Math as a substitute for theoretical physics

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I was watching a video about physics that said people who want to study theoretical physics but do not want to study things like electromagnetism, thermodynamics, experimental physics, etc, should study math, then take some classes in theoretical physics. This way, you could study your favorite parts of physics (and really understand the math behind it) while simultaneously being able to skip over the parts of physics that you do not like. As someone who fits this profile perfectly, and who loves math, this sounds appealing. But as someone who has never studied higher level physics or math, I am not sure if or how this would work. Will this work as well as it sounds if at all, and why?
 

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  • #2
jtbell
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take some classes in theoretical physics
What do these "theoretical physics" classes include, and how do they allow you to skip undergraduate courses in classical mechanics, electromagnetism, quantum mechanics, and thermodynamics?
 
  • #3
What do these "theoretical physics" classes include, and how do they allow you to skip undergraduate courses in classical mechanics, electromagnetism, quantum mechanics, and thermodynamics?
First of all, excuse me if I sound insane but I am just in high school so I do not fully understand how these programs work. Second of all, I was thinking I could Study math and take a few courses on general relativity and I would be able to understand it because I know the math behind it ( that is just a hypothetical )
 
  • #4
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Will this work as well as it sounds if at all, and why?
Sure, it will. The question is what you really intend to achieve. Equipped with all mathematics which is necessary, you can certainly study particular fields of physics and understand them. However, that does not mean you will get any relevant degree in physics, you just get knowledge and only in that particular field of physics.

But there is one thing you should know: Yes, the language of physics is mathematics. Nevertheless, physicists and mathematicians speak different dialects of this language, and a large part of a regular study of physics is to learn this dialect. This usually needs time and a lot of practice. So if you only study a particular field, and know the mathematical mathematics, you will open a book and find a strange dialect. This has to sound funny to you, but to study a certain science has more to do with learning a language than most assume. E.g. lawyers use our common language in quite a different way than ordinary people; look up some contract and its salvatory clause:
If a provision of this Agreement is or becomes illegal, invalid or unenforceable in any jurisdiction, that shall not affect the validity or enforceability in other jurisdictions of that or any other provision of this Agreement.
That's not how ordinary people speak, yet it is ordinary English. It is similar with physics and mathematics and the usual way to study physics gets you used to it.

If you only want to understand, e.g. general relativity, then it won't be necessary to learn thermodynamics or electrodynamics; a good portion of differential geometry might do. However, if you want to take part in discussions why general relativity and Newton's gravity are different, electrodynamics might be useful as it is a frequently used comparison. If you want to understand the physics of black holes, then thermodynamics is necessary.

So as it is always the case with questions like yours: It depends on where you want to end up with your path.
 
  • #5
Sure, it will. The question is what you really intend to achieve. Equipped with all mathematics which is necessary, you can certainly study particular fields of physics and understand them. However, that does not mean you will get any relevant degree in physics, you just get knowledge and only in that particular field of physics.

But there is one thing you should know: Yes, the language of physics is mathematics. Nevertheless, physicists and mathematicians speak different dialects of this language, and a large part of a regular study of physics is to learn this dialect. This usually needs time and a lot of practice. So if you only study a particular field, and know the mathematical mathematics, you will open a book and find a strange dialect. This has to sound funny to you, but to study a certain science has more to do with learning a language than most assume. E.g. lawyers use our common language in quite a different way than ordinary people; look up some contract and its salvatory clause:

That's not how ordinary people speak, yet it is ordinary English. It is similar with physics and mathematics and the usual way to study physics gets you used to it.

If you only want to understand, e.g. general relativity, then it won't be necessary to learn thermodynamics or electrodynamics; a good portion of differential geometry might do. However, if you want to take part in discussions why general relativity and Newton's gravity are different, electrodynamics might be useful as it is a frequently used comparison. If you want to understand the physics of black holes, then thermodynamics is necessary.

So as it is always the case with questions like yours: It depends on where you want to end up with your path.
Okay. So if I am pursuing physics as an interest and not as a career, would it be best to study applied math in my undergrad then be educating myself in physics through books and videos? In that situation would I be able to understand such theoretical, math intensive, concepts like general relativity at a similar level to an actual physicist? Or is an actual degree in physics needed to even understand that?
 
  • #6
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Okay. So if I am pursuing physics as an interest and ... study applied math ... would I be able to understand such theoretical, math intensive, concepts like general relativity at a similar level to an actual physicist?
I'm not certain about the applied adjective here as I think there is a decent portion of pure mathematics involved, too, but in principle yes. You will set yourself in a position to be able to read textbooks about physics and possibly fill gaps, as e.g. in electromagnetics or thermodynamics whenever they occur.

Most important will be curiosity in my opinion. If you're curious and willing to learn, there will be no limits what you can learn, except time perhaps. Whether it will make you an expert in a field is another question.
 
  • #7
Dr. Courtney
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http://www.richard-feynman.net/videos.htm

Watch some of the Feynman videos.

Theoretical physics is about describing reality.

Many descriptions may be right in their math, but wrong in their physics, because they fail to describe reality.

The arbiter of correctness in theoretical physics is agreement with experiment.

Mathematics is different.
 
  • #8
ZapperZ
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I was watching a video about physics that said people who want to study theoretical physics but do not want to study things like electromagnetism, thermodynamics, experimental physics, etc, should study math, then take some classes in theoretical physics. This way, you could study your favorite parts of physics (and really understand the math behind it) while simultaneously being able to skip over the parts of physics that you do not like. As someone who fits this profile perfectly, and who loves math, this sounds appealing. But as someone who has never studied higher level physics or math, I am not sure if or how this would work. Will this work as well as it sounds if at all, and why?
First of all, WHAT VIDEO?

The validity of your source of information here is unknown. It is not even certain if you have understood it as it was intended.

Secondly, what do you think is “theoretical physics”?

Thirdly, if you like math but not physics, why not just major in math? Why is this question even necessary?

Zz.
 
  • #9
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I know a mathematics professor who did work in general relativity, but it involved cleaning up and formalizing the mathematics instead of doing any actual theory. That could be a potentially viable option for you if you pursue a career in math, I just don't know how common that kind of work is.
 
  • #10
I'm not certain about the applied adjective here as I think there is a decent portion of pure mathematics involved, too, but in principle yes. You will set yourself in a position to be able to read textbooks about physics and possibly fill gaps, as e.g. in electromagnetics or thermodynamics whenever they occur.

Most important will be curiosity in my opinion. If you're curious and willing to learn, there will be no limits what you can learn, except time perhaps. Whether it will make you an expert in a field is another question.
I have been thinking about your replies to this thread recently and I had one more question, an answer for which I could not find online. If (hypothetically) I earned a higher level degree in math, and I specified my degree in the right parts of math, would I be able to get a job as a part of a physics research team? I was reading something on quora about how people with a degree in pure math can contribute to projects in things like GR and string theory (purely theoretical concepts). But my question is, is it common (or at least not too improbable) for research teams (mainly at universities) to accept people with a degree in math as a part of their theoretical physics research team?
 
  • #11
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I have been thinking about your replies to this thread recently and I had one more question, an answer for which I could not find online. If (hypothetically) I earned a higher level degree in math, and I specified my degree in the right parts of math, would I be able to get a job as a part of a physics research team? I was reading something on quora about how people with a degree in pure math can contribute to projects in things like GR and string theory (purely theoretical concepts). But my question is, is it common (or at least not too improbable) for research teams (mainly at universities) to accept people with a degree in math as a part of their theoretical physics research team?
I know of a few mathematicians who followed this route to - theoretical - physics, so it is possible. Whether their contributions to physics are of relevance or not is another question. Its answer depends heavily on individual cases. In earlier times many results in mathematics originated from physical problems, and Bernoulli, Euler, Gauß and others left their traces in both fields.
 
  • #12
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I know of a person who graduated with both a mathematics and physics degree for undergrad. Then went to grad school for pure mathematics, while taking some physics classes for fun. Now she works on "string theory."
 
  • #13
I know of a person who graduated with both a mathematics and physics degree for undergrad. Then went to grad school for pure mathematics, while taking some physics classes for fun. Now she works on "string theory."
So let me give you a hypothetical situation. Say I major in math with a minor in CS, then I get a degree in pure mathematics, while “taking a few physics classes for fun.” Will that have been enough for a position like the one you just talked about or do you think an undergrad degree in physics would be required.
 
  • #14
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Im in my senior year in my undergrad degree.

This person did their undergrad at Caltech. I am at a low tier state school. But we have a good few instructors who are very good lectures, and push you to you're limits, only to make you a better student overall. It is good to be ambitious, but also important not to be foolish.

Math and Physics are both hard and time consuming majors. You are still a high school student, so maybe wait till at least you're first year to decide. First year courses for both of the majors tend to be the same. You still need to pass the calculus sequence, linear algebra (sometimes optional for physics majors, but still worth taking), and the intro physics sequence. Then decide if you want to do math, physics, or both.

Also, there can be scheduling conflicts between the two departments. This is something to consider.

Moreover , please be aware that mathematics as math majors know it. Is not the same as high school mathematics. If you are taking calculus, then head to a library and open up Courant Calculus, Spivak Calculus, or Apostol. It won't look the same as you're high school calculus book.

If you are not in calculus, get a copy of Moise/Downs: Geometry. Proof based high school geometry, that is not typically of pure mathematics but it will give you a feel.
 
  • #15
atyy
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I was watching a video about physics that said people who want to study theoretical physics but do not want to study things like electromagnetism, thermodynamics, experimental physics, etc, should study math, then take some classes in theoretical physics.
Theoretical physics includes electromagnetism and thermodynamics, so your question is senseless.
 
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