Projects

Welcome to my projects page! Here you will find some work I've done both in and out of school that I'm proud of. All of the work on this page is completed and entirely my own work. Sources have been cited within the projects as necessary.

BELL'S THEOREM PAPER

March, 2019

During my last semester at Mount Holyoke College, I took a class titled "Philosophy of Quantum Mechanics" taught by Professor Nina Emery. In this class we examine some of the strange phenomena seen in quantum mechanics and discuss the philosophical interpretations of this phenomena.

Throughout the first portion of the class we talked about two odd phenomena known as the Two Path Experiment and the EPRB Experiment. Both of these experiments exhibit surprising results that stun physicists to this day.

In particular, the results of the EPRB experiment exhibit a perfect anti-correlation which is surprising and deserves an explanation. There have been many attempts at developing theories to explain these bizarre results and interpret their implications, including one made by Einstein and two of his graduate students. The three of them came up with a theory known as the "hidden variables theory" which in short, explains the perfect anti-correlation seen in the EPRB experiment using a common cause explanation.

John Stewart Bell responded to this by developing a theorem known as "Bell's Theorem", which states that it is mathematically impossible for one to hold two assumptions known as no conspiracy and locality, and allow hidden variables theory to be true. This leaves everyone with the dilemma of either giving up one of these assumptions or to not accept hidden variables theory and make another attempt to explain the perfect anti-correlation.

This paper that I wrote for the Philosophy of Quantum Mechanics class argues in favor of giving up the locality assumption. I begin the paper by explaining the EPRB experiment, hidden variables theory, and Bell's Theorem. The I make an argument for giving up the locality assumption in Bell's Theorem and defend this response by presenting a possible objection to the argument and explain why this objection is unconvincing.

The PDF of the paper can be found by clicking on the image below.

Bell's Theorem

DREAMING OF A WHITE DWARF CHRISTMAS

December, 2018

During the Fall 2018 semester, I took a course tiled "Statistical Mechanics" at Mount Holyoke College taught by Professor Kerstin Nordstrom. This was a 300-level course that focuses on concepts in thermodynamics and statistical mechanics. Nearly all of our time in class was spent on lectures where we discuss the fundamental concepts in statistical mechanics and solve some complex problems in class.

Towards the end of the semester, we were assigned to come up with an independent project that further explores one of the topics we discussed in class. I was inspired by a lecture on quantum gases which mentioned white dwarfs as an application of the Fermi gas, an example of an ideal quantum gas. Seeing this as an opportunity to merge my interests in physics and astronomy, I decided to do my project on white dwarfs. For this project I completed a problem that derives the relationship between the mass and the radius of a white dwarf star. The relationship between the mass and the radius is directly derived from the function for the total energy of the white dwarf The function for total energy incorporates the Fermi Energy, which is an important property of a quantum gas.

This article walks through the derivation of the relationship between the mass and the radius of a white dwarf. It includes a detailed description of the process, as well as the equations used, calculations done, and some figures I created. Figure 1, the sketch showing the assembly of a sphere shell by shell, was created in Adobe Illustrator. Figures 2 and 3 are graphs I generated using Wolfram Mathematica.

The PDF of the article can be found by clicking the image below.

Stat Mech

ELECTRONICS LAB WRITE-UP

November, 2018

During the Fall 2018 semester, I took a course titled "Electronics" at Mount Holyoke College taught by Kathy Aidala. A lot of physics majors at Mount Holyoke take this course in order to fulfill part of the lab requirement for the major. Most of our time in class was spent working on lab projects that reinforce the concepts in analog electronics that we learn by reading, solving problems for homework, and discussing in a lecture before the lab. The labs we do in class have us building and testing analog circuits that serve a variety of purposes.

The lab I'm sharing in this post is the third lab in the class, and the first one we were assigned to do a write-up on. In this lab we designed, built, and tested two different circuits, both of which function as a voltmeter. Both of the circuits we built had some parameters that we were required to meet with the design. Before we began, we were given skeleton circuits for both voltmeter circuit designs, meaning that we already had a basic layout of what the circuits should look like. The part of the design that we were tasked with figuring out was what we should use for the specific components of the circuit such as the values of the resistors and the model of the op-amp. All of the decisions on these components were made in order to meet the parameters we were given for the circuits. Once we made the appropriate decisions on these components and had a complete design, we built and tested both of the circuits.

This write-up discusses the specific tasks we were required to do in this lab, and walks through the entire designing, building, and testing process. All circuit designs and drawings, as well as the calculations done to find resistor values are included in the document. The final document was written in LaTeX, and all of the figures were hand-drawn by me.

The PDF of the write-up can be found by clicking the image below.

Electronics