# General Relativity in the Undergraduate Physics Curriculum

1. Jun 14, 2005

### ZapperZ

Staff Emeritus
This is an interesting paper. In arguing on why GR can be a part of an undergraduate curriculum via a "physics first" approach, James Hartle has made a rather "understandable" description of GR. I think this might be a terrific introduction to GR to a lot of physics students, whether they intend to go into this area or not.

http://arxiv.org/abs/gr-qc/0506075

Zz.

2. Jun 14, 2005

### robphy

Last edited by a moderator: May 2, 2017
3. Jun 14, 2005

### James R

Sounds like a good approach to me. Many undergraduate students are interested in general relativity. The main problem is their lack of mathematical background.

A "physics first" approach skirts around that problem, while giving students a bit of a feel for the subject.

4. Jun 14, 2005

### neurocomp2003

my GR teacher was decent as an undergrad...i learned more from the problmes he gave...I think they need to strengthen the programming side.

5. Jun 15, 2005

### ohwilleke

I agree with the premise of the article. Mastering differential geometry and tensor mathematics is a non-trivial exercise, yet the vast majority of the epxeriment and observational (and even theoretical) work in the field pretty much limits itself to a handful of greatly simplified cases where the full mathematical suite of tools necessary fully follow GR are not required.

6. Jun 19, 2005

### pervect

Staff Emeritus
I gather Hartle has a textbook he wrote using this approach. I was hoping that it would cover the topic of accelerated observers, but nearly as I can tell it does not conver this topic. This is based on a review where the table of contents is pasted, the "peek into book" function isn't implemented for the book I looked at :-(.

I was looking at some of the other introduction to relativity books via Amazon, and they don't seem to cover the accelerated observer either! (Schutz, Rindler).

Is there anyone who has an introductory level book that does cover this important topic? Or is the treatment in "Gravitation" the simplest one avaliable? (it's a nice treatment, but it does use tensor notation). It seems like the topic of the accelerated observer has come up a lot recently (aside from several recent posts to the relativity forum, it's popped up again in the college homework forum).

7. Jun 19, 2005

### robphy

Try
Leslie Marder, Time and the space-traveller
http://www.worldcatlibraries.org/wcpa/top3mset/36df9466cefce179.html
and
James J. Callahan, The Geometry of Spacetime
https://www.amazon.com/exec/obidos/tg/detail/-/0387986413/104-0842951-1121523?v=glance
http://www.worldcatlibraries.org/wcpa/top3mset/5d5c8379d3e93584a19afeb4da09e526.html

In addition, these may be useful (although I haven't looked at these in detail yet)
http://www.vallis.org/research/res_foundations.html
M. Vallisneri, Relativity and Acceleration, thesis, doctorate in physics (University of Parma, Italy, 2000), http://www.vallis.org/publications/tesidott.pdf
Massimo Pauri, Michele Vallisneri,
Marzke-Wheeler coordinates for accelerated observers in special relativity
http://xxx.arxiv.org/abs/gr-qc/0006095

Last edited by a moderator: May 2, 2017
8. Jun 19, 2005

### pmb_phy

There are several text books out there on this topic. One is called Gravity from the Ground up," by Schutz. Another one is Feyman who connects gravity to acceration. Peacock also includes this in a recent article. There are many more that I mentioned that I have been guided to. Someday I'll get around to that point but is rather tricky,

Pete

9. Jun 20, 2005

### CarlB

I'm very much in favor of teaching GR at the undergraduate level. Heck, I think it would be better if there was more concentration on the practical uses of the various black hole metrics at the graduate level.

Carl

10. Jun 21, 2005

### pmb_phy

I'm sure that you're students would enjoy learning how the knowledge of relativity alowed physics to design the GPS system/

Pete

11. Jun 22, 2005

### metrictensor

I see no reason why GR can't be introduced in the undergrad curriculum. I am reading a very good book that is a mix of a popular and mathematical treatment of GR. Relativity Theory by Amos Harpaz. Very good on the conceptual stuff although it does leave some "examples" unjustified or at least hastly so. But it is the only book I have read where the ideas begin to make sense while not being watered down to the popular level. Popular books are useless anyway if you are serious. In many cases after I understand something as it should the impression I got from the popular books was wrong.

For example, is spacetime really curved in the same way as a road is? I think a better explanation is that the equations of motion are constrained in such a way. To think there is something actually there that is being bent seems wrong.

12. Jun 22, 2005

### pervect

Staff Emeritus
In what way is a road curved? This is a vague enough statement that I'm not sure what you mean by it.

GR has an important entity called the "Riemann curvature tensor" which is nonzero (has nonzero elements) near large masses. This tensor measures something that is called "intrinsic curvature".

http://mathworld.wolfram.com/IntrinsicCurvature.html

The 2-dimensional version of this tensor has the property that the surface of a sphere is curved (has non-zero components in the tensor) while the surface of a plane is flat.

The tensor doesn't apply to a line, you need at least 2 dimensions to have intrinsic curvature as per the quote.

13. Jun 22, 2005

### metrictensor

It is very clear. Curvature is a measure of somethings deviation from flat space.

I understand the math but you are making the assumption that the Riemann tensor is valid. I am interested in the idea of whether spacetime being curved is a model or there is actually something like a road or train tracks that is curved.

If we look at the earth orbiting the sun we can model it as two balanced forces, i.e. the centripetal and centrefugal. We can also look at it as moving in such a way because there are constraints on the equations of motion.

14. Jun 22, 2005

### ZapperZ

Staff Emeritus
Er... hang on a minute. You see nothing wrong with saying that?

If you have "two balanced forces", then what is causing the net central acceleration of the orbiting earth around the sun? Or are you also disputing Newton's First Law?

Zz.

15. Jun 22, 2005

### metrictensor

Maybe that wasn't a good example but that is all it was. Consider a wire loop with bead on it. The bead is constrained to moving only in a circle no matter what forces are acting on the bead. We want to look at the motion of the bead and determine the forces acting on it.

The only force that affects the bead's motion is tangent to the circle, i.ae. it pushed the bead around the circle. Any force acting away from the center of the bead will be balanced by a reactionary force supplied by the bead and acting towards the center.

Now we can look at this in two ways. First, the motion of the bead is constrained by the loop and the only force acting on it is the one that is tangent to the circle. We could alternatively say that there are 3 forces acting on the bead, the one above and an action and reaction force normal to the surface of the loop. Since these two forces are an action-reaction pair they will always be equal and opposite and therefore are independent of the mass of the object.

16. Jun 22, 2005

### ZapperZ

Staff Emeritus
The bead example is even worse, because the bead is confined to move in a circle NO MATTER what the nature and magnitude of the force are. I don't need a central force to have the bead move in a circular motion.

However, this is NOT the same as "earth orbiting the sun" that you brought up. There are no "balanced forces" here. There's only ONE net central force that is responsible for the observed motion of earth. There is no "wire" to constrain the motion.

Zz.

17. Jun 22, 2005

### pmb_phy

If we're talking about spacetime curvature then you've come to the wrong conclusion. If it was I who came to the conclusion then I blame it on the meds I'm on. :rofl:

To give an answer which might give you a better visual understanding think of the three models of the universe. There the is open universe, closed universe and the flat universe. In this example the "flat" does not refer to the spacetime, it referres to spatial flatness. So here we have an example of a spatially flat universe whose spacetime is curved.

Pete

18. Jun 22, 2005

### metrictensor

The point is that you can look at the problem in two ways. Either a constraint on the motion of the object caused by the bead or due to the balance of two forces.

The whole point of GR is that there is a wire. That Newton's explanation does not hold up to the principles of relativity.

19. Jun 22, 2005

### metrictensor

I am talking about curvature and how it is defined.

20. Jun 22, 2005

### ZapperZ

Staff Emeritus
No you can't. Those two are not the same. I have explained why they are not the same.

In plane polar coordinates, if I apply an $$F_{\theta}$$ to your bead, the bead will simply move faster but keeps the identical path. If I do that to the earth, the trajectory will change, and can even change severely. So how can you think these two are the same?

Secondly, look at how you would solve this problem using lagrangian mechanics. Where and what exactly is the nature of the "constraint" here both BOTH situations. You will see that they are clearly not identical.

Zz.