Midterm information

The midterm is Thursday, Feb. 13.  
Closed book. 
One 3"x5" note card. 
Bring a _law_ school blue book. 
Bring a calculator. 

The note card should be way more than enough. There are only a few
equations worth writing down. And there is only one numerical constant,
which you should know now and for the rest of your life.

Our goal has been to understand the relation between physics and
geometry in special relativity. You should know this very well. (The
part about general relativity and gravity is harder, and I comment on
that below.)

The exam will cover R1-R10 and app. B, the handout by Dr. Harris called
General Relativity and Cosmology, and the document on the website called
Four Vector Notation and the Metric. In addition, I will expect you to
understand just a little more about the metric for cases more general
than flat Minkowski spacetime. Namely, I expect you to understand that
the metric equation is the relationship between coordinate differences
and the invariant infinitesimal spacetime interval. I am talking about
the first equation on page two of the document Gravity and Geometry:
ds^2 = g_{mu,nu} dx^mu dx^nu. It is the metric that goes into that
equation to give the relation.  This is true whether it is flat
Minkowski spacetime or the curved spacetime of gravity. The general
relation holds, but the form of the metric changes. This is spelled out
in the other documents, but I do not expect that you can get a handle on
all that. In particular, you do not have the tools to calculate what the
metric is in different circumstances. Here is the one thing that I
expect you to be able to do: If I give you a specific metric and
coordinate changes, I expect that you can put it into the relation above
to get the spacetime interval. However, this will be only a small part
of the exam. Do not spend a lot of time on it until you have all the
other things wired. If you know R1-R10, and the Principle of
Equivalence, you will do fine.

Except for some of the problems on the conservation of 4-momentum, most
of the problems we have done require more understanding than
calculation.  In addition to the ability to calculate, you need to
understand the concepts and be able to explain them in writing.

The Chapter Overviews are useful. 
Here is my list of important stuff:

Principle of Relativity and the speed of light
Time 
   coordinate time
   proper time
   spacetime interval
Metric equation and the metric
Lorentz transformation
   Lorentz contraction
   time dilation
Causal structure of spacetime
Velocity transformation
Four momentum
   definition
   interpretation
   conservation
   Lorentz transformation
Principle of Equivalence

General comment: In preparing for physics exams, it is *not* a good
strategy to try to have a different ready formula for every problem that
might appear. This is not the way that physicists think about physics,
and it is a physicist writing the exam. Physicists like the idea of
using a very small number of general principles, concepts, and laws to
solve a large number of problems. When the fundamentals are understood,
many different kinds of problems can be solved. So you can expect
problems that use the physical principles you have learned, but do not
expect that the problems will be just like ones that you have already
done. It also follows that you should not put much weight on the old 
midterm that is posted. I put it up just to please those who ask for it.