The main law in (quantum) physics is the law of conservation of energy. It is like a cylinder with a piston inside. I can move the piston to and fro but the sum of the lengths at both sides of the cylinder is a constant (invariant). So when I move the piston to the left – position 1, see the image below – I get 2 values: 15 and 17 (sum 32). However, I can express every position of the piston with the help of a sign bit – a negative or a positive position (see the scale division). In this way I can describe every position of the piston at both sides of the cylinder with only one number and a sign bit.
Quantum fields are not composed of cylinders with a piston inside. The typical feature of the basic quantum fields – fields that are existent everywhere in the universe – is the spatial and the homogeneous structure of the volume. So when I want to design a quantum computer I have to simulate the structure of the basic quantum fields with the help of scalar and vector properties.
The unit that composes a spatial structure that have scalar and vector properties is a deformed scalar with an invariant volume. Figure 2 shows the cross section of the unit. The volume of the scalar is grey and the deformed (vectorized) part is blue. To keep it simple the deformed part of the unit is drawn like a cube but keep in mind that the symmetric volume shows any vectors (blue volume).
The only mathematical true scalar is a sphere. So when the cause behind the deformation of the unit is removed, the shape of the unit will become a sphere again. Thus the scalar expands (increases) at the positions of the red arrows (figure 2). However, the deformation of the unit is caused by the existence of all the other units around so theorizing about the alterations of the unit is senseless without considering the environment of the unit. A surrounding that is filled with units which have exactly the same properties as every other unit in the universe. That is why the vectorised part of the unit and the size of the scalar (dotted circles) can be altered by other units.
The image above (3) shows one unit (M) in the centre of its surroundings. Now it is clear that every alteration of the shape of one unit will affect the other units around in a direct way. So all the alterations of the shape of the distinct volumes of the units are synchronized because the volumes of the units are identical and invariant (all the units tessellate space).
Suppose I substitute the red arrows in figure 3 with the cylinder in figure 1. Every alteration of a unit is an internal transfer of volume from one face (or faces) to another face (or faces). Just like the altering volumes inside the cylinder when the piston is moved to and fro.
The result is an alteration of all the binary numbers that represent the joined faces between the units at the same moment. Conclusion: the principle simulates the quantum computer in a perfect way.
Next post: “Topological transformations”