Dimensions by construction

A zero-dimensional space is a point, a dot of zero dimensions.         (1)


We now want to create a line. Classical procedure, founded by the Ancient Greek, wants us then to lay a lot of points in a row.

          . . . . . . . . . . . . . . . . .

Classical procedure now wants us to fill in the gaps between the dots with new dots. There is a classical rule then:

between every pair of dots one can put another dot.         (2)

After filling in till infinite you get a line.

          line segment

According to the first page of the storyline TONE, a dot, a vacuum particle, has a finite dimension and can only be laid next to another dot, touching it, without overlap and without space in between. There is no space behind the space and thus there is no meaning to space between the dots that make up the vacuum.         (3)

Theorem (2) is nevertheless embodied by QED. In QED every real particle that goes from one place A to another place B, splits at A in an infinite number of virtual particles, each of them visits one specific possible place in spacetime and from there returns to B, in doing so making that each possible place in 4-dim spacetime has been visited by one virtual particle. At B all the infinite virtual particles reunite again to the real particle at B. Now each of the visits from A to a point X in spacetime (and each of the returns from X to B) can be regarded as at A splitting in an infinite number of new virtual particles visiting any place in spacetime and then returning to goal X. And so on. Each individual virtual particle from A via any X to B splits in an infinite number of virtual particles - this resembles theorem (2). Theorem (2) is enclosed in this procedure, although QED procedure is considerably more than only theorem (2).         (4)

In this website virtual particles and real particles are all equally real. The so called virtual particles differ only from the real ones in that they never appear in observation, they appear in calculation only. Because there is no observation, the wavefunction of virtual particles never collapses. They superpose and stay superposed, as experienced (see next page) from us, Outside Observers.         (5)

The number of dots equals the number of numbers on the number line, each dot correspond with one number on the number line (this is including QED procedure). The line as well as the number system has fractal structure. A line is a space of 1 dimension. In principle, in the beginning as to speak, it is an empty space, a space without particles.         (6)

The empty line is spatially coherent. Accoring to TONE the line consists of vacuum particles. The points on the line are positioned next to each other and two arbitrary points on the line have a relative mutual distance.

A new dimension can be made by laying a row of points, a row of dots, in a new direction, a direction that cannot be obtained by traveling in familiar directions of already present dimensions.         (7)

line segment

When filling in gaps between the dots with other dots till infinite (Ancient Greek procedure), those row of points make up a line in the direction of the 2nd dimension. These infinite number of dots between the vacuum particles, meant to construct a line, are supplied by QED procedure.         (8)

Now lay a line parallel to the line you already had through one of the new dots. In fact we now do something that is not yet allowed. We state that it is possible to create such a line, a line that has same distance to the original line everywhere. You can only measure that if the space between the lines is already existing. Space exists of dots of finite dimension, that is the opinion of this website. As long as those dots aren't there, the distance between the lines is not defined.         (8)

When through each dot of (7) in the direction of the 2nd dimension is laid a line parallel to the original line we started with, one gets a plane. A plane is a space of 2 dimensions.

When a lot of planes are laid next to each other in the direction of the 3rd dimension, one gets a space, a 3-dimensional space.

The 4th dimension is time. It is the only dimension that has a unique name. The time dimension consists of moments in the same way as a spatial dimension consists of dots. Each number of the number line correspond to one moment of the time dimension. This is in precisely the same way as each number correspond to a point on a line. When one 3-dimensional space is laid through each moment of the 4th dimension, one gets 4-dimensional spacetime. The 3-dimensional spaces are laid parallel to each other in the direction of the 4th dimension. Mind each 3-dim space has zero thickness in the direction of other dimensions than these 3.         (5)

The secret of time is extensively treated in paragraph Building vacuum from gluons at page 2 of QG. But to understand that you have to read the first three pages (nr 31, 32 and 33) of chapter 3 of the TONE storyline.

QED works in 4-dimensional spacetime. (We ignore for the moment possible curled-up dimensions.) In QED it is standard to decompose charge-photon-interactions into 3 different kinds of building blocks and 1 rule of superposition. Any electromagnetic process is described in terms of these 3 components alone.

      1) An electric charge goes from one position to another;

      2) A photon goes from one position to another;

      3) An electric charge couples to a photon (it emits or absorbs a photon).

      A) All possible ways the process can evolve are superposed.

Steps 1, 2 and A presume the pre-existence of empty space. Only step 3 can be done in a single point that doesn't cohere with eventual other points. It seems not possible to derive the coherence of the dots that make up empty spacetime from QED alone.         (9)

How the dots of empty space cohere, is extensively treated in TONE. Gravitation (chapter 1 of TONE) is interpreted as a streaming of the dots spacetime exists of. In TONE the Higgs field, the action of giving mass to the particles, curves spacetime and the subsequent streaming of vacuum dots curve spacetime back to zero net curvature. The dots are filled in with gluon pairs (page 41 of TONE, that's the first page of chapter 4), the dots cohere by the strong nuclear force, the color force.