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
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.
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)|
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.
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