Any tips for doing a PhD in theoretical physics?

[ansabs]

Hello, I am a second-year Data Science and Physics major at Northeastern University (My school has combined majors that are like double majors but cut a few classes out of each major). I am also considering switching to Math and Physics (I've linked the requirements for each major if it's helpful). I want to do my physics PhD in something theoretical (not sure which field yet, but I really do not want to do experimental). So far I have taken Calc 1-3, Diff-eq, physics 1&2, E&M 1&2 (my school does it as two courses), modern physics, stats, electronics, and classical mechanics, and some data science classes. I am a research assistant in this lab and was a research assistant in another lab last summer. I have some questions regarding a PhD.

1. What other courses are essential or useful to take (other than quantum and thermodynamics)
2. Would it make sense to take some graduate-level classes during undergrad, if so, which one?
3. What is a good way to narrow down which field of physics to focus on for the PhD?
4. Would it make sense/be worth it to switch to math/physics?
5. What are some general tips for getting into a theoretical physics program, what should I focus on?

Thank you for your time!

 

[mad mathematician]

Maybe a course on Classical Electrdynamics at the level of Jackson's textbook.
Beware not to burnout too quickly!

 

[Nugatory]

You will get better and more helpful answers from professors in the physics department. But with that said, somewhere in your undergraduate years you’ll want to learn some linear algebra and group theory, and the Hamiltonian and Langrangian formulations of classical mechanics.

 

[CrysPhys]

What is a good way to narrow down which field of physics to focus on for the PhD?

If you have to ask this question, you probably shouldn't be pursuing a PhD. Somewhere along your studies and undergrad research (along with talks, papers, and seminars), some field of interest or specific problem should grab your interest enough to motivate you enough to devote ~6+ yrs to a PhD program. You don't start out with the premise that you want to pursue a PhD for the hell of it and then ask what field you should pursue.

In addition to your core foundational courses you would take advanced undergrad courses in your field of interest (e.g., solid-state physics, astrophysics, nuclear physics, ....) ... when you decide what that is.

 

[Choppy]

I want to do my physics PhD in something theoretical (not sure which field yet, but I really do not want to do experimental).

Sometimes when I hear this from students it's a flag. I'm not necessarily saying that in your case, but I've seen a lot of students who don't like labs because they come ill-prepared, don't like the rigor of follow up analysis, and/or haven't yet developed skills for effective group work and based on that experience, their thinking goes... "well, I still like physics, so I suppose I should work in theory." When it comes time to apply for PhDs, base your choices on directions you want to go into because of your specific interests, the skills you have, and those you would like to develop, rather than what's left when you eliminate the things you don't want to do.

What other courses are essential or useful to take (other than quantum and thermodynamics)

As you move into your senior undergraduate years, this is a time to explore options, so try as much as possible to take a diverse set of courses that will introduce you to the topics you think you might be interested it. Do a senior thesis course if that's an opportunity for you. And if you're interested in theory, make sure you learn how to program.

Would it make sense to take some graduate-level classes during undergrad, if so, which one?

Possibly. But you can take graduate courses in graduate school. It's important not to jump into something too early that you're not ready for. If you say take your most senior undergraduate E&M course early and do really well in it, sure, go ahead and sign up for graduate E&M. But don't push yourself into a course because you think it might look good on an application. Remember, the majority of students in the course will be graduate students. They're the one's who've survived the academic bottleneck of graduate school admissions! The professor will teach to their level and even if you're a high-performing undergraduate student, you're much more likely to be an average student in graduate course work.

What is a good way to narrow down which field of physics to focus on for the PhD?

Read.
A lot.
As you get into your senior undergraduate years you should be reading review articles in fields that interest you.
Also attend as many departmental seminars as you can. Often departments will have professors present the work they're doing, invite other speakers in, etc. Go to these. Some can be boring and filled with jargon, but every once in a while you hit on one that really resonates and can give you some direction. Along these lines I expect there are institutions that provide talks and seminars online, conference keynotes, etc.

Would it make sense/be worth it to switch to math/physics?

I can't help you with this one. I expect the devil is in the details and what skills you specifically would prefer to learn. The data science skills set can also be quite valuable in physics (and once you start looking for a career).

What are some general tips for getting into a theoretical physics program, what should I focus on?

Rather than getting into "theoretical physics," ideally you want to find a specific problem you want to work on, and a specific skill set you'd like to develop. It's also worth investing time in figuring out who you would learn well from as a mentor. You'll likely end up spending a lot of time working with your supervisor, so it's important to invest time up front to make sure that's going to be an effective mentoring relationship.

 

[ansabs]

If you have to ask this question, you probably shouldn't be pursuing a PhD. Somewhere along your studies and undergrad research (along with talks, papers, and seminars), some field of interest or specific problem should grab your interest enough to motivate you enough to devote ~6+ yrs to a PhD program. You don't start out with the premise that you want to pursue a PhD for the hell of it and then ask what field you should pursue.

In addition to your core foundational courses you would take advanced undergrad courses in your field of interest (e.g., solid-state physics, astrophysics, nuclear physics, ....) ... when you decide what that is.

I understand what you are saying. I am only a second year, so I am not completely set on anything yet. It's more that so many fields interest me, and I need to narrow down which one I like best.

 

[ansabs]

Sometimes when I hear this from students it's a flag. I'm not necessarily saying that in your case, but I've seen a lot of students who don't like labs because they come ill-prepared, don't like the rigor of follow up analysis, and/or haven't yet developed skills for effective group work and based on that experience, their thinking goes... "well, I still like physics, so I suppose I should work in theory." When it comes time to apply for PhDs, base your choices on directions you want to go into because of your specific interests, the skills you have, and those you would like to develop, rather than what's left when you eliminate the things you don't want to do.


As you move into your senior undergraduate years, this is a time to explore options, so try as much as possible to take a diverse set of courses that will introduce you to the topics you think you might be interested it. Do a senior thesis course if that's an opportunity for you. And if you're interested in theory, make sure you learn how to program.


Possibly. But you can take graduate courses in graduate school. It's important not to jump into something too early that you're not ready for. If you say take your most senior undergraduate E&M course early and do really well in it, sure, go ahead and sign up for graduate E&M. But don't push yourself into a course because you think it might look good on an application. Remember, the majority of students in the course will be graduate students. They're the one's who've survived the academic bottleneck of graduate school admissions! The professor will teach to their level and even if you're a high-performing undergraduate student, you're much more likely to be an average student in graduate course work.


Read.
A lot.
As you get into your senior undergraduate years you should be reading review articles in fields that interest you.
Also attend as many departmental seminars as you can. Often departments will have professors present the work they're doing, invite other speakers in, etc. Go to these. Some can be boring and filled with jargon, but every once in a while you hit on one that really resonates and can give you some direction. Along these lines I expect there are institutions that provide talks and seminars online, conference keynotes, etc.


I can't help you with this one. I expect the devil is in the details and what skills you specifically would prefer to learn. The data science skills set can also be quite valuable in physics (and once you start looking for a career).


Rather than getting into "theoretical physics," ideally you want to find a specific problem you want to work on, and a specific skill set you'd like to develop. It's also worth investing time in figuring out who you would learn well from as a mentor. You'll likely end up spending a lot of time working with your supervisor, so it's important to invest time up front to make sure that's going to be an effective mentoring relationship.

Thank you so much for your response! If you don't mind me asking, have you done a PhD, and if so, what have you worked on?

 

[ohwilleke]

Would it make sense/be worth it to switch to math/physics?

If I were in your shoes, I wouldn't.

Data Science is an extremely employable major (and fewer schools have it than plain old math, even if they teach the material).

And, I've never heard of someone being rejected from a PhD program because one of their double majors was irrelevant to the program. I know people who were admitted to PhD programs in physics who majored in physics and in piano performance, for example (my undergraduate college had a pretty well regarded music conservatory, so this was pretty common there).

Indeed, big experiment HEP and astrophysics these days have entered the era of "big data" where the cutting edge science primarily involves thoughtful and accurate mining of data collected on an automated basis in amounts too vast to be understood raw by a human being.

Having experimental physics and astrophysics and non-physics data science work as Plans B, C, and D is a good position to be in. Admissions to top Theoretical Physics PhD programs is very competitive and finding employment in that field afterwards is too.

The rule of thumb used to be (and maybe I'm an old fart who is out of date on this) that there are 100 applicants for every theoretical physics job post. An uncomfortably large share of people who earn PhDs in theoretical physics ultimately abandon that career, sometimes after earning a string of post-doc and assistant professor posts but failing to find a permanent position (Sabine Hossenfelder has written several high quality up to date, data based posts on the state of the theoretical physics job market but this one is the only one I found quickly, and Peter Woit has some commentary on a video she made on the subject). 4gravitons is another blog that has quite a few posts on the process of establishing a career in theoretical physics.

You could be the exception. But having the credentials necessary to give you a back up plan is a good idea.

Lots of physics majors ultimately end up in IT. For example, my sister-in-law was an undergraduate physics major, and was planning on pursuing graduate work in it eventually, but the demand for the side knowledge of IT she gained in the process was so great that she ended up doing that right out of college instead, and in the end, she never went back to physics professionally. A physicist with a relevant credential has a leg up in making a transition to a Plan B in IT if that becomes necessary (and given the tight IT market after the latest round of mass layoffs in big IT firms, you might need a leg up).

Also, consider that you could develop some sub-speciality, e.g., technicolor theory, or preon theory, that five or ten years into your professional life, could go bust when it becomes strongly disfavored by new experiments. This could leave you adrift professionally, starting over almost from scratch, even if you find a tenure track position, because it would make it difficult or impossible for you to meet the publish or perish expectations for you as a theoretical physicist to actually get tenure and keep your job. This is not a mere hypothetical possibility. It has happened to lots of physicists in my lifetime, and it has happened even in your, probably thirty years younger, lifetime.

If you want to strengthen your modern physics and advanced math knowledge, nothing prevents you from taking those courses within your current major (I would echo the usefulness in theoretical physics of abstract algebra/group theory). If this is your passion, sacrifice elective courses in history or art and take some of those courses.

What is a good way to narrow down which field of physics to focus on for the PhD?

Take course in many different areas of physics, especially those you know least about, and figure out what you like.

There were certainly areas for me that I found superficially interesting when I was an undergraduate, but decided not to pursue further once I found out what the current dominant research programs in those fields actually involved (e.g. macroeconomics).

You may think that theoretical physics is the way to go now, but once you take a condensed matter physics course, which was a subfield you didn't know much about one way or the other, you might discover that this is really your thing.

Another good way to get a better sense of what fields you might want to specialize in is to read pre-prints at arXiv on a regular basis in the fields that you are considering, to see what the active areas of investigation are in various fields, what methods they use, and what catches your fancy. As you do so, pay attention to the authors of papers you find insightful, who could be your potential advisors in a PhD program. Keep a list, you don't have to memorize them right now. Even if you don't end up working with those particular people, familiarity with the names of physicists who are publishing in the field and what the bleeding edge developments that they are working on impresses interviewers in the PhD application progress.

Reading these papers will also help you learn where the holes in your existing knowledge are, allowing you to patch some of those gaps with undergraduate course work before you apply to PhD programs. But, also, don't sweat it too much. Graduate programs are in the business of teaching you what you don't know and filling gaps in your knowledge. If you've covered the basics, there is no shame in having to learn some advanced topic for the first time in graduate school. This is literally what graduate school is for. If the only place you can learn what you want to learn is in a graduate school course, take it. But don't consider it a pre-requisite to admission to a graduate program.

Also, take advantage of being at a big, good quality university like Northeastern and being "a research assistant in this lab and was a research assistant in another lab last summer."

You have a unique opportunity to rub shoulders with and talk casually with a decent sized pool of physicists who have made it, and they will be happy to spend time discussing things with a major in their department who has also shown commitment to the field by being a research assistant two times in a row. Helping you at this point in your life is literally their job. Bounce ideas off of, and ask questions of, as many professors and graduate students in physics and math as you can.

It is a golden opportunity to gather intel and you don't even have to endure the awkward moments of introducing yourself to someone in a cold call to ask their questions. In the academic and career advising world they call these discussions "informational interviews" but you don't have to be so formal about it. Research labs have lots of down time waiting around for the experiments to do their things. Make small talk with the graduate students and professors running them about different future possibilities and what the state of research is in different fields.

Become clear about the differences between pure theoretical physics work and experimental work, and the places in between like statistical analysis and phenomenological calculations of Standard Model predictions at big HEP collaborations. Ask about what areas over oversubscribed and what areas don't get the attention that they deserve. Discover niches that you weren't even aware existed. There is a good chance that your ultimate career path will be some sub-field that you've never even heard of yet.

Full disclosure: I'm a lawyer and physics is a long time hobby for me. I was a math major and about a course short of a physics major as an undergraduate (graduating in three years to save money). I was good at math and got decent grades in my major, but not PhD level good or PhD level driven to do research in math for the rest of my life. I considered going back to get a PhD later to the point of taking the GREs but life got in the way. But I lived all of my life through finishing law school and beyond, in and around academia. I started reading the Chronicle Of Higher Education on a regular basis when I was 12 or 13. My father was a STEM program director at a university and my mom was a university administrator (primarily she helped professors make their way through the grant application progress and dealt with applying ethics requirements to human subjects research proposals). Almost all of my parent's friends and my friends' parents were academics. My wife spent time as a graduate teaching assistant, as a lecturer at a university, and as a university admissions officer (primarily for international students). In college, as a student government representative, I served as a student representative on faculty-administration committees that hired professors and decided which departments should get new positions or lose existing ones. Many of my close friends became professors and we talk about it. So, while I didn't personally take this path, I'm very familiar with how graduate education and career paths in this area work.

 

[Choppy]

If you don't mind me asking, have you done a PhD, and if so, what have you worked on?

Yes. I'm a medical physicist, specializing in radiation oncology physics, and an adjunct professor.

 

[ansabs]

Yes. I'm a medical physicist, specializing in radiation oncology physics, and an adjunct professor.

Very interesting, the lab I work in now focuses on oncology, mainly on ovarian cancer. The PhD student I work closely with mostly creates mathematical models and simulations of treatments.

 

[CrysPhys]

You may think that theoretical physics is the way to go now, but once you take a condensed matter physics course, which was a subfield you didn't know much about one way or the other, you might discover that this is really your thing.

Not sure of your point here. Under the umbrella of condensed matter physics (or other fields), there are theoretical research and experimental research. "Theoretical physics" is not a field unto itself.

 

[ansabs]

If I were in your shoes, I wouldn't.

Data Science is an extremely employable major (and fewer schools have it than plain old math, even if they teach the material).

And, I've never heard of someone being rejected from a PhD program because one of their double majors was irrelevant to the program. I know people who were admitted to PhD programs in physics who majored in physics and in piano performance, for example (my undergraduate college had a pretty well regarded music conservatory, so this was pretty common there).

Indeed, big experiment HEP and astrophysics these days have entered the era of "big data" where the cutting edge science primarily involves thoughtful and accurate mining of data collected on an automated basis in amounts too vast to be understood raw by a human being.

Having experimental physics and astrophysics and non-physics data science work as Plans B, C, and D is a good position to be in. Admissions to top Theoretical Physics PhD programs is very competitive and finding employment in that field afterwards is too.

The rule of thumb used to be (and maybe I'm an old fart who is out of date on this) that there are 100 applicants for every theoretical physics job post. An uncomfortably large share of people who earn PhDs in theoretical physics ultimately abandon that career, sometimes after earning a string of post-doc and assistant professor posts but failing to find a permanent position (Sabine Hossenfelder has written several high quality up to date, data based posts on the state of the theoretical physics job market but this one is the only one I found quickly, and Peter Woit has some commentary on a video she made on the subject). 4gravitons is another blog that has quite a few posts on the process of establishing a career in theoretical physics.

You could be the exception. But having the credentials necessary to give you a back up plan is a good idea.

Lots of physics majors ultimately end up in IT. For example, my sister-in-law was an undergraduate physics major, and was planning on pursuing graduate work in it eventually, but the demand for the side knowledge of IT she gained in the process was so great that she ended up doing that right out of college instead, and in the end, she never went back to physics professionally. A physicist with a relevant credential has a leg up in making a transition to a Plan B in IT if that becomes necessary (and given the tight IT market after the latest round of mass layoffs in big IT firms, you might need a leg up).

Also, consider that you could develop some sub-speciality, e.g., technicolor theory, or preon theory, that five or ten years into your professional life, could go bust when it becomes strongly disfavored by new experiments. This could leave you adrift professionally, starting over almost from scratch, even if you find a tenure track position, because it would make it difficult or impossible for you to meet the publish or perish expectations for you as a theoretical physicist to actually get tenure and keep your job. This is not a mere hypothetical possibility. It has happened to lots of physicists in my lifetime, and it has happened even in your, probably thirty years younger, lifetime.

If you want to strengthen your modern physics and advanced math knowledge, nothing prevents you from taking those courses within your current major (I would echo the usefulness in theoretical physics of abstract algebra/group theory). If this is your passion, sacrifice elective courses in history or art and take some of those courses.



Take course in many different areas of physics, especially those you know least about, and figure out what you like.

There were certainly areas for me that I found superficially interesting when I was an undergraduate, but decided not to pursue further once I found out what the current dominant research programs in those fields actually involved (e.g. macroeconomics).

You may think that theoretical physics is the way to go now, but once you take a condensed matter physics course, which was a subfield you didn't know much about one way or the other, you might discover that this is really your thing.

Another good way to get a better sense of what fields you might want to specialize in is to read pre-prints at arXiv on a regular basis in the fields that you are considering, to see what the active areas of investigation are in various fields, what methods they use, and what catches your fancy. As you do so, pay attention to the authors of papers you find insightful, who could be your potential advisors in a PhD program. Keep a list, you don't have to memorize them right now. Even if you don't end up working with those particular people, familiarity with the names of physicists who are publishing in the field and what the bleeding edge developments that they are working on impresses interviewers in the PhD application progress.

Reading these papers will also help you learn where the holes in your existing knowledge are, allowing you to patch some of those gaps with undergraduate course work before you apply to PhD programs. But, also, don't sweat it too much. Graduate programs are in the business of teaching you what you don't know and filling gaps in your knowledge. If you've covered the basics, there is no shame in having to learn some advanced topic for the first time in graduate school. This is literally what graduate school is for. If the only place you can learn what you want to learn is in a graduate school course, take it. But don't consider it a pre-requisite to admission to a graduate program.

Also, take advantage of being at a big, good quality university like Northeastern and being "a research assistant in this lab and was a research assistant in another lab last summer."

You have a unique opportunity to rub shoulders with and talk casually with a decent sized pool of physicists who have made it, and they will be happy to spend time discussing things with a major in their department who has also shown commitment to the field by being a research assistant two times in a row. Helping you at this point in your life is literally their job. Bounce ideas off of, and ask questions of, as many professors and graduate students in physics and math as you can.

It is a golden opportunity to gather intel and you don't even have to endure the awkward moments of introducing yourself to someone in a cold call to ask their questions. In the academic and career advising world they call these discussions "informational interviews" but you don't have to be so formal about it. Research labs have lots of down time waiting around for the experiments to do their things. Make small talk with the graduate students and professors running them about different future possibilities and what the state of research is in different fields.

Become clear about the differences between pure theoretical physics work and experimental work, and the places in between like statistical analysis and phenomenological calculations of Standard Model predictions at big HEP collaborations. Ask about what areas over oversubscribed and what areas don't get the attention that they deserve. Discover niches that you weren't even aware existed. There is a good chance that your ultimate career path will be some sub-field that you've never even heard of yet.

Full disclosure: I'm a lawyer and physics is a long time hobby for me. I was a math major and about a course short of a physics major as an undergraduate (graduating in three years to save money). I was good at math and got decent grades in my major, but not PhD level good or PhD level driven to do research in math for the rest of my life. I considered going back to get a PhD later to the point of taking the GREs but life got in the way. But I lived all of my life through finishing law school and beyond, in and around academia. I started reading the Chronicle Of Higher Education on a regular basis when I was 12 or 13. My father was a STEM program director at a university and my mom was a university administrator (primarily she helped professors make their way through the grant application progress and dealt with applying ethics requirements to human subjects research proposals). Almost all of my parent's friends and my friends' parents were academics. My wife spent time as a graduate teaching assistant, as a lecturer at a university, and as a university admissions officer (primarily for international students). In college, as a student government representative, I served as a student representative on faculty-administration committees that hired professors and decided which departments should get new positions or lose existing ones. Many of my close friends became professors and we talk about it. So, while I didn't personally take this path, I'm very familiar with how graduate education and career paths in this area work.

Thank you so much for your very insightful response! You make a great point about remaining in data science, as it is very employable, and I still have the option of taking upper-level math courses such as group theory and abstract algebra. I'm currently at a point where I find out about a new subfield of physics and am extremely intrigued, then I learn about another field and am very intrigued again. I will be taking quantum mechanics next semester which I am very excited about, and I think it will help me round out the required undergraduate physics knowledge (besides thermodynamics/statistical mechanics which I am taking a little bit later). My favorite class so far is electricity and magnetism 2 which I am currently taking.

 

[CrysPhys]

I'm currently at a point where I find out about a new subfield of physics and am extremely intrigued, then I learn about another field and am very intrigued again.

Remember, in the US, applications for grad school are due ~end of first semester senior year. So by the end of your junior year, you should have a reasonable notion of which field(s) you wish to pursue, because that will determine your list of candidate grad schools to apply to (plus how to best present yourself in your applications). It's not important to try out mucho fields to find out the one you find most interesting (and from a practical perspective, you won't have time to do that). It is critical that you find one field that's interesting enough that you're willing to devote 6+ yrs of your life to it. And, you can always change fields later on ... either voluntary (if you find something even more interesting) or involuntary (if your initial choice dries up).

 

[ohwilleke]

Not sure of your point here. Under the umbrella of condensed matter physics (or other fields), there are theoretical research and experimental research. "Theoretical physics" is not a field unto itself.

Usually, when someone says "theoretical physics" they mean something along the lines of HEP-theory, or other investigations that are not directly applicable to experimental testing. arXiv, for example, distinguishes between phenomenology and theory.

This said, the concern raised utterly misses the blatantly obvious point, which is that as an undergraduate physics major, there are all sorts of fields and subfields within physics which you aren't familiar with, and if you look into one of those fields, you might find something exciting and interesting. The particular example chosen is really irrelevant.

 

[CrysPhys]

Usually, when someone says "theoretical physics" they mean something along the lines of HEP-theory, or other investigations that are not directly applicable to experimental testing. arXiv, for example, distinguishes between phenomenology and theory.

To OP @ansabs : By "theoretical physics", did you intend the specific meaning above, or did you merely mean "theoretical" vs "experimental" research (regardless of specific field)?

To practicing physicists on this forum: Do you interpret "theoretical physics" in the above sense stated by @ohwilleke ?

 

[Vanadium 50]

To practicing physicists on this forum: Do you interpret "theoretical physics" in the above sense stated by @ohwilleke ?

I interpret it more as "I have not been attending seminars and colloquia where I could see the breadth of the theoretical and experimental programs". This, of course, is less than ideal.

 

[ansabs]

To OP @ansabs : By "theoretical physics", did you intend the specific meaning above, or did you merely mean "theoretical" vs "experimental" research (regardless of specific field)?

To practicing physicists on this forum: Do you interpret "theoretical physics" in the above sense stated by @ohwilleke ?

I meant "theoretical" research as opposed to "experimental" regardless of field.

 

[Vanadium 50]

Maybe an analogy would help you understand why so many eyebrows are raised.
"I'd like a PhD in history."
"Oh? What period?"
"I don't care about that. So long as its about the Northern Hemisphere."

 

[ansabs]

Maybe an analogy would help you understand why so many eyebrows are raised.
"I'd like a PhD in history."
"Oh? What period?"
"I don't care about that. So long as its about the Northern Hemisphere."

To clarify, it's not that I don't care what field, it is more that I haven't narrowed it down enough yet. But yes I understand what you are saying, and I am still working on narrowing things down.

 

[CrysPhys]

I meant "theoretical" research as opposed to "experimental" regardless of field.

That's what I thought. Thanks for the direct confirmation.

 

[CrysPhys]

To clarify, it's not that I don't care what field, it is more that I haven't narrowed it down enough yet. But yes I understand what you are saying, and I am still working on narrowing things down.

If you haven't picked a field by the end of your junior year, there are other options, depending on your finances. If your university has the option of a senior thesis, that's a great way to get your feet wet. Unfortunately that comes too late for the application cycle at the end of the first semester senior year. So one option is to extend your undergrad program for a 5th yr.

Another option is to graduate and get a job as a research assistant/technician in a lab, where you can get exposure to different research areas. I once served as an industry mentor to a physics senior who hadn't found her passion for a PhD program. She got a job as a research assistant for a company that designed and manufactured accelerators for medical physics applications. She developed a strong enough interest in medical physics that she got her PhD in it.

Good luck in exploring your options. Hope you find a field to be passionate about.

 

[Vanadium 50]

Why do you want a PhD?