Theoretical Physics - How to?

Question

Although I doubt somewhat whether this question is really appropriate for this site, I hope it gets answered anyways. I guess, what I'm wondering is:

1. How does one get to work as a theoretical physicist and - probably more importantly - what do theoretical physicist actually do all day long?

2. How are theoretical physicists distinguishable from mathematicians? Does a physicists day look very different from that of a mathematician?

3. I have a great interest in physics, but I'm not really much interested in doing experiments: Would it be advisable to do my bachelor in mathematics and try to get into theoretical physics later on?

4. Is there a real chance of getting into research afterwards? (not that any kind of answer to this question would ever stop me from trying...)

Well, I hope this question is acceptable.

I think 1) might for example be answered by giving a link to a blog of a working theoretical physicist, who gives some insight into his or her everyday life, or some kind of an essay on the topic. Of course any other kind of answer is greatly appreciated.

Thanks in advance!

Kind regards,

Sam

Edit after several answers: Thanks a lot for all the responses! I found it very interesting and helpful to to get some input from you guys. Although the opinions seem to differ a bit, one can definitely see many overlaps, too.

I do still have some time do decide, and will definitely look at some books suggested here, visit some lectures and try to get a feel for what it would be like to do either physics or maths.

Thanks again for your effort! :-)

Answer 1

If you want to work as a theoretical physicist, it would be advisable to get a little bit of grounding in experimental physics anyway. So my answer to #3 is, if you want to get into theoretical physics, get a Bachelor's in physics, not mathematics, and take at least one or two experimental courses.

I work at a university where students often do shoddy work in the undergraduate experimental courses, because "I came here to study theoretical physics and I'm not interested in experiments." What they don't realize is that most of our professors in theoretical physics are of the opinion that to be an excellent theoretician, you primarily need to be a well-rounded physicist, with both theoretical and experimental skills. These students run into trouble when they're looking for internships or final projects, because no professor will accept them.

(I edited this answer, because I didn't mean to imply that you had to be an excellent experimenter to be a good theoretician. If you don't enjoy experimenting, then you don't enjoy experimenting. Just don't dismiss it or ignore it altogether.)

From Saturday Morning Breakfast Cereal:

Answer 2

1. This I don't know. I think that everyone have his own way of doing research... But you'll need to work hard anyway.
2. I don't think there is a clear distinction now. There is some "gradient" between those.
3. I think that there is a reason beyond teaching students experiment even if they would be theorticians. But matematicians keep coming to physics as if they don't care about my opinion.
4. Everyone I know who tried it -- made it.

Answer 3

This was originally a comment under ptomato's answer but got too long and became point 3.

As for your questions:

1. I am still just a student but I guess what you do is you mostly read papers and study books and try to work on some problems (both your thesis and things from physics.SE ;-) )...

2. ...which is probably the same thing mathematicians do, only the area of research and methods used differ. But I don't think there's a clear distinction. You have people like Witten who won Field's medal but is clearly a theoretical physicist. Now what's that about? :-)

3. I don't think being good experimenter is important at all. Sure, it helps. So does good teaching skills, programming skills, communication skills, algebraic geometry skills, ... But none of that is really necessary for theoretical physics. All that is needed is that person likes science and math and has inquisitive mind that is curious about the ways nature works.

4. Certainly. I know both of physics majors who got into math research and math majors who got into physics research. I think the required skills greatly overlap. The main difference is level of rigor and amount of physical intuition. You can adapt both to the environment you are working in. Of course, it might be excruciating for physicist to be forced to write formal proof where he just sees the answer, or for mathematician to watch hand-wavy derivations in physics.

Personally, I am more on the math side and I hated experiments. So we'll see if I can succeed in being a good theorist :-)

Answer 4

Answer to 2: In mathematics, truth is based on logic and deductive reasoning from axioms and definitions. In physics, the only truth comes from the results of experiments. Furthermore, in physics there can be no true rigor, because in principle it will never be possible to input the initial conditions for a macroscopic number of particles and simulate their motion, or solve the large number of differential equations which arise.

If you want to be a theorist, you really have to be the best of the best to succeed at research. Experimentalist have an easier time getting jobs because they are expected to bring in a lot of grant money (the administration often takes a sizable portion of this money, which is why they love to hire experimentalists), whereas theorists generally don't get nearly as much grant money and therefore need to really be special to set themselves apart.

Theoretical physicists are often doing elaborate and detailed calculations with fairly low level mathematics, in an attempt to explain the results of some recent experiment. Mathematician's also do long calculations, but they mostly are trying to prove things. It is fairly rare for a theorist to predict a phenomenon before it is discovered in the lab, it is much more common that experimental discoveries are made without being predicted in advance (and that theoretical predictions don't pan out); whereas mathematicians "discover" or "invent" things all the time.

Theorists are the companions of experimenters, they support them in many ways; not only by carrying out calculations and giving them numbers, but also by thinking carefully about the physical mechanisms/principles of everything which is going on in the experiment; to perhaps discover an insight which the experimenter has not thought of.

Answer 5

First you must ask yourself what excites you. Is it watching events happen? Comparing what happens to what is predicted to happen? Making the prediction? Understanding the prediction? Making a model for hypotehtical predictions? Understanding what constitutes a model? None of the above? Unless you're just in the business for the money, your research interests should drive your education as much as possible. Otherwise, why bother?

In my case, what excites me is the connection between the concrete and the abstract, which is why I always straddled the math-physics fence.

That said, the general pattern of any researcher is the same. Make observations. Ask questions. Compare with previous questions and snwers. Figure out how to find answers, when none exists. The methods are very different, of course. It is true that a theoretician and a mathematician have similar daily patterns, and even similar methods (talking, reading, writing e-mail, working things out on a chalkboard/tablet/whatever). The nature of the research is different, but there's lots of overlap. When people pose the "what are you?" question to me, I try to punt.

[Note added: Back now to finish. I cut my answer short earlier.]

The main difference between the fields is not so much one of rigor, though that is an obvious one. The more relevant difference is the questions that drive research. In mathematics, one tries to understand the structure behind constructions of objects. In theoretical physics, one tries to understand the structures behind physical models and physical phenomena -- and these can often employ or reveal mathematical structures. Sometimes, the fields work in parallel, with both camps trying to get to the bottom of things. "Bottom" in physics means understanding how hypothetical physical calculations (e.g., correlation functions, metrics) are affected. "Bottom" in mathematics might mean a definition and/or a relation to existing structures.

Answer 6

1. How does one get to work as a theoretical physicist

Go to a good university and get a firm foundation in math and physics. Go to graduate school in theoretical physics. Then apply for post-doc and faculty positions; repeat until you get a faculty position.

3. Would it be advisable to do my bachelor in mathematics and try to get into theoretical physics later on?

Do whichever you find yourself liking better. A background in math could be excellent preparation for theoretical physics. You will either do "mainly physics with a lot of math" or "mainly math with a lot of physics."

4. Is there a real chance of getting into research afterwards?

Of course, if you're good.

A good way to start (right now) is to get yourself a copy of Landau and Lifshitz's Mechanics and work through it. See where that takes you.

Answer 7

John Baez addresses some of these questions on his page "Advice for the Young Scientist". I think it is more oriented towards, for example, someone deciding between grad-schools or later appointments rather than choosing between majors at the university, but it may still be useful to you:

Math or Physics?

This is for people who are torn between a research career in math and one in physics.

Nobody can stop you from learning and thinking about both math and physics - you should go on doing both! The real issue is whether you want to work in a math department or a physics department. It's possible to switch from one discipline to another after grad school, but it's not easy, since departments prefer to hire people with an appropriate degree. So, it's wise to decide which job suits you best before you apply for grad school - if not sooner.

To decide, you need to know how these two jobs differ. For this, it's best to talk to as many mathematicians and physicists as you can, and find out what their jobs are like. Talk to your professors! It's also great to go to some conferences - there's often money for students to attend conferences. I can only summarize:

Mathematicians get promoted by publishing in math journals; physicists by publishing in physics journals. Read both kinds of journals and see which you can best imagine yourself publishing in. Spend time in a good library and browse. I spent my whole undergraduate career doing this! There are some journals at the boundary of math and physics, like Advances in Theoretical and Mathematical Physics and Communications in Mathematical Physics. Look at these. But also look at a bunch of journals that are full-fledged physics, like Physical Review A, B, C, D, and E, and Physical Review Letters, or solidly mathematical, like Annals of Mathematics or the Transactions of the American Mathematical Society. You'll see these come from different worlds! Mathematicians typically write in the definition/theorem/proof style, while physicists write shorter papers, and more of them, often packed with formulas, but usually leaving out all the details of calculations.

Physics is a faster, looser, more energetic discipline. You are also evaluated more heavily on how much grant money you can pull in.

Here's another way to put it: do you like things to be clearly stated in a rigorous way, or do you like to use your physical intuition to get to the answers?

He also has a page titled "How to Learn Math and Physics".

Answer 8

I can see theoretical physicists at work every day, and I've also seen experimentalists... My own field is computer simulations. To my understanding the answers to your questions can be like this:

1. What theoretical physicists do all the day long? Calculate and think.
2. Physics vs Math? Physics is more intuitive than mathematics, and there is more freedom in physics than in mathematics. There is also much less abstraction in physics.
3. Maybe yes, maybe no. This strongly depends on what exactly kind of physics you want to do.
4. Yes, of course. But one has to work really hard for this to happen. Usually everything depends on the level of one's publications. And - in my opinion - if one loves physics he has a REALLY good chance of having good achievements and, as a consequence, publications.

Answer 9

Good question. I did my diploma in Theoretical Particle Physics and therefore worked one year as a theoretical pysicist.

To your questions:

1) The short answer: Find the error in your calculations. One guy at our institute once said: "Theoretical physicists spend half of their time in finding algebraic sign errors." This is to a degree true.

Long answer: It depends on the field you are working at. Actually Theoretical Physics starts at the point the calculations become too complicated for experimental physics. So for the particle physics this is "Phenomenology". (hep-ph on arxiv.org -- don't be surprised if you don't understand anything there) These are the guys that calculate the - theoretical - cross sections for experiments that are tested at the LHC and other colliders. So this is in the end squaring Feynman diagrams, integrating them and analyzing the results. For some problems you can do that completely with pen and paper for other problems it makes sense to do 95% of that work on the computer. Depends on the research group and what they are working on.

On the other hand there is this completely theoretical physics area. Of course they also need to make sure at some point that their work corresponds with the experiments but they mostly concentrate on "model building". (hep-th on arxiv.org) For instance: We are seeing that Standard Model Higgs mechanism is probably not the way nature implemented the Electro-Weak-Force. Well, why don't we check out what happens if we have 2 Higgs fields instead of one? Or what happens if we change the symmetry group? Sounds interesting but you also pay a price: Most stuff you do is really abstract and will probably not be the way nature has implemented things. :D

Of course there is also Mathematical Physics (math-ph on arxiv), but that is usually done in a Mathematics department. Theoretical physcists usually don't have the time to check every mathematical detail. In particular nobody hasn't been able yet to formalize Quantum Field Theory (= Theoretical Particle Physics) like it has been done with non-relativistic Quantum Mechanics or even Newtonian Mechanics.

2) Physicists don't do mathematics in such a formal way. If they we're that detailed as mathematicians are, there wouldn't be able to do actual physics.

The physicists approach is: Let's do this calculation, it looks formally ok and makes sense. If our cross-checks are not consistent, let's check again and pay more attention to the details.

You'll probably want to ask a mathematician how his work day looks like. (stackexchange...)

3) Me not either. And no, please don't do the same mistake as I did by concentrating to much on the mathematics. Except you have enough time to learn all the important stuff about physics you want to work later on.

Make yourself clear: Physics and Mathematics are completely different subjects. Physics is a Natural science. Are you interested in that? Really? Study physics. Of course you need to do some experiments, they are physicists' source of information. But in the end it matters that you are informed about the important experiments that matter to your work.

Are you interested in abstract concepts and the physics doesn't matter to you? Study mathematics.

If you are in between, consider studying Mathematical physics. But make sure your university has a mathematical physics department. I recommend you to talk to students or professors to get some first hand information. Mathematical physics is also really interesting. Take dynamical systems for instance or google for Wightman axioms.

4) Yes of course. Is there a chance to become a professor? Of course, but you need to be focussed and make smart decisions. The process differs from country to country. About Germany I can say it is easy to get into research. But it's not easy to become a professor. Make yourself clear (in one or two years) whether you are a research guy or whether you are just interested about the subject.

Again I recommend you to visit a university and ask as many questions as possible to the mathematicians and physicians there. Most universities have regular events for students interested in studying at their university. At least in Germany there are a lot of student's organizations you can talk to and a lot of mathematics and physics departments have professors that are specialized in helping you with your questions.

EDIT: I want to be more precise about the rigor. Theoretical physicists need to be as rigor as mathematicians. But: Their rigor is focussed on the physics not on the mathematics.