This note summarizes recent revisions in bit operations in binary mechanics (BM) [1] for the electromagnetic (EM) forces. Scalar and vector bit operation components are defined which may in turn result in bit motion.
In the BM tick dedicated to the scalar bit operation, if the scalar force is present, the mite quanta move to the L loci, if they are empty (0-state). With four bits in each concurrent pair of spot units, there are sixteen possible configurations. Table 1 lists the four permutations where a scalar force exists (equals one), showing initial and final states in this tick. In short, the electrostatic scalar force is the product of the two mite states.
Table 1: Scalar Bit Operation
Right Mites Left MitesLegend: State (0,1) of mite (M) or lite (L)
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Initial Final Initial Final Comment
1M 0L 0M 1L 0L 1M 1L 0M Both mites move
1M 0L 0M 1L 0L 1M 1L 0M
1M 1L 1M 1L 1L 1M 1L 1M
1M 0L 0M 1L 0L 1M 1L 0M One mite moves
1M 0L 0M 1L 0L 1M 1L 0M One mite moves
1M 1L 1M 1L 1L 1M 1L 1M
1M 1L 1M 1L 1L 1M 1L 1M No mite motion
1M 1L 1M 1L 1L 1M 1L 1M
A typical simulator [2] result is that the incidence of bit motion due to scalar forces decreases to zero over time, indicating effective repulsion, dispersion or separation of like-charged mites in the simulated space, which is what the electrostatic (scalar) potential is supposed to do.
In countercurrent pairs of spot units, juxtaposition of a mite and a lite produces vector force components (grey rectangles in Fig. 1, eqs. 13 and 14 in [1]). Similar to the scalar force, the vector force requires the product (or AND function) of two loci states to equal one (true). Table 2 lists bit operations that occur if a vector force equals one:
Table 2: Vector Bit Operation
Right Mite Left MiteLegend: State (0,1) of mite (M) or lite (L)
------------- -------------
Initial Final Initial Final Comment
1L 0M 1L 0M 0L 1M 1L 0M Left mite moves
1M 0L 0M 1L 0M 1L 0M 1L Right mite moves
1L 1M 1L 1M 1L 1M 1L 1M
1M 0L 0M 1L 0M 1L 0M 1L Only right mite moves
1L 0M 1L 0M 0L 1M 1L 0M Only left mite moves
1M 1L 1M 1L 1M 1L 1M 1L
1L 1M 1L 1M 1L 1M 1L 1M No mite motion
1M 1L 1M 1L 1M 1L 1M 1L
Similar to Table 1, Table 2 lists the four permutations of bits in the one state in a pair of countercurrent spot units. Only one M quanta may move per vector force instance, whereas a single scalar force instance may result in motion of two M quanta (first bit pattern in Table 1).
Notice that two statements may appear to be true: charge motion creates a magnetic field and a magnetic field causes charge acceleration. However, in BM the magnetic (vector) potential is seen to be the cause of mite motion, not the reverse. However, in a subsequent tick, the lite resulting from the mite motion, may itself create a vector potential. Hence, the above cause-and-effect description is true when time resolution is increased to reveal the order of events at the single tick level.
For both the scalar and vector bit operations, two components of a force may exist (the source and potential quanta) without corresponding bit motion, because the destination locus is already occupied (1-state), which may be seen as a new result of BM.
To review, the common features for all BM forces, the unconditional, scalar, vector and strong bit operations, might be summarized:
1. Bit loci states over BM distance d define a potential which may be zero or one.
2. Coupling constants always equal one and are therefore omitted from expressions. Relative strengths of the BM forces, as might be expressed in non-unity coupling constants, are measured by their counts per bit operation cycle (4 ticks) in larger volumes, which are tabulated by the BM simulator.
3. A "source" bit (at a locus in the one state), called a quanta, moves as a result of a potential only when the destination bit locus is empty (in the zero state).
4. If a potential equals one (evaluates to true), the source bit locus may be zero, rendering the potential without effect.
5. For the EM scalar and vector bit operations, only mite bits, not lite bits, may move as a result of an EM force.
6. The present assumption is that each bit operation occurs in a single tick. Hence, four ticks are required to conduct the four bit operations in a defined order, which might be said to complete one cycle in the time development of a BM state (bit function).
In short,
7. For the intra-dimensional bit operations -- unconditional, scalar and vector, quanta motion is always in the lite direction. For the scalar and vector operations, the potentials require one quanta in the one state at a bit locus perpendicular to the direction that the source quanta may move (if its destination locus is empty).
Further, all countercurrent spot unit pairs reside within the spot cube (Fig. 3 in [3]) which directs attention to the apparent importance of magetic (vector) bit operation within particles such as baryons. In contrast, all concurrent spot unit pairs are located at the six spot cube surfaces, with one spot unit in each pair in a different spot cube, perhaps high-lighting the role of electrostatic (scalar) bit operations in determining interactions among quanta in adjacent spot cubes.
Finally, the classical EM four-vector, still used in legacy quantum mechanics, becomes a six-vector in BM with three components each for scalar and vector operations [1]. Thus, the term "scalar" is not mathematically precise, since the electrostatic bit operation has three components, one in each spatial axis. Likewise, the precise definition of a vector is only analogical to the perpendicular arrangement of spot units in three spatial dimensions [3], where clearly, there is no single point of origin of the "vector".
In short, this six-vector is precisely a collection of six values (0,1) in an abstract space enumerating the EM potentials which may cause bit motion in a spot. "Scalar" and "vector" terminology provide descriptors for the respective bit operations, mostly to suggest their electrostatic and magnetic analogs in classical physics.
This BM postulate may partially explain difficulties experienced in quantum mechanic treatments where the level of fineness involves very small distances and short times, which are low integer multiples of the BM constants for distance d and time tick t. For example, consider the headaches associated with representation of the so-called point charge in classical quantum mechanic simulations [4]. That is, in BM, one has no worry that a M quanta might "explode" due to Coulomb repulstion, since a quanta is, by definition, the smallest unit of energy.
That scalar potentials may exhibit directionality in BM can coexist with the concept of a point charge exerting equal force at a distance in any direction may be due to statistical methods used in classical and legacy quantum mechanics which simply average out such directionality over distances much greater than the BM distance d, near which the directionality under some circumstances may be quite evident. Also, time resolution in typical measurements is much less than the 12 tick electron bit cycle [3], during which a particular M quanta occupies all three M loci in an electron spot. Further, if an electron spot contains 2 or 3 M quanta, electrostatic directionality would be even more difficult to detect even if time resolution were increased.
References
[1] Keene, J. J. "Binary mechanics" J. Bin. Mech. July, 2010.
[2] Keene, J. J. "Binary mechanics simulator updated" J. Bin. Mech. March, 2011.
[3] Keene, J. J. "Physical interpretation of binary mechanical space" J. Bin. Mech. February, 2011.
[4] Keene, J. J. "Captives in a binary mechanical universe" J. Bin. Mech. March, 2011.
© 2011 James J Keene