If you have an existable process and reverse time, invert parity and conjugate charge, the result will for sure be an existable process too. This is called the CPT-theorem. (4.1)
Let's start with the application (3.2) of the previous page, * * * = * k * j * i = 1, which is present in baryons. We start from the assumption this application exists.
At page 1 of the storyline NET FORCES IN QCD is argued:
Quarks have color and antiquarks have anticolor - there seems to be no other way.
Therefore we define color i, j, k as matter and anticolor -i, -j, -k as antimatter. (4.2)
It is tempting to regard the baryonic gluons to consist of half color - half anticolor. But when using the gluon table one sees the baryonic gluons (as well as the 12 so called
shift 1/6 gluons) are equal to i, j, k, -i, -j and -k (right side of equation). Let's trust the gluon table and take the gluons as their single-color outcome, regardless their gluon origin. We can define i, j and k as matter gluons and -i, -j and -k as antimatter gluons. (4.3)
|-i = -1 * i
-j = -1 * j
-k = -1 * k
|i = -1 * -i
j = -1 * -j
k = -1 * -k
Multiplication by -1 changes matter in antimatter or vice versa. (4.4)
We regard now charge conjugation. There is no electric charge but there is color charge. When we multiplied by -1 the color charge conjugation has been done by replacing k by -k, j by -j and i by -i (in colors replaced by , by and by ). Our starting application kji becomes -k -j -i.
We have met that reversing multiplication order is reversing time order. The order of multiplication in fact is taken as time order of multiplication: start multiplying with this, a little later with that and at last with this - as if it were couplings performed one after the other. Reversing time order then is reversing multiplication order. (4.5)
So we reverse time order by reversing multiplication order, -k -j -i becomes -i -j -k, which is eq. (3.3) of the previous page and is an application in the antibaryon.
Multiplication by -1 changes multiplication order which is the same as changing time order. We conclude multiplying by -1 is reversing time order, reversing time. (4.6)
Multiplication by -1 also changes matter to antimatter. So matter (amongst them the matter gluons) go forward in time and antimatter (amongst which are the antimatter gluons) go backward in time. (4.7)
Applied to a single particle, parity inversion means spin swap. Parity inversion is difficult to give physical meaning on a 3-color application like kji or -i -j -k. Particles have spin, but the spin of just a color is not defined.
As said, applying just 3 colors cannot be done. Quarks carry single color; gluons carry two. Permitted is the application of 3 colors twice by means of 3 gluons. The gluon has spin 1 or -1 and when the quark absorbs the gluon, the quark's spin -1/2 or 1/2 is swapped to spin 1/2 or -1/2. Application of 3 gluons would give 3 swaps, equaling 1 swap.
We can replace the gluons by their single color outcome according to the gluon table. Our starting 3-color application kji then not only means multiplication of the 3 quark colors in a baryon with each other, but can also mean the coupling of 3 gluons. We anyway still apply 3 gluons which causes 3 spin swaps.
So when kji exists and we conjugate color charge and change time direction, in the course of which the spin is swapped, we get -i -j -k that exists too. The CPT theorem applies to colors in quaternions. (4.8)
We define time = 1 (our time equals 1) and backward evolving time = -1. (4.9)
1 as well as -1 is colorless white. There is no color in the time axis, the time axis is white.
Unless the white gluons define the time axis. The white gluons are 1, like the time axis is. White gluons have no color and are called glueballs.
Here we for the first time recognize 1 as a gluon, a white gluon with spin 1. And then -1 is a black gluon. Mark if you do so, in QQD there are now 8 gluons (1, i, j, k, -1, -i, -j, -k or , , , , , , , ), two of them are colorless (1 and -1), just as in the old, well accepted QCD. (4.10)
The white gluon 1 goes forward in time. -1 * 1 = -1. This means here: ( the time reversing factor -1 ) times ( the white gluon 1 ) gives ( the black gluon -1 ). The black gluon goes backward in time. (4.11)
Here we conjecture the real time axis in 1ijk-colorspace (pronounce 1-i-j-k colorspace) equals the imaginary time axis in xyzt spacetime. (4.12)
Somehow there is a
real-imaginary swap of the time axis when it comes to observation. (4.13)