Shuttin' Detroit Down

I count my blessing everyday; I get paid to do something I love and my "job" is pretty much locked up for the next 4 years, as long as I qualify for PhD candidacy. Others in this world aren't so lucky... many in this world aren't so lucky. I've lived a blessed life and have not had to struggle to get by; ends have always met. There is one thing, though, that I am a firm believer in, and that's hard work and dedication and I respect all those who do the jobs that make our comfortable lives possible and those who work 10 times as hard as I do just to put food on their table.

My girlfriend would be proud, I am a fan of a country song.

Solution #3

The solution to Physics Question #3 is posted, take a look, see if you're intuitions were correct!

Bessel Functions

Having just encountered Bessel Functions for the second time in my life, I must say that they did not seem any friendlier. For a non-axisymmetric galaxy gravitational potential (think of a barred spiral galaxy), the surface brightness of the galaxy may be defined using a double integral over two Bessel Functions, J0 and J1, both with different arguments. I have to say, it was gruelling and a pain in the ass, but I was finally able to get it to work out earlier today. It involved doing one integral on the computer, but the rest was a lot of calculus to get it to work. As hard as it was, it was fun, and the satisfaction of actually obtaining a result was great. Still, Bessel Functions and I are not close friends. There are relations between them and various integrals that are easier to do than others, it's just a matter of finding which form you need and how to get there. Rather annoying, but worth the time and effort put in. Maybe I'll post the solution later.

Universe Today RSS

I just wanted to bring to everyone's attention that I have added an RSS feed from universetoday.com which is a good website to read up on some current findings in astronomy. They also have good educational podcasts, quizzes, etc. Some of you might find it interesting and informative. If not, no harm done!

Elegance

Here is the derivation of some fairly well known (aka - know them or die) physics equations from electricity and magnetism as derived using the variational principle. I skipped a few steps here and there, mainly with the first couple lines of the variational principle, but the blanks can be filled in if necessary. I am posting this because I found this derivation so elegant and absolutely wonderful. We derived it for General Relativity in order to get familiar with some mathematical tricks; but still, it's beautiful.

Tropicana

Depending on how much you drink orange juice, you may or may not have noticed a new program being put on by Tropicana. The company has teamed up with a conservation group, Cool Earth, in order to protect the Rainforest in Peru. By opening an account, for free, you can enter a particular code on your orange juice container which "saves" 100 sq ft of Rainforest. I'm not entirely sure how this works in the long term. According to the Cool Earth, the funds they receive go to hiring "protection". This protection is in the form of a responsible official whose job is to patrol an area of Rainforest, every so often, in order to make sure that no illegal loggers are operating in the area. It seems that in the long term, funding from the purchase of one bottle of orange juice is not enough to sustain active patrol.

Either way, I have opened an account and whenever I purchase Tropicana I make sure to enter the code in order to "do my part". There is one caveat: the larger the bottle of orange juice you purchase, makes no difference. I didn't find this out by trying it and hoping to get more point, but a bottle double the size of the carton is only a dollar or so more! If you don't want to open and account, but purchase Tropicana, just drop me the code number and I'll enter it. Do not worry, there is no monetary award for any of this and last I checked there was no reward at all for any of it, just the comfort of thinking that you're doing something. Whether it actually is doing something is hard to say, but just in case!

Physics Question #3

Since I know everyone loves a brain teaser, I have another physics question for everyone to ponder! This is nothing new and I am sure that everyone has heard the scenario, if not the solution. It is the infamous Twin Paradox.

One result of Einstein's Special Relativity is that moving clocks run slower! I will not delve into the details of this, but if you would like to know, feel free to inquire. So here is the scenario:

Two twins, Alice and Bob, are both at rest at some point in space, at some initial time, with their clocks synced. Alice moves away from Bob and travels for 30 years, according to her watch, with uniform velocity (near c), in a straight line. After 30 years, Alice returns back to rest where she began, next to Bob, who has remained at rest. When Alice returns, though, she notices that while she is 30 years older, Bob has fared worse than she, and has aged considerably more.

It is obvious to us, the observers, that there is no paradox here, since Alice was moving, thus her clock runs slower. But now consider it from both the reference frame of Alice and Bob, separately. In Alice's frame, Bob is moving away from her at constant velocity, and it would appear that she is stationary, while on-the-other-hand, Bob sees Alice move away from him with constant velocity and he appears to be stationary! So what does this imply? It suggests that Bob would believe that Alice is younger than he is, due to her motion, but Alice would believe that Bob was the younger twin, not her! Yet, he has clearly aged more than she has. How can Bob and Alice reconcile their different views of what should have transpired?