Saturday, March 19, 2011

Electromagnetic Bit Operations Revised

Updated: Oct 26, 2014
This note summarizes recent revisions in bit operations in binary mechanics (BM) [1] for the electromagnetic (EM) forces. Scalar and vector potentials are defined which may in turn result in bit motion.

Fig. 1: Scalar Force in Concurrent Spot Units
Fig. 1 shows right and left pairs of concurrent spot units. Each spot unit contains a mite bit locus (circles) and a lite bit locus (arrows), the direction of which determines unconditional bit motion. The spot unit is thought to occupy a dxdx2d volume of space, with a mite or lite in each of two size d cubes where d is the BM distance unit. A function of spot unit parity determines the sign of mite electric charge (1, -1) (eq. 5 in [1]). Hence, the juxtaposed mites in the concurrent spot unit pairs have the same charge sign, positive or negative. The scalar potential is the presence of a concurrent mite; the scalar force is defined as the presence of two mites, namely that both mite loci are in the one state (grey rectangles in Fig. 1, eqs. 9 and 10 in [1]).

In the BM tick dedicated to the scalar bit operation, if the scalar force is present, the mite bits move to the lite loci, if they are empty (zero 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 Mites-------------  -------------  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`
Legend: State (0,1) of mite (M) or lite (L)

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.

Fig. 2: Vector Force in Countercurrent Spot Units
In countercurrent pairs of spot units, juxtaposition of a mite and a lite produces a vector force (grey rectangles in Fig. 2, eqs. 13 and 14 in [1]). Similar to the scalar force, the vector force equals the product of two bit states. Table 2 lists bit operations that occur if a vector force equals one:

Table 2: Vector Bit Operation
` Right Mite     Left Mite-------------  -------------  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`
Legend: State (0,1) of mite (M) or lite (L)

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 mite may move per vector force instance, whereas a single scalar force instance may result in motion of two mites (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, a force may exist without corresponding bit motion, 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 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), which are tabulated by the BM simulator.

3. A bit (at a locus in the one state) 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, by definition, the source bit 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 distribution).

In short,

B4 = F(S(U(V(B0)))) (1)

where B4 is the final bit state after 4 ticks, one for each bit operation; B0 is the initial bit distribution; and V, U, S and F are the vector, unconditional, scalar and strong operations respectively.

7. For the intra-dimensional bit operations -- unconditional, scalar and vector, bit motion is always in the lite direction. For the scalar and vector operations, the potentials require one bit in the one state at a bit locus perpendicular to the direction that the bit 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) forces 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) forces in determining interactions among spot cubes.

Finally, the classical EM four-vector, still used in 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 force is also deemed to be a "vector" in BM. 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 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 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 no doubt much less than the 12 tick electron bit cycle [3], during which a particular mite bit occupies all three mite locations in an electron spot. Further, if an electron spot contains 2 or 3 mite bits, 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.