# GR

*State 1.*

Let's try to regard the process of mass absorption from the Higgs field and subsequent rearrangement of vacuum particles a little closer. State 1, where we start from, is four-dimensional Minkowski space, as flat as can be.

*State 2.*

Then somewhere in space some particles *couple* and in the course of renormalization mass is absorbed from the Higgs field, which is identical to a vacuum particle being absorbed. This is state 2, a flat space with a hole in it. The hole might react as a particle but it is expected to last very very short.

It is not immediately clear whether the hole will react as a particle or not. A distance is the number of vacuum marbles on the line connecting the mass centers of two objects. When there are lesser vacuum marbles along that line, which is the case when the line crosses the hole, then these objects THUS are nearer to each other. There is no space behind the space (except for the rest of the field of all possible velocities that superposes the specific Higgs field from which is absorbed from), so it can be there is no hole particle

to observe there.

Is there a state transition from 1 to 2? Yes: first there was no hole, at the end there is.

Is vacuum particle rearrangement involved? No, not yet.

Is there an observation? No, not by us. According to accepted QED, every action of a particle going from a place to another place can be decomposed in still smaller displacements and couplings. But these observations - if you can call them observations - do not reach us, outside observers, a separate observations.

*State 3.*

Now opposite sides of the hole glue together and the hole is gone. This is state 3.

State transition from 2 to 3? Yes. First there was a hole, now it's gone.

Observation? No, not yet.

Vacuum particle rearrangement involved? Let's first regard state 3 in Minkowski space, to be called state 3M, M from Minkowski. At first sight, both sides of the hole have displaced (towards each other) over half the diameter of one vacuum particle. But we just said there is no space behind the space. So such a displacement cannot be given meaning. The only thing we can say is: first opposite sides of the hole didn't glue and now they do. But there is a *tension* now in the structure of spacetime. For the vacuum it doesn't feel

right. There is an unequalness of number of gluings and precise direction of the gluings from vacuum particle to vacuum particle around the former hole.

In order to release the tension, spacetime around the hole *curves* OUTSIDE Minkowski space until there is no tension in the vacuum no more. Call this state 3E, with the E from Einstein. The small area around the point that marks the former hole contains lesser space now (space that the hole took, has disappeared) while a little further away space for the moment remains unchanged. This is the recipe for a negative, saddle-like curvature.

Is there a state transition from 3M to 3E? In accepted GR is known that the most complicated curvature possible that still is isotropic, has an embedding space (minimum of flat space containing the curved space) of at least 7 dimensions. While the number of dimensions of Minkowski spacetime always is 4. So at first sight 3M and 3E are not *identical*. However, we already stated there is no space behind the space so distances between vacuum particles cannot be given meaning. Are there dimensions behind the dimensions, other dimensions behind the well-known 4 dimensions of spacetime? Getting ahead of the story, the vacuum particles are governed by *quaternions* and those are shown to extort the 4-dimensionality of spacetime (this is worked out in paragraph Filling in the vacuum marbles at page 2 of QG.) Quaternions need four dimensions to work. But since the space behind the space is considered not to consist of particles, the space behind the space does not exist. The handhold for the dimensionality of the space behind the space is lacking. So curved state 3E without internal tension *is* identical to flat state 3M with internal tension, there is no way to conclude otherwise. So no, there is no state transition from 3M to 3E. And no, when going from state 2 to state 3, there is no vacuum particle rearrangement involved yet.

(If 3M and 3E are *indistinguishable* but not identical states, they would *superpose* and an observation would have forced state 3 to be an *accidental choice* out of the set of all possible states in superposition. However, the first observation will be the act of gravity, the rearrangement of vacuum particles. So the superposition would remain intact until the act of gravitation.)

Is state 3E described by the Einstein curvature tensor G in GR? Or is it a simpler curvature? Once again, the vacuum particles have no way to measure relative distance between neighboring (= gluing) particles. A vacuum particle only counts the *number of gluings* with (by definition) neighboring vacuum particles and, I guess, the angular position of the glues over the surface of the vacuum particle. The actual present curvature seems to be free to choose. No curvature is forbidden, no curvature is compelled. So any mixture partly 3M and partly 3E seems valid too.

The most beautiful way is of course that the curvature equals G and that subsequently vacuum particle rearrangement performs the precise *inverse* of G, in doing so bringing in all GR effects described by the T tensor into the structure of spacetime.

What I mean is this. Masses and their acquired velocities undergo SR (Special Relativity) effects. SR is not in doubt. When the vacuum marble field sags in, it drags along all that is in it and that traverses it, including light rays. As a result the light paths bow and the light is red or blue shifted. So, when one Higgs absorption after the other is taking place, the distortions of the light ray paths caused by vacuum particle rearrangement do add up, in doing so tracing out the curved GR coordinate system. The developing light ray pattern *simulates* curved space. GR's *equations* are right, of course, but the *curvature* is as to speak an electromagnetic illusion, an optical illusion. Rearrangement of vacuum marbles always returns to Minkowski space, the background grid of vacuum particles is not curved. The contribution of gravity to the overall curvature of the universe is zero.

Let's insert some observations. The axis of Mercury's orbit around the sun is observed to rotate with 574 arc seconds per century. 531 of them are calculated to due to the other planets, 43 due to GR. 1/6 part of that 43 is due to the gravitation of the Sun on the gravitational energy between Mercury and the Sun. This means that also gravitational energy gravitates. (Julian Schwinger, Einstein's Legacy, page 198-199-200)

According to observation, let's just take GR to be true.

The wavefunction of an elementary particle is defined relative to the background grid of vacuum marbles (which is not curved), and not relative to the developing light ray pattern (which is curved). When is stated that light rays trace out geodetes in a gravitation field, the wavefunction of that light is not laid along those geodetes. Of course the photons the light consist of are dragged by the rearranging sea of vacuum marbles. But everytime the photon has chosen a next place along its curved track, the wavefunction is defined as new at that place. And that means the wavefunction is defined relative to the flat vacuum particle grid.

*Renormalization procedure* means that between each two subsequent couplings 1 and 2 the particle under consideration splits in an infinite number of itself. Each of those virtual particles (starting at 1) visits one specific place in spacetime and then returns to coupling 2. In doing so all possible places in spacetime are visited by one virtual particle. That is, the wavefunctions are laid along the paths of these virtual particles and at the return at 2 those contributions all add up. This system is set up as new every time a coupling is made. There is no accumulation from one coupling to the next. The renormalization procedure is set up relative to the flat, that is uncurved, grid of vacuum particles every coupling again.

Is this setting-up-as-new every moment really sufficient to decide renormalization performs in flat space? See paragraph Renormalization at page 4 of THE COLLAPSE OF THE WAVEFUNCTION, Argument 1 and Argument 2.

Oktober 2023

The next state is state 4 where the vacuum particles around the point of the former hole rearrange themselves to release the tension of wrong-distributed gluings (3M) or release the tension of the curvature (3E) in order to return to flat Minkowski space. It is a small *streaming* of vacuum marbles that surrounds the hole to fill it in again. But mind, there is no space behind the space. The distance between gluing particles has no meaning. So it is the question in how far well known fluid equations in flat space can give shape to this streaming

.

This is the act of gravity, this IS gravity. This goes on until space is flat and state 1 is reached again. The full act of gravity in state 4 is the precise reverse of the curvature in state 3E. Gravitational action as it is observed - yes, now we have an observation! - described by the matter energy tensor T, is the *reversed version* of the bending of spacetime given by G. So T is the precise reverse of G, from which I hope this reversal includes placing a minus sign before T. It is said Einstein has added a minus sign somewhere for no other reasons than to make things work, otherwise he would obtain a repulsive gravity. The process described so far then would explain this minus sign.

There is absorbed from that Higgs field with respect to which the mass-gaining particle is standing still, that is what is assumed. The other Higgs fields from the set of all possible Higgs fields (differing only a velocity) remain unchanged. When displacement of sagging-in shells has passed by, when *rearrangement* of vacuum marbles within the volumes of the masses and subsequently in the vacuum around them has been completed and Minkowski spacetime is restored, the superposition of all possible Higgs fields is restored again, all its fields neatly filled. Reactions keep on taking place in masses and their Higgs field absorption causes new holes in the vacuum, each hole in (usually) still another choice from all possible Higgs fields. In doing so this ensures ongoing gravitation.

The grid of marbles, spanning empty vacuum, can be called a *solid state vacuum*. All vacuum marble connections are present. The gravitational field in action, the act of sagging-in, acts like a liquid. The gravitational field in action is supposed to be a *liquid Bose condensate*. The vacuum marble connections are partly present and partly disconnected. When fully disconnected, vacuum marbles will not see each other anymore. Their relative distances become undefined. They have become superposed states relative to each other. This can be called the *gaseous state of the vacuum*.

This is the working model of gravitation we use all over my website.

Now there are two ways to proceed. First, the precise description of the mechanism of gravitation given here allows us to formulate the process in backward time direction. This is the way we go in chapter 2, if you are reading the storyline TONE. Second, we are going to fill in the vacuum marbles with particles we already know. We will do so with the colors of the gluons and quarks expressed in quaternions. This is the way we go in chapter 4 of TONE.

In this website a gamma ray, and light rays in general, do not gravitate. Photons have no net absorption from the Higgs field and thus cause no gravitational effects, despite their assigned mass according to E = hf = mc, (Energy = constant of Planck * frequency = mass * lightspeed). But to understand this you have to read the next three chapters of TONE.