Richard Suchenwirth 2002-11-10 - In the beginning there are Tohu (T) and Vohu (V): two very little things ("rishons" because they're the first (Hebrew)), of which T has an electric charge of 1/3 and V has none. And, as symmetry goes, there are also their anti-rishons - conventionally written with a bar over the abbreviation letter, but I use lowercase for easy keyboard input: t (with -1/3 charge) and v.
Rishons (and anti-rishons) always come in groups of three, and if order doesn't matter, we have four distinct triplets of each:
Rishons: TTT, TTV, TVV, VVV; anti-rishons: ttt, ttv, tvv, vvv
Now let's enter the realm of elementary particles (for which a language named Tcl may have some uses ;-), which come in three weight classes: light, medium, and heavy (or scholarly Greek: Leptons, Mesons, Baryons). The particular theory that I'm retelling here says that leptons consist of just one Rishon triplet, if their charges sum up to an integer:
ttt -1 e- Electron (finally, an old acquaintance...) VVV 0 ve e-Neutrino TTT 1 p Positron vvv 0 -ve Electron anti-neutrino
The other four have fractional charge sums, and thus can only be used as building blocks for bigger structures, the so-called quarks (and the complementing anti-quarks):
TTV +2/3 u u-Quark ("up")
tvv -1/3 d d-Quark ("down")
TVV +1/3 -d Anti-d
ttv -2/3 -u anti-uThere are more quarks postulated, with names like "charm", "strange", "top", "bottom", but my physics book didn't tell me how they map to rishons...
Mesons (middle-weight particles - although D-mesons are double as "heavy" as neutrons) consist of one quark and one anti-quark, and also sum up to an integer charge, here demonstrated on "Pions":
u-u 0 pi0 u-d 1 pi+ d-u -1 pi-
The really heavy guys, Baryons, are made up of three quarks, or three anti-quarks, and here we meet old acquaintances again:
uud 1 p Proton -u-u-d -1 p- Antiproton udd 0 n Neutron
Neutrons and protons make up most of all matter. The bad news is that neutrons don't survive long in freedom - typically after 932 seconds (~15 min), the following happens:
n -> p + e- + -ve
The neutron turns into a proton, emitting an electron and an electron anti-neutrino (please pardon my typography - originally there are bars over anti-particles, Greek letter nu where I put the v, and subscripts). Expressed in terms of quarks, the above becomes
udd -> uud + e- + -ve
Or, back to rishons from where we started, the change is only in the second "d" quark, so in rishons that makes:
tvv -> TTV + ttt + vvv
Finally, enter Tcl. Such process descriptions are strings, and Tcl is particularly (if you excuse the pun) good at strings. Here's some code to check whether a process abides by the Rules (which I don't know all, but two are:
Instead of inserting rishons, I start backward by removing matching rishon/anti-rishons from the postulated result, and see whether we get back to the start. But first, some helper routines:}
proc rishon'charge rishons {
# computes the electric charge of a rishon triplet
expr [string map {T +1./3 V "" t -1./3 v ""} $rishons+0]
}
proc rishon'translate rishons {
# turn a rishon sequence to more conventional particle names
set tmp [string map {
TTT e+ TTV u TVV -d VVV ve ttt e- ttv -u tvv d vvv -ve
} $rishons]
string map {
uud p -u-u-d p- udd n u-u pi0 u-d pi+ d-u pi-
} $tmp
}
proc rishon'reduce formula {
regsub -all {[^TtVv]} $formula "" rishons
set rishons [split $rishons ""] ;# turn into a rishon list
while {[has T $rishons] && [has t $rishons]} {
lremove rishons T
lremove rishons t
}
while {[has V $rishons] && [has v $rishons]} {
lremove rishons V
lremove rishons v
}
regsub -all (...) [join [lsort $rishons] ""] {\1 } res ;# group triplets
set res
}
proc has {element list} {expr {[lsearch $list $element]>=0}}
proc lremove {listVar element} {
upvar 1 $listVar list
set pos [lsearch $list $element]
set list [lreplace $list $pos $pos]
}if 0 {Testing:
% rishon'reduce {TTV + ttt + vvv}
tvv ;# so the neutron decomposition appears well-formed
% rishon'reduce {ttv + TVV + TTT}
TTV The latter case is controversial: it describes (backward) how a proton decomposes into a pair of Pi-mesons and a positron - which violates the rule that the number of baryons should remain constant. I can't tell - particle experts, please comment (also on "superstrings", which sound as if they may be food for Tcl too...)