From: platt@watson.ibm.com (Daniel E. Platt)
Subject: Re: Where should beginner begin?
Date: Mon, 23 Nov 1992 16:14:39 GMT
Disclaimer: This posting represents the poster's views, not necessarily those of IBM
Organization: IBM T.J. Watson Research Center

In article <1541700004@gn.apc.org>, antennae@gn.apc.org writes:
|> 
|> 
|> Could anyone please recommend some good books for a complete novice
|> who would like to learn something about physics - particularly
|> relativity and quantum theory?  Is it necessary to have a good
|> grounding in mathematics before you can understand anything?
|> 
|> All the best, Indra

There's a lot that can be said at a qualitative level.  For example,
a dominant feature of quantum mechanics is the idea that momentum
and wavelength are related, and that if the wavelength of an object
is large enough, you start to see wave-like behavior (interference
patterns) -- but you are also seing particle-like behavior at the
same time (people are still arguing about what that means).  There's
also the phenomena of quantum tunneling, where particles can leak
across barriers if the barriers are smaller than their wavelengths.
Interference (constructive and destructive) implies that you will 
also see some regions that are excluded, due to destructive interference.
This implies that you will see only a finite number of discrete constructions
available.  Examples of that include angular momentum, spin, etc.  Then,
there's the possibility of building things out of waves to describe
the behavior of systems that have no classical analogue (particles can
have something called intrinsic spin, for instance).  Then, there's the
problem of consistent observation -- how can two observers always see
conservation of energy or angular momentum for two particles produced
in such a way as to require angular momentum conservation, if both measurements 
are separated by a large displacement, and the quantum description does not
specify what momentum a particle is in before the measurement?  Does this
mean that somehow one particle tells the other what state it was ultimately
measured in, even if the information had to be communicated faster than
light?

The question is, what does the above mean?  Is it possible to talk about
all of this stuff without a basis in mathematics?  If you need a good
grounding in math, what does that grounding look like?  Relativity and
quantum mechanics look glitzy and seem weird and wonderful.  It can be
hard to appreciate that ideas such as momentum, wavelength, and 
interference have specific and specialized technical meanings.  People
who work with them take the meanings for granted.  Einstein's seminal paper
on special relativity was a sort of innocuous looking discussion of
the 'electrodynamics of moving charges.'  It basically looked at the
problem of how Maxwell's equations would look to different observers.  It
was a really hot problem of the day that had the attention of lots of
people.  Einstein's paper used high-school algebra, yet it talked about
lots of ideas that required a lot more depth to really appreciate the
arguments.  I think there's a problem with the kinds of qualitative
presentations as highlighted in the first paragraph.  It says something
about the flavor of the arguments, and states something in a nice
qualitative way about how quantum mechanics fits together.  But it doesn't
do a good job of really getting deep enough to understand even the basic
language (what's 'wavelength'? what's 'momentum'? how do you calculate 
'interference'? what does 'intrinsic spin' really mean?).  That language
and its subtler implications are taken for granted in this kind of development.

Feynmann's 'Lectures on Physics' have a nice discussion of what it really
takes to present some of these ideas.  He talks about this in the preface.
While these lectures were presented to beginning students (freshmen and
sophomores), many physics majors use them to prepare for their PhD qualifiers.
However, he tries to span the gap of saying all kinds of glitzy stuff,
and trying to present enough useful information to really communicate
the concepts.  It's a hard job.  Feynmann himself was not satisfied with
the results.

Dan 
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Daniel E. Platt                                      platt@watson.ibm.com
The views expressed here do not necessarily reflect those of my employer.
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