🚀 go-pugleaf

If you roll a ball without slipping or twisting over the surface of
another ball of the same size, the orientation of the rolling ball is a
single-valued spherically symmetrical function.  Another way of looking
at this function is to say that the orientation of the rolling ball may
be obtained by rotating it by half a turn about the original radial
direction, sliding it to the new position keeping the same orientation,
then rotating it by half a turn about the new radial direction.

I reckon that the function which is the "square root" of this rotation
has spin 0, isospin 0 and charge +2 (with opposite signs for the other
square root).  In four-vectors, the function is (cos pi/4 + iu sin pi/4)
where u is a unit vector in the radial direction, so this is simply iu.
(To see how I get the charge, note that the div of this is 2i/r).

If every baryon was held together by one of these functions (call it a
"baryon quark") with charge Q = +2 and baryon number B = 1, rather than
"gluons", then the ordinary quarks could be identical to the leptons and
would not need fractional quantum numbers.  The "baryon quark" could
also act as a marker to distinguish the sequence of otherwise identical
quarks, avoiding the need for "colour".

The quantum numbers need redefining a little to allow leptons to share
quark properties such as isospin, and quarks to have lepton numbers.
This gives an absolutely conserved quantum number equal to Q - 2B + L/2
which seems to fit correctly as the timelike scalar part of the
intrinsic spin, a generalization of I3.  (Q, B and each type of L are
also conserved separately).  It also equals I3 + (S + C + B* + T)/2
where those stand for Isospin3, Strangeness, Charm, Bottom and Top.

To avoid baryons having unbalanced lepton number +3 in this scheme, the
"baryon quark" could alternatively be assigned a new type of lepton
number Ln = -3 (conserved independently) in which case the generalized
I3 quantum number would become Q - B/2 + L/2.

Does this idea seem reasonable?  I'd like to know about any theoretical
or experimental results which might be relevant.

(For those with long memories, this was one of the less weird ideas I
had when I last had write access to the net in 1987.  I don't have
access to the alt group which I assume to be for REALLY weird new
theories, so I'm trying to avoid being TOO controversial).

Jonathan Scott
jscott@winvmc.vnet.ibm.com