The CPT theorem


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)

Start with the application (3.1) of the previous page,   * * * = * k * j * i = 1, which is present in baryons. We start from the assumption this application exists.         (4.2)

I suppose it is in fact   * * * * = * k * j * i * 1 = 1.         (4.3)

Let's generalize the conjugate charge arguement to color charges. The color charge conjugation is performed by the multiplication by -1.

-1 * i
-1 * j
-1 * k
= -i
= -j
= -k
-1 * -i
-1 * -j
-1 * -k
= i
= j
= k         (4.4)

Although I think that -1 * 1 = -1 and -1 * -1 = 1 should be added too.

In a baryon or antibaryon or meson, multiplication by -1 is done by replacing by respectively . Our starting application kji becomes * * * = -k -j -i = -1.

Or better should be:   * * * * = * -k * -j * -i * -1 = 1.         (4.5)

The real-imaginary swap

Another conjecture: 1ijk quaternion space (pronounce 1-i-j-k colorspace) equals xyzt space. At the following page, page 5 of QQD, are given arguments that there is working a real-imaginary swap when it comes to observation. The imaginary axes of colors i, j and k become the real axes x, y, z and the real axis of colorless color 1 becomes the imaginary time axis t.         (4.6)

The real-imaginary swap is not yet worked out properly. The main difference between the actual use of 1ijk and xyzt is that 1ijk is only used as the 8 quaternion units 1, i, j, k, -1, -i, -j, -k while xyzt is used as r * x + s * y + t * z + u * t, where r, s, t, u are real numbers. The QG storyline works out that the Higgs field (= the gravitational field = our 3-dim space) is built from gluon pairs. I have no calculation how the vacuum particles ( i   -i ), ( j   -j ), ( k   -k ) and ( 1   1 ) would build up xyzt spacetime, in doing so in fact constructing the real-imaginary swap. But the conjecture is that first there is 1ijk colorspace and that xyzt spacetime is a derivative from colorspace.         (4.7)

Multiplication of the 1ijk-space coordinates with color -1 changes all four quaternion values into their opposite directions.           (4.8)

If the real-imaginary swap exists, (4.8) leads to the following conjecture:

Applying color -1 multiplication changes xyzt-space coordinates into its opposite direction.           (4.9)

And this then would include the parity inversion P as well as the inversion of time, the T in CPT. In accepted CPT the parity P only inverts the spacial axes x, y and z. The inversion of time T is mentioned separatedly.

More CPT

Applied to a single particle, parity inversion means spin swap. Let's perform the operation (4.9) piece by piece. First we invert the x-coordinate. As a consequence the spin of the particle (assumed not to be zero) changes direction. When subsequently inverting the y-coordinate the spin changes back to original direction. When inverting the z-coordinate the spin changes direction again. Finally, when inverting the t-coordinate, the T from time (time is running backward now), the spin changes back to original direction again.           (4.10)

The PT transformation so far conserves impulse momentum, conserves spin.           (4.11)

When applied, the C (from conjugation) in the CPT transformation, conjugates electric charge, changes electric charge into its opposite. I conjecture that the t-swap, the inversion of time direction, is sufficient to change the electric charge of the particle into its opposite.           (4.12)

Conjugation in the original CPT theorem means changing the imaginary coordinate of the complex number (one real coordinate and one imaginary coordinate) into its opposite, which would change the electric charge into its opposite. The real coordinate remains the same. Color conjugation then would mean (4.2) rather than (4.3).

If the swap of the x-coordinate would have inverted electric charge, then, I guess, also y- and z-swap would change it. Together with time it leads to 4 inversions in total (as with the spin) that finally leads to no change in the electric charge. I conclude that conjugation of spatial coordinates have no influence on the electric charge. I guess this means that electric charge has no xyz spatial structure. But in principle electric charge could have a 4-dimensional xyzt structure.           (4.13)

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 electric charge inversion should already be in the time inversion. The CPT theorem applies to colors in quaternions.         (4.14)

Color -1

Conjectured is that there are only particles. And there is backward running of time, areas where time is running the other direction as introduced in page 2 of EXPANSION OF THE UNIVERSE.           (4.15)

I first conjecture the real axis 1 in 1ijk-space can be identified with the time axis t in xyzt-spacetime. And then I hope spacetime is built as is indicated in paragraph Filling in the vacuum marbles at page 2 of QG.

This conjecture means there are only colors i, j and k, and the colorless color 1, and when time reverses these colors change into the anticolors -i, -j, -k and -1. 1 as well as -1 are colorless. There is no color in the time axis, the time axis is white.           (4.16)

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.

We define colors i, j, k and 1 as matter and then the anticolors -i, -j, -k and -1 are antimatter.         (4.18)

In the gluon table we 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.         (4.19)

From (4.18) and (4.19) follows that quarks have color and antiquarks have anticolor.         (4.20)

For electric charge and taste this conjecture means there are only u-quarks with electric charge +2/3, d-quarks with electric charge -1/3 and positrons with electric charge +1. When time reverses these particles become the u- and d-antiquarks and the electron (underlining meaning anti-) with respectively electric charge -2/3, +1/3 and -1. The reason why positrons are taken as particle and the electron as antiparticle, is explained in paragraph Electrons as baryons at page 4 of QG.         (4.21)

There is no such thing as pure color that can be conveyed. The nearest thing to conveying the color -1 without any other property is a gluon of color -1, and gluons have spin +1 or -1.

Take a baryon (quark colors i, j, k) or antibaryon (quark colors -i, -j, -k) or a meson (quark colors i -i, or j -j, or k -k) that is hit by a gluon with color -1, coming in from the outside. The gluon couples with one quark and changes the color of it into its anticolor. The other quarks are left unchanged. The baryon or antibaryon or meson is left behind in a colored end state. That is forbidden and therefore the coupling with the color -1 gluon is rejected. The color -1 gluon, since it has only a colorless color, escapes the baryon, the antibaryon or the meson.         (4.22)

Instead of a quark, the coming-in-from-the-outside color -1 gluon can hit another gluon in the baryon or meson, changing its color into its opposite. This disturbs the color exchange processes between those quarks, leaving behind a colored end state of the baryon or antibaryon or meson. This will be corrected immediately by re-emitting the color -1 gluon.         (4.23)

Suppose the color -1 gluon hits an u-quark of color i and spin +1/2 and suppose by this action the u-quark is converted to the u-antiquark entirely. Electric charge +2/3 then becomes -2/3 and violates electric charge conservation. If the color -1 quark did only change the color i of the u-quark into -i, we are left with an u-quark (electric charge +2/3) that has the anti-u-quark color -i. Such a quark is supposed not to exist. In an eventually second change of this kind this is turned back again.

Still, in mesons this can play a role. The two quarks in the meson have colors i -i, or j -j, or k -k. A black gluon starts from the quark with color i, in doing so changing its color in -i. Then the black gluon goes to the other quark and is absorbed by it and changes there the -i into i. Same for j and k. Every first change will leave the quark of the meson with anticolor and the antiquark with color. In a subsequent change of this kind this is turned back again.

A sequence of color -1 exchanges in a baryon is showed in Application 4 page 7 of QQD.

Although color -1 gluons from the outside cannot couple definitively with a baryon or meson, there certainly is a contribution of color -1 in the color reactions between the quarks.