April Showers

Time to really blog again. Well, sorta...
I love Spring!!! Everything about it is just so wonderful! The sunshine, flowers (especially the tulips all over campus), ducks and ducklings, rain showers, the air just before and after it rains, all the beautiful clouds and stars in the sky. Life in the spring time is lovely. (You can quote me on that.) I guess I'm just feeling so blessed with my wonderful friends who stuck around in Provo with me this spring/summer terms. I got my grades from last semester, and I didn't do so shabby. I'm getting started in classes and work/research, and I absolutely love it all. Doctor Who has started up again, and I think I can watch it online... My roommates are great. I love living at Moon Apartments (with air conditioning!!!) I can't wait to meet my ward. I have a really good friend who refuses to give up on me, even when he's seen me at my worst on far too regular a basis. I have so much to be grateful for, which is probably why I love La Primavera. (Yeah, I kinda miss Italian.)

My Favorite Song from this Time Last Year

This is the last day of the 30 day song challenge. Wahoo! We made it! One of my favorite songs any time, but especially this time last year, when I had to say good bye to so many people, is this one, from Wicked.

A Song from my Childhood

Yeah, I played this at my middle school talent show.

A Song that Makes Me Feel Guilty

2 more days of this challenge! We're almost there!

A Song I Wish I Could Play

2 songs today! First up: A song I really wish I could play on the guitar. It's pretty much the best.


And Happy Easter! Today, I played the flute part to accompany the ward choir on this song. I didn't really have to wish I could play this song, I actually did! I hope you enjoy this, and again, Happy Easter

A Song I Can Play on an Instrument

Um... wow. So many choices!! I love playing the piano... and the organ... and the flute...and guitar... and even the piccolo! (but not all at once.) Anyways, I love laying lots of songs of many varieties, but the song I'd like to post today is one of the classical kind.

A Song that Makes me Laugh

Not exactly a song, but it's a rap, and that's kind of close, right? And it's Thomas' birthday, and I'm so glad I could be home to spend it with him and the rest of my family. And it makes me laugh.

A Song I Want to Play at my Funeral

Once upon a time I sang this song in high school choir, and we got a Superior rating at State. When I die, please sing me to Heaven. Here's the lyrics, for those who care:
In my heart's sequestered chambers lie truths stripped of poets' gloss
Words alone are vain and vacant, and my heart is mute
In response to aching silence, memory summons half-heard voices
And my soul finds primal eloquence, and wraps me in song

If you would comfort me, sing me a lullaby
If you would win my heart, sing me a love song
If you would mourn me and bring me to God,
sing me a requiem, sing me to Heaven

Touch in me all love and passion, pain and pleasure
Touch in me grief and comfort, love and passion, pain and pleasure
Sing me a lullaby, a love song, a requiem
Love me, comfort me, bring me to God

Sing me a love song, sing me to Heaven

A Song I Wish I Heard on the Radio

Oops! I missed this one, it was supposed to go a few days back. Oh well, here it is now:

A Song I Would Like to Play at my Wedding

I like this song. It won't be the song I dance to or anything special like that, but it'll probably make it into the playlist whether or not my parents approve.

(100th Post) A Song I Listen to When I'm Sad

Enough said.

A Song I Listen to When I'm Happy

Cliche, I know. But I really do listen to this song when I'm happy!

A Song I Listen to when I'm Angry

This song. No battle.

A Song From My Favorite Album

So...um.... I've missed a couple of days because finals sorta happened. But now I can play catch up! It's hard to pick a favorite song from a favorite album, but here you go:

A Song that I Hear Often on the Radio

I don't listen to the radio often, but when I do, I hear this song often.

Physics 222 Term Paper

Just thought you all should see what my life has been like this semester, in the format of a really cool term paper:


General Relativity in the Big Bang Theory


Jenny Lund
Physics 222 Term Paper
April 13, 2011 

Introduction
Einstein’s General Theory of Relativity is crucial to understanding and modeling the Big Bang, as the current theory for the origin of the universe, because it provides means for accounting for the shortcomings in a classical mechanics model. However, it isn’t a perfect model of the early universe, which creates the need for a Grand Unifying Theory of General Relativity and Quantum Mechanics.

The Big Bang is widely accepted as a model for the origin of the universe. An important distinction must be made, however, that it isn’t a complete theory. Theorists have set various requirements for the initial condition of the universe, dependent on their various theories, such as all matter and energy was concentrated at a certain point, and time didn’t exist. We currently do not know the laws of physics that apply to that initial condition, only that those laws are different than those that operate in the universe today. According to Wikipedia, “the Big Bang Theory cannot and does not provide any explanation for such an initial condition; rather, it describes and explains the general evolution of the universe since that instant. The observed abundances of the light elements throughout the cosmos closely match the calculated predictions for the formation of these elements from nuclear processes in the rapidly expanding and cooling first minutes of the universe.” (Wikipedia, Big Bang)

A Brief History After the Big Bang
What, then, do we learn from the Big Bang Theory? As far as we can tell, the predictions of this model match with observations we have made pertaining to when certain parts of the universe came into existence and have since evolved. From the beginning to 10^-12 seconds, we basically have no idea what is going on, because the laws of physics, as we know them today, were not operating. We call an event like this a singularity. Today, some people study singularities like Black Holes in order to better understand what happened at the first singularity, the origin of the universe. One part of physics that broke down at the universe’s origin involved inflation, in which the growth speed of the universe was faster than the speed of light (some explanation on p.129 BHoT). However, after this point, we can use the known physical laws to describe the processes that occur. (Woolfson)

It is at this point, 10^-12 seconds after the universe came into existence, that we can use Einstein’s General Relativity and Quantum Mechanics to describe what was happening. From 10^-12 to 10^-10 seconds, the universe was a region of intense radiation with very little matter. Photons with extremely high energies produced quarks and anti-quarks which were produced and annihilated at a very high rate. As the universe expanded, it became cooler, and the rate of quark and anti-quark production decreased. For some unknown reason, the Universe was left with more quarks than antiquarks (Woolfson). (The abundance of quarks as opposed to antiquarks led to the origin of matter as we know it today: protons and neutrons made of three quarks each, mesons made of a quark and an antiquark. The world would be very different if matter was made of antiquarks at its most basic level, instead of quarks.)

At about 10^-4 seconds, quarks ceased to exist as isolated independent particles, but combined to make protons and neutrons. After 1 second, these protons and neutrons disintegrated. As the temperature of the universe fell, there were fewer particles around that could collide with a proton and cause its disintegration, and for this reason, the ratio of protons to neutrons increased with time. After 100 seconds, the temperature had fallen to the point (100 thousand million degrees Celsius) where protons and neutrons could permanently come together to form the nuclei of light elements such as Helium and lithium, deuterium. (Woolfson)

After 10,000 years, the radiation and matter of the universe had become independent. As the universe continued to expand, it created more space, so the matter spread out and the density of matter in the universe reduced. The radiation also had a greater space to occupy, the energy per unit volume of the radiation reduced, and so the universe cooled. After 500,000 years, the universe had cooled to the point that electrons could attach themselves to nuclei. (Woolfson). After this point, the universe developed the structure of galaxies that we know today, one piece at a time.

The early universe was very different than the one we know today. We turn to General Relativity to model the particles at high speeds in the early universe. However, as Stephen Hawking points out, General Relativity cannot explain the questions of the universe’s origins before 10^-12 seconds, such as “why was it so hot? Why is it so uniform on a large scale? What is the origin of the fluctuation singularties?” (Hawking, Brief History of Time).

Basics of General Relativity
Despite the fact that we cannot answer all the questions with General Relativity, a basic understanding of Einstein’s General Relativity is important to an understanding of what occurred after 10^-12 seconds. In 1915, Einstein proposed that gravity is not a force, but is a consequence of the fact that space-time is not flat, but curved, or “warped,” by the distribution of mass and energy in it. When a force acts, it affects the curvature of space and time, and the structure of space-time affects the way in which bodies move and forces act (Hawking, Brief History of Time). We use Minkowski space-time diagrams to describe the motion of objects in different reference frames and to reconcile the supposed differences observed in different reference frames, but these diagrams assume no, or relatively weak gravity forces. For the strong gravitational attractions, such as those in the early universe, scientists use four dimensional manifolds to model space and time. “The Einstein field equations are a set of 10 equations in Albert Einstein's general theory of relativity which describe the fundamental interaction of gravitation as a result of spacetime being curved by matter and energy.” (Wikipedia, General Relativity) It is also important to note that in General Relativity, the laws of physics are the same for observers in each frame of reference, and the speed of light is 3x10^8 m/s in each and every frame of reference. In addition, Einstein’s Equivalence Principle states that you can’t distinguish between a gravitational field with gravitational acceleration = g and a uniform acceleration a=-g.

Four Pillars of the Big Bang Theory
We know General Relativity in the Big Bang Theory works because we can observe some of the effects predicted by this model. According to Wikipedia, “The earliest and most direct kinds of observational evidence for the Big Bang are the Hubble-type expansion seen in the redshifts of galaxies, the detailed measurements of the cosmic microwave background, the abundance of light elements, and today also the large scale distribution and apparent evolution of galaxies which are predicted to occur due to gravitational growth of structure in the standard theory. These are sometimes called "the four pillars of the Big Bang Theory". (Wikipedia, Big Bang)

Gravitational Redshifting
Due to acceleration or gravitational effects (General Relativity claims that we can’t tell the difference between the two), Light is bent through gravitational fields in the direction of the gravitational pull or acceleration. If light is traveling perpendicular to the acceleration, its path is curved. If it is traveling parallel or antiparallel to the acceleration, then its frequency is shifted in an effect called gravitational redshifting. Light traveling against the direction of acceleration is redshifted. If the light is traveling in the same direction as acceleration, it is blueshifted. The same effect applies to light that is traveling away from massive source with a gravitational attraction, or “upwards” in the gravitational field; it is redshifted; if the light is traveling towards a source with a gravitational attraction, or “downwards” in the gravitational field, it is blueshifted. The Doppler effect models the same principle, using more familiar sound waves instead of light waves. . From earth, we can observe redshifts, not blueshifts of objects in space, which makes sense, because the Universe is expanding, just as the Big Bang Model predicts.
From Einstein’s equations we thus calculate redshifts: (equation”. The results support those projected by the Big Bang Model. The largest redshift we’ve detected, which corresponds to the furthest distance in time, is that of cosmic microwave background radiation. According to Wikipedia, “it shows the state of the Universe about 13.7 billion years ago, and 379,000 years after the initial moments of the Big Bang.” (Wikipedia, Redshift)

Cosmic Microwave Background Radiation
No matter where in the universe they aim their telescopes, scientists have observed a background radiation in the microwave range of about the same frequency. Wikipedia explains, “The cosmic microwave background (CMB) radiation is an emission of uniform, black body thermal energy coming from all parts of the sky.” (Wikipedia, Cosmic Microwave Background) As pointed out before, “As the universe expanded, adiabatic cooling caused the plasma to lose energy until it became favorable for electrons to combine with protons, forming hydrogen atoms. This recombination event happened when the temperature was around 3000 K or when the universe was approximately 379,000 years old. At this point, the photons no longer interacted with the now electrically neutral atoms and began to travel freely through space, resulting in the decoupling of matter and radiation.” (Wikipedia, Cosmic Microwave Background) The fact that we have found evidence of this background radiation predicted by the Big Bang Theory further supports this theory. We use General Relativity and Quantum Mechanics in the theory to match equations with actual observational data to support the theory.

Abundance of Light Elements
The fact that throughout space we have found an abundance of lighter elements, such as Hydrogen and Helium, instead of heavier elements, further supports the Big Bang Theory. As suggested in the last paragraph, General Relativity provides a way to calculate the energy and mass of particles so small and moving so close to the speed of light. Wikipedia provides more detail: “As the universe expands, it cools. Free neutrons and protons are less stable than helium nuclei, and the protons and neutrons have a strong tendency to form helium-4. However, forming helium-4 requires the intermediate step of forming deuterium. At the time at which nucleosynthesis[(fusion of protons and neutrons into the nucleii of light elements] occurs, the temperature is high enough for the mean energy per particle to be greater than the binding energy of deuterium; therefore any deuterium that is formed is immediately destroyed. Hence, the formation of helium-4 is delayed until the universe becomes cool enough to form deuterium, when there is a sudden burst of element formation. Shortly thereafter, at twenty minutes after the Big Bang, the universe becomes too cool for any nuclear fusion to occur. At this point, the elemental abundances are fixed.” (Wikipedia, Big Bang Nucleosynthesis)

Large Scale Distribution of Galaxies
Galaxy formation is hypothesized to occur, from structure formation theories, as a result of tiny quantum fluctuations in the aftermath of the Big Bang. “cosmic inflation theory] has made a crucial prediction that have been borne out by observation: that the primordial universe would have tiny perturbations which seed the formation of structure in the later universe. These fluctuations, while they form the foundation for all structure in the universe, appear most clearly as tiny temperature fluctuations at one part in 100,000.” (Wikipedia, Structure Formation) Again, we must turn to General Relativity, as well as Quantum Mechanics, to try to understand a little bit of the tiny particle fluctuations that gave rise to the galaxies spread throughout the universe today. We don’t know much about what caused those fluctuations, but we do know the result of those fluctuations.

The Future According to the Big Bang Theory
Although General Relativity does not provide a complete description of every part of the origin of the universe, it does support every part of the Big Bang Theory, and our observations further validate this model. We turn to Quantum Mechanics and continue to look for a grand unifying theory of the two. So far, String Theory is the one that stands up to the theoretical tests.

We can also use General Relativity to extend the predictions of the Big Bang Theory to predict the future of this continually expanding universe. “The future of an expanding universe is bleak. If a cosmological constant accelerates the expansion of the universe, the space between clusters of galaxies will grow at an increasing rate. Redshift will have stretched ancient, incoming photons (even gamma rays) to undetectably long wavelengths and low energies. Stars are expected to form normally for 1×1012 to 1×1014 years, but eventually the supply of gas needed for star formation will be exhausted. Once the last star has exhausted its fuel, stars will cease to shine. According to theories that predict proton decay, the stellar remnants left behind would disappear, leaving behind only black holes which themselves eventually disappear. Ultimately, if the universe reaches a state in which the temperature approaches a uniform value, no further work will be possible, resulting in a final heat death of the universe.” (Wikipedia, Future of Expanding Universe)

Conclusion
Einstein’s General Theory of Relativity is necessary in understanding and modeling the Big Bang, the current theory for the origin of the universe, but it isn’t a perfect model of the early universe. To account for the imperfections, scientists are trying to create a Grand Unifying Theory of General Relativity and Quantum Mechanics. The four pillars of the Big Bang Theory have been validated by concrete observational evidence, so we accept the predictions of the Big Bang Theory to model the early universe. The same model can be used to predict future events in this universe of ours, which we will continue to model and calculate with Einstein’s General Theory of Relativity.
 
Works Cited

1. "Big Bang nucleosynthesis." Wikipedia. N.p., 17 Mar 2011. Web. 13 Apr 2011. .
2. "Big Bang." Wikipedia. N.p., 11 Apr 2011. Web. 13 Apr 2011. .
3. "Future of an expanding universe." Wikipedia. N.p., 12 Apr 2011. Web. 13 Apr 2011. .
4. "General Relativity." Wikipedia. N.p., 9 Apr 2011. Web. 13 Apr 2011. .
5. "Redshift." Wikipedia. N.p., 6 Apr 2011. Web. 13 Apr 2011. .
6. "Structure formation." Wikipedia. N.p., 29 Mar 2011. Web. 13 Apr 2011. .
7. “Cosmic microwave background radiation." Wikipedia. N.p.,11 Apr 2011. Web. 13 Apr 2011. .
8. Hawking, Stephen. A Brief History of Time. New York, NY: Bantam Books, 1988. Print.
9. Hawking, Stephen. The Universe in a Nutshell. New York, NY: Bantam Books, 2001. Print.
10. Woolfson, Michael. Time, Space, Stars, & Man. London, Great Britain: Imperial College Press, 2008. Print.


Other References (not cited, but used in research)
1. Alpher, Ralph, and Robert Herman. Genesis of the Big Bang. New York, NY: Oxford University Press, 2001. Print
2. Penrose, Roger. Cylces of Time. London, Great Britain: The Random House, 2010. Print.

A Song I Used to Love but now Hate

HA! It's still before midnight! Um.... You got me here folks. I'm not sure of a song with this description. On a long shot.... I've heard Waterfall a few more than enough times from freshmen playing the piano in the WILK. So here, it's not terrible, but overplayed (badly) far too often.

A Song that Describes Me

I asked my good friend Joel to pick a song that describes me, and he came up with "She's Got a Way" by Billy Joel. I approve of this song, and of Billy Joel in general, greatly.

A Song that No One Would Expect Me to Love

Given what you've seen of my tastes in music, would you really expect me to like one republic? Well, I do. Now I've given all my secrets away.

A Song that is a (not-so) Guilty Pleasure

http://www.clarrissegill.com/videoclips/amazing_grace.php

I love everything about this song: Amazing Grace.
It is a beautiful message, and a true one at that. I love the location, the instrumentation, the voices, the rises and falls, and the fact that Christ's Grace truly is the only way we can return to our Heavenly Parents, even after all we can do.

So, while there may not be anything "guilty" about this song, for me, it is truly a pleasure to share this with you.

A Song From a Band I Hate

I almost didn't post this. Why promote music I hate? Because I actually do dislike every aspect of this song. You are under no obligation to watch this.

A Song From my Favorite Band

This is a hard one. I really don't have a favorite band in the traditional sense of the word. I listen to and enjoy a wide variety of music (I hope you've been able to tell from this 30 day challenge so far!). One of the groups that I respect above all others though is Queen.
30 minutes later.....
I narrowed it down to a group, but I can't decide what song to post. There are just so many great songs from the genius that is Queen! Killer Queen, Bohemian Rhapsody, Can Anybody Find Me Somebody to Love, Bicycle Race.... the list goes on and on. I will never stop enjoying Queen, so please, Don't Stop Me Now.

A Song That Makes Me Fall Asleep

I don't listen to music as I fall asleep very often. But I think if I did, this song would put me to sleep fairly quickly.

A Song I Can Dance To

Once upon a time in high school I was was part of the swing club. And the jazz band. But I did dance to this song. I wish I could remember all the sweet moves we had.

A Song that I Know All the Words To

Ingrid Michaelson's Parachute. Actually, it was a toss up between this song and about 50 other Ingrid Michaelson songs. At least there's still 22 more days of the challenge!

A Song that Reminds Me of a Certain Event

So this one time, my brothers and I were being goofballs. Actually, that happens a lot. So here's a kind of a goofball sort of song.

A Song that Reminds Me of Somewhere

This song reminds me of Salt Lake City, Utah. It's a gorgeous city. Also, I really love this song.

A Song that Reminds Me of Someone

So this one time I went skiing at Brighton with Ben Mitchell and Luke Pritchett. We could never decide which run to take down the mountain. "Anywhere you go, I'll follow you down" just fits so perfectly to our lack of decision making abilities.

A Song that Makes Me Sad

I dislike listening to sad music, but whenever I am missing home and sad, I identify with this song. I love Michael Buble.