How much mathematics must a theoretical physicist know?/Alternatives to string theory

In summary, the individual is considering becoming a theoretical physicist and is unsure about pursuing string theory due to doubts about their ability to contribute to the field and concerns about its credibility and goals. They are wondering if there are other fields of theoretical physics to focus on in graduate school and how much mathematics is needed for this career path, with the understanding that learning new math is often necessary in specific areas of physics. Some potential areas of study mentioned include condensed matter theory, topology, representation theory, functional analysis, and statistics.
  • #1
Philosopher_k
60
1
Ok, i have come to a realisation that my interests revolve not around pure mathematics (as i once thought) and more around theoretical physics, some people would claim that they merge into one at times, and that leads on to my question. If i wanted to be a theoretical physicist (rather than an experimental physicist), but am not keen on string theory, are there any other fields of theoretical physicis which i could focus on in grad school? Why am i not keen on string theory? well the answer is twofold, one i doubt i could match the contributions of the likes of witten and greene and secondly, i am slightly dubious of the credibility and goals of string theory.

My second Question is, how much mathematics must i complete to become a theoretical physicist? (i use this parameter loosly as i am aware you never stop learning mathematics) say i want to learn quantum field theory or Paticle theory in grad school, will mathematics up to complex analysis/fluid dynamics/advanced PDEs (the applied side) suffice, or will i need to learn topology, representation theory, functional analyisis (the pure side) as well?
 
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  • #2


Philosopher_k said:
If i wanted to be a theoretical physicist (rather than an experimental physicist), but am not keen on string theory, are there any other fields of theoretical physicis which i could focus on in grad school?
Most physicists never even learns string theory so this is a really strange comment.
 
  • #3


Philosopher_k said:
...are there any other fields of theoretical physicis which i could focus on in grad school?

There's all sorts of work going on in all kinds of directions. It's not all strings! Condensed Matter Theory is probably the most obvious one. Google some theoretical physics departments and see what kind of research they're doing - that'll give you a pretty decent idea.
 
  • #4


Philosopher_k said:
My second Question is, how much mathematics must i complete to become a theoretical physicist?

The undergraduate physics program is intentionally designed to give you the minimal set of mathematics so that you can do physics research in graduate school.

(i use this parameter loosly as i am aware you never stop learning mathematics) say i want to learn quantum field theory or Paticle theory in grad school, will mathematics up to complex analysis/fluid dynamics/advanced PDEs (the applied side) suffice, or will i need to learn topology, representation theory, functional analyisis (the pure side) as well?

Yes. But a lot of this will be on demand learning, which is to say that you learn the math at the same time you learn the physics. Also, you'll invariably find in learning any area of physics that you will need to learn new math, and what math you learn is field dependent. For example, if you do any sort of physical cosmology you'll find that you'll need need a lot of statistics that you didn't cover as an undergraduate. If you do computational work, there is a ton of math that you need to learn on the side to do that work.
 
  • #5
I can tell you that the amount of mathematics required for a theoretical physicist varies depending on the specific field and research interests. However, a strong foundation in mathematics is essential for any theoretical physicist.

In terms of alternatives to string theory, there are many other fields of theoretical physics that one could focus on in graduate school. Some examples include quantum field theory, particle physics, cosmology, condensed matter physics, and general relativity. It is important to find a field that aligns with your interests and strengths. It is also worth noting that string theory is not the only approach to understanding the fundamental laws of physics and there are ongoing debates and discussions within the scientific community about its validity.

As for the amount of mathematics required, it is difficult to give a specific number or list of topics as it can vary greatly. However, a strong understanding of calculus, linear algebra, and differential equations is essential. Beyond that, it would depend on the specific field and research interests. For example, if you are interested in quantum field theory, knowledge of group theory and functional analysis would be beneficial. Ultimately, it is important to have a solid understanding of both pure and applied mathematics in order to tackle the complex problems in theoretical physics. Additionally, as you mentioned, learning is a continuous process in science and as a theoretical physicist, you will constantly be expanding your mathematical knowledge.
 

1. How much mathematics is required for theoretical physics?

The amount of mathematics required for theoretical physics is quite extensive. A theoretical physicist should have a strong foundation in calculus, linear algebra, differential equations, and complex analysis. They should also be familiar with group theory, tensor calculus, and advanced mathematical methods such as variational calculus and differential geometry.

2. Do I need to be an expert in mathematics to understand string theory?

While a strong background in mathematics is definitely beneficial, it is not necessary to be an expert in mathematics to understand string theory. String theory involves concepts from a variety of mathematical fields, but a basic understanding of calculus, linear algebra, and differential equations is usually enough to grasp the fundamentals.

3. Are there any alternatives to string theory?

Yes, there are several alternative theories to string theory, such as loop quantum gravity, causal dynamical triangulation, and string field theory. These theories attempt to reconcile quantum mechanics and general relativity without relying on the idea of strings.

4. How important is mathematics in theoretical physics compared to other sciences?

Mathematics plays a crucial role in theoretical physics, as it provides the tools and language to describe and understand physical phenomena. While other sciences also use mathematics, the level of mathematical sophistication in theoretical physics is much higher due to the complex nature of the subject.

5. Can I become a theoretical physicist without a strong background in mathematics?

No, a strong background in mathematics is essential for pursuing a career in theoretical physics. Without a solid understanding of mathematical concepts, it would be challenging to understand and develop theories in this field. However, with dedication and hard work, one can always improve their mathematical skills and pursue a career in theoretical physics.

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