Rough Draft of Statement of Purpose Physics PhD

[Vanadium 50]

I feel this answers clearly why I want to go grad school, what I want to do in grad school and how I'm going to do it.

And the "how I am going to do it" is a problem. First, that's for the faculty to decide (another instance of coming across as naive and overconfident). Second, what you are saying is that before you have learned about the problem in detail, you will reject all but one solution. Does this sound like a good scientist to you? How do you think it will look to the committee?

 

[Dishsoap]

If I may, I'd like to interject with a question. I'm following this thread pretty closely as I seek advice on how to write my own personal statement. You said that the OP saying "the more research I do, the more questions I have" is a middle-school answer. I agree that it could definitely be phrased more eloquently, but is the reasoning in and of itself poor?

Likewise, the OP saying that he is a distinguished tutor you said sounds overconfident, and I agree. However, I mentioned this in my statement (distinguished tutor and TA) because I am having only one LoR written by someone at my university, and I have never tutored nor TA'd for him, though I have won awards for tutoring and TAing within the department. Should you therefore not mention this in your SoP, or just hope they read your CV?

 

[atyy]

@harmony5:

Are you familiar with the Weinberg-Witten theorem?

Are you familiar with the concept of quantum gravity as an effective field theory?

 

[Vanadium 50]

is the reasoning in and of itself poor?

I would say that if it is that general, yes. What would be better is "during my undergraduate project on x-ray diffraction, I became curious about crystalography" or something like that.

Have you seen the movie Animal House? There is a scene where the camera is on a statue of Emil Faber, founder of Faber College. Under his name is a quote, "Knowledge is Good". Why is that funny? Because it is so general as to be almost meaningless. Same problem here.

Should you therefore not mention this in your SoP, or just hope they read your CV?

Your SOP should be a statement of purpose. They will read your CV, and that's the place to put any awards.

 

[Student100]

Here is a quickie I did from some of your previous stuff just to kind of show you an outline.

"
My younger self was only interested in money; as such, my ideal future career revolved around how to make as much of it as possible. This changed, however, while attending [middle school/high school/university] classes. I feel in love with the sciences-physics in particular- for it's ability to quantitatively explain nature. The only future career I could convince of anymore was that of a theoretical research professor in physics.

My time as a physics undergrad has only further cemented this desire.

To help overcome the finical burden of university, I took a job as a physics tutor. While other tutors I worked with may have simply helped the students plug numbers into equations, I would try to guide them and remind them of the importance of the conceptual part of physics. We would walk through the derivations together, and I would point out the physical insight that could be gained from just the equations themselves! [maybe an example, but I don't really even like this tbh in it's current form.] My time tutoring showed me the great responsibility of teaching.

While taking [x classes, what you excelled at, what you did poorly at, how you over came challenges]

The advisement of [name of adviser] helped me to develop the tools I will need as a researcher. When we worked on [X's] research project[ S], [explain what you learned, what you didn't know, and what insights you gained, publication references if you also published], methods, his tutorship, etc.

The program at [X school], and [name of professor doing the work] fascinates me because of [x]. When we spoke through [email/phone] the problem of [x] intrigues me and I'd love to work on [some subset of x that is feasible for a graduate student] I would be a great fit [because why you'd be a good fit]
"

Just remember that you're trying to tell a story here, and that story is "Why should you give me 200K for school over equally qualified candidates. How you can show that you're not a waste of money or time, and how you will be successful as a researcher"

 

[harmony5]

@harmony5:

Are you familiar with the Weinberg-Witten theorem?

Are you familiar with the concept of quantum gravity as an effective field theory?

I wasn't familiar with the Weinberg-Witten theorem until I looked it up right now. In short it says graviton are incompatible with QFT. I'm also familiar that at low energies quantum gravity is an effective field theory.

 

[harmony5]

Here is a quickie I did from some of your previous stuff just to kind of show you an outline.

"
My younger self was only interested in money; as such, my ideal future career revolved around how to make as much of it as possible. This changed, however, while attending [middle school/high school/university] classes. I feel in love with the sciences-physics in particular- for it's ability to quantitatively explain nature. The only future career I could convince of anymore was that of a theoretical research professor in physics.

My time as a physics undergrad has only further cemented this desire.

To help overcome the finical burden of university, I took a job as a physics tutor. While other tutors I worked with may have simply helped the students plug numbers into equations, I would try to guide them and remind them of the importance of the conceptual part of physics. We would walk through the derivations together, and I would point out the physical insight that could be gained from just the equations themselves! [maybe an example, but I don't really even like this tbh in it's current form.] My time tutoring showed me the great responsibility of teaching.

While taking [x classes, what you excelled at, what you did poorly at, how you over came challenges]

The advisement of [name of adviser] helped me to develop the tools I will need as a researcher. When we worked on [X's] research project[ S], [explain what you learned, what you didn't know, and what insights you gained, publication references if you also published], methods, his tutorship, etc.

The program at [X school], and [name of professor doing the work] fascinates me because of [x]. When we spoke through [email/phone] the problem of [x] intrigues me and I'd love to work on [some subset of x that is feasible for a graduate student] I would be a great fit [because why you'd be a good fit]
"

Just remember that you're trying to tell a story here, and that story is "Why should you give me 200K for school over equally qualified candidates. How you can show that you're not a waste of money or time, and how you will be successful as a researcher"

I truly do appreciate the work and effort you put into this outline. It really is a wonderful outline. I'll certainly draw upon it in some way as I write my SoP.

 

[harmony5]

After taking everyone advice I produced this for my SoP. I brielfy mention what I want to do in grad school, I then talk about why I want to do it and what my purpose is for going to graduate school. Finally I talk about what I learned during my research rather then what I did. Unlike my last attempts I feel I don't come across as plain terrible and I don't rabbit hole myself to the point of sounding naive.

"My goal is to research whether or not the accelerated expansion of space can be accounted for by quantum fluctuations predicted in Quantum Field Theory (QFT). To answer this I want to conduct research in theoretical QFT. Specifically, I want to research the consequences of reformulating QFT with the assumption that space is quantized in light of the vacuum catastrophe.This problem is dear to me because it epitomizes everything I love about physics. What drew me into physics was how it answers questions with far-reaching implications using mathematics. The idea that mathematics with a few constraints can derive a theory explaining what we observe is immensely powerful. I also love how you can manipulate the mathematics of a theory to produce a new one or reinterpret an old oneIn college, I was a physics tutor who 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 then they thought possible. In light of everything I want to become a professor and do research in theoretical physics.My research experience consists of working with professor “insert name” at the “insert university” for three semesters on the dynamics of physical double pendulum. (PDP) The experience matured my understanding of how research is conducted. Unlike in class where we learned about systems that have a perfect correspondence to their equations I found that in research that isn’t always the case.I learned the equations of motion I’m solving and animating are not equivalent to the PDP I built in the lab. In light of this I learned how to manipulate theoretical models so they can be more in line with what is actually being studied. Also, I learned many advanced mathematical and programming techniques that will be useful in whatever research I do in the future. Applying these techniques taught me how to extrapolate as much information as I can from a mathematical model.Professor “insert name” gave me a lot of freedom to analyze the dynamics of the PDP in a variety of ways. As a result, I decided to study the topological aspects of its phase space. 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. "

 

[harmony5]

This is the gist of my concluding section. In the future I do plan to modify it because I'm going to talk to them in person sometime between now and december. Is this concluding section a good start. Also my SoP as of now is 616 words is that a appropriate length?"

The Graduate School of Arts and Science of New York University is a good fit for me because it hosts the Center For Cosmology and Particle Physics (CCPP.) My proposed research is at the intersections of cosmology and particle physics and the CCPP specialize in that type of research. Also, because I already live NYC I can devote more time to research and less time worrying about logistics.

Currently I’m interested in working with either professor Mathew Kleban or Roman Scoccimarro. Mathew Kleban research in quantum gravity interests me because it can shed light onto why QFT does not give the correct prediction for the energy density in the vacuum. Professor Scoccimarro research on modifying General Relativity (GR) to account for the cosmological constant is of great interest to me as well for similar reasons.

"

 

[radium]

the WW theorem relates to the restrictions you must put on a theory to get rid of the unphysical polarizations which do not transform in a Lorentz covariant way. With the photon you get the ward identity to get rid of this third unphysical polarization. A way to connect charge conservation in connection to Lorentz covariance is to look at the s matrix elements for p going to zero. You will see here that a spin 2 graviton would interact with everything like gravity, cannot be a composite particle, and lastly higher spin particles are overconstrained and have no dynamics.
The WW theorem doesn't apply to a lot of situations in the standard model however (nonabelian gauge theories) so it is not especially useful there. It does say if you started without gravity you could never get a massless graviton. I don't know too much else about this theorem since my field uses QFT in other contexts where we don't have Lorentz invariance a lot of the time. I do know that classical gravity is nonrenormalizable. You can't get rid of diverges by adding a finite number of counterterms like you can for QED so it breaks down at high energies (so does perturbation theory for QED).

I really am not convinced that you actually want to study quantum gravity. For one, you barely know the basics, and two you have no idea what the research entails. You can get some incredibly messy calculations in QFT, and if you haven't done them, you haven't gotten a full picture of the field. Also, don't mention your plans to solve quantum gravity because you know very little about it and it sounds very arrogant.

 

[harmony5]

the WW theorem relates to the restrictions you must put on a theory to get rid of the unphysical polarizations which do not transform in a Lorentz covariant way. With the photon you get the ward identity to get rid of this third unphysical polarization. A way to connect charge conservation in connection to Lorentz covariance is to look at the s matrix elements for p going to zero. You will see here that a spin 2 graviton would interact with everything like gravity, cannot be a composite particle, and lastly higher spin particles are overconstrained and have no dynamics.
The WW theorem doesn't apply to a lot of situations in the standard model however (nonabelian gauge theories) so it is not especially useful there. It does say if you started without gravity you could never get a massless graviton. I don't know too much else about this theorem since my field uses QFT in other contexts where we don't have Lorentz invariance a lot of the time. I do know that classical gravity is nonrenormalizable. You can't get rid of diverges by adding a finite number of counterterms like you can for QED so it breaks down at high energies (so does perturbation theory for QED).

I really am not convinced that you actually want to study quantum gravity. For one, you barely know the basics, and two you have no idea what the research entails. You can get some incredibly messy calculations in QFT, and if you haven't done them, you haven't gotten a full picture of the field. Also, don't mention your plans to solve quantum gravity because you know very little about it and it sounds very arrogant.

Where did I mention in my recent rendition of my SOP any plans what so ever to solve quantum gravity?

 

[Vanadium 50]

Where did I mention in my recent rendition of my SOP any plans what so ever to solve quantum gravity?

It's in your first post.

For example using a modified form of General Relativity to describe how gravity behaves on quantum scales.

And, while you have not specifically said "quantum gravity" in your latest post, you imply it strongly enough that any reasonable physicist will infer it.

The recent SOPs are good, in that they answer the questions asked and accurately represent your Purpose. I think achieving your Purpose will be quite difficult, as you want to enter one of the most competitive areas of physics with substantially less preparation than your peers, but if that's what you want to do, that's what you want to do.

 

[harmony5]

It's in your first post.
And, while you have not specifically said "quantum gravity" in your latest post, you imply it strongly enough that any reasonable physicist will infer it.

The recent SOPs are good, in that they answer the questions asked and accurately represent your Purpose. I think achieving your Purpose will be quite difficult, as you want to enter one of the most competitive areas of physics with substantially less preparation than your peers, but if that's what you want to do, that's what you want to do.

I do appreciate your honesty. It is true I was not a dual math and physics major. It is also true I have no research experience in QFT let alone quantum gravity. My department did not specialize in either of those field. But isn't graduate school supposed to prepare you to do that research? My GPA right now us 3.665 but I graduated Magna Cum Laude because my school enforces grade deflation. The only reason it isn't a 3.7+ is because of one bad semester. My last semester I had to complete 29 credits of course work and I got a 3.788. I feel I do have a strong application. I'm going to post one more SoP I wrote. It is thicker than this one but it I feel the added details help me. If not I'll change it.

 

[harmony5]

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 (QFT). To answer this I want conduct theoretical research into the consequences of reformulating QFT with the assumption that space is quantized in light of the vacuum catastrophe.This problem is dear to me because it epitomizes everything I love about physics. What drew me into physics was how it answers questions with far-reaching implications using mathematics. What cemented my desire to do research in theoretical physics was the process of manipulating the mathematics of a theory to produce a new one or reinterpret it. The idea that mathematics with a few constraints can derive a theory explaining what we observe is immensely powerful.In college my drive to become a professor and hence teach was introduced when I became a physics tutor. 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 then they thought possible.Through hard work I became the physics Team Leader thus assuming the responsibility of making and grading mock exams. This task meant I had to understand on the grand scale what students who were taking the introductory physics sequence were struggling with so I can make appropriate exams. While as Team Leader I assumed many of the functions of a professor and enjoyed the experience. In light of everything I want to become a professor and conduct research in theoretical physics.My research experience consists of working with professor David Mugglin at the Polytechnic School of Engineering of New York University for three semesters on the dynamics of physical double pendulum. (PDP). The experience matured my understanding of how research is conducted. Unlike in class where we learned about systems that have a perfect correspondence to their equations I found that in research this isn’t always the case. I learned the equations of motion I’m solving and animating are not equivalent to the PDP I built in the lab. Unlike the system of nonlinear differential equations I numerically solved the PDP in the lab had air resistance, friction from the bearing and didn’t have two perfect degrees of freedom. In light of 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 that will be useful in research I do in the future. Applying these techniques taught me how to extrapolate as much information as I can from a mathematical model.While conducting research, I also successfully completed a physics graduate 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 plus work two jobs. That experience taught me how to manage time as efficiently as possible and distinguish important results or finding from trivial ones during research.Professor Mugglin gave me a lot of freedom to analyze the dynamics of a PDP. As a result, I decided to study the topological aspects of its phase space in terms of the KAM theorem so I can discern a route to chaos. In particular I made a Poincare section simulation, which demonstrated how invariant tori disintegrate 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.The GSAS of New York University is a good fit for me because it hosts the Center For Cosmology and Particle Physics (CCPP.) My proposed research is at the intersections of cosmology and particle physics and the CCPP specialize in that type of research. Also, because I already live NYC I can devote more time to research and less time worrying about logistics.Currently I’m interested in working with either professor Mathew Kleban or Roman Scoccimarro. Mathew Kleban research in quantum gravity interests me because it can shed light onto why QFT does not give the correct prediction for the energy density in the vacuum. Professor Scoccimarro research on modifying General Relativity (GR) to account for the cosmological constant is of great interest to me as well for similar reasons.

 

[Vanadium 50]

I feel I do have a strong application

Why do you think that?

A. Your GPA is good, but there are a lot better ones.
B. Your physics GRE is not good.
C. We can't see your letters, but "average" doesn't seem too far from the truth.
D. You were rejected from every school that you applied to.It's possible your application is strong, but the evidence here doesn't show it. And you want to enter one of the most competitive areas of physics with substantially less preparation than your peers. Like I said, if that's what you want to do, go for it. But it is far from guaranteed.

 

[harmony5]

Why do you think that?

A. Your GPA is good, but there are a lot better ones.
B. Your physics GRE is not good.
C. We can't see your letters, but "average" doesn't seem too far from the truth.
D. You were rejected from every school that you applied to.It's possible your application is strong, but the evidence here doesn't show it. And you want to enter one of the most competitive areas of physics with substantially less preparation than your peers. Like I said, if that's what you want to do, go for it. But it is far from guaranteed.

A: You can say that about any stat. I did graduate in the top ten percent of my class.
B: True that's why I'm retaking it
C: I've known all five professors for four years so I do expect excellent letters. I'm going to show them my SOP once it is a 100% complete and that will help make sure the letters further support my purpose.
D: I got rejected because I applied only to 4 schools. Also I didn't take a essential upper level core class at the time I applied.

Despite disagreeing with you on this I do appreciate your critiques and the critiques of others. Do you feel given what I've done in my undergrad the SoP I have above is the best I can possibly do or is it still lacking some essential elements? The last section will be slightly edited once I get into contact with those two professors.

 

[Vanadium 50]

I don;t want to argue, but I will say two things: one is the only evidence we have from people who have seen the whole application is the four or five schools you applied to. You might want to consider those outcomes. The other is that students often grossly overestimate the strength of their LoR's. "Best student in my class this year" is a below-average LoR. Well below average.

 

[radium]

I think rather than providing a specific research question in cosmology/quantum gravity, you should just say what past developments caught your attention. For example, in the end of my GR class we talked about the expansion of the universe which is covered in GR books like MTW, Carroll, etc.

In my statement of purpose, I didn't mention specific research questions I was interested in. For example, I said I was interested in topic a because of what some people have been doing recently. I think I said something like there are proposals to realize Majorana fermions (topological states is one of my interests in my field) experimentally and there have been theoretical proposals to use them for quantum computing so I want to follow in those footsteps. That's more general than what you were doing.

If you have a lower GPA or PGRE, your going to need really strong research experience and letters to make up for it. Do you have any publications?

As I said before, a good way to gauge the quality of your recommendations is to ask the professors where you should apply. For example, when my professors mentioned really great schools, I knew they thought I had a good shot of being accepted and would write a great letter to help.

Overall, I think the content of your statement is getting better, but I am not very enthusiastic about your writing style. You state the obvious in a way that just sounds kind of juvenile

 

[harmony5]

I'll write a new more generalized intro to and see if it is better then the one I currently have. What in my latest statement is obvious and juvenile.?

 

[radium]

Not all of it is stating the obvious, a lot of your writing is just very verbose and needs to be cut. Phrases like "Through hard work", "successfully completed".
"The experience matured my understanding of how research is conducted. Unlike in class where we learned about systems that have a perfect correspondence to their equations I found that in research this isn’t always the case." This needs to be cut down significantly. It sounds like you are lecturing the reader and it just is unnecessary. Basically, for you I would say that you should cut anything that you think you said elegantly since the point is to be direct.

"This task meant I had to understand on the grand scale what students who were taking the introductory physics sequence were struggling with so I can make appropriate exams. While as Team Leader I assumed many of the functions of a professor and enjoyed the experience. In light of everything I want to become a professor and conduct research in theoretical physics."
I would not say you assumed many of the functions of a professor because you didn't. You can say that you were able to become very involved in running the course and enjoyed the experience, but a professor does much more than that.

 

[harmony5]

Not all of it is stating the obvious, a lot of your writing is just very verbose and needs to be cut. Phrases like "Through hard work", "successfully completed".
"The experience matured my understanding of how research is conducted. Unlike in class where we learned about systems that have a perfect correspondence to their equations I found that in research this isn’t always the case." This needs to be cut down significantly. It sounds like you are lecturing the reader and it just is unnecessary. Basically, for you I would say that you should cut anything that you think you said elegantly since the point is to be direct.

"This task meant I had to understand on the grand scale what students who were taking the introductory physics sequence were struggling with so I can make appropriate exams. While as Team Leader I assumed many of the functions of a professor and enjoyed the experience. In light of everything I want to become a professor and conduct research in theoretical physics."
I would not say you assumed many of the functions of a professor because you didn't. You can say that you were able to become very involved in running the course and enjoyed the experience, but a professor does much more than that.

You are right professor isn't the right word. Lecturer would be better. I'll take your advice and be more to the point and less eloquent.

 

[harmony5]

After taking some of Radium's advice I cut some of the fat from my SoP and made my purpose slightly more general. Do you feel that this SoP is a improvement over the one I before.

"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 constantIn college, my drive to become a professor, and hence teach began when I became a physics tutor. 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. Eventually I became the physics tutors’ Team Leader, thus assuming the responsibility of making and grading mock exams. This meant I had to understand what students that were taking the introductory physics sequence were struggling with so I can make more appropriate exams. While I was Team Leader, I assumed many of the functions of a lecturer and enjoyed the experience. In light of everything I want to become a professor and conduct research in theoretical physics.My research experience consists of working with Professor David Mugglin at the New York University Polytechnic School of Engineering for three semesters on the dynamics of a physical double pendulum. (PDP). While doing research I learned invaluable lessons. For example the equations of motion I solved and animated are not equivalent to what 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, which will be useful in research I do in the future. Applying these techniques taught me how to extract as much information as I can from a mathematical model.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.Professor Mugglin gave me freedom to analyze the dynamics of a PDP. 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.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 (GR) 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.

"

 

[harmony5]

I added a paragraph which explained that I was actually part of a research group. Also I did some more edits as well to take out statements that one might view as stating the obvious.

"

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 constantIn college, my drive to become a professor, and hence teach began when I became a physics tutor. 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. Eventually I became the physics tutors’ Team Leader, thus assuming the responsibility of making and grading mock exams. This meant I had to understand what students that were taking the introductory physics sequence were struggling with so I can make more appropriate exams. While I was Team Leader, I assumed many of the functions of a lecturer and enjoyed the experience. In light of everything I want to become a professor and conduct research in theoretical physics.
My research experience consists of working in Professor David Mugglin’s Chaos Theory research group for three semesters. I studied systems, which exhibited Hamiltonian Chaos most notably the Physical Double Pendulum (PDP). While doing research I learned invaluable lessons and gained the habit of constantly reading peer-reviewed physics journals. For example 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. Applying these techniques taught me how to extract as much information as I can from a mathematical model.
Professor Mugglin gave me the freedom to analyze the PDP in anyway 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 his group included quantum chaos and hyperons 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.

 

[Vanadium 50]

This still needs a lot of work. On style, you might remove at least 50% of the commas. Worse, it looks like you are trying to sound erudite. (Why do people try this? It doesn't make them sound smart - it makes them sound like Oswald Bates) This never works. Just sound like yourself and write like you talk.

As an example, "What I enjoyed most from tutoring is seeing students' faces light up when they understood something in more detail than they thought possible." Nobody talks like that. Worse, it's not true. About a week ago you said, "Even though my students weren’t interested in the derivations I loved every second of it." There is not much to be gained and a lot to be lost by embellishing.

 

[harmony5]

This still needs a lot of work. On style, you might remove at least 50% of the commas. Worse, it looks like you are trying to sound erudite. (Why do people try this? It doesn't make them sound smart - it makes them sound like Oswald Bates) This never works. Just sound like yourself and write like you talk.

As an example, "What I enjoyed most from tutoring is seeing students' faces light up when they understood something in more detail than they thought possible." Nobody talks like that. Worse, it's not true. About a week ago you said, "Even though my students weren’t interested in the derivations I loved every second of it." There is not much to be gained and a lot to be lost by embellishing.

I would like to clarify what I said was not true and shouldn't be taken at face value. I was trying to be funny but failed and sounded quite terrible. I was taking advantage of the sterotype that students who take introductory physics aren't interested in derivations and only want to plug and chug. I actually do greatly care if my students are paying attention and feel they are gaining something from the experience. The commas I will remove ASAP. I had to look up who Oswald Bates is and what erudite meant. Before when I was talking about perturbation theory and I sounded erudite but I heavily cut down on it. Can you please explain what you mean by sounding erudite.

 

[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."