Friday, March 31, 2006
Tuesday, March 28, 2006
I was reading my Quantum Mechanics textbook this afternoon and I came across a passage in which the author of the text, David Griffiths, is having a pretend conversation between himself and classical physicist/realist (for definition of a realist see this post) about measuring the angular momentum of a spin 1/2 particle. The whole thing is very funny so here it is-
Realist- "What is the z-component of the particles spin angular momentum?"
Realist- "What is the x-component of the particle's spin angular momentum?"
D.G- "If you measure this the chances are fifty-fifty of getting either +h/2pi or -h/2pi"
Realist- "Are you telling me that you don't know the true state of the particle?"
D.G- "I know precisely what the state of the particle is: chi_+"
Realist- "Well, then how come you can't tell me what the x-component of its spin is?"
D.G- "Because it simply does not have a particular x-component of spin. Indeed, for if both S_x and S_z were well defined, the uncertainty principle would be violated."
At this point the realist grabs the test tube and measures the x-component of its spin, lets say he gets a value of +h/2pi
Realist- "Aha!" (he shouts in triumph), "You lied! This particle has a perfectly well defined value of S_x"
D.G- "Well, sure, it does now, but that doesn't prove it had the value prior to your measurement"
Realist- "You have obviously been reduced to splitting hairs. And anyways what happened to your uncertainty principle? I now know both S_x and S_z."
D.G- "I'm sorry, but you do not: in the course of your measurement, you altered the particle's state. You now know the value of S_x and you no longer know the value of S_z."
He is so condescending towards the realist, it's great. It made me laugh at least.
The concept of spin in particles is a rather interesting one. Let's use an electron (spin 1/2) for example. In high school chemistry and physics we are taught that electrons orbit around the nuclei of their atom and they also spin around a pole. This model is similar to the Earth orbiting the Sun and orbiting on it's axis. They tell us that the electron is actually, physically spinning. They're lying. The electron, along with every other particle does not actually spin. There is an intrinsic property of every elementary particle that appears very much like angular momentum. An electron is not an elementary particle, but it is composed of 3 quarks, 2 which are +1/2 and one that is -1/2 spin thus giving the electron an overall spin of +1/2.
You can picture this, if an electron did actually, physically spin, then if there was another particle sitting on the surface of the electron, it would be rotating at a speed faster then the speed of light. Thus violating relativity. It can't happen.
In other news, this is apparently my 101st post. I completely missed acknowledging my 100th post.
And a quote from one of my favorite episodes of Buffy from season 5, Family:
Magic Box patron (who turns out to be Tara's brother): "So all these books have spells in them, turn people into frogs?"
Xander: "Yes, we're building a race of frog people. It's a good time"
It makes me laugh:)
Silent Hill is coming out on April 21. Anyone want to go see it with me, sometime after exams? I know, crazy me wanting to go see a scary movie. But Silent Hill is based on a video game that my brother Jeremy and I played together back in the day. It was really good and probably the scariest game that I've played. So I want to see the movie.
The picture at the top is really neat. It is of the star Eta Carinae. This is a very cool star. It has a very interesting history. It is estimated to be between 100-120 times the mass of the Sun. It could blow at any time. Very cool. Here is some info on Eta Carinae.
The bottom picture is me and Mom at the Windsor airport before my flight back to Edmonton over Christmas. My Dad took it with his cell phone. It's not a very good picture of me, but it is of me and Mom, so it's awesome.
Thursday, March 23, 2006
as Rankin did slowly
go over the day's physics notes
he went through the problems by rote
While slack-jawed and gaping
he thought of escaping
and his mind toward freedom did float.
But his friend's good intent
instead saved dissent
for she nudged him before his mind went.
His mind was awake
How much more could he take?
How long yet, before the class break?
He glanced at the clock
and started in shock
He's soon (temporarily) free!
by James Dragnuik
Wednesday, March 22, 2006
We got the assignments back today and I got 7.5/8. I lost .5 of a mark because I didn't include the orbital directions of the stars, which was not mentioned in the assignment. The T.A wrote "I like it a lot. Short and relavant" and he put a smiley face. So ha to all of the people in my class who decided to they needed to include everything we had learned in the course thus far in there assignment.
And we'll finish with a picture taken by the Cassini spacecraft in orbit of Saturn. In this picture you can see gigantic Saturn in the background with the moon Enceladus sitting just above the rings. Enceladus has been making the news lately because it's Southern Pole seems to be actively spewing out crystaline water vapour. This is very interesting because the surface on Enceladus is far below the freezing point of water, but there must be some heat source somewhere under the surface for there to be so much activity at the pole.
Monday, March 20, 2006
The snow really is the greatest. I'm so happy that we got the huge dump. Maybe it's because I don't drive and thus don't have to worry about driving through it. Although church being cancelled made Sunday feel kind of strange. The last time I can remember church being cancelled was when we were in Prince George and it snowed 4feet over Friday and Saturday and there was already like 2feet of it on the ground. We couldn't see the fence between the neighbour’s yard and ours. It was cool. Prince George was such a strange place to live. I was there from gr.1-3. All sorts of weird things happened there to make school cancelled. There was the bear in the schoolyard, the cherry bomb disguised as a hockey puck that blew up in a kid’s face, the gym getting struck by lightening. And my all time favorite, the pipe in the girls change room bursting the day we got back from Christmas holidays that extended Christmas break for an extra week. Also I was in the newspaper because I, along with most of the other girls in my class had gotten a Magic Nursery Baby for Christmas and we all brought them to school. So the paper took a picture of us carrying our Magic Nursery Babies from the school to the high school when our school was evacuated. There were also the drug dealers behind the portables. But I don't think we went home for that, they just didn't let us go outside for lunch. Hmm, so apparently a post about how much I like snow has turned into a trip down memory lane.
The bottom picture is my body print in the snow because I decided that I needed to run down the walkway and fly into the snow. It was lots of fun. Then I got to chase 2 of my landlady's dogs around the yard. That was also fun. Then on Sunday I decided that for some reason it would be a good idea to take some gummy bears outside and take pictures of them in the snow. It seemed amusing at the time. (I have since visited Wayne's blog and discovered that he did the same thing with dinosaurs, but I'm posting them anyways). It seemed amusing because gummy bears are cute and putting them in a vast wasteland of snow seemed like something that would make them look even cuter. I think it did. I assure you they managed to scale the huge snow covered cliff beside them and made it back down again in time for tea.
Sunday, March 19, 2006
Friday, March 17, 2006
I've actually learned a number of very interesting things in the last week. First, in last Thursday's Quantum Mechanics class, first we started talking about Bracket Notation for Inner Products. Not to exciting, except that it was funny because of the notation. I was going to show you what the notation looks like, but apparently that means something in html and now this post is a little messed up and thinks that it is linking to something. Did you know that the collection of all bras constitutes a duel vector space? Anyways, that wasn't the exciting part. The exciting part came near the end of the class when our professor started doing some derivation. He didn't tell us where it was leading, but he ended up deriving the quantum numbers l and m. It was so cool. We have been using the quantum numbers in chemistry and physics since high school. My teachers always told us to except that the quantum numbers exist but we were never told where they come from and now finally I have seen the derivation.
Also today in astronomy we learned about Legrange Points in gravitational potentials. Did you know that the Sun puts more of an attractive force on the Moon then the Earth does? And yet the Moon orbits the Earth and not the Sun. This is because the Moon's orbit is within the Jacobian Radius of the first Legrange Point. The first Legrange Point is between the Earth and the Sun, the second one is on the Mars side of the Earth and the third one is on the other side of the Sun from the Earth. SOHO orbits the Sun at the first Lagragne Point. Mechanics is very interesting.
I discovered a couple of days ago that there is a new 400 level physics class called Fundamentals of Continuum Mechanics. It seems to be all about fluids and elasticity and deformation and other stuff like that. I think it will be interesting. I think I will take it.
Today for FAA we were suppose to go tobogganing, but it was only Glenna and I who showed up. So we went to some place that sells ice cream near the university. It was really good, I had Nutella flavor. Glenna and I had a spare together every Monday, Wednesday and Friday for the last 2 semesters, but not this semester. So I don't get to see Glenna as much anymore. So it was good to have some Glenna time.
My sister Katrina got accepted into Wilfred Louriar (I know I'm spelling that wrong but I don't know how to spell it) University. Good job Katrina. Although I am waiting for her accpetance into UofA.
The pitcure at the top of the post I think is really cool looking. It is of course not a giant space monster eating a galaxy, it is a ruptured cometary globule (which actually have nothing to do with comets) that is in our galaxy that is by chance superposed with a galaxy very far away from us. So it looks like the galaxy is about to be eaten.
The picture at the bottom of the post is of the tulips that were given to me by a very good friend and totally made my day last Friday. They are kind of starting to wilt a little now. The picture is a little blurry.
Monday, March 06, 2006
Recently, the Astronomy Picture of the Day website posted a rather tripy picture done by Dr. Clifford Pickover. Along with the picture there was a link to his website. It is a wonderful website filled with all sorts of really neat stuff on physics and math. I spent a good deal of time exploring it (and haven't come close to reading everything) and somewhere along the way I came across a reference to the Mandelbrot Set. You know those crazy, whacked out pictures that you see. Those are fractals and most likely from the Mandelbrot Set. I first encountered the M-Set when I read Arthur C. Clarke's The Ghost from the Grand Banks during the summer between gr.11 and 12 and was completely fascinated. And thus I learned all about fractal sets and complex numbers. I wont 'bore' you guys with the details, but there are links incase you are interested. I also discovered that there are Mandelbrot Set Explorers where you can spend time exploring the Mandelbrot Set. Needless to say, the website sparked my interest again and so I looked up some set explorers. That is where the pictures come from. They are ones that I saved from my explorations. How you get the pictures is by zooming closer and close into set. Most sets (working on the complex plane of course), like for example r=1 gives you nothing interesting when you zoom in. You just have a ring of radius 1 that you zoom in on and all you ever see is black. But with fractal sets, when you zoom in you don't get boring stuff. You get really cool and complex patterns. The colours in the pictures are like colours on a contour map. They represent the number of times a number was iterated to decide whether or not it belongs to the M-Set. You'll have to follow the links for more detail.
The pictures were generated using this set explorer: Mandelbrot Explorer
I like this one because you can save the images that you generate but the resolution isn't as great so you can not go very far into the set and do not see a lot of the detail on the outer limits of the set.
Here is another one that I like Julia and Mandelbrot Sets: An Applet to Explore the Mandelbrot Set. (here is the address because for some reason making a link for it redirects it to some stupid page http://aleph0.clarku.edu/~djoyce/julia/MandelbrotApplet.html)
It has high resolution and gives you lots of options for which type of contours you like to use. The problem with this one is that you cannot save your images. It works best if the resolution is set to it's maximum.
And here is another cool website that I came across a few years ago that has all kinds of really cool math stuff on it. Interactive Mathematics Miscellany and Puzzles
Thursday, March 02, 2006
I love the snow. The snow is so wonderful. The snow makes everything look so pretty. Mazy also likes the snow. Tesseract does not.
Today in Quantum Mechanics, we were shown a proof for the Generalized Uncertainty Principle. Apparently there is an uncertaintly principle for every pair of observables that do not commute (aka [A,B]=AB-BA). The uncertainty principle is refered to Heisenberg's Uncertainty Principle in the certain case of position and momentum observables. It was neat. We talked about HUP in high school and I had to wait until a 3rd year QM course to finally see a proof of it.
I think that the uncertainty principle is a particles way of saying "leave me alone" to all of the scientists. I mean think about it. You're a wave packet nice and relaxed travelling along, minding your own business when some person comes along and tries to measure you. Suddenly you're forced to collapse into this tiny spot. I wouldn't find that very fun. So the particles rebel and force there to be uncertainty in the measuring of them. (Yes, I know I'm geek)