Special Relativity : From Einstein to Strings

Rating:
Summary: All you need to know about SR
Review: This a very fine book if you want to go further than the usual introductory treatment of SR (like the one in Special Relativity by A. French or in the Mechanics book by Kleppner and Kolenkow).

Despite saying on the backcover that this is a book for "anyone with at least a year of university physics and calculus", I don't think this a good for a beginner who should look in books like Spacetime Physics by Taylor and Wheeler or in Special Relativity by A. French, this book actually uses tensors and differential forms and includes a chapter on group theory which I don't find most sophomores are ready to use comfortably. This level of this book is at least for someone that has finished a course on electromagnetic theory (for example using Griffith's book).

But if you are in the rigth audience this book is full of interesting material, the authors rewrite Maxwell's equation in a particulary elegant way, and manage to make accesible some topics that usually aren't even mentioned in common SR courses like supersymmetry and some relativistic quantum theory. The discussions of symmetry and field dynamics are invaluable. Note that the book includes a CD with some useful stuff.

Rating:
Summary: Coherence?
Review: This book contains many topics of interest, but it is
unorganized. As opposed to the distinguished reviewer who found
it "well-written", I find the organization lacking. A
more useful approach that would reach more readers would be to
borrow the styles of Wald in his GR book, and Halliday, Reznick,
Walker in their intro book. Wald has superb exposition that
prepares and leads the reader through the details that are to
come, or those that have just preceded, and HRW has many
examples that solidify the basic ideas. In SR, should a reader
start trying to understand how space and time may rotate into
each other, and the transformations that do this before he has
seen some calculations at the HRW level first?

A more fruitful approach would be to provide an introductory
chapter with well-written exposition explaining how SR came
to be necessary (the author succeeds here somewhat), and then
explain carefully what an inertial frame is (and is not),
state Einsteins two postulates (and explain them with examples
if necessary), and then proceed to work some HRW-level problems
to illustrate time dilation and length contraction. Work examples
to show that time has properties other than those we believed
in Newtonian physics.

The following chapter could develop the tools necessary to
describe what flat spacetime is and how it differs from
Euclidean space. Care should be given to discuss the invariance
of the interval, and extreme care should be given in defining a
tensor not in terms of its transformation properties but as a
multi-linear mapping of 1-forms and vectors into the set R (the
author does this to some extent). The discussion should then
proceed to show how objects like tensors are "geometric objects."
Ex: if a tensor is defined as a mapping of ..."vectors"...,
how is this a geometric object as well as a mapping, and how is
a vector itself defined as a geometric object. Explain how a
tensor may be defined in terms of mappings of vectors, and then
how a vector itself may be defined as a first rank tensor. The
beginning reader will be confused on points like these. Likewise,
a discussion of groups without showing concrete representations
and exposition in sufficient amount will not be adequate. It
would be like defining a topological space formally and then
expecting a first-time reader to immediately see what can be
done in a space having no defined metric.

Great care
should also be given to the meaning of components of a tensor
and what information the components contain.
Examples of tensors in physics, their components and their
meanings would solidify understanding.

The meaning of symmetry and invariance should be discussed with
exposition before the fact, good definitions of these ideas,
and then examples. For example, instead of stating that Maxwell's
Eqns are "Lorentz invariant", do the substitutions and show
the reader that the form of the eqn does not change. Later, the
same can be done with the Schroedinger Eqn to show that it is
not Lorentz-invariant.

After the physical intuition and mathematical tools have been
developed, the book can proceed to discuss flat spacetime in
terms of rotations, tensor operations, manifolds. Examples should
be worked throughout the chapters, as this solidifies ideas at
all levels. Now that the reader knows what flat spacetime is,
physics can be done on it.

The second half of the book seems to be a cut and paste from
various sources that do not fit together well. I would have
preferred an organization of the following type:

1) Exposition on the need for SR and worked problems
showing the properties of time and space in SR.
2) Mathematical development necessary to study flat
spacetime (with examples)at a more advanced level.
3) Physics in flat spacetime with the mathematical tools
learned in 2); properties of spacetime; SR problems
worked out.
4) Discussion of spaces in general with varying degrees of
structure - a manifold, a vector space, etc. Explain
how curvature is determined (in a mathematical sense)
by a metric or connection.
5) Investigate curved spacetime, the reasons that the
Schroedinger Eqn cannot be cast as a relativistic eqn,
(the importance of having a linear time derivative and
second order spatial derivatives), how the KG eqn
and the Dirac Eqn evolved.
6) Leave out the discussion on strings and anything alluding
to the Standard Model. David Griffiths book on Particles
is a good source as an intro to multiplets and particles
and path integrals.
7) Focus on SR and Spacetime and the tools needed to
investigate them; improve the presentation of groups
by giving a few examples of permutation groups and
work a few problems so that the new reader will see
how they work; emphasize the difference between an
abstract group and the representation of that group;

Briefly, there needs to be more clarity of both physical ideas
and of the development of mathematical tools in this book. There
needs to be much more in the way of physical motivation for the
ideas presented. How many times has everyone seen a beginner
struggle to understand *how* two masses in Newtonian physics
cause attraction? They think they are lacking an understanding,
when a simple explanation that the Newtonian law of Grav just
gives the results, not the causes of action-at-a-distance. The
same motiviations need to be given w.r.t. SR in this book and
beyond. Suppose you continued and discussed GR. What would you
tell a reader who asked: "well matter-energy density determines
curvature, and a particle mass subsequently follows that
curvature. But if the field is a vacuum measured exterior to
a massive object, what exactly *is* it precisely that's curving?"
You can pull eqns out and show results, but a little exposition
as in Wald is worth gold.

Final Word: limit the topics of discussion and do a better job
with the writing. I know the author can write a better book than
this.

Rating:
Summary: Special relativity for the 21 st Century
Review: Why has Schwarz chosen to write a book on special relativity?After all its a 100 year old theory whilst Schwarz himself co-founded the extremely new and vibrant string theory. Well thats why I feel this book truely stands apart from the pack in that my opinion is the first attempt to bring to a wider ( 21st century) audience the beauty and elegance contained that lies at the heart of S.R. as a fundamnetal and powerful tool forming the core of our understanding of spacetime in the context of physics as it is today. I think if you have a little previous exposure to S.R. and a nimble and curious mind and a passion for seeing into the how our understanind of space-time works this book will truely fascinate and enlighten you. Its being an 'up-to-date exposition of S.R' is the reason for the non-standard layout and arrangement of some of the material - I believe Schwarz genuinely wishes to take the reader through an breath-taking tour of modern physic at a level that an undergraduate can understand.Consequently,this beautiful and elegant book exceeds the scope of any other book at this level. Sure , there are plenty of 'standard' treatments of S.R. if you want them but I do not know any other book that can give a reader at this level a genuine taste of physics from Pythagoras and Galileo upto differential geometry, groups, particles, fields, supersymmetry and superstrings in one volume. I cannot recommend this more highly. A truely wonderful book.