Theoretical physics

Which is the best route to get into theoretical physics.. is it through a math degree (choosing the physical modules) or a physics, I'm really confused since there is no clear answer?!

Reply 1

ZeroVectorSystem

I once was confused about this and I all learned this too late. When you say get into theoretical physics I automatically assume you mean as a field of research because you want a career out of it and though theoretical physicists are employed in numerous fields from finance to engineering, if it is theoretical physics itself you are interested in, it mainly used in academia or private research groups.

Based on this assumption, Theoretical physics is first and foremost a field of physics, which implores a high level and understanding of mathematics, but without the rigour and elegance considered by mathematicians to be of foremost importance. One who is fluent in theoretical physics can easily grasp 'mathematical methods' for physical models sake up to postgraduate level and knows classical physics as well as modern physics at-least up until quantum field theory, general/special relativity, advanced quantum mechanics, statistical mechanics...

https://en.wikipedia.org/wiki/Physics#/media/File:Physics_and_other_sciences.png

https://en.wikipedia.org/wiki/Theoretical_physics#/media/File:Mathematical_Physics_and_other_sciences.png

I often use these diagram to illustrate to people the importance of mathematics & ontology in the success of physics, though ontology is not something that is necessary to be studied but rather understood in order to be a successful physicist. There is often a vague line between where mathematics and theoretical physics cross, which is why many university departments, notably Cambridge, refer to it as applied mathematics and theoretical physics. However consider this very well written piece from stack exchange...

"Theoretical physics is the field that develops theories about how nature operates. It is fundamentally physics, in that the ultimate goal is to describe reality. It is informed by experiment, and at the same time it extends the results of experiments, making predictions about what has not been physically tested. This is accomplished using the language of mathematics, and often the demands of theoretical physicists force mathematicians to extend this language in new directions, but it is not concerned with developing the language of math. Theoretical physicists are, among other things, physicists who are very well-versed in math (which is not to say other physicists are not - please don't hurt me).

Mathematical physics, on the other hand, is a branch of mathematics. It explores relations between abstract concepts, proves certain results contingent upon certain hypotheses, and establishes an interlinked set of tools that can be used to study anything that happens to match the relations and hypotheses on hand. This branch in particular is motivated by the theories used in physics. It may seek to prove certain truths that were simply assumed by physicists, or carefully delineate the conditions under which certain theories hold, or even provide generally applicable tools to physicists, who can in turn apply them to nature. Mathematical physicists are mathematicians who are intrigued/inspired by physics.

One could say that mathematical physics is concerned with the internal, logical consistency of physical theories, while theoretical physics is concerned with finding the right model to describe the world around us. Very roughly, one might diagram these things as shown below.

Mathematical physics⟺Theoretical physics⟺Experimental physics"

Upon understanding that, this should give you an indication to the route you wish to take. There is no 'best route' in my opinion because learning at the highest level of university at the forefront of the field, you are able to make contributions by thought processes and problem solving. However, there is a more 'standard' route, which would be to take an undergrad in theoretical physics, followed by an MSc/PhD. You could essentially take an undergrad in math which serves concepts in theoretical physics and take a conversion masters to theoretical physics in anticipation of a phd or vice versa, depending on your strengths/weaknesses. The difference between taking a degree in mathematics/mathematical physics and theoretical physics would be that though you may take the same courses, the context in which they are taught or applied may very well vary.

I hope this helps.

BSc Mathematics/MSc Applied Mathematics

Theoretical physics

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