**Table 1: Fundamental forces: previous vs BM**

**1. Fundamental forces deciphered**

*Background.*As described previously [1], BM was developed from the relativistic Dirac equation in quantum mechanics (QM). With the BM quantization of space, time and wave function amplitude (energy), the QM system state vector (wave function) becomes a spatial pattern of bits (

**bit function**), one each located in a cube of size d, the BM fundamental length constant. This BM

**state vector**(eq. 2 in [1]) of 0-state and 1-state bits provides a simple, irreducible representation of any physical system state.

In quantized time intervals t, the BM fundamental time constant, named

**ticks**, four BM bit operations applied sequentially, one per tick, in four tick cycles, determines the exact time development of the state vector (eq. 26 in [1]).

In this context, QM, including quantum electrodynamics and quantum chromodynamics, is seen to be a transitional model between (a) statistical mechanics (wave functions are essentially statistical distributions) with added new bells and whistles (e.g., quantized parameters such as energy and spin and some wonderful math wizardry such as complex amplitudes, spinor matrices, etc) and (b) BM where quantization of space and time requires a higher level of scientific discipline and generates new unexpected, testable hypotheses. QM wave function and time-development operators (e.g., momentum) become the BM bit function and fundamental bit operations respectively.

As an example of increased intellectual discipline, note that QM wave functions may include position coordinates (using real numbers) allowing any arbitrary position in continuous space-time. In BM position coordinates (using only integer numbers),

**these QM wave functions simply do not exist as physical entities,**since they are at best approximations of actual integer positions. Next, consider that the QM operators include infinitesimal increments in parameters such as position or time. However, in quantized BM space-time,

**these QM operators simply do not exist as physical processes**, since only integer increments in position and time are allowed. This result may leave no doubt that the QM wave function is basically classical statistics dressed in new fancy clothes however ingenious and attractive they may be. As such, these QM wave function and time-development operators can only yield approximations, if not outright incorrect predictions, especially at the level of fineness treated in BM. The second section of this report describes the operators that do exist in BM, defining the bit operations.

*Analysis.*Updated from Table 4 in [1], Table 1 shows that a current list of fundamental forces in physics does not map one-to-one to the four fundamental BM bit operations.

**Gravitation.**Recent studies have opened the possibility that gravity is not a fundamental force at all [2]. In a preliminary simulation experiment where two bodies were observed to move toward each other [3], gravitation-like effects were achieved by action of the four BM bit operations alone. Thus, Table 1 shows a check-mark for all four bit operators to map gravitational phenomena to BM fundamental forces. That is, there is no gravity-specific bit operation defined at present.

These results definitely require more study and may be the most exciting area in current gravity research.

Some recent work on gravitation illustrates the ongoing transition from inadequate QM formalism to full quantization in BM. For example, some investigators are "testing the waters" to challenge the faulty assumption of continuous space-time. Half efforts suggest "granular" or "discrete" models of space. One of these is loop gravity theory (LGT) where space is granularized into discrete loops. The intellectual credibility of such half efforts is questionable, if only as measured by whether BM literature is cited (what ever happened to scholarship standards?) or by lack of any contact with the present author from these investigators (is there no curiosity to probe most recent unpublished work in BM?)

**Weak force.**In the initial paper on BM postulates [1], several examples of weak force interactions analyzed were entirely accounted for by the unconditional bit operation. More study is required to ascertain if all weak interactions, if correctly classified as such, can be described completely by unconditional bit operations.

While weak force interactions appear to map one-to-one to the unconditional bit operation, an issue remains. Technically, the unconditional bit operator corresponds to the momentum operator in the relativistic Dirac equation. However, it is not clear at present if the defining components of a "force" in BM occur in the unconditional bit operation. Hence, weak force interactions may not be evidence of a new, unique force as mathematically defined in Table 2. Note that without the discipline required by BM postulates, investigators observing "weak force" interactions would have not known this, nor would grand unification analysts have attempted to unify the "weak not-force" with electromagnetism into an imagined "electroweak" fundamental force.

**Neutral weak force.**The initial BM paper also described neutral weak force interactions accounted for by strong bit operations. Thus, these interactions may correctly be classed as secondary or derivative effects of the fundamental strong bit operation. Note that for both gravity and the neutral weak forces, a second check-mark in a Table 1 row indicates secondary, not primary, force status for the column item.

**Electromagnetic force.**Table 1 shows that the electromagnetic (EM) force category in conventional thinking maps to two different bit operations -- scalar and vector [4] [5] [6]. An electric potential (field) and a magnetic potential (field) are force components which may result in 1-state bit motion in the scalar and vector bit operations respectively, as presented below (Table 2).

**Strong force.**The strong force concept in contemporary physics maps one-to-one to the strong bit operation [7] [8]. However, the mechanism of quark (color) confinement in baryons is different in BM compared to conventional thinking as presented elsewhere [9] [10] [11].

**2. BM fundamental force components**

Table 2 shows algebraic expressions for three components for each of three fundamental forces -- scalar, vector and strong. Each component is a binary expression which may evaluate only to one or zero and may be written in binary logic notation (e.g., {1 - Li} is {NOT Li}).

**Table 2: BM components of fundamental forces**

*Force definition.*The product (or logical AND) of the three force components defines force presence (1 or true) acting on the source 1-state bit or not (0 or false).

**Fig. 1: Spot Unit**

*Mite and Lite Bit Loci.*The unsigned (positive) real components of the complex wave function amplitude of the relativistic Dirac equation may each be assigned to a size d cube of quantized space as shown in Fig. 1 from [1]. As presented previously in detail [1], since the two real components of the QM wave function may have different values, two bit types were postulated to populate the BM

**bit function**-- mites (M) and lites (L). Technically, the specification of two bit types -- M and L, was based entirely on the simple projection from the 2D complex plane of the QM wave function to the positive quadrant of a 2D real plane. Then, as a step toward quantizing energy at the single bit locus level, the positive real values of M and L were restricted to zero and one yielding binary bits.

Keeping in mind that the only restriction in M and L definition is this projection of values from the complex QM wave function to the binary BM bit function, it may be helpful as BM is studied further to think of 1-state bits in M loci as "matter" and in L bit loci as "radiation". Also, M loci might be associated with fermions and L loci with bosons. Again, these labels might be heuristic ideas, but not formal constraints derived from BM postulates.

The bosons listed in Table 1 -- W, photon, gluon and Z -- might illustrate this point. L bit loci, labelled as photons or gluons, have been associated with lepton and d quark loci respectively in BM literature, perhaps only to show where consequences of BM postulates appear to be consistent with important elements in contemporary thinking, for example, in the Standard Model. The bottom line is that theorists may define any physical entity as a bit function, which is essentially a spatial distribution of 1-state and 0-state bit loci. Precise, unambiguous definitions of physical entities require bit functions, if only because M and L bits in spot units are the only options available if our binary universe is fully quantized.

*1-State Bit Acceleration.*Scalar, vector or strong force evaluating to one (true) results in acceleration of a 1-state bit from its source locus (t =0) to its destination locus (t = 1), defining the respective bit operations for the time-development of the state vector. For electromagnetism, the scalar and vector bit operations act only on bits in M loci (Mi), moving them to destination L loci (Li) in the same spot unit. The strong force acts to change direction of source 1-state bits in either M or L loci (Bs), with motion from a source spot unit to an adjacent destination spot unit in another spatial dimension [7] [10].

*Force Potentials.*Each force requires a potential that evaluates to 1 (true). Those potentials are all located in bit loci cubes sharing a face with the source 1-state bit locus cube. Thus, at this single locus level of fineness, the force of any binary potential acts over a distance d, the loci cube size and the BM fundamental length constant. Further, each source 1-state bit has only one adjacent bit locus where a potential for each force can occur.

For the scalar bit operation, the electric potential is an adjacent 1-state mite (Mj) in the concurrent spot unit. The source and potential mites always have the same sign and the result of the scalar bit operation is to disperse mites of the same sign charge (a property determined by spot unit coordinate modulo 2 parity). In a larger volume, the mite distribution

*is*the electric potential field.

The vector bit operation can accelerate a source 1-state mite if a 1-state lite (Lk) occurs in the adjacent countercurrent spot unit. In any spatial volume of interest, the lite distribution

*is*the magnetic potential field. The EM forces (scalar and vector) both result in source 1-state M bit motion to the L locus in the same spot unit. Another result of both the scalar and vector bit operations is confirmation of the EM observation that charge motion (from a M locus to a L locus) produces a magnetic potential, namely the destination 1-state L bit itself [5].

*Destination 0-State Bit Locus.*Since two or more 1-state bits cannot occupy a single locus cube (eq. 1 in [1]), motion of the source 1-state bit to the destination locus can occur only if it is "empty" (0-state). Therefore, any definition of force must include this factor. Indeed, a major objective in the present report is to update the formula for the EM bit operations by adding this factor in Table 2. Previously, the EM forces were described as the product (or AND) of the source 1-state M bit and the associated electric or magnetic potential acting on it, with only textual stipulations that motion occurs only if the L locus "is not already occupied" or "is 0-state" or the like.

The strong potential component (1 - MiLi) of the strong force in Table 2 is equivalent to the logical expression NOT(Mi AND Li).

**Inertia**has been defined as the MiLi product, both M and L loci in the 1-state in a spot unit (Fig. 1). At first, this may seem like an arcane definition of the strong potential as absence of inertia, namely NOT inertia. On the other hand, this potential definition is consistent with several facts. (1) The strong bit operation results in capture of 1-state bits in baryon and lepton bit cycles [9] [12]. Capture means that a 1-state bit, if not otherwise disturbed, will return to its initial location after a number of ticks in which the four fundamental bit operations are repeatedly applied. (2) The foregoing is equivalent to stating that inertia disables the strong bit operation ({NOT inertia} enables it as its potential component). When strong force scattering is disabled, 1-state bits can continue motion in the same direction in the next unconditional bit operation tick. This is basically how inertia is conventionally defined in physics.

*Uniform Force Definition Criteria.*The present addition to the EM force formalism (Table 2) produces several interesting results.

First,

**the three forces -- scalar, vector and strong -- are all defined by three similar factors**. Lack of any obvious presence of any of these factors for the unconditional bit operation might argue that this time-development operation is not a fundamental force. This interpretation is consistent with the derivation of the unconditional bit operation from the QM momentum operator and with the conclusion that the associated so-called weak force is not really a fundamental force at all.

This "weak force snafu", if you will, illustrates the utility of the formal definition of a fundamental force in physics. Without it, almost any observations of apparently new phenomena that do not readily fit into current theories may result in proclaimed discovery of a "new force" and "Oh, now we need to name a new boson to mediate these interactions" and on and on into seemingly endless confusion. Applying the scientific discipline attribute of BM, theorists can determine if they have "the goods" to declare discovery of a new force by filling in a new row of Table 2 with their specific new force-defining components.

Second, for all three fundamental forces -- scalar, vector and strong, the required destination 0-state locus meets the neutrino definition (eq. 37 in [1]). Thus, for every 1-state bit movement in these bit operations, a 1-bit neutrino "moves" in exactly the opposite direction. This report may be the first to stipulate that

**1-bit neutrinos are required and move in the bit operations for any of the three fundamental forces which evaluate to 1 (true)**.

Third, at higher 1-state bit densities in a spatial volume, two force factors will tend to increase: (1) source 1-state bits and (2) potential field strength. However,

**disassociation between potential field strength and its observed effects on particle motion is predicted**, since the incidence of 0-state destination bit loci will decrease. This decrease in the third force factor lowers the odds that any of the three fundamental forces would evaluate to 1 (true). In other words,

**as density increases, a non-linear relation between potential field strength and particle acceleration is predicted.**In plain English, a 1-state source bit cannot move if it has no place to go (a 0-state locus), regardless of how much energy is pumped in to create intense potential field gradients.

**References**

[1] Keene, J. J. "Binary mechanics" J. Bin. Mech. July, 2010.

[2] Keene, J. J. "Physics news: gravity game-changer" J. Bin. Mech. October, 2014.

[3] Keene, J. J. "Gravity looses primary force status" J. Bin. Mech. April, 2011.

[4] Keene, J. J. "Electromagnetic bit operations revised" J. Bin. Mech. March, 2011.

[5] Keene, J. J. "Quantized electromagnetism" J. Bin. Mech. May, 2011.

[6] Keene, J. J. "Electron acceleration and quantized velocity" J. Bin. Mech. April, 2011.

[7] Keene, J. J. "Strong operation disabled by inertia" J. Bin. Mech. March, 2011.

[8] Keene, J. J. "Baryogenesis" J. Bin. Mech. May, 2011.

[9] Keene, J. J. "The central baryon bit cycle" J. Bin. Mech. March, 2011.

[10] Keene, J. J. "Matter-antimatter asymmetry mechanism" J. Bin. Mech. October, 2014.

[11] Keene, J. J. "Physics glossary" J. Bin. Mech. May, 2011.

[12] Keene, J. J. "Physical interpretation of binary mechanical space" J. Bin. Mech. February, 2011.

© 2014 James J Keene