Re: [Phys-L] Special Relativity for QFT

[John Denker <jsd@av8n.com>]

On 07/19/2018 01:37 AM, David Craig wrote:

> the key is finding something that gets students to the point of some
> degree of comfort with the basics concepts and notation of SR
> required for QFT in a reasonable period of time without overwhelming
> them.

That's a tall order.  By the time students are ready for a
first graduate course in QFT, they have almost certainly
"seen" special relativity before.  The problem is, the
class will be heterogeneous:
 -- Group "A" will be up to speed with the modern (post-1908)
  spacetime approach.
 -- Group "B" will be burdened with pre-1908 ideas of clocks
  that can't be trusted, rulers that can't be trusted,
  velocity-dependent mass, et cetera.

This sort of heterogeneity makes life difficult for the teacher.

In my experience it's easier to explain relativity to naïve
high-school students, because there's less heterogeneity,
and less unlearning required of group B.

Any reference that is good for group "A" will not be good
for group "B" and vice versa.  Most books on the subject are
heavily compromised, because they try to serve both groups
at the same time.  From the students' point of view, narrowly
speaking, it would be best to divide the class and teach the
two groups separately, using different references.  That may
not be as impractical as it sounds.  It might sound like it
doubles the teacher's workload, but not really, because
group A doesn't need as much help.  They can mostly fend
for themselves.

If you want an example of an uncompromising post-1908 spacetime
approach, aimed at group A, try this:
  https://www.av8n.com/physics/spacetime-welcome.htm

As for group B, I don't know what to recommend.  For some
of these guys, the misconceptions are lightly held, so you
can just tell them to forget everything they know about
contraction and dilatation, and to start over.  Then throw
them in with group A.  Meanwhile, others are so stuck on
pre-1908 ideas that it could take years to get "comfortable"
with the subject.  Unlearning is always hard.

I reckon the less time spent on pre-1908 ideas the better.
There is a ton of pedagogical and psychological evidence
that says that merely mentioning an idea tends to reinforce
it, even if that's the opposite of what you intended to do.

Taylor and Wheeler _Spacetime Physics_ was (and remains)
influential, but is heavily compromised by pre-1908 ideas,
not because the authors think that way but because they
expected their readership to think that way.  The second
edition is more compromised than the first.  It contains
some useful analogies, but also contains a surprising amount
of soporific algebra, making the subject look messier and
more inelegant than it really is.

Also it contains more coverage of "paradoxes" than I
would like to see, i.e. more than zero.  SR is not weird
or paradoxical.  It is the geometry and trigonometry of
spacetime, nothing more and nothing less.  It is possible
to construct "paradoxes" in any subject area -- even
introductory Newtonian mechanics -- by misstating the
basic laws.  But we don't teach mechanics that way,
because it would be pedagogical malpractice.

The first chapter can be downloaded for free from here:
  http://www.eftaylor.com/download.html

> It needs to cover Lorentz transformations in  matrix form 

I don't really disagree with that, but I am reminded of a
quote from Charlie Peck:
  «The goal of this course is not to teach you how to do
   Lorentz transformations, but rather how to /avoid/
   doing Lorentz transformations.»

All of the concepts and the vast majority of the calculations
are best formulated in terms of invariant /vector/ operations
... addition, subtraction, dot product, etc. applied to each
vector as a whole (not to components).  Components are not
invariant.  "Sometimes" you have to write out the Lorentz 
transformations component-by-component, but this is rare
and should be seen as an uninteresting corollary of the
underlying concepts -- not as a starting point or a focus
or a goal.

I assume the QFT book treats a vector as a first-class
frame-independent spacetime object unto itself (not as
a bucket of components).