**bit function**replacing the wave function for an irreducible representation of the state of any physical system and (2) four fundamental

**bit operations**replacing infinitesimal operators for system time evolution [2]. With time quantization in discrete

**tick**t units, Planck's constant h for an action quanta could then be parsed to define energy quanta as 1-state binary bits independent of time or frequency considerations. Another consequence of BM postulates was discovery of a cyclical circulation of 1-state bits in a quantized spatial structure named a

**spot cube**(Fig. 3A in [1]). With a physical interpretation of BM space [3] and simulation software [4], this 1-state bit circulation was further described as an 84 tick

**central baryon bit cycle**, detailing the physical basis for quark confinement [5].

**Fig. 1: 1-State Bit Density in Central Baryon Bit Cycle**

Legend: Centers (0 - 4) of bit loci (approx. 0.6 fm cubes of quantized space) with densities of 1 (light grey), 2 (grey) and 4 (black) 1-state bits viewed from the XY plane and rotated 90 degrees, the YZ plane.

**Methods and Results**

Using data presented previously (Table 2 in [5]), Fig. 1 presents "x-ray" images of the central baryon bit cycle from two perspectives -- the XY plane and rotated 90 degrees, the YZ plane. The central baryon bit cycle has 42 bit locus cubes sequentially occupied by a 1-state bit, which moves distance d in each time interval, where d is the BM fundamental length constant and bit locus size. A previous report estimated length d as approximately 0.6 fm [6]. The coordinates of these loci range from zero to four in each of three dimensions. In sum, Fig. 1 shows the density of these 42 bit locations.

Thirty of the 42 1-state bit positions are located in a spot cube {0-3, 0-3, 0-3} (Fig. 3 in [3]). The remaining 12 positions are outside the "home" spot cube, in three neighboring spot cubes with four 1-state bit positions each: {4, Y, Z}, {X, 4, Z} and {X, Y, 4}. This arrangement is not symmetric. First, only one of each pair of parallel faces of the home spot cube shares a face with one of these three neighboring spot cubes. Second, a vertex of each of the three neighboring spot cubes shares a point with a vertex of the home spot cube, as may be visible in Fig. 1.

In general, the bit function contains equal numbers of mite and lite bit loci featured in fermion and boson representation respectively. In the present analysis, one half of the 42 bit positions in the central baryon bit cycle are mites with electric and color charge attributes completely determined by modulo 2 parities of spot position (eqs. 5, 29, 31-34 in [1]). These 21 mite bit positions have net positive electric charge of 3 yielding a particle charge of +1 (eq. 29 in [1]) consistent with the proton (Table 3 in [1]). Fig. 2 shows density images of the 21 mite positions, which exhibit a spatial asymmetry similar to the images for total energy (1-state mites and lites) in Fig. 1.

**Fig. 2: Mite Bit Density in Central Baryon Bit Cycle**

Legend: Centers (0 - 4) of bit loci (approx. 0.6 fm cubes of quantized space) with densities of 1 (light grey) and 2 (grey) 1-state mite bits viewed from the XY plane and rotated 90 degrees, the YZ plane.

**Discussion**

*Central baryon bit cycle as proton model.*The 12 tick electron spot cycle has been used to calculate electron intrinsic spin and hence, Planck's constant h, based only on electron rest mass and BM length constant d [6]. This was apparently the first time Planck's constant was calculated from first principles of a comprehensive, fundamental physical theory. In addition, electron magnetic moment has been calculated from the electron bit cycle based only on elementary charge e and length d [7]. Likewise, the central baryon bit cycle may be the physical basis for proton observations. For example, as cited above, it exhibits a net positive charge of +1 while the electron bit cycle has net charge of -1.

*Non-spherical proton shape.*Whether viewing total energy content (Fig. 1) or mite (fermion) energy content alone (Fig. 2), the bit locus cubes traversed by a single 1-state bit in the central baryon bit cycle is clearly not spherical. Indeed, proton shape as assessed by the central baryon bit cycle is markedly asymmetrical. Inspection of the raw data (Table 2 in [5]), reveals three volumes within a proton with increased 1-state bit density, accounting for much of the observed asymmetry: namely, the three right-handed d quarks (drR, dgR and dbR) which BM postulates determine to be matter particles. Specifically, a 1-state bit was found located in these matter d quark spots during 18 of the 42 time intervals in the cycle. In contrast, a cycling 1-state bit occupied anti-matter left-handed d quarks in the home spot cube during 12 of the 42 time intervals. Hence, as reported previously [5], matter d quarks were occupied 50 percent more often than anti-matter d quarks in the central baryon bit cycle home spot cube. This finding revealed one of the basic mechanisms for real-time matter-antimatter asymmetry by ongoing processes in the present [8].

The density images in Figs. 1 and 2 depend on the assumption that the tick duration of 1-state bit positions resulting from the unconditional bit operation equals that from positions resulting from the strong bit operation [2]. When the correct order of the four fundamental bit operations for exact time development of a system state is well established, this tick duration assumption can be either verified or the density images adjusted to reflect the applicable tick durations.

An unexpected result in the present analysis was that the positron component of the proton was not located in the home spot cube as suggested originally in 1994 (Table 3 in [1]). Instead, not only was the positron component outside the home spot cube, but one third of it (one spot unit) was located in each of three neighboring spot cubes as described above.

*Proton shape fluctuations.*Observed proton shape fluctuations are also predicted by BM postulates.

First, the 42 bit loci positions in the central baryon bit cycle may be occupied by zero to 42 1-state bits at a time tick t. That is, there are 2

^{42}possible states. These permutations may account for essentially all hadron phenomena including hadron resonances, energy levels, particle half-lives, particle time phase [9], particle categories, etc. Increasing the number of 1-state bits in the central baryon bit cycle increases energy level and the density images but does not change proton size (Figs. 1 and 2). Some reported QCD work purports to document proton size changes at higher energies, contrary to the present findings. This discrepancy may be due to the unwarranted assumption of continuous space-time in QCD.

Second, 1-state bits in adjacent baryon bit cycles may also affect proton size and shape measurements. Recall that the central baryon bit cycle includes one positron spot unit in each of three neighboring spot cubes. In other words, the positron spot (3 spot units) in the "home" spot cube may contain 1-state bits circulating in baryon bit cycles in one to three neighboring spot cubes. These possibilities no doubt pertain to both proton measurements as well as atomic nuclei with multiple nucleons. Further, 1-state bits in the electron spot of the home spot cube may neutralize the net positive proton electric charge, yielding a neutron. Indeed, in principle, with little more than a decent lap-top computer, the entire range of possible particles and phenomena in nuclear physics might become available in downloadable databases.

*Proton spin source.*The central baryon bit cycle is the source of intrinsic proton spin. Hence, with the specific geometry of this bit cycle, proton properties such as electric dipole moment and magnetic moment may be calculated for the first time from fundamental theoretical postulates (Keene, in preparation).

*BM precision vs QCD magic.*This report further supports the time development engine in BM simulation software as a leading tool in nuclear physics research. It replaces magical thinking in QCD with precision description of physical quantities and processes. Consider, for example, two 1-state bits circulating in a central baryon bit cycle. Clearly, they are confined since after repeated application of the fundamental bit operations, they return to their original position. No "force between quarks" of any kind beyond the four fundamental bit operations [2] needs to be invoked. As in many magic tricks, distraction from the basic facts is evident: "We don't see individual quarks floating around, so there must be a 'force' confining them which magically does not decrease with distance."

When space, time and energy are quantized, the bit function -- a spatial distribution of 1- and 0-state bits -- is the only way to define any physical object (or "field"). Instead, QCD invokes mysterious "gluon fields" which magically are strong enough to "create quark pairs" and if this violation of energy conservation were not enough, the "QCD vacuum" has miraculous powers able to fill any gap in understanding -- you name it, whatever you need, quark-antiquark pairs, "vacuum condensates", whatever. In contrast, BM precisely defines the vacuum [10]. And unlike BM calculations, whatever numbers that QCD generates, renormalization is typically needed, which is tantamount to explicit admission that the values needing it are seriously flawed (e.g., obsolete assumption of continuous space-time). Indeed, considering the vague, imprecise and ill-defined terrain of QCD, it appears that QCD as a physical theory is neither fundamental or comprehensive compared to BM. The scientific discipline attribute of BM simply does not allow this sort of sloppy, magical thinking. For example, there either is or is not a symmetry; there are no "approximate symmetries". In BM, there are no fudge-factors or off-the-shelf excuses (e.g., Heisenberg uncertainty); something is either correct or incorrect physics.

Figs. 1 and 2 may appear to be low-resolution, crude, grainy images. It might be supposed that improved technology might yield higher resolution images. On the other hand, BM predicts that Figs. 1 and 2 show the highest resolution possible if the fundamental BM length d is correctly estimated at approximately 0.6 fm. Note that the physical size of a 1-state bit is stipulated by BM to be less than length d, so it fits into a bit locus cube. Otherwise, this size is unknown. But reported measurements of 1-state bits emitted from electron spots are very small values. In sum, as illustrations, Figs. 1 and 2 paint the entire bit locus cubes with the density values rather than the 1-state bits of perhaps much smaller size within the cubes.

Experimental data on hadrons continues to accumulate confirming numerous BM predictions. However, although some progress has been achieved (e.g., the CLAS collaboration) indicating substantial interest in the physics community, search of physics literature reveals that the present report along with the discovery of the central baryon bit cycle in 2011 may be the first to describe in precise detail the internal 3D structure of the proton.

*Homework assignment.*In analysis of the simpler case of intrinsic electron spin, involving only one spot composed of three spot units, a first-ever calculation of Planck's constant h was based only on electron rest mass and BM length d [6]. Use the central baryon bit cycle data to calculate proton rest mass based only on Planck's constant h and BM length d.

**Editor's note: The reader is invited to post comments in agreement or disagreement with this or other**

*Journal of Binary Mechanics*articles at the Binary Mechanics Forum. The Journal also welcomes on-topic articles from other investigators and persons considering serving on the Journal's editorial board.**References**

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

[2] Keene, J. J. "Fundamental forces in physics" J. Bin. Mech. October, 2014.

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

[4] Keene, J. J. "Binary mechanics simulator updated" J. Bin. Mech. March, 2011.

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

[6] Keene, J. J. "Intrinsic electron spin and fundamental constants" J. Bin. Mech. January, 2015.

[7] Keene, J. J. "Intrinsic electron magnetic moment derivation" J. Bin. Mech. February, 2015.

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

[9] Keene, J. j. "Particle up-down spin and quantized time parity", J. Bin. Mech. January, 2015.

[10] Keene, J. J. "Vacuum thresholds" J. Bin. Mech. March, 2011.

© 2015 James J Keene