1-State Fermion Mite Bit Velocities
Distance d = 1. Bit velocity v = d/t where d and t are the fundamental quantized length and time constants [5]. Distance d is presently thought to be approximately 0.6 fm. Time interval t was calculated based on the speculation that so-called "light speed in vacuum" c = v/π (eq. 2 in [5]), approximately 6.34922E-25 seconds in the BM frame. In one time tick t of the unconditional bit operation, all 1-state bits (fermion mites and boson lites) and 0-state bits (1-bit neutrinos) move exactly one distance unit d at bit velocity v. With four bit operations each thought to have duration t, the average unconditional bit velocity over one cycle of bit operations application is v/4. It may be convenient to express these velocities in bit velocity units where light speed is 1/π and average velocity over 4 ticks t due to the unconditional bit operation is 1/4, less than purported light speed.
Legend: States of spatial objects named spot units over successive ticks (top to bottom). Each spot unit contains two bit loci named mite (circles) and lite (arrows) with 0 (blue) or 1 (black) allowed states. The last row adds view of a bit locus in an adjacent perpendicular spot unit. Strong bit operation direction (purple arrow).
This article examines maximum bit velocities over specific distances and over one cycle of bit operator application for four bit categories: 1-state mites and lites associated with fermion and boson particles respectively and 0-state mites and lites associated with fermion and boson neutrinos respectively. With four bit operations, the duration of each operator cycle is four ticks t. If none of the primary force operations (S, V and F) evaluate to one (true), the unconditional bit operation accounts for all bit motion over distance d = 1 (see Table 1 below). This result is identical for all four of the bit categories itemized above.
Distance d = 2. In Fig. 1, the velocity = 1/4 due to unconditional motion over 4 ticks t may be doubled over distance d = 2 to 1/2. This scenario requires only that either the scalar or vector bit operations, or both, precede the unconditional bit operation in one application of the four operations over 4 ticks. Note that only one of the bit operations order permutations can be physically correct [6], since different orders may produce different time-development results. The VSUF, SVUF and SUVF orders are presently the best contenders for the one correct order, defined as the order with which all known results from physical phenomena measurement can be reproduced. Notice that these three orders all meet the criteria needed to produce instances of velocity = 1/2 over a 2d distance.
The t = 0 initial state is a 1-state mite (fermion) bit in the top row of Fig. 1. In the next row, a scalar or vector force [7] may accelerate this 1-state bit to the lite locus. Notice that if both the scalar and vector potentials are one (true) and act before the unconditional bit operation (VSUF or SVUF), the initial state bit can move only once due to action of the operation that is applied first per the mathematical definitions of the scalar (electrostatic) and vector (magnetic) forces [2]. The next row in Fig. 1 shows a further 1d motion due to the unconditional bit operation. Without any further motion due to the strong bit operation [8], motion over 2d in 4t is velocity 1/2. In summary, with the bit operations orders listed above, bit motion may occur at velocity 1/2 in the specified directions, 57% faster than light c speed at 1/π, which is about 0.3183.
Distance d = sqrt(5). The bottom row of Fig. 1 adds an axial view of a perpendicular spot unit adjacent to the horizontal, longitudinal illustration of the other spot units. In the axial view of this additional spot unit, only one of its bit loci is visible. From the initial position (top row), the distance to this adjacent bit locus is sqrt(22 + 12) or sqrt(5).
A somewhat greater velocity may occur over this distance d = sqrt(5) if three conditions are met. First, the strong bit operation follows the unconditional bit operation as seen in the three bit operation orders highlighted above. Second, the strong force must evaluate to one (true) in the strong bit operation tick. Part of this criterion is that the handedness (R; right or L; left) of the spot in which the spot unit pair is located allows bit transfer in the direction shown. Third, given the position of the 1-state fermion bit in row three of Fig. 1, there must be a bit locus in the adjacent perpendicular spot unit given the geometry of the spot in which these two spot units are located [9].
With these conditions, bit velocity may be sqrt(5)/4 or 0.559 over distance d = sqrt(5), 75.6% faster than light speed c at 1/π.
1-State Boson Lite Bit Velocities
Distance d = 1. The scalar and vector operations do not affect 1-state lite bits (Fig. 2), which in fact prevent the scalar and vector forces from evaluating to one (true) [2].
Legend: States of spatial objects named spot units over successive ticks (top to bottom). Each spot unit contains two bit loci named mite (circles) and lite (arrows) with 0 (blue) or 1 (black) allowed states. The last row adds view of a bit locus in an adjacent perpendicular spot unit. Strong bit operation direction (purple arrow).
Distance d = sqrt(2). However, if the strong force equals one (true) along with the other criteria described above, a 1-state lite maximum velocity of 0.354 is possible, some 11% greater than the nominal light speed.
0-State Fermion Neutrino Bit Velocities
Distance d = sqrt(2). The shortest distance over which fermion neutrino bits may achieve faster-than-light motion is sqrt(2), but the bit velocity is only 0.354 (Fig. 3). This example examines motion of the 0-state bit (v). By convention, the direction of strong operation bit motion (purple arrow) is illustrated pegged to the motion direction of the 1-state bit. Indeed, in all primary force operators (S, V, F), positions of a 1-state bit and a 0-state bit are exchanged [2].
Legend: States of spatial objects named spot units over successive ticks (top to bottom). Each spot unit contains two bit loci named mite (circles) and lite (arrows) with 0 (blue) or 1 (black) allowed states. The last row adds view of a bit locus in an adjacent perpendicular spot unit. Strong bit operation direction (purple arrow).
0-State Boson Neutrino Bit Velocities
Distance d = sqrt(2). For boson neutrino bits, two scenarios may occur. First, in the absence of scalar and vector forces without a 1-state source mite bit [2], motion depends on the unconditional bit operation described above and if applicable, with strong force evaluating to one (true), a velocity of 0.354 occurs for distance d = sqrt(2) (Fig. 4A).
Legend: States of spatial objects named spot units over successive ticks (top to bottom). Each spot unit contains two bit loci named mite (circles) and lite (arrows) with 0 (blue) or 1 (black) allowed states. The last row adds view of a bit locus in an adjacent perpendicular spot unit. Strong bit operation direction (purple arrow).
In a second scenario, with a source 1-state mite bit and a scalar or vector potential of one (true), a boson neutrino moves "backwards" exchanging its position with the accelerated 1-state mite [2], and then "forward" again with the subsequent unconditional operation, with a net position change (and velocity) of zero. However, with strong force action, a slower-than-light 0.250 velocity over sqrt(2) distance may occur (Fig. 4B).
Legend: States of spatial objects named spot units over successive ticks (top to bottom). Each spot unit contains two bit loci named mite (circles) and lite (arrows) with 0 (blue) or 1 (black) allowed states. The last row adds view of a bit locus in an adjacent perpendicular spot unit. Strong bit operation direction (purple arrow).
In Figs. 1 to 4B, the destination bit locus in the perpendicular spot unit seen in axial perspective was always depicted as a mite bit (circle). In fact, this bit might be a mite or lite in this destination locus depending on the location in the spot cube [9] of the pair of illustrated spot units. That is, there are four possible 1-state bit transfers in the strong operations: mite to mite, mite to lite, lite to lite and lite to mite.
Summary and Discussion
"A Change is Gonna Come" (Bobby Womack). Table 1 summarizes the velocity data for the four possible categories of bits in a spot unit over a time interval spanning the 4 tick bit operations cycle, a sort of "looping program", producing exact time-evolution of any system state. Several highlights may be noteworthy:
Legend: Velocities expressed in bit velocity units for comparison with hypothesized light speed c = 1/π = approx. 0.3183
1. Light speed c appears to be close to or exactly 1/π, a conclusion requiring more study, not yet well-settled [5] [10] [11] [12].
2. 1-state mite bits, associated with fermions, exhibit the greatest possible faster-than-light velocities in a 4t operator cycle, 50% or more faster (Fig. 1).
3. 1-state lites, associated with bosons, and fermion and boson neutrinos also can exhibit faster-than-light speeds, but only 11% above light speed (Figs. 2 to 4A).
3. Without strong force action, a perhaps surprising result is that EM force action (scalar or vector operators) produces zero net motion of boson neutrino bits -- zero velocity in one operator cycle (Fig. 4B). Even with strong force action combined with an EM force action, boson neutrino bit velocity is only 0.250, slower than light speed.
4. At present, aside from the basic definition of neutrinos in binary mechanics as 0-state bits, mapping the fermion and boson neutrinos as described above to the proposed set in the Standard Model is a pending task. Nonetheless, the "neutrino field" is presently thought to be the ones bit complement of the 1-state mite and lite spatial distribution, named the bit function representing the quantized quantum mechanical wave function. For example, absolute vacuum [13] is apparently equivalent to maximum possible neutrino density.
5. The information presented depends only on the postulates and bit operations at the core of binary mechanics and a physical interpretation of BM space [9].
6. A frequent observation in light speed studies at Binary Mechanics Lab is presence of some detected bits arriving several BMLS Ticks [11] before the main wave front (e.g., Fig. 1 in [10], Fig. 3 in [11], Fig. 4 in [12]). The present analysis affirms that binary mechanics predicts faster-than-light speeds under specific conditions over short distances. The early onset bits often observed in the light speed experiments might be a confirmation of this prediction, representing a number of instances of faster-than-light bit motion.
7. Strictly speaking, demonstration of faster-than-light speeds violates Einstein's postulate of "constant light speed c in vacuum" fundamental to the mathematical formalism in his Special Relativity theory. Who could have imagined in the early 20th century that the assumption of continuous space-time was without scientific merit at more microscopic levels of fineness in both space and time units, was a superstition of a by-gone age totally contrary to the meaning of word "quantum"? So Einstein expressed his insights the only way he knew, using math based on the now obsolete continuous space-time assumption. In any case, a rewrite of the basic Special Relativity mathematical formalism incorporating quantized space, time and velocity is clearly needed for physics theory to advance and is an agenda item. Recall that binary mechanics was developed in part from a pair of relativistic Dirac spinor equations of opposite handedness [1].
8. Remember the snafu a few years ago when many first voted for faster-than-light muon neutrinos [14] and then voted against them. In the context of the present analysis, it might seem that the choice of a neutrino as the test particle might have been ill-advised (Fig. 4B).
9. This article may be a "go" signal for engineers to find or create new materials that provide the conditions described herein with the objective of increasing the incidence of faster-than-light events perhaps for practical use in communications exceeding light speed. High-frequency traders on Wall St. will pay almost anything to get an edge on competitors by increasing communication speed. Warning: keep alert with eyes open to avoid injury, especially in narrow hallways, if caught in an stampede of crazed nanotechnology engineers headed to their laboratories.
10. [Insert reported apparent faster-than-light measurements in literature here. Seem to recall some experimental reports presenting data claiming same...]
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. "Captives in a binary mechanical universe" J. Bin. Mech. March, 2011.
[4] Keene, J. J. "Physics glossary" J. Bin. Mech. May, 2011.
[5] Keene, J. J. "Intrinsic electron spin and fundamental constants" J. Bin. Mech. January, 2015.
[6] Keene, J. J. "Bit operations order" J. Bin. Mech. May, 2011.
[7] Keene, J. J. "Electromagnetic bit operations revised" J. Bin. Mech. March, 2011.
[8] Keene, J. J. "Strong operation disabled by inertia" J. Bin. Mech. March, 2011.
[9] Keene, J. J. "Physical interpretation of binary mechanical space" J. Bin. Mech. February, 2011.
[10] Keene, J. J. "Light speed amendment" J. Bin. Mech. March, 2015.
[11] Keene, J. J. "Binary Mechanics Lab Simulator update" J. Bin. Mech. December, 2015.
[12] Keene, J. J. "Light speed at zero Kelvin" J. Bin. Mech. January, 2016.
[13] Keene, J. J. "Vacuum thresholds" J. Bin. Mech. March, 2011.
[14] Opera collaboration. "Measurement of the neutrino velocity with the OPERA detector in the CNGS beam" Arxiv. September 2011. © 2016 James J Keene
