Dimensions by construction
A zero-dimensional space is a point, a dot of zero dimensions.
Lay a lot of points in a row, one next to the other.
Now fill in the gaps between the dots with new dots. There is a rule: between every pair of dots one can lay down another dot. After filling in till infinite you get a line. The number of dots equals the number of numbers on the number line. 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.
The empty line is spatially coherent. Somehow the dots of empty space cohere to make up the line. The points on the line are positioned relatively to each other and two points on the line have a mutual relative 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 the familiar directions of the dimensions already present. Start with one dot only.
Now lay a line next to the line you already had through the dot.
When filling in gaps till infinite, those lot-of-points make up a line in the 2nd dimension.
When a lot of lines is laid next to each other in the direction of the 2nd dimension, one gets a plane. A plane is a space of 2 dimensions.
When a lot of planes is 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. When a lot of spaces is laid next to each other in the direction of the 4th dimension, one gets 4-dimensional spacetime.
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. The 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 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 doesnít cohere with eventual other points. It seems not possible to derive the coherence of the dots that make up empty spacetime from QED as it is formulated now.
We donít know how the dots of empty space cohere, but somehow they do. If we understand, we probably will understand gravitation too as well as the expansion of the universe since both phenomenons are distortions in/ streaming of the coherence of the dots.
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