Time reversed gravitation

Pages 2 and 3 of this storyline are based on the theory of gravitation of this site, described in page 3, 4 and 5 from the storyline NEG (NEWTON EINSTEIN GRAVITATION). To understand this page you need to read those pages 3, 4 and 5 carefully.

The storyline QQD (QUANTUM QUATERNION DYNAMICS) replaces the colors of the strong nuclear force by quaternion units. Page 2, 3, 4 and 5 of the storyline QG (QUATERNION GRAVITATION) uses this to describe the vacuum marbles (the particles our vacuum consists of) as quaternion unit pairs (pairs of gluons we take them to be). For this page QQD as well as QG are not important, except for the 2nd paragraph of this page, Dark multiplication rules, that uses the quaternion description of the vacuum intensively. You can skip that paragraph and read it later.

1. Time reversed gravitation

In the first place we use

dark matter = backward time evolving matter

bright matter = forward time evolving matter


Only in second occasion we state

dark matter = antimatter

bright matter = our kind of matter


We go for the view that dark mechanics, ruling dark matter in dark vacuum, is in fact bright mechanics, the film of events being played backwards.

Vacuum streams out of a dark star. Still we see a planet orbiting it, a dark planet. Against the outflow of vacuum it deviates its track towards the star. Dark mechanics. Antimatter mechanics.

We don’t actually see it violating laws of mechanics, not in the light of its dark sun. For more about the visibility of dark matter, see page 4 in the storyline FORWARD BACKWARD TIME DIRECTION.

The left picture here is fig. 5 from page 1 of storyline NEWTON EINSTEIN GRAVITATION. There the inward flow of vacuum adds a velocity increment to the blocks that go with the flow.

Event A := Event B

means Event A becomes Event B by means of time reversal. In this page time reversal means the film of the event being played backwards.

              Forward vacuum                                           Backward vacuum

In the right picture, as to speak, outward flow of vacuum removes velocity from the blocks. As if there is a hidden supply of velocity (in equal amounts in both directions, carefully adding up to zero) from which the outward stream of vacuum erases one. The complement velocity, directed towards the dark star, remains and pushes the planet a bit towards the star, thus forcing it in orbit around the star.

Dark flow erases velocity.         (1.3)

A laborious formulation, but using the view of vacuum flow, I see no other way to create the film of events in backward time direction.

But then again, in the picture given at page 3, 4 and 5 from the storyline NEWTON EINSTEIN GRAVITATION, when gravity is in action, space is disappearing. Shells of vacuum marbles after rearranging have smaller surface than before rearranging of the vacuum marbles. Space is shrinking when gravitation is in action, observable by all things floating in the vacuum being dragged by it.

In the dark matter Higgs marbles are emitted in the course of backward time evolving renormalization. The new Higgs marbles - after conversion to gravitons, see QUATERNION GRAVITATION page 3, paragraph 1 point (3.6) - constitute new vacuum marbles that are immediately absorbed by the vacuum, enlarging it by their volume. Space expands then. Despite we observe the orbiting dark matter (in so far we can observe dark matter) being dragged by as if space was shrinking there (caused by the erasing of velocity), space in fact is expanding there. There is more space between them and us, the number of vacuum marbles connecting them and us has grown.

              Forward vacuum                                           Backward vacuum

Reconsider the two-picture scene in item 13 at page 1 of this storyline. This scenario is not wrong when performed in forward time evolving vacuum alone. That results in repelling gravity that observably doesn't exist here. What is meant to depict backward time evolving gravity is to time-reverse the process of sagging-in shells of gravity and to do so in backward time evolving vacuum.

2. Dark multiplication rules

At this page only this paragraph uses the quaternion description of the vacuum intensively. You can skip this paragraph and read it later.

In this site is assumed there is forward time evolving vacuum and backward time evolving vacuum, separated by the time border. At page 1 of the QG storyline vacuum is treated as a sea of vacuum marbles. At page 2 up to 5 of QG is described how the vacuum marbles are filled in with gluon pairs, the colors of the gluons described as quaternions. It must be then that also the computation rules at both sides of the time border are different.

Our computing rules are:
1 * 1 = -1 * -1 = 1 (2.1)
1 * -1 = -1 * 1 = -1 (2.2)

Regard the 2 vacuum pairs ( 1   1 ) and ( -1   -1 ). We assume multiplying by the time reversing factor -1 yield these vacuum pairs in backward time evolving vacuum; which turned out to be the same 2 pairs. Applying ( 1   1 ) means   * 1 * 1, applying ( -1   -1 ) means   * -1 * -1.         (a)
Assumed is a backward time evolving vacuum pair equals -1.          (b)
(a) and (b) together forces us to set equal  * 1 * 1 = * -1 * -1 = * -1.

OR this is nonsense, OR this means their sign multiplication rules, as observed by us, are:
-1 * -1 = 1 * 1 = -1 (2.3)
-1 * 1 = 1 * -1 = 1 (2.4)

Swap all signs in one set of rules, that gives the other set. Another way of stating this is: start with our rules and multiply every factor with -1 (multiplying with -1 reverses time), this gives their set. When they multiply every factor with 1 according to their rules, one gets our set back again. As observed by us, 1 is the factor that reverses time in their world.

Since this should be all there is to the direction of time, to the difference between forward and backward time evolving vacuum, one states also:

-i * -i = i * i = 1 (2.5)
-i * i = i * -i = -1 (2.6)
and in the last line one recognizes the vacuum marble pair ( i   -i ) yielding -1, the backward time evolving vacuum as observed by us.

A little more about square root -1.
Us 1 * 1 = 1 1^2 = 1 (1^2)^0.5 = 1^0.5 1 = 1^0.5
Them -1 * -1 = -1 (-1)^2 = -1 ((-1)^2)^0.5 = (-1)^0.5 -1 = (-1)^0.5       (2.7)

So the square root of minus one is extracted here without introducing complex numbers. The outcome is minus one. And you have to do it there, not here. In backward time evolving vacuum as is supposed to be present in dark antimatter galaxies. You have to do it there, but observe it from here, not there. As observed by them it is here that the square root of minus one is extracted without the use of complex numbers.

There is little difference between forward time vacuum and backward time vacuum. The vacuum neutrino field swaps spin. The multiplication rules swap sign.

3. The sink drain

A similar problem like this in item 13 of page 3 of the storyline FORWARD BACKWARD TIME DIRECTION is the following.

Imagine a large shallow lake with in the middle a large sink drain. Water violently flows away through the drain, causing a radial stream of water onto the middle of the lake.

Or imagne a small Niagara Falls, however not a straight wall of water in a river but a closed circular wall of water in a lake. We assume the radial stream in the lake is without vortices. (I am not sure this is feasible with a real lake, but assume it to be so here.)

Then a jetski circumvents the rim of the cirular falls. It steers straight forward with constant speed and perpendicular to the stream. The stream drags it sideways toward the falls. The velocity of the jetski is precisely such that the jetski not escapes into the open, nor is it dragged in the Falls. The jetski keeps on circumventing the pool at constant distance of it center at constant speed.

Now time is reversed. The water streams out of the drain now, or the falls speed upward and push the water present there aside. pushing the jetski away from the drain. The jetski still can circumvent the drain by steering sufficiently toward its center, at an angle with the direction perpendicular to the stream. But I want the reversed sequence of events of the original situation. Why doesn’t that work?         (3.1)


Maybe more advanced techniques hint for a solution.
Elie Joseph Cartan, 1869 - 1951, found solutions to the Einstein equations with torque-description. These were equal to Einstein’s but more complex, so they chose Einstein’s.         (3.2)

Observed from the dark planet - time runs the other way now - there is nothing special there. Vacuum is flowing into the dark star, it drags the dark planet along with it and because of the planet’s velocity it orbits the star. They experience themselves as bright. If they look up to the sky they see us, our kind of matter, as being dark. They don’t see us. So they don’t have to observe the earth’s velocity to deviate towards the sun while vacuum is streaming out of the sun, as they observe it.

4. Dark and bright planets and stars of equal mass

What happens when two planets of equal mass, one bright, the other dark, pass each other by? For convenience assume equal radius too. There is outflow of vacuum from the dark mass and inflow of vacuum into the bright mass. At all times the outflow of vacuum from the dark mass equals precisely the inflow of vacuum into the bright mass. As a consequence there is only a flow of vacuum between the planets. The amount of vacuum between the planets remains the same. They will not change each other's motion, they will not deviate each other’s paths. They will pass by each other with constant rectilinear motion, their orbits just any pair of straight lines. They feel no signs of their mutual passage - as long as they do not collide, of course (matter-antimatter explosion).         (4.1)

When relative velocity is zero, they will keep on hanging there, motionless relative to each other.         (4.2)

Visibility depends on the light source. In the light of the dark sun you will not see anything. Our eye is not adapted to light that is drawn from us, instead of light entering the eye. In the light of a matter sun or the lights of your ship you will see both planets (dark and bright) alike. More about this in The dark meteorite at page 4 of FORWARD BACKWARD TIME DIRECTION.         (4.3)

Two stars of equal mass, one dark, one bright, will act like the planets do. A dark star cannot orbit a bright star of equal mass.         (4.4)

Compare the vacuum, the sagging-in of shells and dragging by of all that floats in it, with a conveyor belt. Since the velocity of the belt out of the dark planet equals the velocity of the belt into the bright planet, there is no tendency of the belt to reduce nor enlarge their mutual distance. The belt doesn't lengthen nor shorten.         (4.5)

What happens when the bright mass measures e.g. 7 units of mass and the dark mass 3 units of mass, and then they pass by each other? Using the view of the conveyor belt connecting the masses, now 7 units of length of vacuum flows into the bright mass against 3 units of length of vacuum in the same time flowing out of the dark mass. The flow between the masses decreases distance with 7 - 3 = 4 lengths in the same time, constituting an attraction. The force is considerably smaller than with Newtons gravitation law between bright masses.

Now shift view to the 3-units dark mass, so it is bright now. Time runs the other way now, the 7-units is dark now. We see 7 units of conveyor belt streaming out of the 7-units dark mass against 3 units streaming into the 3-units bright mass. The 7-units wins but since its surrounding vacuum is dark it erases velocity. So the gravitations subtract but then is still attractive because the dark vacuum erases velocity instead of adding it. This is laborious, but I see no other way to make things fit.

Imagine a dark snowball, an antimatter snowball of 5.97 kg. From the depths of the void it had made it to the earth, just above the atmosphere. The mass of the Earth is 5.97 * 10^24 kg. Imagine the conveyor belt. For every 10^24 meters of conveyor belt streaming into the earth, is there about 1 meter streaming out of the snowball?

In The calculation of the time border will be derived that the time border around such a snowball is not there. There only are very tiny time borders around each quark. As far as is concerned their mutual gravitational influence, even the antiquarks react bright at the Earth surface. This doesn't withhold the gravitational force from the dark snowball to be repulsive, as observed from our point of view. As observed by us, the quarks the snowball consist of, emit to the Higgs field, causing expanding shells, a repulsive gravity. As long as this enlarging of space is behind the time border (behind from our point of view), it erases velocity. However, very soon it has passed the time border around each quark and then it is just repulsive gravity that is left.

So the dark snowball is dragged along with the gravitational field of the earth, just a tiny little bit slower than a bright snowball would do (1 meter conveyor belt streaming into the bright snowball against 1 meter conveyor belt streaming out of the dark snowball). The behavior of a dark snowball in the earth atmosphere is nearly precisely that of a bright snowball. Both snowballs obey bright mechanics, mainly. (Except for annihilation effects of atmosphere molecules on the antimatter snowball.)

So a bright snowball can orbit a dark planet, obeying dark mechanics. Or a rocket can. I can land there. (Not wisely, but I can.)

Don't you see Don't you see

And now for the formulas. To imagine what happens, keep in mind two things.

First the picture of gravitation around a bright mass (matter). Sagging-in shells, inward displacing shell content, drag everything in it along with the shells. Around a dark mass (antimatter) expanding shells, outward displacing shell content, also drag everything in it along with the shells. This is the main picture.         (4.10)

Second, there is the time border, a mathematical plane separating forward and backward vacuum. Forward vacuum is the vacuum we know. In backward vacuum the laws of physics are different. Velocity is erased there to keep planets in orbit, see paragraph 1. The multiplication is different, -1 times -1 equals -1 there, see paragraph 2.         (4.11)

Gravitational force is a vector. If vectors are given in bold, the Newton gravitational law for matter in bright vacuum is:

F = G * M1 * M2 * r / r^3         (4.12)

which is just the well-known gravitational law F = G * M1 * M2 / r multiplied by r/r, a unit vector made from the vector r that points from point mass M1 to point mass M2.

Instead of this we better use gravitational field strength g (gravitational force on a point mass of 1 kg). Set M2 = 1 kg.

g = G * M1 * r / r^3         (4.13)

In this site we will use g/G and equal that to M1 / r times the unit vector r/r.

g/G = M1 / r * r/r.           (4.14)

This is the field strength around M1 (and caused by M1), r is the vector pointing from a point you want to know the field strength of to M1.

With this formulas we are not yet able to reproduce (4.1) and (4.2). It is not true that between two planets of equal mass, one bright, one dark, at every point the amount of sagging-in cancels the amount of expanding-outward. (So when a planet rotates sufficiently fast around its axis and the planets are near enough to each other, then tidal effects are expected!) But one can image that, from the vacuum between the planets, the total decrease of vacuum by the bright planet cancels the total increase of vacuum by the dark planet. And since the amount of vacuum between them doesn't change, their relative distance is maintained.

As said, we better talk about gravitational field strength instead of gravitational force:

g/G at the location of a bright test point mass m caused by a bright mass M1 and a dark mass M2 is:

g/G = M1 / R * R/R + M2 / r * -r/r           (4.15)

where R is a vector pointing from m to M1 and r is a vector pointing from m to M2. So m is in O, the Origin. It is precisely the same as force in the usual Newton gravitation law. The force F on m is

F = G * M1 * m / R * R/R + G * M2 * m / r * -r/r           (4.16)

The actual effect of the gravitational force from dark matter is repulsive only in bright vacuum. In the dark part of the vacuum it erases velocity.

Are the orbits of the masses elliptic? And if velocities too high, hyperbola's?

Original text, start

The formula for the gravitation F between the dark and the bright mass seems to be:

F = G ( m-bright - m-dark) / r           (4.1)

r being their mutual distance, G = gravitational constant. When m-bright = m-dark then F = 0.
Mechanics, dark and bright together.

But I should not be surprised when the formula turned out to be:

F = G ( m-bright / m-dark) / r           (4.2)

When m-bright = m-dark then F = G / r, which for planets is also about 0.

If (4.1) is right, then a particle and its antiparticle don’t annihilate under the force of gravity since particle and antiparticle have equal mass. They exert no gravitational force on each other.

When (4.2) is right, a particle attracts its antiparticle by a gravitational force F = G / r, becoming as strong as the particles are permitted to approach each other before actual annihilation.

Original text, stop

Don't you see Don't you see

Regard again the two identical planets M1 and M2, one bright, one dark, and suppose them at rest relative to each other. As said, they stay at rest relative to each other. The time border between them necessarily is the flat plane halfway between them, perpendicular to the line connecting the planets. Regard the point at the bright side (in bright vacuum) nearest to the cross point of the connecting line and the time border. There the force of both planets are equal and work in the same direction. Everywhere along the route from M1 to M2 the acceleration is the sum of accelerations working in the same direction and proportional to M1 / R + M2 / r. When free floating and put at rest relative to the planets, a test mass m cannot remain standing still on the time border.

One can launch mass m straight up to the other planet. While climbing it reduces speed and we can launch it such that precisely at the time border it comes to a standstill. The next moment it starts falling back, in a time-reversed version of the climbing path. Eventually mass m doesn't climb completely straight up but in a kind of elliptical orbit. Then, when one moment being tangential to the time border, it would just complete its orbit. (I am not sure the orbit is elliptical.)

When starting speed was just a little higher, we observe mass m to pass the time border and fall with increasing speed to the dark mass. Mind, at the dark side the force erases velocity. Finally m collides with the surface in a matter-antimatter explosion. But well, it is not precisely an explosion.

In fact m doesn't fall to the dark planet, despite we observe it so. Evolving backward in time we know m being launched from the surface of the dark planet. As they observe it, in an anti-entropic fashion an antimatter mass m is drawn from their planet's surface and speeds upward, reducing speed while climbing.

Since free floating, matter mass m, as we observe it, reduces speed when climbing to end at some none-zero speed at the time border. It ends its evolution there. It clicks on to the course of events of mass m at our side being launched towards the time border.

To be frank, mass m has no natural source at M2. So at the time border there exist a superposition of all possible ways m could have come to existence there. From the superposition then is taken the most likely event, that's the way it usually happens. The described course of events is not the most likely, maybe.

Similar considerations are made in The time border, page 4 of FORWARD BACKWARD TIME DIRECTION, and page 6 and 7 of the same storyline. Skip The diamond at page 5.

5. The bouncing ball

Imagine bright planet M1 and dark planet M2 sufficiently far from each other to cause no significant tidal effects. Suppose the planets don't rotate around any of their axes and just hang there motionless with respect to each other. Where the line connecting their centers crosses the surface, a platform is laid, its perfectly flat surface precisely perpendicular to the connecting line. A bouncing ball with sufficient energy bounces up and down between the platforms, from planet to planet all the time. But no, let's not start with such an entropic thing as a ball (temperature rises in an atmosphere, radiation is emitted in empty space). We start with one single particle. No, we start with one single photon. We know its speed and it has no trouble with the antimatter composition of the platform at M2.


6. The gravitational field and the expansional field

Move the cursor from left to right over the lightgreen-lightblue bars to show the mechanism of gravity as proposed in the storyline NEG page 3, 4 and 5. The left side row of bars, denoted as Forward show gravitation, the row of bars at the right side denoted as Backwards show the mechanism of expansion of the universe - in fact antigravitation, the gravitation of antimatter.

yellow = three dimensional vacuum, consisting of vacuum marbles. For convenience, regard each shell as consisting of a layer of one vacuum marble thickness.
gray = a hole in the vacuum
A = a mass center


Forward vacuum
Backward vacuum


Mass A absorbs one or more vacuum marbles (Higgs particle/gravitons) from the vacuum, leaving a spherical hole there (cursor at second bar of first row, shown is a gray triangle-like part of it only)
Shaded = vacuum marbles at the brink of falling into the hole. When they actually do, they leave behind a new, shell shaped hole. Each shell shaped hole has the same volume as the original sphere in the center, so when the surface of the shell increases, the thickness of the shell decreases by the same factor.           (6.1)
(For the shells hold that there is lesser space inside than there ought to be, due to disappearance of one or more vacuum marbles, while the space outside hasn't changed yet. This meets the requirements for a local - and temporal ­- negative curvature.)

Suppose, in the depths of the nearest void is a cluster of galaxies, evolving backward in time. They are immersed in backward vacuum, they consist of antimatter and they are dark. (We follow arguments from page 1 of this storyline, item 9 and further.) Regard a dark star there, with some dark planets around it. The mechanism of gravity in backward vacuum as observed by us, is depicted by the second row of bars. As observed by us, it comprises an outward flow that drags by everything floating in it: a repelling gravity. But mind, as observed by us, in backward vacuum the outward flow erases velocity from the dark masses, still making the dark planets to orbit their dark sun.

(The only hint for an explanation of this strange behavior comes from quaternions, where is suggested forward and backward vacuum to differ in their multiplication rules, see paragraph 2. We adopted forward vacuum to equal 1 and backward vacuum to equal -1, see The CPT-theorem in the storyline QQD. This makes them distinguishable from each other - if not the first moment then at the second.)

As observed by them themselves, they are bright. The particles they consist of absorb vacuum marbles and a subsequent inward flow of vacuum drags everything floating in it towards the gravitational centers according to the picture of the first row of bars. The sequence of sagging-in shells proceed outward and finally meets the time border, somewhere in between the void and us. And then, what happens there?

The time border is a plane separating forward and backward vacuum. From quaternion considerations (see paragraph Dark multiplication rules) we concluded the border is seamless. It is by no means a special place and there is nothing special to see. A photon proceeding in forward vacuum and then entering backward vacuum, traces out a straight line in spacetime. Also particles show nothing special in their track when passing the border, see also Cross roads, page 6 of FORWARD BACKWARD TIME DIRECTION. Then, since rearranging of vacuum marbles is regarded as a kind of particle reaction, also the outward bound series of sagging-in shells around the dark sun, as observed by them, will pass the border without changing shape in spacetime.           (6.2)

Only the judgements differ. We judge the photon or particle to proceed towards the time border, leave our vacuum and enter theirs - and they from their point of view judge precisely the same!           (6.3)
The time border itself is a mathematical plane, it does not consist of anything. In quaternions, there are forward vacuum marble pairs equaling 1 and there are backward vacuum marble pairs equaling -1 and that's all there is to a vacuum. For more about the time border, see page 4 and 5 in the storyline FORWARD BACKWARD TIME DIRECTION.

When the sequence of sagging-in shells around the dark star as they observe it, passes the time border and enters our vacuum, then we judge the sequence as an outward flow, an antigravity. IF the sagging-in of shells in our vacuum drags by masses floating in it (constituting gravitation) THEN the inward bound series of outward expanding shells in our vacuum is dragging by masses in precisely the same way. What is ordinary gravity in their vacuum, becomes repulsive gravity in our vacuum when passing the time border.           (6.4)

The packages at the conveyor belt are free falling. When in forward vacuum (from the time border nearer to the bright mass) they fall with increasing speed to the bright mass. But this velocity is increased by the now repulsive gravitation of the dark mass. When in backward vacuum (from the time border nearer to the dark mass) they fall with increasing speed to the dark mass, this velocity now increased by the repulsive gravitation of the bright mass. Without any propulsion you cannot stay at rest at the time border. When in case of two matter galaxies there is a point between them where the attractive forces of both galaxies cancel out. But in the case of a matter galaxy and an antimatter galaxy of equal mass the forces to deviate anything, bright or dark, away from it, are twice as strong as the gravitational force of one of the two galaxies alone. At the time border the effect of the force switches between erasing velocity and usual F=ma, but a point of zero force does not exist. This keeps the time border free from anything hanging around there. There is very little matter (or antimatter) there to show this. Dark matter (in the sense of backward time evolving matter) remains well hidden!           (6.5)

Is backward evolving matter a candidate for the Dark Energy?           (6.6)

It might be another piece to the puzzle why our space is flat on large scale. As is pointed out at page 6 of GRAVITATION at the end of paragraph 1, vacuum marble absorption curves space but subsequent rearranging of vacuum marbles restores flat spacetime, good old Minkowski spacetime. For backward matter this works precisely the same in their frame of reference, and that doesn't change when observed by us then.           (6.7)

The conclusion of item 13 at page 1 of storyline THE DIRECTION OF TIME is wrong. It is right when performed entirely in forward time vacuum. In backward time vacuum rules dark mechanics, the outflow of gravitational field erasing velocity. The shown conclusions - the pictures - in item 3 of page 1 from FORWARD BACKWARD TIME DIRECTION are restored.

7. The calculation of the time border

Let's state as a theorem:


Where gravitation and expansion equal each other, there is the time border.

For a test mass m on the time border between mass M and mass bM holds:
( b is a real number larger than 2, d is the distance between M and bM, all masses are point masses )

G * m * M / r = G * m * bM / R

1 / r = b / R

r * b = R

(x + y + z) b = (d - x) + y + z

                        = x - 2xd + d + y + z

(x + y + z) (b - 1) + 2xd = d

x + y + z + 2xd / (b-1) = d / (b-1)

(x + 2 * x * d/(b-1) + ( d/(b-1) ) - ( d/(b-1) ) + y + z = d / (b-1)

(x + d/(b-1) ) + y + z = ( d / (b-1) ) + d / (b - 1)

(z-axis not shown)

b-1=a, b=a+1, a is larger than 1

For a test mass m on the time border between mass M and mass aM holds:

(x + d/a ) + y + z = d / a + d / a           (7.2)

The time border is a sphere around mass M with radius r(tb) = SQRT( d/a + d/a ) and off-center over distance d/a; Take d=1 so r(tb) = SQRT( 1/a + 1/a )

a 2 3 4 5
1/a 0.50 0.33 0.25 0.20
r(tb) 0.87 0.67 0.56 0.49
r(tb) -1/a 0.37 0.34 0.31 0.29

When a is very large then the time border is a sphere of radius r = SQRT( d/a ) = d / SQRT a
and M is in the center of the sphere.           (7.3)

Regard an antiquark in an antiproton at the Earth surface. There is a bubble of backward time evolving vacuum around the quark of radius r. Then a = 3.57 * 10^51 * 3, that is the number of nucleons the earth consists of (see calculation of the vacuum marble radius) times 3 (there are 3 quarks per nucleon) and d = the radius of the Earth = 6.38 * 10^6 m. The radius r of the bubble

= d / SQRT a

= 6.38 * 10^6 / SQRT( 3.57 * 10^51 * 3 )

= 6.2 * 10^-20 m.

In its own frame, in its tiny bubble, the antiquark absorbs a vacuum marble in the course of renormalization. In our frame this bubble is experienced as a backward time evolving vacuum wherein the quark did emit a vacuum marble. The emission causes shells around the quark to expand (the time reversed version of sagging-in of shells) that nevertheless erases velocity from present particles (if there were particles inside). Once outside the bubble, the expanding shells are repulsive gravity indeed.

Compare this to the radius of the proton that is (a little less than) 10^-15 m and the vacuum particles that are supposed to maintain a relative distance of between 10^-20 and 10^-21 m. So the backward bubble around an antiproton at the earth surface is about 10 to 100 vacuum particles across and is residing as a tight jacket around the quark that emitted (in our frame emitted) the mentioned Higgs particle. So for 1 antiproton at the earth surface even between the antiquarks the vacuum is still forward. No anti-entropic behavior to be expected there!

The mass of the quark. There is little known about the quark mass. The mass of a quark might be larger than the mass of the proton and being reduced by the so-called mass defect when the 3 quarks clump together. The mass of a quark might be smaller than 1/3 of the mass of the proton and then being enlarged by its high average speed in the proton and special relativity. But we don't have to know the mass of the quark, we only need the ratio between the number of quarks in the Earth and in the quark (1 of course). We don't isolate that single quark. It is thought as to keep its presence within the baryon and so we assume no further corrections are necessary.

Only when the number of clumped together antimatter atoms grows, they first conquer the space in the antiprotons, then win backward vacuum in the atom's volume, and finally occupy the space between the anti-atoms and anti-molecules. And then anti-entropic behavior is expected.

What happens then is worked out at page 7 of FORWARD BACKWARD TIME DIRECTION. Time border behavior is worked out there. But you better start reading page 4, skip The Diamond from page 5 and then read page 6 and 7.

An antiproton - its own gravitational field negligible - falls in the earth’s gravitational field just as a proton would do (well, nearly as a proton would do), compare the dark snowball in paragraph 3. And likewise when an electron-positron pair emerges, they are supposed to be separated from the first moment and to obey forward vacuum behavior.

If one has followed argumentation in page 3 and 4 of NEG (or, what is the same, paragraph 1.1 and 1.2 in TONE), then it is clear that by the absorption from the Higgs field and subsequent action of gravity, vacuum is shrinking. While at the same time the backward time evolving vacuum by the emission to the Higgs field, is expanding. As a consequence the time border (the border between forward and backward evolving areas) starts moving towards forward time masses, and away from backward time masses. While the calculation above shows the time border not to be dependent of time. So I assume it is time for another theorem:


In doing so we assure the time border to remain stable at its calculated position. Also, if the vacuum marble is a structure, it changes into its enantiomer. More about this at page 2 of QUATERNION GRAVITATION, especially (2.13) and (2.14).

8. Massless coinciding

And what if the pair does coincide? The proton mass is about 2000 times the electron mass and at the earth surface the distance r becomes SQRT 2000 or about 50 times smaller. So by coincide we mean: within a distance of about 10^-20 m and this is near to the highest resolution the vacuum marbles can support.

The electron absorbs Higgs particles from the vacuum. The positron inside the time border, as observed by us, emits Higgs particles at the same pace. As a consequence the composite does not absorb nor emit Higgs particles and thus is massless and has zero gravitational field.

Since the particles have no mass, they immediately gain lightspeed. They force each other along the same path, because the slightest separation (10^-20 m) would separate the forward and backward vacuums and then the electron and positron would get mass, for which the energy is lacking.

By now the composite is resembling the photon too much to ignore. See more about it at page 5 of the storyline NET FORCE IN QED.

If this is the photon, then also the gluon might consist of a quark and an antiquark, massless coinciding. The spin-story would be identical. The electric charges would cancel likewise. If the taste of a quark is u, then the taste of its antiquark must be anti-u, and u and anti-u should cancel then to zero taste. See more about this in paragraph Meson exchange at page 4 and especially Four quarks in the shell at page 5 of the storyline QCD.