Instantaneous Spreading of the g-Qubit Fields

The Geometric Algebra formalism opens the door to developing a theory deeper than conventional quantum mechanics. Generalizations, stemming from implementation of complex numbers as geometrically feasible objects in three dimensions, unambiguous definition of states, observables, measurements, Maxwell equations solution in that terms, bring into reality a kind of physical fields, states in the suggested theory, spreading through the whole three-dimensional space and values of the time parameter. The fields can be modified instantly in all points of space and time values, thus eliminating the concept of cause and effect and perceiving of one-directional time.

where V is a set of (Boolean) algebra subsets identifying possible results of measurements.
The importance of the above definitions becomes obvious even from trivial examples.
Let's take a point moving along straight line. The definitions are pictured as ( Figure 1).
In this example it does not formally matter do we consider evolution of "state" or of "measurement of observable by the state" or of "the result of measurement" because they differ only by an additive constant or the map of one-dimensional vector to its length. In the conventional quantum mechanics similar formal identifications are commonly followed without justification.
The above one-dimensional situation radically changes if the process entities become belonging to a plane, that's dimensionality of physical process increases, though we continue watching results in one dimensional projection ( Figure 2).
In a not deterministic evolution the randomness of observed values is due to the fact that their probabilities are associated with partition of the space of states The option to expand, to lift the space where physical processes are considered, may have critical consequence to a theory. A kind of expanding is the core of the suggested formulation.

Lift of Qubits to g-Qubits
The very first critical thing for the whole approach is to generalize algebraically formal two-dimensional complex number vectors to geometrically clear, unambiguous objects-elements of even subalgebra 3 G + of geometric algebra over the three-dimensional space. Such objects are identified by an arbitrary oriented plane in three dimensions and angle of rotation in that plane. I will call such objects g-qubits, if they have unit value, to distinguish them from qubits as 1 Correctly would be to say "by a state". State is operator acting on observable.
It can be conveniently written in exponential form: e e The g-qubit on the right side of Figure 4 has the right-hand screw orientation.
Take arbitrary qubit x iy x iy , is an arbitrary triple of unit value bivectors in three dimensions satisfying, with not critical assumption of right-hand screw orientation , the multiplication rules, see Figure 5:

Maxwell Equation in Geometric Algebra
Let's show how the system of the electromagnetic Maxwell equations is formulated as one equation in geometric algebra terms [4].
Take geometric algebra element of the form: The electromagnetic field F is created by some given distribution of charges and currents, also written as geometric algebra multivector: ρ 3 and multiplication is the geometrical algebra one, to the F. The result is:

Without charges and currents the equation becomes
The circular polarized electromagnetic waves are the only type of waves following from the solution of Maxwell equations in free space done in geometric algebra terms.
Indeed, let's take the electromagnetic field in the form: requiring that it satisfies (4.1).
The geometric algebra product ∇F is: kh I e .
The result for the case 3= S I kI is that the solution of (4.1) is where 0 e and 0 h are arbitrary mutually orthogonal vectors of equal length, lying on the plane S. Vector k should be normal to that plane,  and − F saving the structure of (4.2) will also be a solution.
Let's write: is solution of (4.1). The item in the second parenthesis is weighted linear combination of two states with the same phase in the same plane but opposite sense of orientation. The states are strictly coupled, entangled if you prefer, because bivector plane should be the same for both, does not matter what happens with that plane.
One another option of linear combination saving the structure of (4.2) is:    The expression (4.5) is linear combination of two geometric algebra states, g-qubits.

Clifford Translations of States (4.5)
For is associated with a Hamiltonian, that's the translation is is lift of a Hermitian matrix α β γ δ γ δ α β is generalization of imaginary unit in the current theory, then: with:

Conclusions
The seminal ideas: variable and explicitly defined complex plane in three dimensions, the 3 + G states as operators acting on observables, solution of the Maxwell equation(s) in the 3 G frame giving 3 + G states, spreons, spreading over the whole three-dimensional space for all values of time, along with the results of measurement of any observable, allow putting forth comprehensive and much more detailed formalism replacing conventional quantum mechanics.
The spreon states, subjected to Clifford translations, change instantly forward and backward in time, modifying the results of measurements both in past and future. Very notion of the concept of cause and effect, as ordered by time, disappears.

Conflicts of Interest
The author declares no conflicts of interest regarding the publication of this paper.