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