs, importance of the electron gas to Solid State physics, even define what Solid State physics is. A little overview of relativity and the different types of wormholes. Problems in high energy physics. All this maybe to the limitation of just mentioning names and dates... but I think that would be enough to motivate the students to stay in physics and try to go as far as possible.

I good freshman year will give the student the idea that the remaining years in college will be rewarding.

Hawking goes weightless!

Quantum Crops would like to congratulate Stephen Hawking on his recent weightless experience. I can imagine how much this would mean to professor Hawking, a man that has spent his life studying gravitation, among other things.

Via Reuters.

Who wants to be a theoretical physicist? - Part I

On this post I would like to comment on the "difference" between being a theorist or an experimentalist.

First of all, what the hell do I know about being a theorist or an experimentalist? After all, I am only a first year (almost second year...) graduate student. Well, guess what? I want to do theory. No surprise, since the majority of the students want to do theory when they go to school. The first point is, I am not really sure I want to do theory. That is, my experiences so far consist of field work in laboratories. I really do not know for certain whether I want work with theory. I just like it.

To tell you the truth, I also liked working in the lab. Last summer I had the opportunity to work at SLAC. My project involved putting together an apparatus that assembled water samples for x-ray transmission experiments. It was fun, since I had to manipulate the fluid cells really carefully. I came up with an array of micrometers that slowly assembled the sample. I also went and try them at the Advanced Light Source in Lawrence Berkeley National Laboratory. I know, I am talking about fancy labs, whatever that means. But I was a bit hesitant about working in the lab. My undergraduate years included two semesters of "Intermediate Lab", something that was really depressing. I know that science labs education is a big challenge. My advanced lab experience made me feel really frustrated. Sometimes the experiments were not working; once I even burned one of the detectors. Most of the experiments consisted of a well organized series of steps, that appeared to be really straight forward to carry out in theory. In practice it was not that way. I guess the fun and excitement lies in encountering problems along the way and coming up with solutions. I guess that is how experiments are actually carried out.

There is a little demon inside my head that wants to suggest the following format. Learn about some phenomena (i.e. diffraction). Now device an experiment that will let you measure something (i.e. diameter of a human hair from the diffraction pattern). This type of format will require a considerable amount of equipment, but hey it is just a proposal. Students will learn that the whole process of carrying out an experiment is long and hard. One will have to go not only through the stages of the scientific method but also through the whole design of the experiment.

There is also a little angel inside my head that is suggesting another format for a lab course. How about keeping all this pre-arranged experiments, but having meetings with the professor or the instructor and going through the lab. A quick lecture of the theory behind the phenomena that is to be measure. Also some comments on understanding the instruments and methods used to get the measurements. This way the students will understand better what is actually going on during the experiment. What I am trying to avoid is mindlessly sitting down and pushing buttons to get numbers and just going around with them to get standard deviations and etc.

Having bad experiences with undergraduate labs does not justify that I do not want to become an experimenter... So why do I want to be a theorist?

It never pays

Procrastination never pays...

During my spring break, which coincided with "Holy Week", I did little homework and no reading. I really wanted to relaxed. I did worked, but basically I felt like a sloth: slow. Or maybe I should say stupid. Whatever, I was just not processing anything. I did not even finished with taxes, which was very annoying. Taxes were like taking a test on something you never heard about in your life.

But this week, I straighten up. By Friday I had finished the EM homework and had half of the SM homework already written. I guess I have been more motivated since I started reading the Harry Potter and the ... books. They are pretty good, I cannot help but compare myself with Harry in Hogwarts, with physics as magic.

I have also been feeling a bit less stressed out. I did not contacted anyone else regarding summer research. Instead, my plan is to read Frankel's The Geometry of Physics and Zwiebach's A first course in string theory. Both should keep me busy during the summer, before I probably start TAing during July. More on that later, now I should finish my QM and my SM and maybe grade a little.

Calmness, finally

Things are finally settling down around here. Yesterday was my second statistical mechanics midterm: it was easy, but I am very disappointed at myself. I worked very slowly and only had time to work half of the first problem.

There were two problems. First we were given a 2-D electron ideal gas and were asked to find all thermodynamic characteristics for the case of zero temperature and temperatures very small compare to the Fermi energy. The other problem was to discuss an aparent contradiction with Bose-Einstein condensates. Below the critical temperature we know that the chemical potential is zero. This would imply that the Gibbs energy is zero. Generally the entropy of a system can be found by differentiation of the Gibbs energy with respect to temperature while fixing the volume and number of particles. Since the Gibbs energy is zero, then the entropy will also be zero. But in class the professor found an expression for the specific heat of the Bose gas as a function of temperature below the critical temperature. This specific heat can be integrated to yield the entropy, which in this case will be a non-trivial function of temperature. WTF?

I am disappointed at myself. I spent to much time organizing my thoughts during the test. First I quickly started calculating the energy and occupation number for the electron gas when the temperature was zero. Then I found the other potentials, but not the specific heats nor the entropy. All I found were things in terms of the area, surface tension and number of particles, so I could not take any derivatives, of course, since the temperature was fixed. It turns out that for any temperature you can calculate the number of particles in the system exactly since the integral can be evaluated analytically. But Melvin here just stared at the paper for a long time trying to remember how to integrate such things as one-over-e-to-the-x-plus-one.

In the end I do not think all the work I handed in is worth 50 points (out of the 100 points the first problem was worth). I did not even worked on the case for temperatures below the Fermi energy. I presume that some sort of series expansion was needed. I have realized that I am not good with series expansions and I need a lot of time to set everything up. This makes me very sad because I believe that being able to work with series expansions is very important for physics. I should settle down and learn them right once and for all, before this goes to far... if it does...

For the second problem I just wrote down some garbage on how I believe the Gibbs energy was not zero dealing with the fact that there are two phases present below the critical temperature (the condensate and the gas). Now that I think of it, well no. The entropy when the temperature tends to zero should tend to zero too. Also in phase equilibrium both phases have the same value for the chemical potential. Anyways, the whole point is that the test made me feel really stupid.

Yesterday at the electrodynamics recitation the professor stated the following problem. Consider a charged particle at rest in a region of constant electric and magnetic field, with the fields perpendicular to one another and having the same magnitude (in Gaussian units!). What is the trajectory of the particle?

We fiddled with the problem by writing down the Lorentz force law. Because of the Lorentz-gamma factor, the differential equations for the velocity or momentum components look kinda nasty. The professor believed that there was an analytical solution, but he said he was to lazy to find it so he would prefer to solve this problem numerically. This was just for fun, but I kept on thinking about it and decided to work on it during the night. I discretized the two equations and found a nice system of couple differential equations. It is not very complicated, but I just suck at debugging code, so it was not until this morning when I was able to make the program run properly. I found what was expected: the magnitude of the velocity tends to the speed of light, and the trajectory just blasts off to infinity with slight distortions. I felt happy, since I had accomplished something that appeared to be correct. So I emailed the professor some of my results and went to my class.

It turns out that the professor had found an analytical solution for this problem, so I seem not to pay much attention to my results. My ego was just demolished :-(.

And it has been like this during the past weeks. I am feeling like a forgotten piece of crap, very useless. On my previous SM midterm I got something like an 84 out of 150, on the QM midterm I did slightly better with 14.8 out of 20, the average being around 14 so I guess I am above average. But I have not been doing that well in the homeworks, there is alway a bloody problem where I do not have a bloody clue on what to do. A more positive picture is on EM where I was able to score a 95/100 in the midterm, and my homeworks are not that bad. But in SM... oh boy. Two homeworks ago we had to calculate the third virial coefficient for the hard-sphere model of a non-ideal gas. It was way more complicated than I thought, so I only got half credit. In fact, only two students got the correct result, most of the class got half-credit. Then on the previous homework we had to find an expression for the vapor pressure of the van der Waals model. Again, I did not worked this problem completely and expect to do very poorly. All this added to not doing well on this second midterm may imply that I could fail this class. Ahh!

I do not even want to think about it. Currently I have been over worried thinking about next semester. I am planning on taking Quantum Field Theory and Relativity and hopefully a breadth course. At the same time I should attend more theory seminars and maybe the Strings course.

Summer plans

My summer plans currently consist of just trying to absorb as much as possible from Srednicki's Quantum Field Theory and Frankel's The Geometry of Physics. I emailed some professors in the math department here in Stony Brook. My idea is that I do not have the background to work on a string-related project yet, but I could take a mathematics project. I know that I also do not have the mathematical background for a math project, but I figured it would be more effective for me to learn some math during the summer and in the end do some sort of calculation than learn some partial stuff with strings and then have to wait another year to continue. I still have to email some other professors... who knows!

Divergent Series (The Haunt of)

So one class ago my QM professor talked about how infinite series creep on you and sneak on you to come and blow up on your face if you do not truncate them, say like for the Hydrogen atom problem.

I guess these are what a theorist's nightmares are made off...

Srednicki's

Also, I got a copy of Srednicki's QFT textbook. Should be fun!

Before the tempest...

Well March is going to be hell month. Three midterms and a seminar presentation. I gave the seminar this past Wednesday. It went better than I expected, with not so many annoying questions. Next week starts the one-midterm-per-week with EM.

Sometimes one has to know when to stop. I have been struggling with a problem from SM. A two-level system, approaching it with the grand canonical distribution. I just cannot get anything to come out like the results from the canonical or micro canonical. Anyways, I am sick of it. Tomorrow I will check the library for other sources. Now I shall start with this week's EM homework, which finally has some problems on relativity ;-).

Wordpress

I am going to be doing some blogging over at Wordpress, since they have enable LaTeX typesetting! That is so cool! :-).

Destroyed

Phew! Just finished grading this week batch of lab reports. Last week saw my ego completely destroyed by the first midterm on statistical mechanics.

It was an easy exam. The first problem was a collection of two-level systems; we were asked to find thermodynamic quantities and analyze them. I started doing things the wrong way, until I finally realized I had to find the partition function and calculate everything from there. It was to late when I figure things out. The second problem was a rotating cylinder with a pressure in its axis, we were asked to find the pressure in the boundary. Again, I started walking the wrong path and by the time I realized what I had to do it was to late. Literally, time was up. So I handed in two less-than-half-way done problems.

I was angry at myself. So angry that during lunch I bit my own tongue. I hated myself for not thinking things right. Then I felt in this thinking storm of how I sucked as a physics student, how I was alright back in Puerto Rico and how I am never going to make it to work with quantum gravity. It made me feel really low. I went to Boston during that weekend and worked on homeworks.

I had worked on EM previously during the week, but on Sunday night I realized that what I did was very wrong. It turned out I only had solved correctly one problem, out of 4. Again, it made me feel so hopeless. I ended up arriving at Stony Brook around 8:30 PM to grade my part of the midterm grading for the class I am TAing. It turned out that the professor wanted the grades early, so he had started grading my part with another instructor. I felt so bad when I saw somebody doing my job. I graded a bit of what was left and helped entered all the grades to the spreadsheet in the computer. This lasted until 3:00 AM.

While walking back to my apartment I saw the snow falling down on the campus. That night and Monday we had like 3 inches of snow. I think most of it is melted now, since it had been relatively warm lately. On Tuesday I got my grade from the midterm and it was not that bad, 85/150. The average was around 100, so I am well below average. I do not feel that bad, because I know that (at the end) I had an idea on how to solved the problems.

I also email some professors in the mathematics department asking for summer research. Three out of four already replied with a negative answer, mostly the same; they are busy, they are going to be gone during the summer, they do not have anything to offer, and I can always take courses to learn. I get a bit annoyed by the fact that they tell me I can take the courses. While it is true, I can take the courses at some point, I also have to take a lot of other courses. I am tired of taking courses and solving textbook problems. I want to work with somebody, and to learn things in a non-linear way. Oh well, there is still one professor who has not replied, but I do not have my hopes high...

Still, I am a happy person.

Is it fake?

It is about time I bring some graduate school experiences to this blog, so let's all get worried about my future!

I have been thinking about it. It might not be the best thing to do now, since there are other things more pertinent at the current moment (like passing my classes with better grades than last semester), but I believe that I should think about it for a little while. The first thing in my head is

summer work.

This is related to the problem of

housing.

If I do not have a summer job, how am I going to pay for my housing? I cannot just walk to the YITP and tell everyone "Hey, give me a project for the summer and I will work on it". First of all, I do not anything about string theory yet, and my quantum field theory is very rudimentary. My special relativity is better, and my math skills are so and so, but still. I do not have a good reason why I want to do research in string theory. Is is fake? Of course it is, after I read (and watched) The Elegant Universe and Hyperspace I just wanted to learn about all this theories and work with them. But just a popular approach is not even close to what it actually is.

Have this semesters being a waste of time? I do not think so. Like professor Likharev said once, "This is the basic core knowledge of physics" (or maybe he said something along this lines...). I needed to take these classes, I really lacked that knowledge. So maybe I am rushing to much. The plan for next fall is to take course on field theory and relativity, and maybe the breadth courses and graduate lab. Which brings me to my second thing,

what to research?

Either I read on my own, or take courses on strings (which I will take at some point), but I need to learn about this topic before I even think of what particular aspect I would like to study. The thing is, time may not be enough. Money is a crucial part of my survival, which is a sad thing. Gotta go to class now...

During one year...

...my girlfriend went and came back from New Zealand, I graduated from college, went to California for the summer, spent some weekends in the Sierra Nevada Mountains, moved to New York, started graduate school in Stony Brook, got a lot of experience commuting to Boston from New York, went to San Antonio for Christmas and met little Vonn, went home for new year's eve, saw the first falling snow in Wellesley and started my second semester at Stony Brook.

Phew!

Happy Birthday QC!

This blog just turned one year old. Happy Birthday Quantum Crops! It was a long and arduous labor, but it is growing healthy.

Well that is annoying...

Life is a beach.

Today classes were canceled at 2:00 PM due to the current weather conditions. This morning while walking to my office I almost got blown off the sidewalk by the wind, the chilling wind. It was not that cold. It was even raining, with about two inches of snow in the ground. But the wind... the wind was blowing from all directions! Oh boy, my poor umbrella was torn to pieces.

Today at 2:20 PM I was presenting my seminar talk on the search for supersymmetry. I must confess I was not 100% prepared for it. During this past weeks I have been paying the price of my procrastination during the first week of classes. It has been one homework right after the other, with almost no rest between. I am very sleepy now. The first EM homework was handed in with almost all problems partially solved. For the second I choose not to solve one of them. Statistical mechanics was done the night before. This class is scaring the shit out of me, since I feel I am not following the professor during lectures. And QM. For the first "set" I had to work on it just the night before, and literally solved only one of the problems the morning it was due. I have been out of it. And my dedication to the seminar presentation was very little, in the sense that I have not read that meaning papers related to experiment concerning "the search for supersymmetry".

I put some slides together in the course of these past two weeks and really wanted to get it over with today. Oh well. I guess now I have more time to work on it. Make a better presentation.

I also need to start working on the QM problem set due tomorrow.

No rest for the wicked.

First week of classes: Spring 07

Monday was OK. Electrodynamics started without any mercy, jumping right into waveguides calculations. Pretty intense. This is just what I wanted to test my masochistic change from coffee to tea.

A very unscientific feeling tells me that coffee is bad for me. I spent the week before classes started at Merideth's and there was no coffee there. So I drank tea. And I felt different, better. So now I am drinking tea instead. I bought a box of green teas. On Thursday the I had a ginseng tea, which I suppose did not had that much caffeine. I got a massive headache by the afternoon. Yesterday I bought some regular black tea, hopefully this will work.

Tuesday I had the other two classes, Quantum and Statistical Mechanics. In Quantum we had a review of to much stuff, it got pretty boring, pretty fast. In Statistical Mechanics, the professor talked about thermodynamics. Now I had a pretty good thermal physics class in the RUM, but it was a long time ago. Time just flies! So I have to review my thermo... I also had my first TAing meeting on Tuesday afternoon. It was pretty boring, since it is the type where all the course staff comes, so they focus more on the professors. I got to pick my lab sections: last fall I had sections L06 and L08, so this semester I went with the odd ones, L03 and L05. This time I am going to TA for four hours straight! It is going to be nasty, and nasty to grade, but I think I shall survive.

On Wednesday I got to pick my graduate seminar topic! Nobody wanted one of the first slots, on February 14. So I thought to myself, I can just get this over early! So I signed up for the first day, and I got to pick my topic first: The search for supersymmetry. It is going to be awesome.

The rest of the week was alright. Lots of procrastination, to much in fact. Friday was the COLDEST day ever. It felt like -10 degrees Fahrenheit. It was horrible. Today I went to the post office and applied for a passport. Oh yeah, passports are expensive!