What a beautiful land we live with.

Let's keep it that way :-)

Who needs drugs.

Another garden post. It just rocks my socks every time I walk past. I think what amazes me so much is not that I did anything (Nick and Aaron did all the hard work) or even that we did anything by planting it, but that the earth did it. That out of a bunch of bare dirt and a couple seeds the earth spit out edible food! Call me simple, but my socks are still rocked.

Here are some more pictures. I decided to change my blog title to reflect my obvious garden-mania. Plus I think it is a nice metaphor to my life, so it works.

Can you believe how tall the corn is!

We are going to make salsa with these chile peppers sometime soon.


The bean seeds Nick planted are all sprouting.

And, when I went to take pictures of the pumpkins, this guy was there waiting for me. He was beautiful in life and vibrant. He even sat there long enough for me to dig out my camera and didn't fly away even when I stuck the camera in his face. There are angels everywhere.

The point.

Okay folks, this is a long one.

As most of you know, I am working on a quantum mechanics research project this summer. Since 1) I think it is really cool and 2) I'm not very good at explaining it on the fly, I thought I'd post what I'm doing here so if anyone is interested you can see what I'm doing. Plus there is a movie at the end...that was one of my major accomplishments (don't laugh, my adviser thought it was really cool too!).

In the largest sense, I am applying an alternate interpretation of quantum mechanics to a basic concept in physics, namely, the harmonic oscillator. The harmonic oscillator is used as a model in almost all subdivisions of physics. Photons are modeled as harmonic oscillators in theories of light, pendulums in classical mechanics can be modeled as harmonic oscillators, etc. The quantum harmonic oscillator is one of the few systems that can by solved analytically in quantum mechanics (that is, the answer is exact equations instead of making approximations and using a computer to hack through). But even though an analytical solution is possible with standard quantum mechanics, the results are not necessarily conceptually fulfilling.

Standard quantum mechanics works on the assumption that a particle’s positions or velocity or any other feature is inherently probabilistic. Whereas on a human scale I can tell you the exact position I am sitting or exactly how fast I am moving, on the scale of an electron the best I can tell you is a range where the electron will be found and a position where it will most likely be.

This is a pretty unsatisfying view of the microscopic world. And since the macroscopic world is built from these probabilistic particles, quantum physics has profound implications for how we view the world. Einstein’s dissatisfaction with these ideas prompted the quotable line, “I am convinced that God does not play dice with the universe”.

As standard quantum mechanics was being developed (well before it was referred to as “standard”), other theories to explain experimental results were being developed. Why one theory becomes accepted and the others get relegated to footnotes, I am not enough of historian to explain. But so it happens. One of these “alternate” theories is now known as Bohmian mechanics, after its conceiver David Bohm.

Bohmian mechanics works on the principle that a probabilistic wave-function can be seen as a collection particles that can be treated just like particles in classical mechanics. We envision that each of these particles has a probability of existing until a measurement is made at which point only one particle actually exists. The true value of this interpretation comes from the fact that the behavior of wave-functions can be understood in terms of classical forces. All of those Physics I concepts like Force = Mass * Acceleration become useful tools in Bohmian mechanics. In standard quantum mechanics many problems can’t be understood conceptually, one just has to “shut up and calculate” as theoretical physicist Richard Feynman is quoted as saying. Bohmian mechanics gives us a way to picture the quantum world in terms of graspable classical concepts.

My specific project this summer is to apply Bohmian mechanics to the time-dependent harmonic oscillator. The simplest example of a harmonic oscillator is a weight on a spring sliding along a frictionless surface. The weight is pulled back from its equilibrium point and let go. It oscillates back and forth with a certain period and maximum distance from the equilibrium point depending on how far it is pulled back and the strength of the spring. This is a time-independent harmonic oscillator since the strength of the spring is constant in time. A time-dependent harmonic oscillator would be one where the strength of the spring changes over time. This isn’t a very meaningful model in the spring/mass example, but time-dependent harmonic oscillators are very useful models in quantum mechanics.

What we do is start with a specific wave-function whose shape is a Gaussian. A Gaussian is a distribution useful in statistics, you may know it as a normal distribution or a bell curve. A Gaussian is useful for our purposes because when the forces of a harmonic oscillator are applied to it, it stays a Gaussian. Its width and height changes, but it never loses the properties of a Gaussian. This makes it exceptionally nice to follow through time since we only have to worry about how one function changes in a harmonic oscillator.

Bohmian mechanics works by adding the force from the harmonic oscillator with the so called quantum force that is derived from the Schrödinger equation (the equation that governs standard quantum mechanics). By looking at how these forces cause the Gaussian’s width to grow or shrink we can predict how the probability distribution will change with time and where we are most likely to find the electron that this distribution models. Although there are still probabilities and uncertainties in this treatment, why they behave like they do is much more clear than in standard quantum mechanics. And since we come to the same conclusions as people who use standard quantum mechanics and as are achieved experimentally, our interpretation has validity.

My end results are best viewed as movies. The blue curve is the Gaussian probability distribution which represents where the particle is likely to exist. The green line is the quantum force that depends on the width of the probability distribution and the red line is the classical force which I can make change as any arbitrary time-dependent function. Sometimes physics is watching squiggly lines move on a screen!

Baby pictures.

Our little garden is growing up so fast (sniff, sniff).

Actually it is pretty awesome, and at the risk of seeming like an overly proud mother shoving pictures of her kid is unsuspecting bystanders faces, here's the latest:

Several lovely ears of corn are showing up!













A few baby yellow squashes making their first appearance in the world.

The bush bean seeds Nick planted last week are starting to sprout!

And the snap peas are ready to eat, and oh so tasty!

Family.

Amy got married! Amy got married! Amy got married!

I spent the last five days in San Diego seeing my aunt (my mom's younger sister) Amy get married to a wonderful man named Tony. It was an amazing experience. Tony's family is from Chicago and is very Italian and sooo similar to mine. We both play pranks on each other and love to laugh, two things that happened a lot this weekend.

The wedding was on a paddle boat that sailed out on Mission Bay. It was beautiful and scenic and perfect for themed prank pulling. Tony's family went with Love Boat while mine went with pirates (I have a little sore spot in my throat from saying "Arrrggg..." all weekend). In addition to flying a pirate flag off our balcony and passing out eye-patches at the reception, we introduced a new member of the family, Uncle Arrrrggg-nold (pictured below).

On of the best parts of the whole trip was dancing at the reception. Bopping around with my cousins and Amy in her beautiful dress was a blast. Then my great-Aunt Kay came on the floor. She was amazing and is officially my hero. How many 73 year-olds do you know who dance to Gettin' Jiggy with It (na na na na na nana)? Yea Aunt Kay!

It was wonderful to spend time with family, even parts that I haven't seen since I was little. I learned a lot of names, heard lots of stories about my grandma and grandpa, and generally felt blessed to be part of such an awesome group of people.

Here's some pictures from the trip.

Uncle Arrrggg-nold.

Pirating can be dangerous work!

Two of my cousins and me at the beach.

Self-explanatory.

Thanks Mr. Salinger

I just finished a collection of two stories (Raise High the Roof Beam, Carpenters and Seymore: An Introduction) by J.D. Salinger and I wanted to share a couple of my favorite quotes:

Please accept from me this unpretentious bouquet of very early-blooming parentheses: ( ( ( ( ) ) ) ).

My atoms, moreover, are arranged to make me constitutionally inclined to believe that where there's smoke there's usually strawberry Jello, seldom fire.

...all we do our whole lives is go from one little piece of Holy Ground to the next.

The next adventures.

I've moved back to Flagstaff, Arizona for the summer and since I'll no longer be posting about Europe, I thought I'd change the look of the blog. I have no idea how much I'll be updating this in the future, but hopefully enough to keep your interest.

Flagstaff is beautiful in the summer. It is hot, but nothing like Las Cruces or Phoenix. I ride my bike to work every morning, somtimes stopping by our little Canterbury garden to water. And speaking of the garden, it is doing wonderfully! When I left seven weeks ago there was just dirt and soaker hoses to show that something was special about that plot of land. Now there are three rows of corn plants, each a foot tall. Pea plants climbing up stakes with buds where pods will someday appear. Pepper plants, lettuce leaves, potatoes, huge pumpkin and squash bushes...it is beautiful! Here's a couple of pictures that I couldn't resist taking...

The corn plants

Tomatoes, peppers, squash, potatoes, lettuce, garlic, and peas!

It is a little weird being in Flagstaff over the summer. I am use to the busy university life when I'm in this town. Not that I'm complaining about not doing homework every night, but I'm finding that I don't really know what else to do on weeknights. I'm sure I'll figure it out.

And so there you have it, the next adventure begins!