How Limited is the Impact of General Relativity in Theoretical Cosmology?

[magicfountain]

When is the first time a student of physics works with Einsteins field equation and does Friedmann cosmology?

 

[f95toli]

For most students that would be if they decide to do PhD student in cosmology.
There are Masters programs that cover GR, but they are not very common.

Note that GR is complettely unneccesary for the vast majority of physicists simply because there are few fields of modern physics where gravity plays a role at all, and when it does you can get away with Newtonian mechanics.
Hence, most will never study GR "properly" (I certainly never did).

 

[haushofer]

I did it in my Bachelor/undergraduate (third year) at the level of Carroll's notes and the book by d'Inverno, which is quite feasible I think.

 

[DrewD]

If you want GR you need to seek it out. Some schools offer it at undergrad level, but I don't think any require it. I have a professor who has never taken a GR course. He knows a fair amount about it because he's a bright guy, but he did his PhD in Quantum info which doesn't require any knowledge of GR.
Currently my school doesn't offer a PhD, but will starting Fall '13 (they have it planned out, but didn't finish in time to accept students this year). There is no plan to offer any GR courses.

 

[George Jones]

When is the first time a student of physics works with Einsteins field equation and does Friedmann cosmology?

I have Ph.D. in physics, but I never took any courses on GR or cosmology.

 

[bcrowell]

It's relatively recently that GR has started to be offered widely as an elective undergrad course. I think the most influential book is Hartle's Gravity, which dumped the traditional pedagogy of developing tensors and then deriving everything from the field equations.

My PhD program (at Yale) didn't require GR, but I took it. Some of my colleagues never took GR in grad school.

If the motivation for the OP's original question is that s/he wants to learn GR now, then I would just suggest simply going ahead. There are GR books at all levels, including books like Geroch's Relativity from A to B, which uses no math at all but is nevertheless very logically rigorous. Just pick a book that's way too easy and go ahead and read it. Keep going until you reach the point where self-study becomes too difficult or time-consuming, then quit and wait to take a formal course.

 

[GRstudent]

I began learning GR when I was 15.

 

[TheEtherWind]

It's a shame that, at least intro, GR isn't typically required at the undergrad level...

 

[soothsayer]

At my school (I go to a UC) you can take GR as an elective for physics/astro. It's not required. It's also got so many pre reqs that you probably wouldn't be able to take it until your senior year.

 

[bcrowell]

It's a shame that, at least intro, GR isn't typically required at the undergrad level...

One of the great things about majoring in physics is that the number of units of required courses is relatively small (compared to, e.g., engineering or music), so you can get a real liberal arts education. I'd hate to see that changed by throwing in more requirements.

 

[George Jones]

The June 2012 issue of Physics Today has an interesting article, "Teaching general relativity to undergraduates"

http://www.physicstoday.org/resource/1/phtoad/v65/i6/p41_s1

Click on the figures to expand them. Fig. 2 is quite interesting. I once taught a course that used Taylor and Wheeler's Exploring Black Holes as text, and that had only first-year physics and calculus as prerequisites.

 

[Doc Al]

I took a GR course as an undergrad. (A long, long time ago.) We used Adler, Bazin, & Schiffer. But long before that I read Lillian Lieber's delightful book which I found in my high school library.

 

[soothsayer]

One of the great things about majoring in physics is that the number of units of required courses is relatively small (compared to, e.g., engineering or music), so you can get a real liberal arts education. I'd hate to see that changed by throwing in more requirements.

Where did you major in physics? I have to take a fifth year! (granted, only part of it, but still.)

 

[bcrowell]

Where did you major in physics? I have to take a fifth year! (granted, only part of it, but still.)

Berkeley. I'm not saying it's an easy or low-unit major, but it does require far fewer units than engineering or music.

 

[mfb]

If you are lucky, you can find a course which covers the required mathematics, too - not in depth as a mathematical course would do, but enough to get the concepts of GR. In this case, the usual bachelor courses should be sufficient to follow.

Usually, it is not required, but it is one of the two fundamental theories of modern physics. It is my personal opinion, but I think without GR, you are missing something.

 

[alialice]

I studied GR for the first time at the third year of university, but it was an optional course for physicist. And at master level there is a second exam about GR.
It depends on what your university offers, or if you want to study it by your self, you can start after high school!

 

[GRstudent]

GR requires a lot of effort to fully grasp it. Those tensors are real headache and they have practically very few real-life applications. Had I not spent so much time doing GR I would have easily learned 1 year of college-level physics instead. Yet something always fascinates me to understand GR. I think that only at GR level you can really appreciate the hidden deep beauty of mathematical thought.

 

[vanhees71]

GRstudent, I've to contradict you vehemently :-).

GR is a pretty straight-forward subject, concerning the physics. It's just a classical field theory for gravity and thus doesn't cause too much headaches (compared to quantum theory, which is much harder to swallow).

Scalars, vectors, tensors, and the corresponding fields are applicable everywhere in physics and engineering, and thus are affecting our everyday life to a great extent.

Last but not least GR is simply beautyful!

 

[GRstudent]

^
If you are so comfortable with messy equations why don't you help me find the Einstein Tensor of Schwarzschild Interior metric? You help on this important issue would be much appreciated!

Math part of GR consists of all math: Calculus, Multivariable Calculus, Linear Algebra, Differential Equations, etc. What I mean what differential geometry which is used only in topology and GR.

 

[soothsayer]

Berkeley. I'm not saying it's an easy or low-unit major, but it does require far fewer units than engineering or music.

Santa Cruz. To be fair, I started on my physics requirements a little late, so I had to play a bit of catch-up, but my schedule was always packed with classes. I'm not sure how it compares to a lot of other majors though. I do know it is a highly regimented major, once you get in, it's basically a straight road as far as what classes you're taking when, and there's little chance for deviance outside of your elective choices (And there aren't many to choose from). Compared to, say, the psychology major, where I happen to know, at my school, you pretty much take classes willy-nilly. I do know a lot of physics majors who were able to do a minor (usually math, though I have no idea why they would have wanted to do that.)

 

[PeterDonis]

they have practically very few real-life applications.

I guess this depends on what you consider "real-life applications". A quick list:

* GR is essential in making GPS work;

* GR is essential in understanding cosmology;

* GR is essential in understanding neutron stars and black holes.

 

[GRstudent]

* GR is essential in making GPS work;

Special Relativity is used in GPS making. The speed of a satellite is ~4km/sec so it has some time dilation. What strange is that, when I challenge the applications of GR, people always defend by making GPS example.

* GR is essential in understanding cosmology;

* GR is essential in understanding neutron stars and black holes.

These skills are not so crucial for most engineers. I doubt that average Engineer needs geometry of neutron stars or black holes to do his job. GR is purely theoretical insight--no more than that.

 

[PeterDonis]

Special Relativity is used in GPS making.

So is GR. And SR is a subset of GR.

The speed of a satellite is ~4km/sec so it has some time dilation.

The GPS satellites are also orbiting at 4.2 Earth radii, which is high enough that gravitational time dilation has a significant effect. So both SR and GR are necessary to make GPS work. But, as above, since SR is just a subset of GR, this is really the same as saying that GR is necessary to make GPS work.

These skills are not so crucial for most engineers. I doubt that average Engineer needs geometry of neutron stars or black holes to do his job.

This is true, unless he's an engineer working on devices that are meant to observe these phenomena. But not everyone is an engineer. There are a lot of working scientists who deal with neutron stars and black holes, and cosmology.

GR is purely theoretical insight--no more than that.

I assume you mean "for most engineers". For people like those working scientists who deal with neutron stars and black holes, and cosmology, GR is required to explain observed data.

 

[GRstudent]

There are a lot of working scientists who deal with neutron stars and black holes, and cosmology.

I highly doubt that there are more neutron star and black hole physicists in the world than there are Engineers. I don't think that many students would do arduous work for relatively low salary.

 

[mfb]

While effects of GR are relevant for GPS, the system could work without knowledge of the theory, too: With classical mechanics, you could simply observe the frequency shift, and correct for it.

These skills are not so crucial for most engineers. I doubt that average Engineer needs geometry of neutron stars or black holes to do his job. GR is purely theoretical insight--no more than that.

Most engineers do not need any modern physics, classical mechanics is a good approximation in most applications.

 

[PeterDonis]

I highly doubt that there are more neutron star and black hole physicists in the world than there are Engineers.

I would certainly agree with that. But that doesn't mean the much smaller number of such physicists can't be working on "real world applications". Unless you are defining "real world applications" such that only engineers can work on them? That seems like quite a restrictive definition.

I don't think that many students would do arduous work for relatively low salary.

Grad students typically do "arduous work" for peanuts. When I was a grad student all I got, other than having tuition paid for (which was not insignificant, of course, but I never saw any of it), was a stipend for being a teaching assistant or research assistant, which was barely enough to pay for housing.

 

[PeterDonis]

While effects of GR are relevant for GPS, the system could work without knowledge of the theory, too: With classical mechanics, you could simply observe the frequency shift, and correct for it.

When GPS was first launched, this was exactly what was done; they ran the satellites for a while *without* turning on the additional oscillators that compensated for the frequency shift, because a number of non-scientists involved didn't really believe the scientists' prediction that there would *be* a frequency shift. Only after they had confirmed that the clocks aboard the satellites were in fact running faster than ground clocks, by exactly the amount predicted by GR, did they turn on the additional oscillators on the satellites that corrected their "clock rates" to match those of ground clocks.

In principle you are right, this could have been done without knowledge of GR. But in practice, what would have happened without knowledge of GR is that the satellites would have been launched with no way of compensating for the clock rate difference, and once that difference was observed, the whole thing would have had to be scrapped and re-done. So knowledge of GR certainly had a large practical effect in this case.

Most engineers do not need any modern physics, classical mechanics is a good approximation in most applications.

Quite true.

 

[GRstudent]

^
Yeah, I agree with you guys.

If we wish to discuss the need of GR we should start a new thread because I recall some guy saying to me not to go off topic ("hijack a thread"). I mean this thread is related to the timeline of learning GR so it has little to do with its importance.

 

[Nabeshin]

Usually, it is not required, but it is one of the two fundamental theories of modern physics. It is my personal opinion, but I think without GR, you are missing something.

This. Restricting the discussion to only physicists (i.e. not engineers), it seems ridiculous to have someone not learn ANY GR. With the pedagogy of Hartle, you can tackle the subject easily in 3rd year of undergraduate or earlier, with no more difficulty than an upper division classical mechanics course. So in terms of educational difficulty, there's really no barrier.

A degree in physics is not, in my opinion, a collection of real world job skills to be used in future employment. It's largely a theoretical endeavor, which can be evidenced pretty well by the development of thermodynamics from a physics perspective. So to have a physics degree without even having encountered one of the two fundamental pillars of modern physics...

 

[GRstudent]

there's really no barrier.

Tensors and Differential Geometry is the main obstacle to me (and to many other students as well, I am sure). The problem is that nowhere is given a clear (in normal simple language) and explanation of GR ( in particular, Einstein Field Equations). I as a beginner, can only see the a lot of complicated formulas which are not accompanied by conventional thinking. For example, Walter Lewin's lectures; when he talked about Mechanics he made me "see through equations"; not just stare at them as I do now; but to really understand the logic. I think we have this problem because GR as a college level class is highly undervalued.

 

[WannabeNewton]

Tensors and Differential Geometry is the main obstacle to me (and to many other students as well, I am sure). The problem is that nowhere is given a clear (in normal simple language) and explanation of GR ( in particular, Einstein Field Equations). I as a beginner, can only see the a lot of complicated formulas which are not accompanied by conventional thinking. For example, Walter Lewin's lectures; when he talked about Mechanics he made me "see through equations"; not just stare at them as I do now; but to really understand the logic.

Well you're also comparing, at the level of Lewin, a theory based on a very simple set of DEs to the EFEs which are non - linear and MUCH more complicated in terms of the entities involved. Things aren't going to be as "visual" per say. But GR does have a very clear and incredibly elegant explanation with its formulation using riemannian manifolds. Many textbooks explain it well; Hartle's text was mentioned above and my personal favorite, Carroll's text.

 

[WannabeNewton]

This. Restricting the discussion to only physicists (i.e. not engineers), it seems ridiculous to have someone not learn ANY GR. With the pedagogy of Hartle, you can tackle the subject easily in 3rd year of undergraduate or earlier, with no more difficulty than an upper division classical mechanics course. So in terms of educational difficulty, there's really no barrier.

Funny you should say that because I have seen many unis where a very good amount of general relativity is added on to the intermediate classical mechanics classes (the Taylor level ones).

 

[Nabeshin]

Well you're also comparing, at the level of Lewin, a theory based on a very simple set of DEs to the EFEs which are non - linear and MUCH more complicated in terms of the entities involved. Things aren't going to be as "visual" per say. But GR does have a very clear and incredibly elegant explanation with its formulation using riemannian manifolds. Many textbooks explain it well; Hartle's text was mentioned above and my personal favorite, Carroll's text.

I agree, Hartle's motivation seems pretty good to me. After all, he takes a 'physics first' approach and although it takes 22 (or 24, I can't remember) chapters to get to the EFE, once you do get there I feel like it's very well, perhaps overmotivated.

Also the tensor issue is something a student shouldn't really have -- they should encounter these objects already in upper division E&M and classical mechanics courses, although perhaps not quite so many of them. It's perhaps frustrating algebraically, similar to keeping track of minus signs, but really shouldn't impede the understanding very much.

 

[Nabeshin]

Funny you should say that because I have seen many unis where a very good amount of general relativity is added on to the intermediate classical mechanics classes (the Taylor level ones).

Really? Is this just in the sense of adding an extra term from the post-Newtonian expansion into the Lagrangian from the Kepler problem? Or calculus of variation on the Einstein-Hilbert action? I'm curious!

 

[WannabeNewton]

Also the tensor issue is something a student shouldn't really have -- they should encounter these objects already in upper division E&M and classical mechanics courses, although perhaps not quite so many of them. It's perhaps frustrating algebraically, similar to keeping track of minus signs, but really shouldn't impede the understanding very much.

Indeed and even if they haven't had that exposure, going back to Hartle's text, there are copious amounts of worked examples as well as problems to get the person acquainted with the necessary algebra and calculus of tensors. From some people I know at cornell and carnegie mellon I know there are one semester courses on GR that use the very same text. I'm sure other places do as well for undergraduate courses.

 

[WannabeNewton]

Really? Is this just in the sense of adding an extra term from the post-Newtonian expansion into the Lagrangian from the Kepler problem? Or calculus of variation on the Einstein-Hilbert action? I'm curious!

From what I've seen they don't go into the Einstein lagrangian; its more like, after the general curriculum is done you get an intro to GR like you would any other undergraduate GR class but probably more brief (this is for the two semester intermediate mech courses at least those are the ones I've seen this done).

 

[George Jones]

From what I've seen they don't go into the Einstein lagrangian; its more like, after the general curriculum is done you get an intro to GR like you would any other undergraduate GR class but probably more brief (this is for the two semester intermediate mech courses at least those are the ones I've seen this done).

I don't see how this is possible. Even one semester is not enough time to do anything more than a brief introduction to GR. From a thread comparing quantum mechanics and GR:

In my opinion, students could find physics courses in general relativity easier than courses in quantum mechanics. I think that students become more familiar with quantum mechanics because they spend more time studying it.

For example, when I was a student, I:

saw bits of special relativity stuck here and there into a few courses;

did not have the opportunity to take any lecture courses in general relativity;

was required to take three semesters of quantum mechanics as an undergrad and two semesters of advanced quantum mechanics as a grad student;

was required to take two semesters of linear algebra, which gives the flavour of much of the mathematics of quantum mechanics;

was not required to take any maths courses that give the flavour of the mathematics used in general relativity.

Because of the importance and widespread applicability of quantum mechanics, my programme offered much more opportunity to learn quantum mechanics than to learn relativity.

If physics students spent as much time studying general relativity and its mathematical background (say 4 or 5 semesters) as they spend studying quantum mechanics and its mathematical background, then general relativity would be understood by possibly millions of people. I understand why students spend much less time studying relativity than they spend studying quantum theory, and I am not necessarily saying that students should spend more time studying relativity (see the post above by Haelfix), but I do think that this time difference is a big part of the reason that general relativity still has a bit of a reputation.

Fortunately, there are many more good technical books on general relativity (pedagogical, advanced, physical, mathematical, etc.) available now than were available 25 years ago.

 

[WannabeNewton]

I don't see how this is possible. Even one semester is not enough time to do anything more than a brief introduction to GR. From a thread comparing quantum mechanics and GR:

It isn't any more than a brief intro to GR indeed. It isn't a substitute for an actual GR class, I was just agreeing with Nabeshin's comment that the Hartle level undergrad GR class shouldn't be much harder than the intermediate mechanics class and that it is even introduced in such courses.

 

[twofish-quant]

* GR is essential in making GPS work;

* GR is essential in understanding cosmology;

However, the amount of GR that you need to understand cosmology is pretty minimal. You need a tiny bit of GR to derive the Friedman equations and maybe a little more to derive perturbation, but most people just use the "cookbook equations."

* GR is essential in understanding neutron stars and black holes.

It's actually not. For most astrophysical work in black holes and neutron stars, you use "cookbook" equations. And even sometimes that isn't necessary. For most neutron stars computations, you don't need or want to use GR, because that unnecessarily complicates the calculations and you miss the things you really are interested in. You can show that the impact of GR on neutron stars is minimal, and once you run your calculations using Newtonian gravity.

The reason that GR isn't taught very much in comparison to QM is that for all but a few specialist problems, it's not that necessary, and you can get by with either ignoring it, or having a specialist give you "cookbook" equations.

 

[twofish-quant]

For people like those working scientists who deal with neutron stars and black holes, and cosmology, GR is required to explain observed data.

In most situations, it's not. If we had very good measurements of black holes and neutron stars then you need GR. However, with some exceptions (i.e. binary pulsars), the black hole, neutron star, or cosmology data isn't good enough for GR to matter, and there are about a dozen things that matter more than GR.

For my Ph.D. supernova code, I had a GR module which I used to confirm that GR didn't make a difference. Once I confirmed that, then I ran everything else using Newtonian gravity, because it was a waste of CPU cycles which could be used to calculate something else.

 

[romsofia]

Wow, I'm surprised that people didn't take GR. You'd think that people would want to learn gravity to the degree that they learn electromagnetism, as both are introduced in introductory course (well, one is a full semester, while one is probably only a chapter :P).

As others have said, if you want to study GR, go with Carroll's text.

Good luck!

 

[f95toli]

Wow, I'm surprised that people didn't take GR. You'd think that people would want to learn gravity to the degree that they learn electromagnetism

It not a question about what you want to know . It is what you need to know. A good grasp of EM is absolutely essential to every working physicist, simply because EM is used in almost every field of physics. The same can not be said of GR.

Remember that something like 80% of alll physicists work in solid-state physics or one of its subfields; and that the vast majority are experimentalists. Theoretical cosmology is a tiny field.

 

[lsaldana]

I also recommend Hartle as a starting point in learning GR; that is if you're an undergrad or wish to start learning the theory without learning the full-fledged diff geo behind it first. I thought it was a great book, very intuitive and easy to follow. Personally, I took a GR course as a junior in college and then a Cosmology course as a senior. I believe this is just the right time to start. I plan to take further units in grad school. GR is a beautiful theory and differential geometry alone makes it quite interesting. If you have time though, I recommend learning some diff geo first. It is also quite a beautiful field of mathematics.

 

[mfb]

It not a question about what you want to know . It is what you need to know. A good grasp of EM is absolutely essential to every working physicist, simply because EM is used in almost every field of physics. The same can not be said of GR.

This might be true for the concepts of electromagnetism, but knowledge is not the main goal of a degree in physics. You learn how to work in a scientific context, you learn how to learn new things, and how to solve problems. Those things are important. The science you need directly for work is so special that you have to learn it separately anyway.

Concrete example: Which knowledge do you need for a master thesis in experimental particle physics at the LHC? You should know which particles you study, and the relevant decay channels - the basic part (which you learn in courses) can be learned in 10 minutes, a feeling for those things needs practice. You need some basic concepts of special relativity, but probably not in calculations. You need an idea how your particles (or their decay products) behave in the detector - this is very specific, and probably not part of usual courses.

In principle you are right, this could have been done without knowledge of GR. But in practice, what would have happened without knowledge of GR is that the satellites would have been launched with no way of compensating for the clock rate difference, and once that difference was observed, the whole thing would have had to be scrapped and re-done. So knowledge of GR certainly had a large practical effect in this case.

Fix the receivers, if you cannot fix the satellites?

 

[PeterDonis]

Fix the receivers, if you cannot fix the satellites?

In principle it would be possible to apply the corrections in the receivers (although that would have its own problems--millions of copies of the algorithm to convert GPS satellite time to UTC time, and many more opportunities for receiver makers to screw something up). But the real problem is that, in this alternate universe where nobody knows about GR, even *after* the frequency shift is observed, nobody has a theory to explain it, so nobody knows how it behaves. It's not as though people would instantly be able to figure out the correct GR equation for the shift just by observing it, if GR as a theory was unknown.

 

[GRstudent]

Can we say that Hartle is soft of "Walter Lewin" in GR?

 

[twofish-quant]

Remember that something like 80% of alll physicists work in solid-state physics or one of its subfields; and that the vast majority are experimentalists. Theoretical cosmology is a tiny field.

And the use of GR in theoretical cosmology is surprisingly limited. Someone works out the equations, and the rest is cookbook, and the symmetry conditions of the universe vastly reduces the complexity of the equations.

There are people that specialize on applying GR to cosmology, but that's a small subfield of a small subfield. What most people who are GR specialists do is to try to reduce the equations so that "mere mortals" can use it. You have people writing pages and pages of tensor equations and the punchline is that under conditions X, Y, and Z, you probably can get away with just using Newtonian physics.