Tues. about 2:30 p.m. 3rd day of June 2014. Hoo boy. It’s been 40 years since I enrolled in my first physics class.
Here’s a statement that I
keep thinking about, mainly because I can’t remember it. It’s from Freeman Dyson’s article in the NYRB
of 6 March 2014: “We can divide
particles into two types in three different ways.” This is a statement that I can’t forget, but
also can’t precisely remember. In my mind, I start it as “We can divide two
particles…,” so I’m immediately lost. I
guess the unhelpful choice of the words “divide particles” just throws me off
the track. Then, if I do remember to
start with “We can divide particles” I can’t figure out how to bring the “two”
in properly. We can divide particles in
two? We can divide particles into two
groups? Or what?
One thing: “types” and
“ways’ together—that bothers me somehow.
When I first read the sentence back in late February, I was impressed
with how cleverly it covered that whole territory of charged vs. neutral,
strong vs. weak interaction, and fermion vs. boson. The three-fold way! But where are the two types? I’m sorry, that’s of course obvious. But particles each have all three
properties. Once the properties are
assigned, we have eight types, not two, or “eight possible combinations” as
Dyson says later.
So can I say it better than
Mr. Dicey Dyson does? Not right
now. I need a nap here at 2:51 p.m.
4 pm. Nope, I can’t say it
better. Except “types” and “ways” still
bothers me the way he used it. Okay, so
I’ll reverse it. “We can divide
particles into three different types in two different ways.” I’ll think more about that. Still bugs me.
3 types based on charge,
interaction, spin.
2 ways: yes/no, weak/strong, integer or
not.
About 9 pm Friday, June 20th. Just a note to myself, a reminder of what
books I’m currently keeping in mind as far as research is concerned (learning
is concerned). Lawrie’s Grand Tour,
A&H’s Gauge Theories, Low’s Classical Field Theory, José & Saletan’s
Contemporary Dynamics, J. Townsend’s Quantum Mechanics Intro, Holstein’s Weak
Interactions in Nuclei, and some others that don’t come to mind right now. Also I’m presently reading “Matrix Mechanics
of the Infinite Square Well and the Equivalence Proofs of Schrödinger and von
Neumann.” A fine and richly referenced
(rich with references of great interest) article in AJP.
7:15 a.m. June 21. Summer Begins.
What bothers me about
Dyson’s description is that by itself it makes no sense—at least not to me (see
previous page). In a way, it’s a parody
of Dyson’s inclination to put numbers to his proclamations. I may look up an example later but it’s
something like saying there are two ways we could improve our understanding of
so-and-so, or there are three reasons why we should improve such-and-such. “Particles can be divided” is also a bad way
to start off the sentence. Nothing is
being divided.
Electric charge, spin, and
means of interaction are particle properties.
Actually, these are all “means of interaction,” a term I was using [as it is commonly used among theoretical physicists] only
to describe the force—what type of force—the particle recognizes and responds
to. But charge or no-charge is a
property that determines whether a particle responds to the electromagnetic
force. (Well, what about the neutron’s
magnetic moment?) (To be discussed
later!) Dyson, however, leaves out the
electromagnetic force in his “divide into two types,” or maybe he includes it
in the weak force without saying so. His
two types of force are strong and weak.
Spin is integer [boson] or half-integer [fermion].
Charge is either neutral or weak, oops, neutral or charged.
So I would say—as a first
attempt to correct the indecipherable numerical shorthand of Dyson’s
sentence—that elementary particles have three properties, each of which
manifests itself in two ways.
But of course, this
categorization [Dyson's categorization] leaves out the further property of plus or minus charge. And I don’t know what all else (strangeness comes to mind, but I don’t recall its importance at the moment).
One thing I’ve managed to
accomplish here is to again bring out the point that spin does have an
influence very much like electric charge.
The exclusion principle causes Fermi-Dirac particles to interact in such
a way as to prevent them [any two of them] from being in the same quantum
state. This is like particles of the
same charge repelling each other. The
Bose-Einstein particles can all be in one quantum state, which gives them a
property or means of interaction like neutral particles: that is, no means of interaction!
