What is the Difference Between a Theoretical Physicist and a Mathematical Physicist?

[CPL.Luke]

hmm I'm intrigued, how does your knowledge of n dimensional calculus help you understand work? I can certainly see how ones understanding of work would improve with a good foundtion oin basic calculus, but I cannot see how knowledge of n dimensional calculus (something I am aquainted with) benefits you beyond the ability to calculate the work done on a particle moving in more than one dimension.

 

[complexPHILOSOPHY]

Tom,

You are misconstruing some of the points. No one said 'learn the bare minimum' and no one said 'tons of maths are useless'. Certainly, none of us only do the bare minimum, or we wouldn't be posting on physicsforums. I would also assume that your broad knowledge of calculus significantly helps you with calculus-based physics, so I am not sure what your point is. Learning tons of calculus to do calculus-based physics, obviously helps.

Perhaps you should look into string theory more, because when you do your PhD, its HIGHLY SPECIALIZED areas of string theory, which I don't believe have direct applications outside of academia. Again, I am NOT discouraging you from taking tons of maths and physics and to do tons of mathematically rigorous physics. I am simply warning you of String Theories lack of empirical support in lieu of it's ridiculous popularity.

 

[imastud]

the posts about beer pong may be some of the funniest that I have seen in a long time, being a freshmen myself, they hit home nice and well

yeah you should enjoy your intro beer pong class while it lasts because if your a science major the advanced classes will be way too much of a time commitment to take as electives. they require 5-6 night a week commitments and if you are doing A level work in them it probably means that not only your nights are being tied up, but you spend the morning/early-afternoons afterward in bed with a headache. in my experience this has been too much for science majors to handle, but business and poli-sci (not to mention the kids who major in beer pong) and other crap majors tend to be able to fit them into their schedule without too much detriment.

 

[Tom1992]

hmm I'm intrigued, how does your knowledge of n dimensional calculus help you understand work? I can certainly see how ones understanding of work would improve with a good foundtion oin basic calculus, but I cannot see how knowledge of n dimensional calculus (something I am aquainted with) benefits you beyond the ability to calculate the work done on a particle moving in more than one dimension.

1st year physics teaches work in only one dimension and assumes a point mass only, which is unrealistic, and after all physics is supposed to study the real world, right? why the restricted viewpoint of work? one and only one reason--the limited math used in 1st year physics.

kepler's law of equal areas teaches us the non-uniform speed of planetary motion, but do first year physics textbooks teach us why the law holds? physics is about "why", not just "what", right? again the reason they don't is because of the limited math being used. i can explain the physics of it in one sentence: planets move faster at greater curvatures, but you would have to know what a geodesic is. this is just an example of how much physics is being missed just because of the restriction caused by unlearned math.

another example: 1st year physics textbooks does not explain why fermat's principle of least time holds. knowing true physics is to also know why it is true. again, the reason for no explanation is because the calculus of variations is not taught at that point.

the more math you know, the better you will learn physics. so I'm going to maximize my mathematical toolbox in order to learn physics in the most appreciative way.

 

[imastud]

1st year physics teaches work in only one dimension and assumes a point mass only, which is unrealistic, and after all physics is supposed to study the real world, right? why the restricted viewpoint of work? one and only one reason--the limited math used in 1st year physics.

i think it has more to do with the fact that they don't want the students to get bogged down with computations. its not hard to go from 1 dimension to 3 dimensions or pointlike mass to ridgid body, but the problems become much more computationally-intensive and that takes time away from learning the concepts the 1st year course is looking to survey.

just too follow up on stuff said before too, in the math sequence from calc 1 to diff eq the profs know they are not only teaching math students but also physics, engineering, comp sci, etc... so the courses are tailored with more applications. as you go higher up the classes become much more proof based and abstract (some find that fun, I don't). not that taking them isn't useful, but its a lot less useful. i learned that this year taking complex analysis where we spend half the time verifying if a complex function is analytic and proving that the deritive of whatever doesn't exist rather than doing fun stuff like solving pde's of circuits and stuff.

 

[^_^physicist]

Posted by Tom1992:
physics is about "why", not just "what", right?

See and here is where you are wrong...physicists like to wonder why (at least in my experance); however, physicists don't deal with why on any real level. Physics deals with the "how" "what" and "when" questions. 'Why' is what the humanties deals with.

 

[Tom1992]

See and here is where you are wrong...physicists like to wonder why (at least in my experance); however, physicists don't deal with why on any real level. Physics deals with the "how" "what" and "when" questions. 'Why' is what the humanties deals with.

?

people wanted to know why planets move in elliptical orbits and it was Newton who solved the problem, right?

anyway, i feel that i know physics better if i know why the result is true instead of just knowing the result.

 

[imastud]

?

people wanted to know why planets move in elliptical orbits and it was Newton who solved the problem, right?

anyway, i feel that i know physics better if i know why the result is true instead of just knowing the result.

i think what physicist was referring too was the "why" question philosophers ask, like "why is the speed of light ~ 3*10^8 m/s?" or "why does the universe exist?" and other questions that can't be answered using science or any other method of human rationale that has been used before. physicists only answer questions that they can use science to answer.

 

[Tom1992]

but i never in this thread referred to that type of "why". i only referred to mathematical "why"s. and it is the "mathematical whys" that many physics students are missing out on because of the restricted math used in their classes. at least that's what i believe.

 

[tmc]

those are hows, not whys.

 

[Tom1992]

those are hows, not whys.

ok, the semantics put aside, the bottom line is that these extra math courses should be help me appreciate my physics studies more.

 

[Gott_ist_tot]

I have noticed that language comes into play in scientific research. It all depends on your field. I am doing research in high energy physics and have seen a need for french and japanese. Quite a few japanese institutions working with KEK, such as the BELLE collaboration, do write quite a few papers in english, since it is most logical to reach a large portion of the scientific community, but there are quite a few papers in japanese. Also, I am sure not all of the english translations are as good as they could be when you need information on some of their methods. If you ever wanted to work at CERN you may want to know French (and German too if possible). Even undergrads doing an REU at CERN are expected to know french.

I have not gone too far in mathematics but I have noticed that russian would be good to know when researching (and just keeping up) with topology.

I also feel that one who takes only science and math regrets it a bit later on. Richard Feynman did quite a lot to not take the humanities required at MIT but began to appreciate them later on. He later did art, music and learned Portuguese. This had a big impact on his life. He picked that language, if memory serves me right, because a girl he saw was taking it. It had no immediate benefit to his career. Richard Feynman's biographies are pretty good examples that you can surround yourself with all the science and math in the world but if you study some art or read some literature then it all might mean something. (I think that's from star trek.) :)

 

[imastud]

feynman only learned Portuguese so he could pick up chicks in brazil

 

[^_^physicist]

Another reason for learning a language, if you are going into mathematics at least, is that some graduate programs in math require competancy in either French, German, Greek, Latian, or Russian, because so much work does get done in these languages (at my school from what the math students have been telling me, from their talks to advisors, is to pick up Russian if you plan on doing anything with Geometry or Mechanics).

 

[Gott_ist_tot]

Edited to fix typo

I left the computer and came back so my post is from a conversation a few pages back.

As for knowing as much math as possible. I don't think anyone here is saying you should not study those subjects. What I did is I took humanities since I knew I was not as likely to study these on my own when I could do math (I'm a nerd like that) and I studied the math on my own. Believe me, knowing topology and differential geometry will come in handy. The problem with your list of math that one needs to know for string theory is it refers to a familiarity with that subject. You can get that from self study. Very few people would be experts in all of those fields and string theory. I don't think you could even keep up with all the advances in all of those fields. Your research will probably be a tiny bit better with all of that math, but your life would benefit significantly with some humanitites.

In the end it is you decision but I would really listen to some of their advice.

 

[CPL.Luke]

meh personally I like to study the humanities on my own rather tha in a class, 18 years of dinner conversation has taught me that they are a subject best treated in good company.

make friends with a couple philosophy majors their usually fun.

 

[tmc]

Another reason for learning a language, if you are going into mathematics at least, is that some graduate programs in math require competancy in either French, German, Greek, Latian, or Russian, because so much work does get done in these languages (at my school from what the math students have been telling me, from their talks to advisors, is to pick up Russian if you plan on doing anything with Geometry or Mechanics).

I'd like to know who told you that a lot of work gets published in latin...

 

[Gott_ist_tot]

Maybe some physicists really like to study 17th century physics. Principia or Corporum in gyrum anyone?

 

[^_^physicist]

Posted by tmc:
I'd like to know who told you that a lot of work gets published in latin..

If you are doing any form of study relating to mechanics or possibly math history (which is what a sub-set of mathematicians do study), knowing Latin or Greek is a necessity. Many of the texts that you are dealing with are in these languages.

Other times, just knowing these two languages makes it easy to pick up other languages as necessary for your work though journals.

In fact to get into the graduate mathematics program at my univeristy you must have competensy in any of those languages I stated in my eariler post.

As for Russian, French, and German...just the standard languages to know in the math community according to my math department when asked about it.

 

[verty]

but i never in this thread referred to that type of "why". i only referred to mathematical "why"s. and it is the "mathematical whys" that many physics students are missing out on because of the restricted math used in their classes. at least that's what i believe.

Yes, not the philosophical why but the scientific why. Perhaps philosophy is a distraction from the business of science, and perhaps people turn to philosophy as a result of the starkness of science, that we have a mystical urge for the grandiose. If you (Tom) lack such a frivolous urge, so much the better.

 

[^_^physicist]

Posted by Verty:
Yes, not the philosophical why but the scientific why. Perhaps philosophy is a distraction from the business of science, and perhaps people turn to philosophy as a result of the starkness of science, that we have a mystical urge for the grandiose. If you (Tom) lack such a frivolous urge, so much the better.

Ahh but you forget, what we practice is natural philosophy . Ever wonder why they call it a PhD a Doctor of Philosophy?

Moreso, philosophy is something everyone should have some experance in; it is not frivolous, it is merely a form to allow one to cope and question the universe around oneself. Science is a particular class of philosophy, in that it limits itself to that which can be observed and can be varified with multiple observations and tests.

Additionally philosophy puts into perspective the human "element" when developing new technologies. Ethics are something a scientist should understand.

Sorry to ramble, or sound preachy, its just something I think would add to this.

 

[verty]

I'm not calling philosophy frivolous, I'm calling an urge for the grandiose frivolous. I haven't ever looked it up but I would think that Doctor of Philosophy means someone who doctors with/by means of philosophy, someone who uses knowledge to make the world better.

 

[^_^physicist]

So long as that is cleared up.

Though, based on Tom1992's knowledge and what appears to be intellegance level, visualizations of the gradiose are something that he might have the potential to reach.

Granted it wastes time, but hey having a visualization of what you want from your work, even if it frivous to some extent, it is still worth having.

 

[verty]

Yes, but I worry that when people suppose that one should have a visualization or that one should consult philosophy that they want that person to have a particular purpose. Hearing that scientists should understand ethics, I worry that it is meant that scientists should understand ethics as *I* understand it.

Read like this, it becomes a moral imperative and I am against that, especially with someone young and potentially impressionable like Tom. I think the best we can do is to let him run his own ship.

 

[Schrodinger's Dog]

Ahh but you forget, what we practice is natural philosophy . Ever wonder why they call it a PhD a Doctor of Philosophy?

Moreso, philosophy is something everyone should have some experance in; it is not frivolous, it is merely a form to allow one to cope and question the universe around oneself. Science is a particular class of philosophy, in that it limits itself to that which can be observed and can be varified with multiple observations and tests.

Additionally philosophy puts into perspective the human "element" when developing new technologies. Ethics are something a scientist should understand.

Sorry to ramble, or sound preachy, its just something I think would add to this.

Actually it's mostly historical, the term philosophy originally was meant to indicate the broad range outside of Medicine, law and theology; since science wasn't actually a part of the language at the time. Whether we can consider science a natural philosophy or not is kind of beside the point. It's pretty much tradition.

 

[^_^physicist]

Posted by Schrodinger Dog:
Actually it's mostly historical, the term philosophy originally was meant to indicate the broad range outside of Medicine, law and theology; since science wasn't actually a part of the language at the time. Whether we can consider science a natural philosophy or not is kind of beside the point. It's pretty much tradition.

True, it is maintained primarily historical purposes; nevertheless, my point still holds because by the vague defination of philsosphy, the natural sciences still fit into there place. The natural sciences are just an outgrowth of philosophy with a distinct set of rules to indicate how it is different, from say ethics.

But we both agree on the roots and where the term comes from. (in my education a large degree of time in my humanties studies (which are required) are deticated to the development of the scientific professions).

 

[Stingray]

I'd forgotten to get back to this thread. Anyway, my main point was that some people who are starting out tend to have an impression that physicists use much more math than they really do. The reality is that very few theorists have a particularly strong mathematical background. It's possible to find "applications" for just about anything in any part of physics, but this hasn't been particularly useful in most cases. While learning more math is certainly helpful at the lower levels, it's not at all clear that it's worth it beyond a certain point. Saying "it can only help" is misleading. All of that time spent learning math is time taken away from learning physics. Again, I'm not saying to avoid math. I'm just trying to point out the "been there, done that" point of view. I've spent a good amount of time learning extra math on my own. Pretty much the only thing I've found useful beyond what I'm already supposed to know is distribution theory.

Anyway, some mathematical topics that are commonly used in certain fields of physics may take a very long time to get to in a standard math sequence. Hardly any physicists learn them that way, however. For that, there are several excellent books on the mathematics used in physics which are very good and essentially self-contained. These have more material than almost anyone will ever use outside of a few very specialized topics. Geroch, Nakahara, Frankel, Baez/Muniain, and Choquet-Bruhat/Dewitt-Morette are all good to read. Working through them is much more efficient than trying to take 10 math courses (there's a lot of overlap between those books).

 

[complexPHILOSOPHY]

What is the distinction between a 'mathematical physicist' who does theoretical physics and a 'theoretical physicist,' who does theoretical physics?

Does a mathematical physicist rely more on logically rigorous formal mathematics and mathematical intuition to derive theories whereas the theoretical physicist, interprets experiments and observations and then models the phenomena?

Are they colloquialisms for the same profession or is there a dichotomy?

 

[Stingray]

A mathematical physicist is usually a mathematician who studies problems inspired by physics. What they do is usually not actual physics in the way most people would see it. Sometimes people use the term to mean any theorist though.

 

[math_owen]

complex philo

What's up complex?

I have no clue what came before any of this. This is only a reply to the difference between a mathematical physicist and a theoretical physicist.

To begin, the difference can be subtle if you like, and in both depts math/ physics you'll find crossovers.

Straight to the point. A mathematical physicist (MP) would work on something the theoretical physicists (TP) already considered solved. The MP is more worried about showing how these new ground breaking ideas are mathematically solid, i.e. they worry about proofs and tying in this "new physics" with the mathematical foundations of it.

A quick, obvious example is Newton. Yeah, he was a god and did it all, fine. But, with his calculus, he had these little quarks, that were unexplainable. So back in the day, the rave of mathematical physics was figuring out the mathematical frame work of his calculus. Now we consider that analysis, and a part of a "pure" mathematical training, but once, it was mathematical physics. (Correct me if I'm wrong people)

I'm only an undergrad, so I can only pass on what little I know.

Now a TP, wouldn't care about "why" you can do this or that in math. He uses a more heuristic and approximating approach. What he cares about, is that strange unexplainable phenomenon in the labs that keeps popping up.

Then there's the grey area. Things like String Theory. My school is pretty good at it. But I know the mathematicians and the theoretical physicists work together a lot on it.

I'll give you the ultimate difference, it's the defining one. Ready?

A mathematician who studies mathematical physics has to teach math classes.

A theoretical physicist who knows a ton of math, has to teach physics classes.

And of course, there is always the option for a joint appointment.

Hope that helps.

Cheers