Rough Draft of Statement of Purpose Physics PhD

[Vanadium 50]

what I said was not true

This time or the time before? I suppose that doesn't matter - what matters is that everything in the statement you send must be 100% true. If the admissions committee gets even a whiff of dishonesty, they will almost certainly decide "more trouble than it's worth" - because dishonest students (and postdocs, and faculty) are more trouble than they are worth.

As far as the text, you keep focusing on what not to write. It's better to focus on what to write: be brief. Be clear. Use everyday language. Make each sentence count. Make each sentence flow into the next. Separate different ideas into paragraphs.

 

[radium]

Vanadium hit the nail on the head. The content of your statement is a bit better, but your writing style is very unnatural and makes it seem like you are trying to sound impressive (you aren't succeeding) which is what I did not say so well earlier. You need to go through this statement and edit anything you think sounds especially impressive because what you seem to think is well said actually sounds quite bad for the reasons just mentioned.

"My goal is to research whether or not the accelerated expansion of space can be accounted for by quantum fluctuations predicted by Quantum Field Theory. Recent work in modified gravity, such as the DGP model has spurred my interest in this problem because it can explain the observed acceleration of space without postulating dark energy. I would like to conduct theoretical research in these models to determine if they can explain the value of the cosmological constant"

You yourself have mentioned that you know practically nothing about QFT and GR. How can you open the statement by claiming that this is the goal for your PhD? People have been working on this for years and you think you can say that you will solve it before you know anything about the problem? What I was trying to say before is that while you can say this problem interests you, don't say your goal is to solve it. That's not how a theory PhD. You find an advisor whose interests you share and go from there. People in my group can work on a variety of different things in their PhD and the thesis is usually just a summary of the main areas you worked in. For an example A PhD student I worked with in undergrad wrote his thesis on two parts which each contained his work in a distinct area from the other. Right now I am currently working in a very interesting what I would call a sub-subfield but I still want to explore other slightly different areas in the future (all in quantum condensed matter systems) since many of the skills in my topic translate to other related areas.

 

[harmony5]

I understanding both of your points. Do you feel I'm spending to much time talking about my tutoring experience? Also am I mentioning to much fluff about my research experience? Everything I have said in my last statement was the plain truth. One of my recommendation letters is coming from my boss where I tutor. He'll attest that many students come specifically to see over other physics tutors because I explain things in the most depth.

 

[harmony5]

Well I did take a class in cosmology and a class in classical fields and I got -A in both. Those two were my to favorite physics classes. After doing research in classical mechanics for three semesters I decided not to devote 3 plus more years of research into it. I like to do research which is at the intersection of field theory and cosmology.

 

[harmony5]

"My goal is to conduct theoretical research that is at the intersection of Cosmology and Particle Physics. A particular problem that interest me is the vacuum catastrophe. Recent work in modified gravity, such as the DGP model has spurred my interest in this problem because it can explain the observed acceleration of space without postulating dark energy. I would like to work on this problem and further advance the contributions of others." Is this better for my opening paragraph?

 

[radium]

That is good except for "further advance the contributions of others". It's not necessary to include that part and it gives the impression that you have a big ego.

 

[harmony5]

"My goal is to conduct theoretical research that is at the intersectionof Cosmology and Particle Physics. A particular problem that interest me is the vacuum catastrophe. Recent work in modified gravity, such as the DGP model has spurred my interest in this problem because it can explain the observed acceleration of space without postulating dark energy." So it is okay that I end the first paragraph this way? I don't have access to a computer now but when I do I'll change the rest of it. Do you feel like I talk to much about my tutoring experience? Also am I still mentioning unnecessary details about my research?

 

[harmony5]

"My goal is to conduct theoretical research that is at the intersection of Cosmology and Particle Physics. A particular problem that interest me is the vacuum catastrophe. Recent work in modified gravity, such as the DGP model has spurred my interest in this problem because it can explain the observed acceleration of space without postulating dark energy. Eventually I want to become a professor of physics and continue to conduct research in theoretical physics.
In college, I was a physics tutor and became the physics tutors’ Team Leader. As a tutor, I would show my students the derivation of equations as opposed to just applying them. What I enjoyed most from tutoring is seeing students' faces light up when they understood something in more detail than they thought possible. As Team Leader I made and graded qualifying and mock exams for prospective tutors and students respectively. While I was Team Leader I assumed many of the functions of a lecturer and enjoyed the experience.
While doing research in Hamiltonian Chaos in the Double Pendulum I understood that the equations of motion I solved and animated are not equivalent to the pendulum I built in the lab. From considering this I learned how to manipulate theoretical models so they can more accurately represent what is being studied. Also, I learned many advanced mathematical and programming techniques from constantly reading peer reviewed physics journals. Applying these techniques taught me how to extract as much information as I can from a mathematical model.

My advisor gave me the freedom to analyze the Double Pendulum in any way I wish. As a result, I decided to study the topological aspects of its phase space in terms of the KAM theorem. In particular, I made a Poincare section simulation that demonstrated how invariant tori disintegrated as I varied a parameter. While doing so, I learned the importance of using computational methods to witness the consequences of a theory. Prior to my research I downplayed the importance of numerical methods in theory. But after conducting my research I now strive to use computational methods to bring the theory I’m studying to life.
Other projects in my adviser's group included quantum chaos and hyperon's orbit. I would attend weekly meeting discussing what progress everyone in the group was making. During these meetings I assisted my fellow undergraduate researchers in troubleshooting their code and in constructing programs to measure Lyapunov exponents. The meetings taught me how to clearly express the weekly to monthly results of my research. Also, I got to learn from others how they conducted their research and that enriched my own understanding.
While conducting research, I completed a graduate physics class at the Graduate School of Arts and Science (GSAS). I further incorporated the theories and programming techniques I learned in that class in my research. During my last semester of research in order to graduate on time I had to complete 29 credits of course material while working two jobs.That experience taught me how to further manage time as efficiently as possible and distinguish important results or observations from trivial ones during research.
The GSAS of New York University is a good fit for me because it hosts the Center For Cosmology and Particle Physics (CCPP.) The CCPP has pioneered models which explain cosmic acceleration without dark energy such as the DGP. As a result, it is the ideal place for me to conduct research in determining if dark energy is needed to explain cosmic expansion.
Currently I’m interested in working with either professor Mathew Kleban or Roman Scoccimarro. Mathew Kleban’s research in quantum gravity interests me because it can shed light on why QFT does not give the correct prediction for the energy density in the vacuum. Professor Scoccimarro’s research on modifying General Relativity to account for the cosmological constant is of great interest because it can determine whether or not modified gravity can explain the value of the cosmological constant without dark energy."

This is what I have so far. Did I take out to much details or is this draft the best one so far?

 

[harmony5]

I managed to condense my words to 599 words in this draft and I took out some parts and added others. Is this a excellent statement of purpose given my background?

"
My goal is to conduct theoretical research that is at the intersection of Cosmology and Particle Physics. A particular problem that interest me is the vacuum catastrophe. Recent work in modified gravity, such as the DGP model has spurred my interest in this problem because it can explain the observed acceleration of space without dark energy. Eventually I want to become a professor of physics who works in theoretical physics.In college, I tutored physics and became the physics tutors’ Team Leader. I taught my students the derivations of equations as opposed to only applying them. What I enjoyed most from tutoring is seeing students' faces light up when they understood something in more detail than they thought possible. As Team Leader I made and graded exams for prospective tutors and students. During my tenure, I assumed many of the functions of a lecturer and enjoyed the experience.During my three semesters of research on the dynamics of a Double Pendulum I understood that the equations of motion I solved and animated are not equivalent to the pendulum I built in the lab. From considering this I learned how to manipulate theoretical models so they can more accurately represent what is being studied. Also, I learned many mathematical and programming techniques from constantly reading peer reviewed physics journals. Applying these techniques taught me how to extract as much information as I can from a mathematical model.My advisor gave me much freedom to analyze the Double Pendulum. As a result, I studied the topological properties of its phase space in terms of the KAM theorem. I made a Poincare sections simulation that demonstrated how invariant tori disintegrated as I varied a parameter. While doing so, I learned the importance of using computational methods to witness the consequences of a theory. Prior to my research I downplayed the importance of numerical methods in theory. But after conducting research I now strive to use computational methods to bring the theory I’m studying to life.Other projects in my adviser's group involved quantum chaos and Hyperion's orbit. I attended weekly meeting discussing what progress everyone in the group made. During these meetings I assisted other researchers in troubleshooting code and in constructing programs to measure Lyapunov exponents. The meetings taught me how to clearly express the weekly to monthly results of my research. Also, I got to learn from others how they conducted their research and that enriched my own understanding.

During my last semester of research my father died and I had to complete 29 credits to graduate on time while working two jobs. That experience taught me how to further manage time as efficiently as possible and prioritize my work. Most importantly, I learned how to persevere during tragedy and stress.

The GSAS of New York University is a good fit for me because it hosts the Center For Cosmology and Particle Physics (CCPP.) The CCPP specializes in research that intrigues me and hosts those who proposed the DGP model. As a result, it is the ideal place for me to conduct my research.Many of the faculty engage in research I’m interested in but currently I would like to work with either Professor Mathew Kleban or Roman Scoccimarro. Professor Kleban’s research in quantum gravity interests me because it can shed light on why Quantum Field Theory does not give the correct prediction for the energy density in the vacuum. Professor Scoccimarro’s research on distinguishing between modifications of general relativity and dark energy interests me because it can help determine which type of model can best solve the vacuum catastrophe."

 

[harmony5]

I had others read the above SoP. They said it was very dull, uninspiring and I didn't go into enough detail of what I did during my research. So I wrote a new SoP. This one has a very standout introduction and goes into great detail about my research. Also I go into more detail of what I expect to gain from going to NYU for grad school. All critiques are welcomes. Specifically I'm interested if this is an improvement of what I had before or not.

"
Catastrophe. The word invokes a feeling of discouragement and destruction. However, in physics it invokes excitement and creativity. It gives license for paradigm shifts. Today such a paradigm shift is possible due to the vacuum catastrophe. Attempts to resolve it such as the DGP model require radically rethinking our understanding of gravity and the dimensionality of space. As a result, my goal is to conduct theoretical research that is at the intersection of Cosmology and Particle Physics. The parallels between the vacuum and ultraviolet catastrophes draw me to be part of this field of research.

In college, I honed my research skills by working with Professor Mugglin for three semesters. Initially we sought to simulate the motion of a Physical Double Pendulum (PDP) we built. To do this we took into account air resistance, friction and multi planar motion. To account for the multi planar motion I proposed adding a coupled harmonic oscillator third degree of freedom. The more it oscillated in the z direction the more energy it would sap from the other two degrees of freedom. Using a high speed camera we tracked the motion of our PDP and it reasonably matched our model.

During this phase of our research I learned many mathematical techniques. These techniques to name a few included Rayleigh’s dissipation
functions and variational principles for non conservative systems and canonical transformations. Applying them taught me how to extract as much information as I can from a mathematical model and how to enhance existing models.

After reading a paper on the integrability of the PDP my goal was to determine if it exhibited seperatix motion. Treating g as a small perturbation I expanded the Hamiltonian and converted it to action angle variables to determine the frequency. To simplify my calculations, I derived simple polynomials which matched the behavior of transcendental functions between the angles of -Pi and Pi. While converting the Hamiltonian to action angle variables I found another parameter which, if set to zero makes the PDP integrable.

I made a Poincare sections simulation as this small parameter was increased. Interpreting the results in terms of the KAM theorem I observed invariant tori disintegrating. The manner in which their disintegrated though, was unusual. First, they collapsed into themselves to form periodic orbits. If the parameter was increased slightly further the collapsed tori exploded into a sea of points. I concluded I was observing an unexpected route to chaos. As this parameter starts off at zero and is increased the motion is quasiperiodic; it then abruptly becomes periodic and if increased further chaotic. None of the professors in my department observed this before and this became the most prominent result of my research. Deriving this result taught me how to use computational methods to bring the theory I'm studying to life.

Despite all of the mathematical work I did the most important thing I learned while conducting research was how to persevere through tragedy and stress. In the fall of 2014 I took two very difficult graduate classes and learned my father was sick. Despite those difficulties I did not decrease the hours I devoted to research. Tragically, in the spring of 2015 my father died. In addition to my father's death, I had to complete 29 credits to graduate on time while working two jobs. The experience prepared me to overcome any challenge I faced whether it be academic or personal

At the GSAS of New York University I can continue to hone my research abilities by working with faculty who represent the frontier of their field. NYU hosts the Center for Cosmology and Particle Physics and I would like to conduct research there. I'm drawn to the center for what it specializes in and because it hosts the founders of the DGP model. As a result, it is the ideal place for me to conduct research. I also wish to increase my knowledge of physics in areas outside my specialization. My long term goal after graduate school is to become a professor of physics.

Many of the faculty engage in research I’m interested in but currently I would like to work with either Professor Mathew Kleban or Roman Scoccimarro. Professor Kleban’s research in quantum gravity interests me because it can shed light on why Quantum Field Theory does not give the correct prediction for the energy density in the vacuum. Professor Scoccimarro’s research on distinguishing between modifications of general relativity and dark energy interests me because it can help determine which type of model can best solve the vacuum catastrophe."

 

[micromass]

Catastrophe. The word invokes a feeling of discouragement and destruction.

Are you actually being serious right now?

 

[harmony5]

Are you actually being serious right now?

Are you actually being serious right now?

I saw an example SoP where someone started with the word perturbation and supposedly everyone said that was a really good one. So I figured I would do something similar.

 

[harmony5]

"My goal is to conduct theoretical research that is at the intersection of Cosmology and Particle Physics. Recent work to resolve the vacuum catastrophe such as the DGP model convinced me to pursue this path. In the same way resolving the ultraviolet catastrophe revolutionized physics, resolving this catastrophe may revolutionize physics again by radically changing our understanding of gravity and the dimensionality of space. Due to the vacuum catastrophe I feel Particle Cosmology is an exciting field to be part of as of today" Is this better?

 

[radium]

A statement of purpose is not the time to be dramatic. Who did you have read your statement? You want to be concise and too the point. It's not some creative writing piece.

 

[micromass]

I saw an example SoP where someone started with the word perturbation and supposedly everyone said that was a really good one. So I figured I would do something similar.

Who is "everyone"? The only people you should care about is the admission committee really.

 

[harmony5]

A statement of purpose is not the time to be dramatic. Who did you have read your statement? You want to be concise and too the point. It's not some creative writing piece.

Because I wasn't getting replies to this thread anymore I moved on to academia sub reddits for. They all said it was boring and I didn't talk enough about my research. I will say though that I trust this forum far more then any physics or grad school sub reddits. The perturbation part I got from a university Web site though.

 

[harmony5]

Who is "everyone"? The only people you should care about is the admission committee really.

The perturbation part was from a university website saying I need a strong hook.

 

[micromass]

So let's pretend I'm in your admission committee (I've never been in one so I wouldn't know, but hey). I see your record and your statement of purpose. I see on your record that you don't really have any experience with QFT and with GR. And I see in your statement of purpose that you want to go into precisely that field. This raises a pretty major red flag to me. You need to use your SoP to convince me that you are a qualified candidate and that my worry is unnecessary.

 

[harmony5]

So let's pretend I'm in your admission committee (I've never been in one so I wouldn't know, but hey). I see your record and your statement of purpose. I see on your record that you don't really have any experience with QFT and with GR. And I see in your statement of purpose that you want to go into precisely that field. This raises a pretty major red flag to me. You need to use your SoP to convince me that you are a qualified candidate and that my worry is unnecessary.

I just got an idea. I should emphasis how I knew nothing about Nonlinear dynamics when I began my research. But after three semesters I knew more about it then the professors in the department. Is that what you mean?

 

[harmony5]

@micromass do you feel that in my latest draft I went into to much detail about my research. I did that because I wanted to show how I was creative.

 

[Vanadium 50]

Look, we've given him (or her) the same advice, over and over. (S)he clearly doesn't want to take it. No point in giving it again. And again. And again.

Harmony5, best of luck to you.

 

[harmony5]

Look, we've given him (or her) the same advice, over and over. (S)he clearly doesn't want to take it. No point in giving it again. And again. And again.

Harmony5, best of luck to you.

Are you saying I have made no progress in my SoP.

 

[harmony5]

I do want to take everyones advice and I'm not here to waste anyone's time. I'm quite amazed how much difficulty I'm experiencing writing this. It's been three weeks and I went from a horrible SoP to a slightly less horrible one. Is it because I go into much detail about my research? Not enough detail. Is my research experience so bad that the more I talk about it the worse I look? Is it still unfocused? I know my last two renditions have been terrible but I don't know why

 

[Vanadium 50]

Are you saying I have made no progress in my SoP.

No, although the latest one is a step backwards. I am saying that you have gotten some good advice that you aren't taking. Starting at message #2. I don't see where repeating it will do any good.

 

[harmony5]

No, although the latest one is a step backwards. I am saying that you have gotten some good advice that you aren't taking. Starting at message #2. I don't see where repeating it will do any good.

The latest was a step back I understand. How about the one prior the latest. I know the 599 word one isn't good but I did model it on the advice you all gave me. To be clear it being bad was due to me misunderstanding all of your advice. My problem is Idk why that 599 word one in which I tried to not sound erudite Is still a abomination.

 

[atyy]

My background: I'm a biologist, and I wrote in my grad school essay I was interested in consciousness (which is way worse than anything you've written), so I'm not qualified. But what exactly is the vacuum catastrophe? In what sense is it a problem that QFT cannot predict the cosmological constant? After all, there are free parameters in the standard model too that we cannot predict. If one treats the cosmological constant as a free parameter, there is no deviation between theory and observation.

 

[harmony5]

My background: I'm a biologist, and I wrote in my grad school essay I was interested in consciousness (which is way worse than anything you've written), so I'm not qualified. But what exactly is the vacuum catastrophe? In what sense is it a problem that QFT cannot predict the cosmological constant? After all, there are free parameters in the standard model too that we cannot predict. If one treats the cosmological constant as a free parameter, there is no deviation between theory and observation.

Don't look back at previous drafts. They were rejected for a reason. Please look and ask questions about my current SoPs. According to QFT the energy density in a vacuum is one Planck unit. If we attribute this energy density in the vacuum to the acceleration of space we calculate the density should be 10^-120.

 

[atyy]

Don't look back at previous drafts. They were rejected for a reason. Please look and ask questions about my current SoPs. According to QFT the energy density in a vacuum is one Planck unit. If we attribute this energy density in the vacuum to the acceleration of space we calculate the density should be 10^-120.

I'm looking at the one in post #70?

My question is: what is the problem with the density being 10^120? Are there any observable consequences?

 

[harmony5]

I'm looking at the one in post #70?

My question is: what is the problem with the density being 10^-120? Are there any observable consequences?

The observable consequence is that this energy density of 10^-120 is caused a negative pressure in the vacuum of space. This negative pressure is driving the expansion. The problem is that we have no way to accurately predict this energy density. QFT which attributes this energy density to the constant creation and annihilation of virtual particles in the vacuum gives a answer 10^120 times greater.

 

[atyy]

The observable consequence is that this energy density of 10^-120 is caused a negative pressure in the vacuum of space. This negative pressure is driving the expansion. The problem is that we have no way to accurately predict this energy density. QFT which attributes this energy density to the constant creation and annihilation of virtual particles in the vacuum gives a answer 10^120 times greater.

Please state the predicted value of the energy density and the observed value.