The sea of possibilities
Travel AXC - mark we situate the Earth now at A - doesn't violate any law, not even the 2nd law of thermodynamics. According to the 2nd law AXC is improbable but not forbidden. (Well, it might be improbable-up-to-the-impossible, which is nearly the same as forbidden.) AXC fits in with the view that there is nothing special to see there happening, at the time border.
The dark meteorite of previous page, it must have come from the antimatter area, isn't it? How had it looked when it passed the time border? The time border is situated in the middle between the dark and bright galaxy. There is little light there. We can see it before, during and after passage of the time border in the light of matter stars and light from eventual matter spotlights we direct on it. We will not be able to see it in the light of antimatter stars. As said, we will see nothing special. The antimeteorite moves along a straight line at (nearly) constant speed towards the border, passes it and is here, in our matter vacuum. If the antimatter meteorite is inert (no events happening there except for light reflection on its surface) there will be no sign whether it is in bright or dark vacuum. We can see it coming from the antimatter galaxies toward us all the time, as far there is light to see in.
But observed from their point of view it looks precisely the other way around. They see the antimeteorite coming from our part of the universe passing the border towards them, along the same line and at the same speed - in opposite direction. Well, as long as there are no processes involved with a time arrow, everything will be alright. But what happen when, in stead of the antimeteorite coming to us, your spaceship in forward vacuum approaches the time border and passes it, entering dark vacuum? Will you carry a bubble of forward time vacuum around you, or what?
As our background view we take eq. (4.15) and (4.16) from paragraph Dark and bright planets and stars of equal mass at page 2 of EXPANSION OF THE UNIVERSE. And we take (6.4) and (6.5) from paragraph The gravitational field and the expansional field at the same page.
Two galaxies of equal mass, one dark, one bright, don't affect each others motion. But a small mass half way between them will be carried by the
conveyor belt. Sagging-in shells around our bright galaxy drag your ship towards it. And at the time border, at our side of it, the expanding shells of the dark galaxy drag it too, in the same amount and the same direction. The force of gravitation of both galaxies on your ship at the time border is twice the force of our galaxy on the ship.
Now comes a difficult part: to estimate a realistic situation. The situation is not just our galaxy and an antimatter galaxy. Item 14 at page 3 of this storyline joins in with the view that we are in a kind of cluster of bright galaxies in the soap-bubble structure of the cosmic web. The cosmic web is a distribution of galaxies over space in the shape of
knots (high density of galaxies),
filaments (average density of galaxies) and
planes (low density of galaxies). The filaments connect the knots and span the planes. In the voids enveloped by them there should be present clusters of dark galaxies, a similar structure of knots, filaments and planes of dark galaxies. A knot of dark galaxies in the middle of each void, the dark filaments between them crossing the planes of bright galaxies somewhere in the middle. At the cross point of a dark filament (average density) and a bright plane (low density) there is a dim chance to find a bright galaxy between more dark galaxies. Where a bright filament crosses a dark plane there you might find a dark galaxy between more bright galaxies.
As far as I know, there is no clue these days whether our galaxy is in a knot, a filament or a plane. So it is difficult to judge what distance between a bright and a dark galaxy is reasonable. Andromeda is about 2 * 10^6 light years away from us. Let's guess we are in a filament, not too far from a knot. In a bright knot the mutual distance between galaxies might be 10^6 light years and in the filaments about 10^7 ly. Let's take the distance D from us to the center of the nearest void to be about
D = 2 * 10^8 ly = ( 2 * 10^8 ) * ( 10^16 m ) = 2 * 10^24 m.
The mass of our galaxy is about 2 * 10^12 solar masses
= ( 2 * 10^12 ) * ( 2 * 10^30 kg )
= 4 * 10^42 kg
Shall we set our environment at 100 galaxies? And the antimatter cluster in the void at 1000 galaxies? We take all galaxies of equal mass.
A test mass of 1 kg is at the time border and on the line between us and them. R is the distance from the kg to them and r is the distance from the kg to us, D = r + R, G is the gravitational constant.
G * 100 * ( 4 * 10^42 ) * ( 1 kg ) / r = G * 1000 * ( 4 * 10^42 ) * ( 1 kg ) / R
100 / r = 1000 / R
R = r * SQRT 10 = 3.16 * r
D = 2 * 10^24 m = R + r = 3.16 * r + r = 4.16 * r
r = 0.5 * 10^24 m
You have a large ship similar to the dark meteorite of page 4, its size is comparable to the Mount Everest.
For convenience we take it as a homogeneous sphere with radius 10^4 m and mass of about 10^16 kg. You are at the location of the 1 kg test mass at the time border, the test mass is on the surface of your ship. The gravitational force g between the 1 kg test mass and the mass of an object x according to Newton is
g = G * m(1 kg) * m(x) / radius.
We leave out m(1 kg) and calculate some field strength g/G = m(x) / radius:
mass(100 matter galaxies) / r
= 100 * ( 4 * 10^42 ) / ( 0.5 * 10^24 ) = ( 4 / 0.25 ) * 10^( 2 + 42 - 48 ) = 16 * 10^-4 = 0.002
mass(1000 antimatter galaxies) / R
= 1000 * ( 4 * 10^42 ) / ( 1.5 * 10^24 ) = ( 4 / 2.25 ) * 10^( 3 + 42 - 48 ) = 2 * 10^-3 = 0.002
mass(You and your ship) / its radius
= 10^16 / ( 10^4 ) = 10^( 16 - 8 ) = 10^8
The gravitational force of your ship at its surface is about 10^11 times larger than the force from the matter galaxies together, or from the antimatter galaxies together. So yes, you will carry a time border around you when entering the dark vacuum. The gravitational field around your ship from the galaxies is a homogeneous field, and the field of your ship is spherical, so the time border around you is a sphere, see also EXPANSION OF THE UNIVERSE, page 2, paragraph The calculation of the time border.
g/G (all matter + antimatter galaxies) = 0.002 + 0.002 = 0.004
g/G (your ship) = 10^16 / r = 0.004,
r = 10^16 / 0.004 = 2.5 * 10^18,
r = SQRT(2.5) * 10^9 = 1.58 * 10^9 m.
That is a little more than the 149.6 * 10^6 km diameter of the Earth orbit around the Sun.
When you are at the large time border between the galaxy clusters - shall we call it the Large Time Border from now on? - you and your ship (10^4 m radius, 10^16 kg), then cross that border and invade dark vacuum, you will carry a bubble of forward vacuum around you of diameter 3.2 * 10^6 km.
(To be frank, we took the gravitational field strength that determines the time border far too large. We took all gravitation there is there, in the empty space at the time border. But the time border is determined by the difference of forward and backward time gravitational strength, to be 0.002 - 0.002 = 0 at the time border. Near to the LTB (Large Time Border) this difference will deviate from zero still very little.)
From The time border, page 4 of this storyline, we know when you go down into the ship, gravitational field strength decreases proportional to the distance from you to the ship's mass center. Is there a time border deep within the ship?
(gravitational field strength g/G) / (distance to center) = constant,
10^8 / 10^4 = 0.004 / x,
x = 0.004 * 10^4 / 10^8 = 4 * 10^-7 m.
This is a sphere of diameter of about 10^-6 m, a micron.
So yes, there is a time border deep withing the ship, but it is very small. Within it time runs backwards.
g/G (proton) = 1.67 * 10^-27 / r = 0.004,
r = 0.42 * 10^-24,
r = 0.65 * 10^-12.
So there, at the Large Time Border, the time border around every single particle is larger than the nucleus, but smaller than the atom. It lies somewhere between the electron orbitals. Within this smallest time border time runs forward again.
From page 4 of this storyline we know when the ship is near to the surface of an Earth-like antimatter planet, there is no time border any more, nor outside nor inside the ship. There only is a very tight bubble around every fundamental particle (quarks, electrons) the ship and you consist of. So somewhere on the track, from the 1.6 * 10^6 km wide sphere at the large time border between the matter and antimatter galaxy clusters, onto e.g. the surface of an antimatter planet, a transition must take place. At the end of page 4 is said that the gravitational strength is largest at the ship's surface and this will maintain to be the case. So when you approach antimatter masses and the surrounding field is increasing, the more than 10^6 km wide, spherical time border around the ship will shrink while the micron-sized time border in the ship's center will grow. A shell of forward time evolving matter remains, diminishing in thickness until they finally meet at the ship's surface and the whole ship, all its particles, react dark.
Between the myriad bubbles around the elementary particles now reigns backward time evolving vacuum. The particles react anti-entropic, with respect to the normal entropic behavior of the part of the universe you have left. The metal skin of the spaceship, stable as it is, will not show different behavior. But that doesn't hold up for life, for our human bodies and our human brain functioning.
Life-on-Earth's main property is that it consists of matter and is unstable. Left to its own it deteriorates but it takes action to stop this. This is life: deteriorating matter that takes action to stop the deterioration. (Life's second main property is its DNA base. All life on Earth is based on DNA. But we will not go into that.)
Without doing anything, your body breaks down and you die. Then you breathe in and out, take in food and drink and go to toilet, you sleep and life is maintained for quite a while. You get children and they get children too and life is maintained for millions of years to come.
Both the deterioration as well as the action-against-it obey entropy increase. If there is anything that has a time arrow in this universe, then it is life.
So when the processes in your body reverse fast enough (that means sufficiently simultaneous), you will survive the approach of the dark galaxy. All the particles you consist of will carry a tiny bubble of forward evolving time deep within them, but they now interact backward time evolving, obeying dark mechanics. When it happens fast enough, you will not notice having reversed time.
But you will still entirely consist of matter.
In fact, when you are frozen in, it should be possible. You will defrost backward time evolving - as observed by us at Earth. Also when time has come to a nearly complete stand still by moving at very near light speed, it should be possible. When decelerating, you will do so as a dark human being.
The decelerating process is a kind of bottle neck. When at near light speed, time is hardly elapsing. The time it takes for the computer to start the decelerating process might take years as observed from the outside. You easily overshoot your goal. So you have to decelerate sufficiently early, a bit too early in fact, to be sure. So near light speed travel might be accompanied by freezing in.
Since you react dark now, you will see the planet in the light of its dark sun. But when entering the dark atmosphere of the dark planet, your ship will experience severe annihilation effects of the dark antimatter air molecules. And when in contact with the surface your ship will explode as a matter-antimatter bomb.
When you manage to enter sufficiently strong dark gravitation sufficient fast, making reversing entropy taking place at the same time all over your body, you can go back in time, kill one of your ancestors by a matter-antimatter explosion, return to bright gravitation in the same way and cause timetravel inconsistencies.
But wait, we forgot something.