About time I put something on here again.
So first I'm going to talk about my project, what exactly I'm doing, how I'm doing it, etc. Some parts I will go further in depth with later. Then, I'm going to talk about my general experience actually doing the project. Here we go!
At the beginning of my project, I knew little about how
physicists go about discovering “the secrets of the universe.” They can’t exactly
just observe black holes in their natural habitats like you would a troupe of
chimpanzees. Instead, physicists often have to observe the universe as if the
chimpanzees are invisible and all they can see is how the chimps affect the
space around them. Like if some physicists saw a floating banana slowly peel
itself and disappear at a rate within the accepted range for chimpanzee consumption,
they might think, “Hmm, that there might be a chimp.”
Same deal with the universe. In fact, the discovery of
gravitational waves was so exciting mostly because now we can use gravitational
waves to observe other aspects of the universe. That’s actually what I’m doing
with my project. Physicists think there are these things in the universe called
cosmic strings. They are hypothetical objects made of mass-energy that formed
in the early universe during phase transitions. In the
beginning, these strings were smaller than quarks, but as the universe
expanded, the strings expanded. They’re a lot like the lines you see in ice
when it cools from liquid, except cosmic strings can stretch, interact, oscillate,
and disintegrate. These mass-energy strings are extremely dense—just a 1.6 km
long string would be as massive as earth. They are also one-dimensional—no height
or width. If cosmic strings existed, they could give us valuable insights into
the early universe, so scientists have been trying to detect them. One of the
most promising ways to find cosmic strings would be to detect the gravitational
waves they emit when they decay. As explained by the LIGO Scientific
Collaboration, “Gravitational-wave emission is the main mechanism for cosmic
strings to dissipate energy. When a string in a cosmic string network crosses
itself, a loop separates from the string. Once formed, a loop is doomed. It
oscillates, radiates gravitationally, shrinks and eventually evaporates. Strong
gravitational emission occurs at the pinch-off points of the loop, the cusps,
which move with a velocity [expected to be] the speed of light. Powerful bursts
of gravitational waves are expected to be produced by cosmic string cusps. The
amplitude of the signal depends on the tension in the string and the size of
the loop. These signals could be detected by the ground-based laser
interferometers, LIGO and Virgo.”
But before
we start sifting through data collected from LIGO and Virgo, we need to know
what the interferometer can measure (not all the features of these cosmic
strings may be equally easy to measure). The gravitational waves emitted from
cosmic strings have a mathematical form with depends on physical parameters,
such as amplitude, lower frequency, and higher frequency.
It is also important to understand that the noise in LIGO
depends on the frequency. We want signals to have as little noise as possible
because with less noise the actual signal is much more prominent. In other
words, we want a high signal to noise ratio (SNR). See the graph below:
Graph explanation: As you can see, between approximately 10^2 and 10^2.5 Hz, LIGO and Virgo experience the lowest noise spectral densities (approximately between 10^-22 to 10^-23 1/(Hz)^1/2). The lower noise spectral density, the lower the noise, and thus, signals that are between 10^2 and 10^2.5 Hz give LIGO and Virgo scientists the most precise data.
The goal of my project is to understand how precisely the laser
interferometers can measure these physical parameters. These errors in turn
will tell us which physical conclusions LIGO will be able to make and which are
beyond the current reach of the instrument. Just to give an analogy, when
people tested the prediction of general relativity that light from distant
galaxies get bent by the sun (gravitational lensing), it was necessary to have sufficient
precision in measuring the trajectories to distinguish between general
relativity and Newton's gravitational theory.
The work will involve first estimating the error
with a technique called the Inverse Fisher Matrix approach. Then we will use a
more accurate technique (which is also computationally much more intensive)
developed by Dr. Zanolin, which uses asymptotic expansions of the covariance
matrix of maximum likelihood estimators. The idea is to compare the prediction
of these analytical studies with previous studies that were performed with
computer simulations done by X. Siemens et al.
So that is what my project is all about. So how has it been going in practice? First, I've had to learn SO much stuff. I've had to learn new math and some programming (although my work buddy does most of the programming) and of course, lots about cosmology and gravitation. Here are some of the topics I've had to learn to do my calculations:
general info about LIGO and gravitational waves
cosmic strings: what are they and how do they work?
inverse matrices
estimation theory, maximum likelihood error, and cramer rao bound
dirac delta functions
fourier transforms
gamma functions and incomplete gamma functions
gaussian distributions
noise spectral density
how to use Mathematica
I don't even completely understand all these topics yet. Some I'm still learning as I go, but basically, my brain has been exploding. But it's pretty great. Also, it's cool to see how the math we learn in school is actually applied to learn things about the universe. Yes, calculus is actually used in the real world. And I didn't realize there is so much math I haven't learned yet. I remember thinking in 5th grade that once you've learned calculus, you've basically learned everything. Ha was I wrong! There is a lot more math out there I haven't even heard of, but now, I'm having to use a tiny fraction of this more advanced math, which really makes me realize how much I haven't learned.
Well, that's enough for now. In my next post, I'm going to talk about the people I've been working with because they're pretty awesome! But anyhow, ciao!
Carissa
