Spin is measured in values called the reduced Planck. The spin corresponding to one is a rotation in space (3+1+1 ) at three hundred and sixty degrees. Its multiples correspond to rotations by angles equal to one divided by the corresponding multiples of angles (for example, spin 1/2 is equal to the angle of rotation by 720 degrees). Most likely, spin resembles the spatial spiral of Archimedes in ( 3+1+1 ) space. The value of the Planck constant divided by 2p ( two pi ) corresponds to the step of the spiral "a" in it. Spin, like a spiral, can have a right and left direction. Let's consider some interesting coincidences between spin and the Archimedean spiral. Both branches of the spiral ( right and left ) are described by one equation. The positive values of the angle f in it correspond to the right spiral, the negative values correspond to the left spiral. If a point moves from negative values to positive values through the center of rotation, it will describe both branches of the spiral. This is very similar to the movement of quarks in the space of weak interactions, when a quark behaves simultaneously as a particle and an antiparticle. And another interesting coincidence: suppose that a point object moves in a Cartesian coordinate system with a constant velocity V directed parallel to the X axis relative to the X1Y1 plane. If the plane X1Y1 rotates with a constant angular velocity w around the Z axis , then the velocity of the point relative to the Z axis can be written as :
| Vo| = ( V2 + ( w x V x t)^2)^1/2.
The projection of the velocity V on the X and Y axes will be equal :
Vx = V x cos w x t - (w x ( V x t )) x sin w x t ;
Vy = V x sin w x t + ( w x ( V x t)) x cos w x t
Shown in Fig. 1
Now let's turn to the theory of the electroweak interaction, and compare the above formulas with the formulas of this theory for the photon Y and the boson Zo , which are a superposition of the other two particles - Bo and Wo :
Zo = Wo x cos Os - Bo x sin Qs ,
Y = Wo x sin Os + Bo x cos Os ,
where Os is the electroweak Weisberg angle.
It is possible to notice the coincidence of formulas for particles in a single space of electroweak interactions and formulas for velocities in a flat two-dimensional Archimedean spiral, according to their structural component, which indicates the similarity of their physical meanings. Later, when the splitting of the electroweak space into the space of electromagnetic interactions and the space of weak interactions occurred, the relationship between the spaces of electromagnetic, strong and weak interactions most likely took the form of a spatial Archimedean spiral with spin transitions between the spaces.
The term "Archimedean spiral" is sometimes used for a more general group of spirals, which are denoted by the formula :
r = a + b x S^1/s , where
S - is the angle of rotation of the spiral,
s - 1 is a normal Archimedean spiral,
When the dimension of space changes ( after splitting the electroweak interaction ) the flat energy Archimedean spiral has acquired the appearance of a more general case of the Archimedean spiral, which is a spatial spiral. At the same time, when the electroweak interactions were one, gravity did not exist. Gravity appeared when the splitting of electroweak interactions occurred. A spatial spiral with transitions between electromagnetic, weak and strong interactions is shown in Fig. 2. The spins of the particles have the appearance of a Mobius strip coiled into a spiral with transitions between electromagnetic, strong, and weak interactions.