Why is theoretical physics useful?

A question that you'll get thrown your way from all angles throughout your career. From the public, physicists from different areas, other areas of science and mathematicians. The work of theoretical physicists is increasingly under attack from those outside it and also those within it. Now of course science should always be subject to critique, but it easy to feel shaken by the level of criticism thrown at theory.

Jibes from fellow students who have taken a more experimental route suggesting theorists don't really do science. Mathematicians saying that theorists never prove anything and aren't thorough enough, suggesting maths is a more 'intellectually superior' route. Those from other scientific disciplines can also be very harsh. I had a chemistry teacher once say that theoretical physicists just turned up to conferences with their "pony-tails" to talk about nothing (I have long hair now so I find this even more offensive...). More rightly come questions from the public as to how theorists can benefit them.

Perhaps this is a bit of karma though, it is not unheard of for theoretical physicists to be associated with a superiority complex. Now that a lot of the work of popularised particle theory (like string theory and super-symmetry) is under stress due to the exploration of higher energy scales at the LHC, perhaps all those who felt bullied by theory now have the ammunition they need to exact vengeance!

(Image Credit: Quora)

This is absolutely not about starting arguments but giving you confidence that theory is useful! Both historically and at present. I'll throw in a few examples to counter specific critics as well though... (just for fun). Here's a few reasons why theory is important!

Theory develops new mathematics! (one for the mathematicians)
Most of the time theorists are busy trying to apply mathematics to develop new methods for physics, but sometimes theorists end up solving problems in mathematics or even developing entire new ideas in mathematics! Dr Robert Dijkgraaf (a mathematical physicist) gave a lecture at the Perimeter Institute titled 'The Unreasonable Effect of Quantum Physics in Modern Mathematics' in 2014 (find it on YouTube and watch it). He explains how a problem in algebraic geometry was solved by string theorists working with Calabi-Yau manifolds. 

(Image Credit: Newcastle University)

The problem was to find the number of solutions to the so called 'quintic equation' (not a degree five polynomial, you can prove this to be unsolvable using Galois theory), specific to a given degree of curve. In other words to find the number of linear, quadratic, cubic etc. solutions to the quintic equation. Mathematicians worked out the numbers for linear and quadratic solutions analytically, but when it came to cubics they ended up turning to computational methods. Turns out that string theorists had not only the number of cubics but knew the number of every degree of solution analytically! Dijkgraaf adds much more detail and tells the story very well so go watch the lecture, but the point is sometimes theorists beat mathematicians to it (if not very often).

Historically theorists have made good predictions
Concerns regarding string theory and super-symmetry draw current theorists predictions into doubt but historical theory has done very well. Paul Dirac correctly predicted the existence of anti-matter (specifically the positron), Peter Higgs did the same for the Higgs boson. Glashow, Salam and Weinberg formulated electroweak theory which was validated by the discovery of the W and Z bosons. And all these just in particle theory (there are many others in particle theory)! BSC theory has been immeasurably successful in predicting super-conductor phenomena for condensed matter physics. Outside of specific fields of theory, quantum mechanics (specifically QED) has been shown to be ridiculously precise.

(Image Credit: Know Your Meme)

I think a lot of the present distrust of theory is due to the public nature of string theory and super-symmetry. It's not 'in' publicly to be improving cross-section calculation methods for the LHC or researching condensed matter, but these are two areas that come to my mind when I think of areas of theory that are being very productive at present. So whilst theory might be perceived to be going through a rough patch, that might not be entirely the case and it certainly hasn't been previously.

Knowledge moves down the chain
Lets address my chemistry teacher's attitude. Modern chemistry is dependent on the foundations quantum mechanics laid nearly a century ago. Quantum information science is moving into computer science, biology is utilising statistical mechanics. My point is that there is a progression of techniques and knowledge moving from science to science. Physics (well all sciences) use mathematics as a tool, new tools are developed by mathematicians and these (usually slowly) find a use in science. Physics studies fundamental (arguably simple) situations and knowledge/methods of/for these move into sciences that study more complex situations, chemistry, biology, neuroscience, psychology and these all feed in to each other. That's science! 

What people often don't think about is that the feedback for these fields takes different amounts of time. Physics may often be the first science to utilise new mathematics (along with computer science) but that doesn't happen quickly. Pure maths is often said to be a hundred years ahead of application, for theoretical physics there can also be a reasonable gap. Experiments take time to build and after validation of methods other fields take time to accept and utilise techniques developed in theory.

Failure is a key part of science
When theory gets it wrong, that's part of science and its not a bad thing. In fact getting it wrong is REALLY important. Theory is crucial because it provides research with a direction and despite some people opinions... theory is not plucked out of the air, not good theory anyway. Good theory is focused on trying to solve problems where we are at now and with minimal new assumptions, or at least making those assumptions testable. Theory can also be about testing the water with new tools that are still in development.

(Image Credit: OrthoCuban)

Particle phenomenology is about predicting new particles to solve current problems in particle physics, like dark matter candidates for example. These are testable and candidate particles are based on knowledge of current particle physics and therefore the best idea of what could exist that hasn't been found yet. Often these models are phased out as experiments explore the energy scales and processes which should feature these particles. In the current climate, this often results in theorists having to adjust their predictions and that's ok!

Often the problem comes from (string theory cough cough) theorists extending their predictions to far or making assumptions/jumps that are simply too big. In fairness this has often led to serious progress in mathematics but often criticism from the scientific community. Some of these culprit areas have since reigned things in, but over the last forty years some ridiculous statements have been made along the lines of theory not needing to be testable. Theory is not a one way street there are lots of directions theorists take and they all have their strengths and weaknesses. But just because their predictions aren't fore-filled doesn't necessarily mean they're doing a bad job, sometimes it turns out to be really useful!

Theory leads to new technology
Most modern electronics can be traced back to quantum electrodynamics, a theory that started development in the 1920s. So it's not unreasonable to argue that modern technologies like I don't know... the internet, personal computers, satellite navigation, I could go on, would simply be impossible if it wasn't for the endeavour of the theorists who laid the ground work for QED. GPS wouldn't work without relativity either, you might know that from A-level! All stages of science are crucial to the development of technologies that benefit human kind. Theoretical physics works quietly in the background, laying the foundations often decades before tangible effects are seen. But that doesn't mean theorists are any less important!


So if you're feeling a bit insecure about studying/pursuing theory because of the mentioned pressures, have a real think about where those opinions come from and whether they actually make sense!

Can you have a social life whilst studying physics?

This might seem like a more light hearted topic in comparison to my other articles but its a serious subject worth consideration no matter what stage of studies you're at. Whether you're just starting or in a final year, so called 'work-life balance' is important. I'll confess that I hate the term 'work-life' because it implies that work is bad and I hope that most university students enjoy their studies. But academic study is hard/stressful and engaging in social activities and past-times is not only fun and enjoyable but also stress relieving!

How do you find a right balance for you? How do you deal with the pressures from either side? Hopefully I can provide some answers.

Disclaimer: Inevitably my own approach to this has an effect on how I answer these questions, nevertheless I'll try to answer as objectively as I can. But you should probably know I'm not a very social person (surprise surprise) and whilst I tend to be reasonably flexible with my work schedule in my last academic year I almost always handed in problem sets a good few days before deadlines. Not everyone does it that way and with good reason, different things work for different people.

Can I really afford to spend time on things outside of physics?

Yes of course you can! There is often a perception that most successful physicists spent all their time doing nothing but study, to my knowledge that is certainly not the case (though they probably spent a lot of time on physics).

I'm not going to reel off all the research that thousands of articles have talked about regarding how down-time and certain types of activities can really boost your productivity. Instead I'll give some examples of some of the things successful students in my cohort did on a regular basis outside of physics:

• A number of them regularly went swimming multiple times a week with the college club. This was particularly beneficial for them as they had a structured way to socialise outside of lectures, I noticed it strengthened their friendships and it made them happy! Most people participated in some kind of sport, some of them played a role in running sports clubs.
• They took part in physics society social events, including many of the top of the class students. Events included pub crawls and bowling nights. This gave people a chance to let off some steam and converse about non-physics stuff, this usually had a good impact on people provided they didn't get absolutely plastered.
• I myself and I think a few others managed to spend a significant amount of time a week practising an instrument, I actually managed to be an instrumental teacher (part-time) for about 2 years over the course of my degree. I found this to be a very good relaxation tool whilst still feeling like I was progressing at something, I imagine the results would be similar for any more technical activity like (sorry to be stereotypical) playing chess or something more craft based if you can do that in your uni accommodation.
• Plenty of people were members of societies, I know at least one person wrote a number of physics articles for the university magazine for example. So its certainly not impossible to have pretty serious commitments outside of your studies.

Not only can you spend time away from physics but my experience (and research) points towards it being very important. I think the benefits of exercise cannot be ignored but if you don't want to go to the gym I really do sympathise with you, I hate gyms. But if you can find a sports class with a comfortable environment or even if you just do a bit of exercise in the privacy of your own accommodation I think you'll reap the benefits.

Humans are also fundamentally social beings, this is something that stereotypically students of sciences grapple with more than others I think, particularly physicists. The fact is that social interaction is crucial to your health, both physical and mental, that is under no doubt whatsoever. Keeping yourself healthy maximises your productivity and effectiveness when working. You'll find that if you work whilst in a bad mental state you are likely to perpetuate it, as you're unlikely to make much progress for the amount of effort you'll feel like you're putting in. 

There has been a lot in the news recently about student mental health and the statistics regarding suicide rates in the student population. It is more apparent than ever that we need to look after our minds whilst we undertake this tough but (hopefully) rewarding journey. Social interaction is the cornerstone of this and taking part in more organised events as well as spending time casually with friends is very important for any student.

On a less serious note, I think its important not to let study suppress your other hobbies/interests. Keep doing the sports you've been pursuing, same goes for any hobbies like instruments, crafts etc. I did reasonably well in my degree and I still managed to practise guitar and listen to music, play Skyrim, watch films/TV and spend a good amount of time cooking!

So now I've convinced you spending time away from physics is good, I now have to reign it in and convince you that you must be careful how much time you spend away from it...

I want to be a physicist but I still want to 'live'

My first answer to that question is: if you want to be a physicist you should live physics. But that's kind of a cheap answer so for those unsatisfied let me elaborate. Having spent three years doing my degree I've seen people change from having dreams of working in physics to not really caring so much. And there's nothing wrong with that, but sometimes the reason for that change was valid, other times it wasn't. If after studying the subject for such a long time you become dis-interested fair enough, but for some it was a case of their grades dropped because they didn't dedicate enough time to their studies and they saw that as them not 'being right for physics'.

Now I'm not judging people with drops in grades, some people get them for legitimate reasons (I've been there). But I'd be lying if I didn't say that some people get in that situation because ultimately they didn't put the time in. There's no 'I'm just not that smart' card you can pull here in my opinion, if you want the grade you have to put the time in. That amount of time is different for different people, I know for me that's usually longer than others! 

The fact is you get one shot at your degree, sure there's opportunities to retake a year etc. but that can cause serious problems with regards to academic record and whilst again this can happen for very legitimate reasons it is best avoided. Here's a couple of examples of ways I've seen people distracted from their studies to their detriment:

• Going out too much: You knew it was coming, it applies a lot of students. The fact is spending multiple hours in the late-evening/early-morning drinking several times a week isn't going to do your studies any good. Going out once our twice a week seemed not to cause people too much trouble but I tended to notice that when people did three or more heavy nights in the week the would have serious problems getting multiple problem sets in on time. What I can't escape is that the top of the class students went out once a week at most. I'd attribute a lot of my successes in my degree to the fact that I never go out drinking! But all in moderation, its about taking a serious look at whether your studies are being impacted by the amount you are going out (sometimes people find this difficult to assess though...)
• Devoting too much time to sports: I saw this happen to at least a couple of people. This was due to either being part of running a club or being involved in competitive matches. The key thing in both situations is to ensure that when you get into it there needs to be an escape route you can take if its impacting your studies. You MUST put your degree first. If you can't do that, that might suggest something about how much interest you actually have in the subject. It's fine if your passion for the subject is dead and gone but at least be ready to put some damage control in place so you can still come out with a degree.
• Procrastination: Whilst I've never experienced the first two I think this one can affect all of us. This often goes in line with your mental health, many of us when feeling down will occupy ourselves with unproductive and non-beneficial tasks. Now a bit of procrastination (a bit) has shown to be good, but it's important to keep it in check. Some use schedules to tackle this, that doesn't work for me so I simply monitor what I'm doing and whether I'm on track for meeting deadlines and getting the best marks I can.

So how do you achieve a balance? We here's my take on it.

Finding a 'balance'

Whilst I'll discuss my approach I think in the interests of objectivity its only fair that I'll give a counterexample. One of the top students in my year almost always did their problem sheets the night before they were due, they also did a ridiculous number of activities outside their studies. Whilst I'm pretty convinced they were a polymath it does show that everyone has their methods. Some people work incredibly well under pressure and enjoy having to manage multiple aspects of their life on an hourly basis. At the other end are more straight arrow types, they often still have hobbies but do work significantly in advance and have rigorous structure to their time. I'm somewhere in the middle...

I've already spoken about problem sets and not leaving them till a day or so before the deadline. But I also understand sometimes this is unavoidable, sometimes you have to do a set the night before its due in. My thought is that if you're facing this situation on a weekly basis you either aren't structuring your time correctly or you aren't spending enough time studying/working. Grades are a different matter, for some people where they are at now means that they need five hours on a sheet to get a 2:2, for others they only need an hour to get a 1st. If you're in the former position this can be very disheartening if you hear how the latter is doing. But if that's where you're at you have to make a choice, is that grade worth your five hours? This is perhaps worth an entirely new article, I'll probably write one about it soon.

I think your own happiness is ultimately the best measure. Because the fact is not everyone wants to put in the work they need to in order to graduate with a 1st, that's fine! But you don't want to be in the position where you graduate with something less than you expected/wanted. The best way to keep track of this is to pay attention to your problem set grades, they are highly indicative of how you are progressing and you should feel an emotional impact from them. I'm not saying if you get a 2:2 when you're after a 2:1 you should feel bad but that you should care that its not what you wanted and do something about it.

That could mean implementing a tighter schedule, going out less etc. Likewise if you consistently get what you want and you feel like you could still get it with some more free time injected into your life, give it a try! There are no set rules but the key is to be willing to change your lifestyle to fit what you want in the hope that it might make you a bit happier.

External pressures that push you to work

Lecturers in physics can often be very demanding (very very very demanding). They can expect you to put in a lot of extra work, completing exercises for the reader etc. There is also little sympathy for your commitments outside of your studies, you can't ask for a coursework extension because you had a sports match on during the weekend. To some this seems harsh but I'm afraid I'm with the lecturers on this, just be aware of it and plan accordingly.

Problem sets are perhaps where things get a bit more hazy. They can vary in difficulty drastically and in my experience lecturers can be very poor at structuring their coursework. We all have our limits, if for you four hours on a sheet is max then work to that. But don't expect lecturers to sympathise with you as students regarding the length of problem sets. Sometimes changes are made but in my experience its often a 50:50 chance at best. Having a personal limit on your work time is a good resolve to have when facing such pressures.

You also might find that your fellow students unintentionally push you to get things done. If you chat with a straight arrow type you might find yourself pressured to complete coursework ahead of your own personal schedule. For some people this might be the push they need, but if your system works for you and is getting you the marks you want its important to remember that everyone does things differently.

External pressures that push you away from work

First lets note that some of these pressures are justified, health (and that of those close to you), family matters etc. If you are experiencing such difficulties please talk to your department and get your deadlines moved and such.

The more... unjustifiable pressures mostly come from your fellow students. Being convinced to go out for drinks again and similar situations are often continuous social pressures that students are under. A willingness to say no is often not common amongst the general student population, I would encourage you to develop such a willingness. 

I think this is especially important if you have friends studying degrees with a different workload or deadline structure. Some other courses require fewer hours of work per week or they have an essay based coursework system, this can offer a different level of flexibility unlike physics where you have to manage a number of weekly deadlines. It's important that your friends recognise the pressures you are under. 

If I'm being completely honest and bias, science students tend not to have the same amount of free time as some other degrees, sorry BAs if that offends you its just what I've seen. Physics in particular is seen as a pretty 'hardcore' subject, if you're studying it you probably know that. Don't forget it and understand what that means for your social life in comparison to students of other subjects.

Ways not to deal with the pressure

Using drugs (including legal ones like alcohol and 'legal' study drugs) to prop yourself up is a really, really bad idea. Whether it be aiming for stress relief, to keep you awake so you can study/party all night, or anything else really, I've never seen someone who used drugs at uni end up in a good position. Not to mention that if you get found to be storing/using on university property you are at serious risk of being expelled from your university. If you feel that you are reliant on any substance please seek help with the relevant services at your university.

Running away from issues like falling grades is a really bad idea as well. Get in touch with your tutor or relevant members of staff and get help. Also, talk with your friends! I know I'm always willing to help out a friend with managing work, you should do the same. That said, never give someone a copy of your coursework, its ok to talk about problems but don't simply hand over a copy. It doesn't help people in the long run. Likewise don't ask someone for a copy of their work, it puts that person in a very difficult position.

A lot of opinions/information for you there, with any luck that gives you a clearer idea of how to achieve the fabled 'work-life balance'. Everyone does it differently but it's crucial that you find it as soon as possible!

Series Introduction (IP 1.1)

I've decided to start a running series of short articles, a way of generating content more regularly alongside my longer pieces. I might expand the number of the series in the future but we'll start with this one.

As in the title the working title is 'Information Processing', I'm going to discuss any science material I've been reading, watching, listening etc. I'll chat about what it covered, how I thought it was delivered and how useful it was to me.

Let's get started with Information Processing 1.1! I'm not back at uni yet so I'm really just warming up ready for the first term.

"What are quarternions, and how do you visualize them? A story of four dimensions." - 3Blue1Brown:

I've been a big fan of 3Blue1Brown for about 6 months now, his focus on visualisation and trying to make mathematics more intuitive suits me, he exhibits a level of detail which many YouTube creators do not. 

This particular video is on a topic that I wasn't familiar with previously, it's part of a short series of videos that should be coming over the next few weeks. Quarternions certainly have applications in physics but for me the more interesting aspect of this video was the focus on stereographic projections and dimensions. These are subjects I'm more familiar with. The example of projecting a 4D hyper-sphere into 3D space is definitely worth a look at for anyone interested in theory. 

As always with 3Blue1Brown, the animations are on point and as a classical music fan the soft piano in the background helps me absorb the material presented. Definitely worth a watch.

Various presentations by Dr Don Lincoln - FermiLab:

The FermiLab channel offers some nice (if short) introductions to topics in particle physics. I used these for a quick conceptual refresher over a couple of days. They are a lecture style presentation with a few basic animations.

I covered a number of topics, QFT, QCD, QED but the Twin Paradox one probably sticks in my mind most. This had better animations and covered it from the point of reference frames, something I only covered in detail this academic year gone. The ones on general particle physics were a good terminology reminder but I found them too low level personally.

Solid explanations, but the presentation can sometimes be a bit slow and cheesy, only sometimes though. Still a good refresher though.

QFT lecture notes - Imperial College London:

For anyone interested these notes are available on the Imperial theory group page, freely available to anyone, on the 'Information for Current Students' section of the masters pages. I've read through the PhD note-takers material for the first few lectures, their handwriting is very good with clear diagrams as well. The material is reasonably introductory and as yet hasn't got me running scared (I stress yet). The QFT course seems to seen as the most introductory and 'basic' course in the first term, it leads on nicely from the advanced classical physics course I took last year.

I'll try and cover more ground before I start the course next month!


That's it for this week, I'll check in next time with a few more entries!

How to approach your first problem sheets/sets... 5 points of advice

As far as I am aware most physics courses in the UK have coursework in the form of problem sheets (a.k.a problem sets). These are a series of (often connected) problems designed to challenge you to implement the techniques you have learnt in lectures to textbook problems or examples from more front line research topics. 

If you've just received your offer for a physics course you might well be receiving your first problem sheets in freshers week (that should give you a good idea of what you've let yourself in for). For many people it can take a while to get into the swing of doing these sheets, my uni certainly didn't give me general advice on how to tackle problem sheets. This can be a bit disheartening, especially seeing as looking back there are simple steps you can take to make things easier.

Not like A level problems/homework:

This is something I'm sure that you're all aware of, but my main point is that by recognising this you'll be better prepared. With higher study comes more independent work (inevitably) and tougher material. Typically undergraduate problems require you to make more leaps on your own, fill in gaps in your knowledge of your own accord and to be more thorough in your explanations. I'll expand on these below.

Lectures may not give you everything:

You have to understand what lectures are designed for, they are to provide you with a base line of knowledge and skill. You may need to search elsewhere for information or methods that will enable you to solve a problem. 

Sometimes this involves looking through the course textbooks or reading more widely through your university's library. Many often turn to the internet, a technique which is a source of much debate. In my personal experience looking online is usually useful for finding good textbooks or a bit of background information, but I don't find it often leading me to solving problems asides from the occasional online textbook or university PowerPoint.

(Image Credit: Wired)

Often students who do well on problem sheets are familiar with a wide range of textbooks they can turn to on various subjects. I would suggest familiarising yourself with the books at your disposal in the library, they are crucial tools for problem sheets and might save your skin more than once!

Draw on other areas:

The solution to a problem might be found outside the immediate vicinity of the course that set the sheet. Skills that another course is teaching you might be the key to your solution, if you're doing a quantum mechanics problem you might find a linear algebra technique you learnt in maths gives you a quick solution!

Another common occurrence is using programming or software to overcome a problem. Can't solve an integral because it's freaking huge? Well unless the question is literally 'solve this integral', use Mathematica, its what any sensible physicist would do. Can't visualise a function, graph it on a computer! You can also use these methods to check your answers if using them as part of your solutions is not valid.

(Image Credit: Wolfram)

Be thorough:

Undergraduate problems are often more open-ended than in A-level, with less direction to the realms of the correct answer provided. In order to arrive with confidence at an end point each step you take must be very water tight. The problems are often designed so that if you take steps lacking in security you will often arrive at the wrong answer. Question the appropriateness of your mathematical methods at each point in your calculations and whether your assumptions are appropriate also.

I have also found that thoroughly explaining my steps and choices in my solutions often helped the marker understand my intentions and direction. This enabled my markers to give me more feedback and sometimes to give me a few more marks where I had made mistakes.

Communication and Persistence:

Obvious but talk with your colleagues (don't copy, but talk) and also academic staff if you are struggling to make progress. You might also find you learn more than you expected to if you talk to an academic!

Some problems you will solve like *that*. Others might occupy you for hours. The key is to not give up unless it is occupying an 'unreasonable' amount of your time. My limit personally is about 10 hours for a sheet (I had about 2-3 sheets a week) but I'm unnecessarily stubborn and I work slowly. I know people who regularly got firsts that never spent more than 4 hours on a sheet. Find your limit and work to it!

In your first weeks its important to make lots of time for problem sheets in order to get to grips with them before the increase in difficulty (which can happen suddenly). DO NOT leave them to the last minute and do not trust yours or your colleagues estimates of how long the sheet will take, it will take as long as it does and you just have to deal with it! Hopefully some of the above advice will come in useful and the best of luck with your first problem sheets!

Eight theoretical physics masters options!

Masters courses! Searching for them can be a bit trickier than undergraduate and a summary is always helpful too. If you're looking to study particle theory or mathematical physics these courses may well be up your street. Some of them have plenty to offer to prospective condensed matter theorists, theoretical astrophysicists and cosmologists. The courses I've mentioned are geared almost solely (if not solely) towards theory, but there is nothing to stop you going into theory if you go for the MSci route or take a general physics MSc with lots of theory options. But here are some of the top choices for getting into a theory PhD!

Disclaimer: This list is not necessarily exhaustive and if you're interested in a course do the full research and don't take my word for any details. The main aim of this article is to inform you of some of whats on offer to you in terms of UK theoretical physics masters courses. Lets get started...

Cambridge - Part III - MMath/MSaT
The reputation of this course proceeds itself. A huge number of prominent theorists took this course, that much cannot be denied. There's a plethora of courses on offer from pure mathematics modules to applied mathematics and theoretical physics modules covering all you can imagine. 

The course is purely taught, there is no dissertation/project or research component. The cohort is also quite large to my knowledge, though I can't comment on class sizes. There are also non-examinable graduate courses available to you. The entry requirement is set at first class honours and the course also requires serious preparation over the summer, but I imagine that's more than worth it!

For fans of: Loads of options, pure mathematics, established course, all exams.

Suited specialisations: Everything except condensed matter!

Imperial College London - Quantum Fields and Fundamental Forces MSc
Second disclaimer: I've been admitted to this course, so quantify my bias as you like!
Imperial has a serious reputation for theoretical physics, this long running course (it hasn't always had this name) also has a serious reputation. Unlike Cambridge, the options on this course are much more limited, half your modules are compulsory. The course is very much geared towards particle theory, studying the standard module is compulsory to a certain level for example.

There is a reasonable selection of options to fill the rest of your taught credits and a dissertation over the summer. The taught modules on this MSc are longer than the average taught course length, typically 30 hours as opposed to 16 hours at Oxford for example. It's up to you how you see this, some people prefer more independent study, others (like myself) want as much lecture time as possible. The entry requirement for this is also a first class honours, they have a recommended topic refresh list as well.

For fans of: Avoiding option paralysis, established course, lots of lecture time.

Suited specialisations: Particle theory, mathematical physics. There are some courses that touch on cosmology but the general relativity exposure is mainly designed for mathematical physics applications, I wouldn't go here for cosmology. Furthermore I wouldn't go here for particle phenomenology, Imperial doesn't really research in that area. This is certainly not a course of theoretical astrophysicists or condensed matter theorists.

Kings College London - Theoretical Physics MSc
Third disclaimer: I applied and was offered a place on this course.
Like the Cambridge Part III, this course is run by a maths department. KCL offers a core set of theoretical physics courses for you to choose from with the option to throw in some pure/applied mathematics if that takes your fancy. 

The number of these mathematics courses is large and there are many options available, some of the applied maths options are particularly unique. These are University of London accredited courses, some of which are offered on the popular inter-collegiate MSci. You would have the option to take courses from other University of London Institutions. The course includes a dissertation which is carried out over the summer and has a upper second class honours entry requirement.

For fans of: Plenty of options, mathematics, University of London.

Suited specialisations: Particle theory, (potentially) astroparticle theory, mathematical physics, applied mathematics. Cosmologists might be ok with this course, there are physics department modules you could take to supplement this interest.

Oxford - Theoretical and Mathematical Physics MMathPhys
This course is reasonably new on the scene, but a particle theorist I spoke to about nine months ago said the course was going very strong and had become very desirable. He also mentioned that the places were very limited and application processes were arguably tougher than Cambridge Part III! There are a huge number of options on this course, though many of them are third year maths courses, take that for what you will. The course teaching is organised by both the maths and physics departments.

The course is typically entirely taught, although there is the option to do a dissertation. Something I note in particular about this course is that it offers a very high level of training for perspective condensed matter theorists. Again the entry requirement is a first class honours.

For fans of: Lots of options, small class sizes (so I hear), a new/fresh course.

Suited specialisations: Mathematical physics, applied mathematics, particle theory, condensed matter physics, theoretical astrophysics.

Durham - Strings, Particles and Cosmology MSc
Durham has a strong reputation in theory, this course is certainly a good option for a prospective theorist. It differs from many others in that almost all modules are compulsory, there are some optional extra courses offered that vary year to year. This would force you to cover a broad range of topics with particle theory, cosmology and gravitation. In my opinion the main focus is on particle theory and links from other areas to this. Courses are of a similar length to those at Oxford and you take a large number of them due to some of them being half length. 

There is a dissertation as with many of these masters, but this accounts for half of the MSc. There will always be a debate as to whether taught courses or dissertations are more important (I'll probably write about this another time). Unless the answer to this is clear in your mind, I would follow your gut on what you want more of. The grade requirement is an upper second class honours.

For fans of: Keeping it broad, large dissertation, Oxbridge style university, no choices.

Suited specialisations: Particle theory, astroparticle theory, (potentially) cosmology. This masters would provide a very strong route into phenomenology in any of these areas, there is a lot of time spent on the standard model and links the theory to active experiments. Not really suited to theoretical astrophysics and definitely not condensed matter theory.

Nottingham - Gravity, Particles and Fields MSc
Nottingham has established itself a centre of research in theoretical and mathematical physics, particularly with regards to gravitational research. In this guise the MSc focuses greatly on gravity. This is a pretty unique feature of the MSc, if you want to focus on gravitational physics this should be a serious consideration for a masters. Consequently if you're interested in traditional particle theory this would not be the best option for you (in my opinion).

As far as I am aware there are no taught course options, all compulsory. Topics included advanced general relativity as well as quantum information. There is a dissertation component of this course, I believe it is slightly large than usual, but don't take my word for it (the information they provide on their website is a bit sparse). The course is run out of the maths department so expect mathematical rigour and the grade requirement is an upper second class honours.

For fans of: Heavily structured course, no choices, mathematical perspective, a pretty unique masters.

Suited specialisations: Cosmology, gravitation, mathematical physics. If you want to focus on gravity this would be a great choice, would probably suit cosmologists as well.

Edinburgh - Theoretical Physics or Mathematical Physics MSc
Held at the Higgs Centre for Theoretical Physics at the reputed University of Edinburgh. The course offers a very wide range of options with a general structure. There is research skills core, then a choice of base knowledge modules then additional optional courses which build on these. There are a wider range of topics available than some other courses with some different fields than usual on offer, i.e. an advanced material science module. This might suit someone who is interested in more esoteric combinations of physics topics. In addition, I would suggest that those interested in condensed matter theory would find this MSc might suit them.

There is a dissertation which accounts for a third of the course, slightly larger than usual. The entry requirement is an upper second class honours degree.

For fans of: Lots of options, unusual topics, structured programme.

Suited specialisations: Pretty much everything! There are many options you won't find on any other course (atmospheric physics and computer science for example) so worth a look if you're into something niche.

Queen Mary - MSc Physics - Theoretical Physics
QMUL is renowned for string theory and cosmology research and is part of the University of London. The MSc has half of its courses as compulsory, focusing on methods for quantum field theory. The course is an intercollegiate, so you can fill your options with any eligible course from the University of London (that's a very big list!). This capped off by a dissertation worth a third of your final mark. Unlike the KCL programme this is run from the physics department. The entry requirement is an upper second class honours degree.

For fans of: University of London, structured core study, lots of options.

Suited specialisations: Pretty much anything! QMUL itself is suited to particle theory, cosmology and theoretical astrophysics but with the other uni's thrown in you could do pretty much anything.

Some closing comments:

If you are leaning towards a serious interest in maths and are thinking about working in this area I would suggest Cambridge and KCL are the places to look. It's true that Oxford has plenty of maths courses on offer but these aren't quite as broad, they focus on geometry (which in my mind is a good thing) but if you want less related maths you'd be better looking a Cambridge/KCL.

I think Oxford alongside Edinburgh and QMUL are excellent options for those pursuing pretty much any area of theoretical physics, specifics above taken into account. In particular Oxford for theoretical astrophysics and condensed matter, QMUL for cosmology and Edinburgh for more niche subjects. All all are strong for particle theory with QMUL a bit weaker for condensed matter theory.

Durham, Nottingham and Imperial are far more focused. Durham would be an excellent for a prospective particle theorist, particularly for phenomenology. The course would also complement links from this interest to cosmology and/or astroparticle physics. Nottingham is perfect for someone who's interested very specifically in gravity and/or mathematical physics with a gravitational focus. Cosmologist would also be served well here if the don't want to focus on a particle physics perspective. Imperial is very focused on particle theory and mathematical physics. You should absolutely want to be linked to particle theory if you're thinking about Imperial but again it doesn't do phenomenology, it's a very specific course like the MSc Nottingham offers.

Condensed Summary:

• If you love maths and are thinking about being part mathematician: Cambridge and KCL (maybe Oxford) are for you.
• If you have mixed interests, like condensed matter, astrophysics or want lots of choice: Try Oxford, QMUL and Edinburgh.
• If you love particle theory: Durham and/or Imperial (depending on the specificity of your interests) but all those above are also very valid.
• If you love gravity (and maybe cosmology): Nottingham is a great fit.

Application choices example:

Lets say you love particle theory, aren't a huge fan of pure maths and aren't sure where you want to end up in particle theory. I would suggest you apply to Durham and Imperial then broader optioned courses like Oxford, QMUL and Edinburgh. Obviously locations have an effect so you might not apply to all five, I applied to three masters courses for example.

Hopefully that's been helpful! Eight masters that could be your route into a theory PhD. If you're a perspective masters student weigh up the nuances of the courses and apply to a number of them if more than one fits. And as always, do in-depth research on the courses and see if there are any alternatives out there.

How is studying theory different? What do YOU need to do differently?

Different physicists need different tools in their lines of work, the two main groups in physics are theorists and experimentalists. It's fair to say that there are a lot more experimentalists than theorists (rightly so), so often the path for experimentalists is quite well laid in the structure of physics courses. Sometimes it's not so clear for theorists what they need to be doing to get to where they want to be. Asides from choosing theory options in your degree there are some general points of advice I'd like to give, hopefully they'll be useful! So here's some things I think you'll need to do differently to your experimental colleagues, regardless of your specific direction.

(Image Credit: Lib Quotes)

More Maths!

This is not a stab at experimentalists, not some 'theorists are smarter than experimentalists' rubbish. Physicists need tools to solve problems and experimentalists need to use tools outside maths to solve the problems they look into. They use engineering, electronics and other skills which although related to maths don't necessarily require them to be actively solving maths problems constantly. For theorists, maths is their domain and their only real tool.

Theorists often need very specific mathematical tools relevant to their research, for example fluid mechanics researchers often need techniques from non-linear dynamics. But there are areas of maths that are practically ubiquitous throughout all physics, and crucial for both the experimentalist and theorist. Theorists must be particularly well versed in these, fluent in common mathematical language and having a good understanding of it. So here are three areas I think are key.

Calculus is an essential tool for almost all scientific fields, but theorists need serious calculus abilities. In particular geometric integrals involving volumes and surfaces of spheres and cylinders crop up a lot. Vector calculus is also an important arrow in your quiver, useful for topics like electromagnetism.

Differential equations crop up in physics all the time, solving them is a common necessity in problem solving. As a theorist you will almost certainly work with differential equations at some point in your career. You should be well versed in how to solve many types of differential equation problems analytically and potentially numerically (more on numerical methods later).

(Image Credit: Clement Mouhot - Wordpress)

Linear algebra is arguably the least fundamental of these three, but undoubtedly a key piece of your tool kit. Studying this leads to group theory which is essential for a number of fields. Understanding vectors and matrices along with the relevant techniques and manipulations is an important part of a theorists skill set.

Most importantly, if you want to do theory you better love maths! I've known plenty of experimentalists who view maths as a necessary evil but never a theorist who shared that view.

Programming:
Whilst there are areas of theory that don't use computers as a primary tool I'd be lying if I said they aren't crucial to most areas of theory. They can perform calculations that simply aren't worth your time, or calculations that are impractical for humans to carry out. Computers are key for a number of theoretical activities such as:

• Constructing simulations of many-particle systems
• Modelling fluid dynamics
• Finding numerical solutions to systems of differential equations
• Computing large matrix operations symbolically or numerically
• Kinematics calculations from track measurements in particle detectors

You can imagine how the above can be relevant to multiple fields. The main programming language used is C++, but Fortran is also used by some theorists. Symbolic manipulation languages like Mathematica are also used, with C++ extensions like Eigen often used by particle physicists.

Python is often the starting point for most physicists, it leads nicely into C++. All of this said don't feel pressure to take programming courses, I only have a compulsory 2nd year programming course under my belt and it hasn't caused any problems yet. I spoke to a UCL Particle Theory PhD about half a year ago (he'd done an MSci at Oxford), he said that plenty of PhD students teach themselves programming as and when they need such capabilities.

Quantum Mechanics:

Alongside your maths courses, quantum mechanics is a subject any prospective theorist should absorb thoroughly. It is the basis for almost all modern physics outside of relativity, so being quick with quantum is pretty much a pre-requisite for being a theorist except in a few areas (fluid mechanics comes to mind). Topics like quantum field theory (a graduate level topic) build on this foundation and are the primary tool of both particle physics and condensed matter physics (along with others).

Whilst knowledge of quantum mechanics is key for both experimentalists and theorists, theorists should be well versed in the mathematics of the theory, experimentalists often focus more on the physical phenomena that arises from quantum mechanics.

Statistical Mechanics:

This is an increasingly required area of expertise for theorists of all walks. Last academic year I spoke with a condensed matter theorist, Dr Andrew Ho, who told me that whilst previously areas like particle theory weren't expected to be well versed in statistical mechanics that has been changing. Within statistical mechanics is the most modern interpretation of thermodynamics, which is often used in calculations for various experiments.

Monte Carlo methods are increasingly prevalent in particle physics, as well as various data analysis techniques are also used for the large data sets that come out experiments like the LHC. Whilst data analysis can be a discipline of itself in physics, theorists can be heavily involved in statistics and data analysis. These are often contextualised in the setting of statistical mechanics.

So whilst this discipline may be seen as more relevant to experimental studies, it seems that statistical mechanics is increasingly relevant to many theorists.

Classical Mechanics:

And to a high level, we're not talking SUVAT style here! Specifically the topic of Lagrangian and Hamiltonian formalism is an essential requirement for most fields in theory. In depth knowledge of rotational mechanics is also likely to be useful. Experimentalists are often very familiar with calculations for specific mechanical systems they work with (though plenty of them are great with Lagrangian and Hamiltonian mechanics). As a theorist you need to be familiar with a high level of generalised classical mechanics. The primary reason for this is that Hamiltonian and Lagrangian formalism is the basis of field theory, a cornerstone tool for most theorists. If you have the option to take an undergraduate course in advanced mechanics you must absolutely take it!

Numerical Methods:

This is a slightly unspecific comment but it should suffice. There are plenty of problems in physics that can't be solved exactly, even with algebraic approximations. Systems of differential equations come to mind, some of them are only solvable numerically. There are algebraic alternatives to numerical methods like perturbation methods and asymptotics, but numerical methods are incredibly relevant to current research. You might find that none of these come up in your undergraduate course and that's absolutely fine. But if you have the opportunity to study them, consider if they are relevant to your current interests, I'd strongly suggest studying them if there is even a bit of relevance.

(Image Credit: The Great Courses Plus)

So there's some points about what you might need to do differently in your studies to your experimental colleagues and some general advice about what you might find useful if you want to pursue theory. This list is not at all exhaustive, but I hope it highlights some important areas to focus on.