Re: Fundamental composition of matter?

rim317-ava wrote:
What exactly is an electron and a quark?

Different states of a single particle.

Do we have any experimental proof of their underlying structure?

There is, in fact, interesting (but little-known) structure in the
Standard Model which underscores the fundamental unity of the entire
spectrum of particles.

[In the following, "particle" refers to a particle of matter -- i.e.,
fermion. The particles of energy are the bosons and are not addressed
here directly.]

(1) The fermion cube.
The symmetry group for the force binding quarks is what is known as
SU(3). Contrary to what's widely asserted, there are NOT 3
"fundamental" types of quark charge. Rather, there are 3 primary
"colors" (red, green, blue) for the quarks and 3 other "colors" (cyan,
magenta, amber; though usually called anti-red, anti-green, ant-blue)
for the anti-quarks.

The analogy to color theory is, in fact, quite deep. The symmetry group
SU(3) is associated with 8 modes, each identifying a separate type of
"gluon". Two of the modes (usually taken as the 3rd and 8th) are
normally associated with the scales that define the charges:
respectively L3, L8 (lambda 3, lambda 8, but I don't have a lambda
key).

They play the analogue to what in color theory are called chromaticity
coordinates. In a L3-L8 plot, the 6 colors, red, amber, green, cyan,
blue, and magenta will occupy the positions of a hexagon situated about
(L3,L8) = (0,0). The total charges add up as
red + green + blue = 0 = cyan + magenta + amber
as well as
red + cyan = green + magenta = blue + amber = 0.

There are only TWO independent charges for quarks, not 3.

You may then wonder: what about "brightness"? Who plays that role? The
corresponding quantum number would be the same for all quarks (and
opposite for anti-quarks), therefore it's just the baryon number.

However, there are certain restrictions in quantum field theory on just
what numbers may serve as candidates for a bona fide charge. Baryon
number is not allowed, but the combination G = (Baryon - Lepton)/2 is.

The assignments of G are:
quarks = 1/6; leptons (electrons, neutrinos) = -1/2
anti-quarks = -1/6; anti-leptons (positrons,
anti-neutrinos) = 1/2.
Correspondingly, one might define 2 additional colors:
white = anti-lepton; black = lepton.

So ... what do you get, when you plot the 8 colors on the (L3,L8,G)
axis? A cube! (Provided you scale G appropriately).

Associated with this is 1 invariant and 3 operators.

The total L charge for quarks and anti-quarks is given by L^2 = 4/3
(long story); for leptons and anti-leptons, L^2 = 0. Thus
L^2 + 6 G^2 = 3/2
is the same for all leptons. Correspondingly, one also finds 3
operators that each take on the values +/- 1/2. Under a standard
scaling for (L3,L8), the 6 colors are
red = (1/2, sqrt(1/12)), green = (0, -sqrt(1/3)), blue =
(-1/2, sqrt(1/12)),
cyan = (-1/2, -sqrt(1/12)), magenta = (0, sqrt(1/3), amber =
(1/2, -sqrt(1/12)).
The 3 operators are
c = G - L8/sqrt(3) + L3, d = G + 2 L8/sqrt(3), e = G -
L8/sqrt(3) - L3.

For all the particle states, they each have the values +/- 1/2. The 8
combinations of (c,d,e) are related to the colors as:
white = (+++), red = (++-), green = (+-+), blue = (-++),
black = (---), cyan = (--+), magenta = (-+-), amber = (+--).

(2) The Mass Modes
Each type of particle comes in left-handed and right-handed modes. In
the Standard Model, the neutrino's right-handed mode and
anti-neutrino's left-handed mode were considered neutral and
(therefore) unobservable or otherwise non-existent.

The handedness of a particle is determined by its chirality. This, in
turn, for an object moving at light speed is related to the direction
of the axis of its internal angular momentum relative to its motion. A
particle that has counter-clockwise spin seen from ahead of its motion
(I think) is the one called left-handed.

For particles moving under light speed this concept is not
well-defined. If you switch to another reference that moves at a speed
greater than the particle, then that reference is overtaking the
particle and, in it, the particle is moving in the other direction. Yet
its spin stays the same. Therefore, the relation to the spin axis and
direction of motion are observer-dependent.

For the Standard Model, this forces a quandry. The weak nuclear force
only interacts with particles in the left-handed state, and
anti-particles in the right-handed state. The question of whether an
interaction is taking place is NOT observer-dependent.

The only way out is to assert that neither is the particles'
handedness: i.e., all particles are fundamentally massless.

The appearance of mass has to be explained by other means. In
relativistic quantum theory, a particle's motion is already given by
what's known as the Dirac equation. Even there, it's already the case
that (in the Heisenberg picture at least) the equation effectively
treats the particle as moving at light speed, but in such a zig-zagging
motion that its average motion is under light speed. The frequency of
this zig-zagging is proportional to the particle's mass. In effect, it
represents an alteration between left and right handed modes.

Since the Dirac equation for a particle in the Standard Model has no
mass. So, the left-rught mode switching is explained by something else.
It is hypothesized that a universal energy field exists that is
switched permanently in the "on" state.

In effect, it fills the vacuum and has several notable effects. First,
it makes the vacuum opaque with respect to 3 out of the 4 components of
the electroweak force. The only mode that remains transparent is also
the only mode that is left-right symmetric -- that corresponding to the
electromagnetic force. Therefore, light can travel freely through a
vacuum and electromagnetic forces are long-range; but the other parts
of the electroweak force are not and while photons have no mass, the
other particles associated with the force now do.

Second, it causes an interaction between left and right modes of a
particle and causes the very left-right switching required to produce
the appearance of mass. In effect, though the massless particles move
at ligth speed, under interaction with the universal field, they move
about in a zig-zagging fashion such that their average motion is that
of a massive particle.

That universal field is called the Higgs.

As I pointed out at the very top, there is a fundamental unity of the
entire spectrum of particles. The apparent disunity is entirely tied up
in the strength at which each mode of this particle interacts with the
Higgs. The modes that interact the strongest have appearance of the
largest mass. So they would be thought of as "different" particles from
the other modes, even though at the root, they are all just different
states of a single particle.

(3) The electroweak diamond.
The electroweak force, like the color force, reveals an second
structure in the particle spectrum. Here, there are 2 fundamental
charges -- hypercharge (Y) and isospin (I3). The values of the two are
left-right dependent and are as follows:

A right neutrino/right up/left positron/left anti-down: Y = G + 1/2, I3
= 0
B left neutrino/left up/right positron/right anti-down: Y = G, I3 =
+1/2
C left electron/left down/right anti-neutrino/right anti-up: Y = G, I3
= -1/2
D right electron/right down/left anti-neutrino/left anti-up: Y = G -
1/2, I3 = 0,

where G is the quantum number described previously under "fermion
cube".

These are the 4 "isocolors".

For right neutrinos since G = -1/2 (and left anti-neutrinos, G = 1/2),
you'll see that here Y = 0 and I3 = 0. They are completely neutral and
therefore invisible.

In light of the previous discussion "Mass Modes", if the neutrino were
massless, that would actually means they didn't interact with the Higgs
at all and acquired no mass as a result. In such a case, the right
neutrino and left anti-neutrino were be absolutely neutral, as far as
the Standard Model would be concerned and effectively non-existent
(except for taking into account their gravity).

With massive neutrinos, that means interaction with the Higgs. Then,
the question as to the existence of these otherwise invisible neutrino
modes is back on the table. But the Higgs has never been seen, so
nothing can be said about the right neutrinos or left anti-neutrinos
yet.

The electric charge of a particle is Q = Y + I3. For electrons that
works out to either (G) + (-1/2) or (G - 1/2) + 0, depending on the
handedness. In both cases, that works out to -1. For the quarks, you
get +/- 2/3, +/- 1/3 for the up/anti-up and down/anti-down. For the
neutrino and anti-neutrino you get 0.

The diamond is formed by the 2 units
Right isospin X = Y - G, Isospin I3,
with the settings (X,I3) for the respective isocolors:
A: (+1/2, 0), B: (0, +1/2), C: (0, -1/2), D: (-1/2,
0).

The isocolors B, C the total isocharge is given by I^2 = 3/4 (another
long story), and for isocolors A, D, it's just I^2 = 0. Therefore, you
find a 2nd invariant:
I^2 + 3X^2 = 3/4.

Associated with this are 2 operators, a and b, which each have the
values +/- 1/2:
a = X + I3, b = X - I3,
with the respective (a,b) assignments:
A: (+,+), B: (+,-), C: (-,+), D: (-,-).

(D) What is a particle?
So ... to answer your question, the particles of matter form a
fundamental unity which consists of 3 generations, each having a
spectrum arranged in a 4 x 8 array. The 4 refers to the 4 isocolors,
the 8 refers to the 8 colors.

Since they are all -- at a fundamental level -- of the same mass (0),
then they are all best regarded as just being different states of a
single particle -- the Fermion.

.

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