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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! :-)

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Do a math/physics double major! You will appreciate both perspectives. Then you can decide what you want to do after. There are times when physicists think that mathematicians are missing the point and vice versa! –  Greg P Dec 6 '10 at 15:46
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@SamL: What is your current level of education? Do you enjoy maths even abstracting from physics? –  Piotr Migdal Dec 6 '10 at 17:00
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@Piotr: As for "current level of education". Technically, I'm only in the first semester. But I've spent A LOT of time learning maths working through books suggested by older students last year (when I actually was enrolled for medicine). So I essentially have covered the basics: analysis, linear algebra, a first introduction to algebra, topology, measure theory, some complex analysis, a little bit of functional analysis. Besides the usual curriculum I'm taking a course in differential geometry now. Which should also answer the second question I guess ;-) (a big yes). –  Sam Dec 6 '10 at 19:49
    
Come to think of it, I actually have done a lot of maths so far, and not so much physics. But since now I can understand Lagrangian mechanics and the math behind the "fancier" topics in physics, the subject has gotten increasingly exciting from my perspective! –  Sam Dec 6 '10 at 20:05
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@Sam: the subject is exciting and it's certainly very useful to know math. But be prepared for feelings of frustration when you are not able to solve (at the intuitive level) even the simplest problems with gyroscopes, fluids and heat engines. That doesn't go away even after years of studying physics :-) But maybe I just wasn't meant for physics and am better in math, hard to say. –  Marek Dec 6 '10 at 21:16

10 Answers 10

up vote 4 down vote accepted

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:

Saturday Morning Breakfast Cereal

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I would strongly advise young budding theorists to take ptomato's advice seriously, and add that graduate school is also the time to start networking with publishing experimental groups at your school. In my experimental group we had close working relationships with several groups of theorists; the collaboration was fantastic and benefited all tremendously. Your employability will be significantly enhanced if you stay involved and form relationships in active fields related to your area of interest, not necessarily an exact match to your dissertation topic. –  Pete Dec 9 '10 at 16:10
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I disagree with the emphasis you are putting on having an experimental background. In many of the top universities theoretical and experimental physics are different departments, and there is a reason for this. Theoretical physicists need a very different set of skills than experimental physicists. Their ability to do path integrals, for example, tends to be of much greater importance than their ability to align optical elements. Both fields require a huge amount of background knowledge, and it is very rare to be successful at both (I can think of examples, but they are few and far between). –  Joe Fitzsimons Sep 12 '11 at 6:32
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@ptomato: If they trying to seal a vacuum chamber? Sure. It's simply not relevant to that specific task. Very few experimentalists will have ever studied differential geometry, or example, but it is absolutely fundamental to much of theoretical physics. –  Joe Fitzsimons Sep 13 '11 at 6:30
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@ptomato: Of course I don't think that's all they do, but experimental physics is fundamentally different from theoretical physics. They are distinct subjects, and while there are some people who are good at both, they are few and far between. You are asserting that experimentalists need to know differential geometry, but the fact is that most don't know any, and with good reason. It is simply not relevant to whatever they are working on. Similarly, theoretical physicists often come from purely mathematical backgrounds, and are unfamiliar with many experimental techniques. –  Joe Fitzsimons Sep 13 '11 at 9:37
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@ptomato: I don't think it is at all reasonable to assert that theorist "who think they can be a good theoretical physicist with a background in pure mathematics, are not well-rounded enough to be good physicists." In fact, it seems trivial to find counter examples. –  Joe Fitzsimons Sep 13 '11 at 9:39

I was in the process of writing several comments all over the place, and realised it would be better structured to put them together as an answer. I answer specifically questions 3. and 4. of your question.

$\\$ "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?"

$\\$

Firstly, my response to some of the answers above encouraging you do a physics degree, including the accpetd answer by ptomato, is do not listen!

$\\$

I realise that it may be hard to do before you've even gotten an undergraduate degree, but if you can try to decide which area of theoretical physics you think you might like to work in, it would help you greatly to decide how to specalise your undergraduate degree.

By that I mean that theoretical physics is a large area of research these days. I have some friends who switched into mathematics to go on to become string theorists, black hole physicists, cosmologists, particle theorists, quantum information researchers etc. as well as fields outside of theoretical phyiscs like meteorology, many kinds of maths biology (from cancer to nuroscience to informatics), genomics etc. On the other hand, some, such as myself, stayed with physics to go on and become cosmologists, astrophysicists, computational physicists, geophysicists, complex systems physicists etc. all doing theoretical work.

(I should say that we are only at PhD student age now, not university lecturers or anything like that, but this gives you an idea of the many fields that you can go into).

What you'll notice is that absolutely none of us went into condensed matter physics, a very large area of theoretical physics. And this is why I highlight ptomato's answer as terrible terrible advice; If you fore people to do things again and again that they are not enjoying, they will more likely learn to resent it, than grow to love it! His claim that

$\\$ "These students run into trouble when they're looking for internships or final projects, because no professor will accept them" $\\$

is pure and utter rubbish, again, in my humble opinion, which is based on the experience of my fellow class-mates. In fact, I vividly remember one physics lecturer saying that he prefers to take on the maths-physics students for PhD research. Using a metric of "number of students who went on to further research", the maths-physics degree had the highest number, by a long shot!

The university I went to is quite big in condensed matter physics, and there was always a high focus on this in our lectures and labs (labs were compulsory in all years. We had no choice in our lecture courses. I believe this is not common in some other countries, so maybe it is not a worry for you?). Many of us did not like it, which resulted in over half switching into pure maths. The only reason I did not was because I was stubborn, proud and arragont (which, as a side piece of advice, don't be stubborn, or overly proud etc. I can tell you, you won't get anything out of it, and will loose a year playing catch-up to your more humble maths-physicists friends who took the leap!).

$\\$

From the sounds of your comments, it is obvious that you really like maths. So why not do a maths-physics degree? That way you'll see both sides, learn lots of interesting things from both departments, and keep your options open.

I just repeat that doing a straight physics degree, in my opinion, given that you want to become a theoretical physicists, would be a very bad idea.

$\\$

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...)

$\\$

For your second question, again, I can only offer an answer from the point of view of a current graduate student.

To start, that attitude is definitely the right sort of one to have! People will tell you that it's very hard, which it is, and that you'll need a bit of luck, which you will, but most of all, you need to not give up before you've even begun!

As far as how likely it is to get into research, again, for starters, it depends on what you want to do. I have friends who switched into maths biology, and money is thrown at them. Others who want to be string theorists and algebraic geometrs, not so much!

Moreover, it depends on your country. I come from a country with very little funding in fundamental physics (theoretical particle physics, string theory, maths-physics etc.). Most of the funding goes to materials physics, experimental physics, computational physics etc.

I now like in a country with more funding for maths-physics, which is great, but they are a little hostile to forigners, and funding for foreign PhD students and post-doc researchers is far harder to get than for nationals. But there is still some money out there, so it's not too bad.

In other countries, the US, Netherlands, Germany mainly, there is lots of funding, if you're good, and most PhD students once accepted get funding, and post-doc researchers even get a good wage (relative to where I am now, in case that angers anyone!).

$\\$

For now, my advice would be to hold on to your ambition, and work hard at your undergraduate degree. Assumedly you have several years before you need to think about these things.

$\\$

And with that, I wish you the best of luck!

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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.

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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.
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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.

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Positrons, the charm quark, the Z boson, black holes, the expansion of the universe (almost)... all were theoretical predictions before they were actually discovered. And those are just some of the "big names" I can think of off the top of my head. So I don't think it's fair to say that it's almost unheard of for a theorist to predict a new phenomenon prior to its discovery - in fact, it happens rather often. –  David Z Dec 6 '10 at 17:54
    
@David: I agree and it's even more true today when theorists have no experiments to confirm their predictions. With tongue-in-cheek one might say that there are some many theories today that some of those predictions are bound to be discovered :-) –  Marek Dec 6 '10 at 18:06
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@Matt: I just finished reading your story. It seems that you think that theoretical physicists are slaves who essentially have to compute trivial things anytime experimenter asks them. Well, this isn't quite how it works in the real world. If you want to know how it works, go to arXiv and pick any a paper from hep.th, statistical mechanics, or anything else that is theoretical and you'll see that theorist are most of the time just playing around and inventing new things. If the situation were such as you describe, I'd be better off doing experimental physics (and that's saying something)... –  Marek Dec 6 '10 at 19:24
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@Matt: But I wanted to contend with your (maybe wrongly taken) tone that theorists are there just for experimenter's sake. It's true that experiment is the key to everything in science but people often forget that we already have hundreds of years of experiments done and our theories are amazingly verified, so theoretical physics has a live of its own (thanks to the old experiments). –  Marek Dec 6 '10 at 20:17
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@Matt: You must be looking at different journals than I scan. In order to even do an experiment, you need to have a theory about why you are doing it and what you are looking for. You aren't just randomly collecting data from the environment. –  Gordon Feb 10 '11 at 4:52

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".

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Heh, it's comforting to know that Baez sees the same difference as I do (in the last paragraph), namely that in rigour and intuition. –  Marek Dec 6 '10 at 19:42
    
+1 for all about intuition and rigour. Go intuition! . –  Dimensio1n0 Aug 29 '13 at 12:33

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.

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+1 for the recommendation of Landau & Lifshitz's Vol. I –  Flint72 May 23 at 18:55

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.

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I don't agree with the last paragraph. Saying that mathematics is just about abstract structure and theory building completely denies existence of huge number of problem solvers (as in Gowers' Two Cultures). I believe the same two cultures also exist in theoretical physics: the ones who build models and abstract theories and the ones who apply them to actually solve something. –  Marek Dec 6 '10 at 18:36
    
So I think the main difference indeed is in rigor and nothing else. You could also say that physics is based on the real world, so the physicist can just look out of the window and just watch the answer (instead of deriving it abstractly), but this point of course doesn't apply to modern theoretical physics at all. –  Marek Dec 6 '10 at 18:39
    
Clearly there are finer points of distinction, and lumping all of Math on one side and Physics on the other side will always be a poor generalization. Gowers' article points to an important divide within mathematics, and physics does have a similar divide. But the central difference between physicists and mathematicians, in my experience, is not just rigor. It's in the taste for problems. In short, a physicist is much more than a non-rigorous mathematician! –  Eric Zaslow Dec 6 '10 at 19:05
    
yeah, it's also about intuition (as I said in my answer, but not in these comments) and the divide is definitely not sharp. Still, mathematicians are in love with proofs in a way that no physicist will ever be. And physicists understand nature in a way that no mathematician will ever do. Of course there are some exceptions to these observations (e.g. I honestly can't tell in which of these groups do I belong) but I think this is a reasonable distinction. –  Marek Dec 6 '10 at 19:49

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 :-)

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Being a good experimenter (...had a grad school buddy who was a positive danger in the lab, but smart) is completely unnecessary for a theorist. Having done enough hands-on work that you can appreciate what we deal with is probably a good idea. Similarly, I settled on experiment early but was still sent to theoretical summer schools to soak up some of the culture and language. –  dmckee Dec 6 '10 at 17:12
    
Looking back on my answer, I see you might have interpreted it as saying that a theorist had to be an excellent experimenter too - I've edited it to say what I really meant, which is just that it's important not to ignore experimenting. –  ptomato Dec 7 '10 at 0:37
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@ptomato: I agree with that. And I actually like doing experiments on my own sometimes. But I hated courses with long hours of boring measurements of long-known things then protocols with statistics, graphs..., I guess you know the drill. There was no creativity in that and I don't think I gained anything from it. We didn't get to build our own devices and measure what we wanted. Just get to machine, push the button, record the data and explain why what you obtained is correct (or isn't). Thinking back on it, it is probably just a problem of how our school conducted those experiment courses. –  Marek Dec 7 '10 at 0:53
  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.
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Have you been a professional theoretical physicist? There's not enough information on your profile. –  John McVirgo Aug 7 '11 at 21:11
    
@John -- fixed that. What about your profile? –  Kostya Aug 9 '11 at 10:35
    
I have never been on a PhD program in theoretical physics which is why I wouldn't be able to answer this sort of question. My answers are given to basic questions which can be verified by a text book and so I don't think there is a real need to add information to my profile. –  John McVirgo Aug 9 '11 at 13:02

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