Re: [Phys-l] An introduction to MTW?

[John Denker <jsd@av8n.com>]

On 02/02/2012 07:01 PM, Ken Caviness wrote:

> I have a memory of an article (perhaps in AJP, perhaps 50pp?) that
> provided an introduction for physics students wanting to tackle
> Misner, Thorne & Wheeler's "Gravitation", giving extra help to get
> started.
>
> An hour's worth of searching hasn't turned it up.  Anyone remember
> this one?  Any pointers?

That's quite a good question.  I don't have any good answers, and
strictly speaking the question might not even be answerable, but 
that doesn't make it any less of a good question.

Here are some very sketchy partial answers:

1) As to the broad question of what to read in preparation for MTW,
 possible answers include "nothing" and "everything".  It depends 
 on whether the emphasis is on merely "getting started" as opposed 
 to "tackling" (in the sense of Oklahoma powerslam).  The extremes 
 include:

1a) You can read the first couple of chapters (70 pages) of MTW with
 no background beyond first-year college physics plus math at the 
 level of partial derivatives and some matrices and linear algebra.
 It might take you 70 days to read those 70 pages, but I can't think
 of any preparation that would speed up the overall task, because
 the introductory chapters of MTW are the best introduction I know.
 Anything else you could read would take just as long ... and might
 take longer, because it would be less modern and less correct, and 
 some of it would have to be unlearned.

1b) At the opposite extreme, halfway through the book we come to
 chapter 22, entitled "Thermodynamics, Hydrodynamics, Electrodynamics, 
 Geometric Optics, and Kinetic Theory".  This is a "Track 2" chapter,
 meaning you don't need to deal with it at all on first reading ...
 but if you do want to "tackle" such topics in curved spacetime, it
 would be helpful if you had already seen the flat-spacetime versions,
 such as
   Thermodynamics at the level of Sturge or Schroeder or Kittel&Kroemer
   Fluid dynamics at the level of Lamb.
   Electrodynamics at the level of Feynman volume II or Jackson.
   Optics at the level of Fowles.
   et cetera

 Similarly, chapter 9 is Track 2 but bills itself as an "easy chapter".  
 The title is "Differential Topology".  I suppose that chapter is easy
 for everybody who already knows about differential topology ... i.e.
 practically nobody.

 In other words, you could get a PhD in physics from a first-rate school 
 and still not have enough background to "tackle" everything in this
 book.  

 On the other hand, this reinforces the point made previously:  MTW
 is itself the best introduction to differential topology that I know
 of.  The only math books I know on the subject are not introductory
 at all:  they assume to much at the beginning, and then pursue the 
 subject much farther than is necessary.  MTW sneaks in the crucial
 ideas early and builds them up gradually, starting in chapter 1, always
 keeping the mathematical formalities in contact with the physical
 intuition.

 Tangential remark:  Basic ideas of differential topology are exceedingly
 valuable for reasons having nothing to do with general relativity.  In
 particular, I don't see any other way to make sense of _thermodynamics_.
 This is discussed at
   http://www.av8n.com/physics/thermo-forms.htm
 Another amusing example along this lines allows us to visualize the 
 topological basis for the cyclic triple chain rule, as discussed at
   http://www.av8n.com/physics/spontaneous.htm#sec-cyclic-triple-derivative

 If anybody knows of a better introductory discussion of differential 
 topology as it applies to physics, please let us know!

 So, returning to the question of what to read in preparation for MTW:
 I'm sticking with my original answers: "nothing" and "everything". 
 Both answers are correct.  The only way I know of to deal with this 
 book is to read it N times.  Read it once early, then study physics 
 for a couple of years, then read it again, then study some more physics
 ... and so on, iteratively.


2) As to the specific question that was asked:  I don't recall any 50-
 page article that is focused on preparing for MTW ... but any article 
 on the modern (post-1908) approach to special relativity might fit
 the bill.  Obviously a good background in special relativity is super-
 useful as preparation for anything involving general relativity.

 The canonical (but not perfect) reference in this area is 
   Taylor and Wheeler, 
   _Spacetime Physics_

 The nice thing about Taylor & Wheeler is that it "contains" an 
 introductory discussion of the modern spacetime approach to relativity.
 The not-so-nice thing is that for some reason it also discusses the 
 premodern contraction/dilation approach, which IMHO is unnecessary 
 and indeed quite unhelpful.

 If you want to see an example of an introduction to special relativity
 using the modern approach, not even mentioning the other approach, see
    http://www.av8n.com/physics/spacetime-welcome.htm

 (That document is new and not fully polished, but IMHO it suffices to
 prove the point that the modern approach is far simpler than the other
 approach.)

 It should be noted that MTW does not even mention contraction and/or
 dilation, not even in passing, if I recall correctly.  As such, MTW
 is itself the best introduction to special relativity that I know of!
 This gets back to the central point made in item (1), namely that 
 "preparing" for MTW will be less helpful than you might have hoped, 
 because the preparatory material won't be as good, and some of it will 
 have to be unlearned.


3) Another suggestion:  When reading this book, be prepared to be treated 
 as an adult.  This will come as a shock to some students.

 For example, consider exercise 1.2, which calls for calculating the height
 of the spring tide and the neap tide.  The first time I read that, I was
 completely mystified, because I couldn't find anything in chapter 1 that
 explained how to do such a calculation.

 Eventually I realized that the question did not say "Using the methods
 of chapter 1, calculate the height ...."  It just said "Calculate the 
 height ...."  You are supposed to use _everything you know_ as input to
 calculation.  MTW plays by real-world grown-up rules, not nursery-school
 rules.  I don't know of anything students can read to prepare for this 
 ... but you can pass the word.