Why are there so few General Relativity courses?

[hitmeoff]

Why is it that colleges offer very few courses in General Relativity at the upper div or grad level?

Seems like 2 quarter to year long sequences are always offered for Classical Mechanics, E/M and Quantum, but only 1 or so courses on G.R.

Is G.R. treated as a topic in Classical mechanics and special relativity covered in Q.M. courses?

 

[twofish-quant]

Usefulness. In most areas of physics, you can model the system without using GR, or with GR as a correction, but it's pretty much impossible to do anything even as a rough approximation without quantum.

 

[greeezy]

Also the mathematical background required for GR is quite specialized and most physics programs do not go too in depth into the mathematics required for GR outside of GR courses. The course would not have much interesting content since the majority of the course would be learning the basic mathematic mechanisms used rather than interesting GR stuff.

There are some formulations of basic GR that is done with nothing more than trig an a bit of calculus. There is a book by Wheeler which does this; i feel it is perfect for undergraduate students who want to get as much out of GR as they can without spending the entire quarter learning a years worth of tensor analysis.

 

[f95toli]

Just to add to what twofish-quant has already said. GR might be interesting but it is completely useless to 95% of all physicists (as opposed to SR which IS used and is usually covered in e.g courses mechanics).
Quite a few student take an introductory course in GR just for fun, but unless you do a PhD specializing in e.g cosmology it is unlikely that you will ever learn GR "properly".

 

[Andy Resnick]

I disagree with the above responses. GR (or continuum mechanics in general) should indeed be more frequently taught. Unfortunately, continuum mechanics is (unfairly) given over to engineering, and GR is a nonlinear theory. The mathematics of differential geometry is enormously applicable, and there really is no excuse for physicists not knowing it.

 

[George Jones]

Also the mathematical background required for GR is quite specialized and most physics programs do not go too in depth into the mathematics required for GR outside of GR courses. The course would not have much interesting content since the majority of the course would be learning the basic mathematic mechanisms used rather than interesting GR stuff.

There are some formulations of basic GR that is done with nothing more than trig an a bit of calculus. There is a book by Wheeler which does this;

Exploring Black Holes by Taylor and wheeler

i feel it is perfect for undergraduate students who want to get as much out of GR as they can without spending the entire quarter learning a years worth of tensor analysis.

At a slighter higher level, but still at an undergraduate level (prerequisites: second-year calculus; special relativity; elementary Lagrangian mechanics) there is Gravity: An Introduction to General Relativity by James Hartle. This book waits until until page 427 to start its treatment of tensors. Look at what is covered before this!

http://www.pearsonhighered.com/educ...nsteins-General-Relativity/9780805386622.page

Unfortunately, the table of contents given at this link does not list the individual sections of chapters.

 

[mal4mac]

This really highlights what physics education is about -- usefulness to the military-industrial complex rather than cultural education of the student. Anyone who has read Greene or Hawking or Einstein's popular works knows how important GR is, which makes it a real shame that students can't easily get to study GR up to the level of, say, understanding Einstein's serious papers. I took an MSc in astronomy and even that didn't teach GR! After the 'powers that be' tried to force me to do some drudge project, I insisted on doing something involving GR. I was encouraged out of the field soon after my MSc :) But at least I got somewhere near the intellectual frontier of physics. So, if you *really* want to learn the nuts and bolts of GR, see if you can do a project in GR and learn it while doing the project - just realize it might not help your physics career. GR isn't any help in building new weapons or the latest hi def TV, so there aren't many jobs in GR.

 

[LithiumHelios]

It's probably worth noting that many of the higher level courses offered in university will bear a strong resemblance to the research interests of the department. If the department is strong in condensed matter, instrumentation and solid state would you really expect a high level of expertise in general relativity?

Many institutions with strong research interests in general relativity, gravitational physics and areas of astrophysics will often have courses running for advaned undergraduate and postgraduate students.

Saying that it seems fairly typical for an undergraduate to have studied GR up to the level of Hartle/Schutz by the end of their degree in the UK.

Much like f95toli alluded to.

 

[Andy Resnick]

And just to add: the basic physics of curved surfaces can be taught in an introductory physics course. We all have seen maps, and we all live on a curved surface. Even a non-science major can understand what happens if two people, separated in longitude, both head north (or south).

 

[twofish-quant]

The mathematics of differential geometry is enormously applicable, and there really is no excuse for physicists not knowing it.

Agree. I think the problem here is that if you insert a GR course, what do you take out? Also I don't think that GR or differential geometry is inherently harder than QM. The way that it is taught normally requires a large amount of math knowledge, but it took a lot of effort to get QM teachable to undergraduates.

 

[twofish-quant]

This really highlights what physics education is about -- usefulness to the military-industrial complex rather than cultural education of the student.

True. For that matter, universities exist more to churn out worker bees for corporations than to impart cultural education.

Not to say it's a bad thing. If it weren't for the military-industrial-corporate complex, there wouldn't be funding for physics, and it would be likely some topic that only the idle rich can study. If a student wants to be culturally educated, money from the military-industrial-corporate complex will let them do it, but it requires some amount of effort on the part of the student.

 

[f95toli]

This really highlights what physics education is about -- usefulness to the military-industrial complex rather than cultural education of the student. Anyone who has read Greene or Hawking or Einstein's popular works knows how important GR is, which makes it a real shame that students can't easily get to study GR up to the level of, say, understanding Einstein's serious papers.

That is partly true. The "problem" is of course is that if you ask the average tax payer (if you can find one that has some interest in science) if he/she thinks what Hawking&co are doing is interesting the answer will probably be yes. However, you should also ask the same taxpayer how much of his/her money should go to research (and training student) in quantum gravity etc, and how much should go to research that benefits society more directly (financially, finding cures for diseases etc)..

Also, remember that the vast majority of all physicists work in solid-state physics or related areas where GR is simply not relevant (I don't know what the 2nd biggest field on physics is, probably optics?). The kind of theoretical physics Hawking, Green and the other are working on is a tiny, tiny field.

The only time I ever come across "real" problems that has anything to do with GR is when I listen to talks by people who work on clocks (uncertainty in the gravitational potential is starting to to be noticeable in good clocks) and/or satellite based positioning systems. I can't think of any other "real world" applications.

 

[cristo]

However, you should also ask the same taxpayer how much of his/her money should go to research (and training student) in quantum gravity etc, and how much should go to research that benefits society more directly (financially, finding cures for diseases etc)..

But, fortunately, the 'average tax payer' does not get to make these decisions, otherwise we would have no government funded research in any of the sciences that cannot be immediately applied to something the 'average tax payer' deems necessary.

 

[Shackleford]

I want to learn physics for the sake of physics, certainly not to just build something. I want to learn the "frontier," as someone put it. To me that is absolutely thrilling to be on the threshold of knowledge. How the military-industrial-corporate complex operates it's a bit counterproductive. The focus by and large is on science strictly pertinent to application and such. However, what paved the way is the breakthrough theoretical physics. Look what became possible because of QM, etc.

 

[Andy Resnick]

Agree. I think the problem here is that if you insert a GR course, what do you take out? <snip>

I assert the Physics curriculum is ready for an overhaul. The material addressed in nearly all introductory physics textbooks was essentially written in the early '60s. The 'canonical' physics curriculum was set even earlier, in the 40's- 50's. When were all the 'standard' texts first written? Goldstein was 1950. Jackson was 1962. Halliday and Resnick was 1960.

Surely, there have been a few changes in our understanding of Physics between then and now- never mind the stupefying range of applications that now exist.

 

[Shackleford]

I assert the Physics curriculum is ready for an overhaul. The material addressed in nearly all introductory physics textbooks was essentially written in the early '60s. The 'canonical' physics curriculum was set even earlier, in the 40's- 50's. When were all the 'standard' texts first written? Goldstein was 1950. Jackson was 1962. Halliday and Resnick was 1960.

Surely, there have been a few changes in our understanding of Physics between then and now- never mind the stupefying range of applications that now exist.

Don't you have to start at the basics, though, and the "everyday" Newtonian physics? It seems the curriculum is logically progressive.

 

[mordechai9]

I think it's a really good question and I've noticed the same thing. I tend to agree with the viewpoint that the curriculum is old, outdated and that relativity should be taught more, or offered more. I know at Texas they only offered undergrad relativity like once in the five years that I was there.

The complaint that relativity isn't as commonly used is probably valid. Also, the complaint that the mathematics may be too sophisticated may also have some validity. But this is really an issue with the educational structure. Mathematics and physics should be much more integrated in undergrad hard science curriculums (like engineering, physics, astronomy, computer science, and so on.) That's pretty much how it is already, only informally, or people wind up double majoring when they realize for themselves how kind of ridiculous it is. Formal mathematics shouldn't be the obstacle, because if that was truly considered the obstacle, then really we wouldn't learn anything of worth in undergraduate.

 

[Nabeshin]

With a textbook like Hartle (the one George Jones mentions), the complaint that the mathematics of GR is too complicated is pretty much baseless.

 

[George Jones]

When I was a student, my school didn't have a course in general relativity. I have never taken a course in general relativity.

 

[hitmeoff]

True. For that matter, universities exist more to churn out worker bees for corporations than to impart cultural education.

Not to say it's a bad thing. If it weren't for the military-industrial-corporate complex, there wouldn't be funding for physics, and it would be likely some topic that only the idle rich can study. If a student wants to be culturally educated, money from the military-industrial-corporate complex will let them do it, but it requires some amount of effort on the part of the student.

I guess there's where my issue lies. Although I'd eventually like to go into research, I am not really interested in joining the private sector outside of academia. Id like to be more on the theoretical side than the experimental side, even within an academic environment.

I guess what I'm trying to say is that I's like to become a professional student :D

 

[Flat]

Why is it that colleges offer very few courses in General Relativity at the upper div or grad level?

Seems like 2 quarter to year long sequences are always offered for Classical Mechanics, E/M and Quantum, but only 1 or so courses on G.R.

Is G.R. treated as a topic in Classical mechanics and special relativity covered in Q.M. courses?

At my school, there is a two quarter GR series offered by the math department.

I just happened to stubble upon it the other day. It seems to only be offered every few years.

 

[Andy Resnick]

Don't you have to start at the basics, though, and the "everyday" Newtonian physics? It seems the curriculum is logically progressive.

Of course the curriculum seems logically progressive; the curriculum was not created by dolts. That, and it is what you are familiar with.

Here's another example. I have 6 different introductory physics textbooks: 2 versions of Halliday and resnick, Fishbane etc., Giancoli, Serway, and Hecht. These cover calculus-based and algebra based approaches, are designed for physics/science majors (or not)... a wide variety of texts.

Even though these books were written by different people at different times, and the topics are all presented in *exactly* the same order! For example, "energy" is *always* presented in chapter 5, 6, or 7, right after Newton's laws and right before momentum. Also, in every book, translational motion is first discussed, then a side track to energy/momentum, and then back to motion, except it's rotational this time.

Why is this? Contrast the table of contents in one of those books with the Feynman lectures, also written in the early 1960's. A *very* different ordering occurs. So no, there is not one single allowed progression of topics.

The way electromagnetism is developed is also archaic. Why is the circulation of the electric field called the "EMF" (which is explained as some warped form of voltage) while the circulation of the magnetic field left as B*dl? Why are the electric fields and magnetic fields treated as distinct, independent entities?

And I don't think it's got anything to do with 'mathematical sophistication'- remember, I am comparing books written using both calculus and algebra. They present the same conceptual material.

 

[f95toli]

But, fortunately, the 'average tax payer' does not get to make these decisions, otherwise we would have no government funded research in any of the sciences that cannot be immediately applied to something the 'average tax payer' deems necessary.

Not directly no, but the overarching goals of the various funding agencies ARE ultimately controlled to politicians and those politicians are elected by taxpayers. At least in theory that means that the opinions of those politicans at least to some extent reflects the opinons of the electorate.

Id like to be more on the theoretical side than the experimental side, even within an academic environment.

Which is fine. But again, even if you end up working as a theoritician (which is already a minority) in academia you will most likely be working on problems in e.g solid state physics or something similar simply because that is where the jobs are. There simply aren't that many positions available in the few fields where GR is relevant. Remember that you can't freely choose the topic of your research (unless you happen to be famous), and at some point you need someone to approve your grant application meaning you have to be able to persuade people that the research you are doing is worth spending money on.

This in turn means that it would frankly be irresponsible for universities to put too much focus on GR, it makes sense to prioritize subjects that are more relevant to what the student are likely to be doing AFTER they graduate.

I work as a physicist because I enjoy it, but I am always aware that the people who pay me do not care whether or not I am having fun. What they are interested in is if the research I am involved in might one day lead to applications in areas they deem important (which at the moment seems to be security).