**Quantization of electron velocity is predicted**. Fig. 1 shows the X1 level of the YZ surface of two adjacent spot cubes (left and right) as might be seen from above the YZ plane of the page.

**Fig. 1: X1 Plane of YZ Surface of Two Adjacent Spot Cubes**

One electron spot bit in the 1-state (black circle in Fig. 1) in the Z dimension will be examined as an example of similar events in the X and Y dimensions. Events affecting motion of this mite bit along the Z dimension to the next electron spot in the left spot cube shown over 4 BM distance units

*d*will be described.

Let the 1-state mite in the Z3 electron spot be the tick 0 initial state. In tick 1, the strong bit operation has no effect since the mite is in a destination locus, causing the strong potential to be zero [3].

The electromagnetic (EM) scalar and vector bit operations [4] and the unconditional bit operation [1] are pending. Different results are obtained depending on the order of the EM and unconditional operations. If the vector bit operation is applied before unconditional bit motion,

**fast motion**of the electron mite may occur.

**Fast Electron Motion**

In tick 2, the vector bit operation can move the mite bit to the lite locus in the electron Z3 spot unit. If the adjacent countercurrent lite in the dwR quark spot shown above the electron mite is in the 1-state, a vector force moves the mite to lite in the electron Z3 spot unit (Fig. 2). [Note: The dwR quark was renamed to the dgR quark, replacing the white (w) color charge designation with green (g). The physics remains the same, but physics 101 textbooks are now more colorful.]

**Fig. 2: EM Vector Potential Accelerates Z3 Electron Mite**

Let us assume this vector force and result occurs.

Then, in tick 3, application of the unconditional bit operation moves the lite out of the electron spot and into the mite locus in the adjacent dbR quark spot.

**sequence 1**. On the other hand, if the scalar potential equals one in tick 4, the mite is accelerated again to the Z2 lite locus, denoted as

**sequence 2**.

**Fast Sequence 1:**In tick 5, the next operator cycle begins with the strong bit operation. However, the 1-state bit, now a mite in the Z2 spot unit, is a destination bit for the strong potential, as shown by the direction of the purple arrow in Fig. 1. Therefore, nothing happens in this tick.

In tick 6, the vector potential, if present, may produce the same effect of mite-to-lite motion as described in tick 2. If so, in tick 7, the unconditional bit operation moves the Z2 spot unit lite to the mite position in the Z1 electron spot unit. In summary, a 4

*d*bit motion is completed with average velocity

*v*= 4/7, meaning the 1-state mite bit moved 4 distance units in 7 ticks, where each movement was at velocity

*v*= 1.

**Fast Sequence 2:**As described above, with a scalar potential in tick 4, the Z2 spot unit mite moves to the Z2 lite locus. Hence, it must not be scattered in tick 5 when the strong bit operation is applied again, else it will not arrive at the Z1 mite position. If this Z2 lite survives as described in more detail below, then in tick 6, the vector force has no effect on lite bits. Finally, in tick 7, unconditional bit motion causes the Z2 lite to arrive at the Z1 electron mite position.

In summary, for both fast sequence 1 and 2, the four electron-to-electron distance units may be completed in 7 ticks. While the average velocity is the same in the two sequences, their probabilities of completion may be different. Both sequences depend on a vector potential at tick 2. However, sequence 1 depends on the absence of a scalar potential at tick 4. With the presence of a tick 4 scalar potential, sequence 2 requires the absence of a strong force at tick 5.

**Slow Bit Motion**

What if there were no magnetic forces in this thought experiment? In tick 2, without a vector potential, the mite shown in Fig. 1 would remain exactly where it was and then move to the lite locus in the Z3 spot unit via unconditional motion in tick 3. In tick 4, the scalar bit operation would have no effect, since it accelerates mites, not lites.

The tick 5 strong bit operation may scatter this lite bit in the electron spot. Specifically, the 1-state lite bit in an electron Z dimension spot unit could scatter to the X dimension per the strong bit operation (purple arrow in Fig. 1). Indeed, if the time development is not modified by the presence of other bits, this bit will cycle in the electron spot and return to the same lite position after 12 ticks. Although this internal bit cycle proceeds within the electron spot, the electron as a particle is said to be at rest.

However, such scattering is disabled by two mechanisms causing motion to exit the electron spot as shown in Fig. 3.

**Fig. 3: Strong Bit Operation Disabled by Two Mechanisms**

First, a 1-state mite in the destination locus in the X dimension causes the strong potential to evaluate to zero. Second, even in the absence of this X 1-state mite, if the Z spot unit has inertia -- both mite and lite in 1-state, the strong bit operation is also thought to be disabled. In short, if either or both of these additional bits are in the 1-state, the 1-state lite bit is unaffected.

Finally, in tick 7, the electron spot emits one unit of energy. That is, by unconditional bit motion, the lite moves to the mite position in the Z2 quark dbR spot. The tick 8 scalar operation may accelerate the Z2 mite to the lite locus in the spot unit, if a scalar potential is present. Hence, two slow sequences may be considered.

**Slow Sequence 1:**Without a tick 8 scalar potential, the Z2 mite remains and the tick 9 strong operation has no effect since this mite is a destination bit as shown in Figs. 1 to 3 (purple arrows). If there is also no vector force in tick 10 (as seen in tick 2) in this slow electron bit motion scenario, again the unconditional bit operation is needed for the mite-to-lite motion in the Z2 spot unit in tick 11. This lite is motionless in tick 12, unaffected by the scalar bit operation.

In tick 13, the strong operation again needs to be aborted as in tick 5, else the electron-to-electron bit motion is aborted by scattering in a baryon bit cycle. If the Z2 quark spot lite survives tick 13 (strong force = 0), it also remains unaffected by the vector bit operation in tick 14. Finally, the tick 15 unconditional bit operation moves it to the destination Z1 electron spot, with average velocity

*v*= 4/15.

**Slow Sequence 2:**With a scalar potential in tick 8, the Z2 mite moves to the lite position where in tick 9, it remains motionless if the strong force is zero. The tick 10 vector operation is null since it acts on mites, not lites. Finally, in tick 11, unconditional bit motion completes the journey to the Z1 electron spot mite locus, with an average velocity

*v*= 4/11.

**Quantized Velocity**

In summary, fast motion is more rapid than either slow motion sequence. Even so, this maximum electron velocity is only 4/7 of maximum BM bit velocity. To the extent that experimentalists succeed in accelerating electrons to near the speed of light, such efforts may be viewed as calibrating maximum bit velocity as approximately 1.75x (7/4) the speed of light, consistent with previous BM predictions [5].

**BM predicts that only three electron mite velocities are possible 4/7, 4/11 and 4/15 over a 4**.

*d*distance between electron spotsIn short,

**on any distance scale, electron mite velocity is quantized**. That is, electron mite velocity cannot assume any arbitrary value as might be wrongly assumed by models using the obsolete concept of continuous space-time, such as in the EM Lorentz force, Maxwell's equations or the Special Theory of Relativity by Einstein.

However, the finding of velocity quantization, obvious at very short distances, does not negate the basic empirical results at larger distances based on the work of Lorentz, Maxwell, Einstein and many others. In fact, EM potentials were seen above to cause increased bit velocity.

While the present results may modify some Special Relativity effects at short distances or small time intervals, basic empirical results such as time dilation, length contraction, etc, remain intact at larger scales. Associated invariant quantities are apparently preserved at these larger space-time scales by using the speed of light as a maximum velocity in Lorentz transformations. Since "light velocity in a vacuum" is thought to be much less than BM maximum velocity, partly supported by the present results, relativistic effects pertaining to measurements at larger space-time differences may be seen as consistent with BM. Also, recall that BM was originally derived from the relativistic quantum mechanical Dirac equation [1].

**Electron Particle Motion**

How do electron particles move? Rephrasing, how is the present one-bit motion analysis and its results relevant to motion of electrons as particles? The following picture is emerging.

As absolute vacuum [6] is filled with bits, one may assume that most, if not all, electron spots contain at least one bit, given their strong tendency to capture and hold bits in their 12 tick bit cycles. A particle threshold, then, might require two or more bits in an electron spot [5].

If one of these bits moves to another electron spot as described above, the source electron spot (Z3 in Fig. 1) may cease to be an electron, depending on its initial energy level in terms of its bit count up to the maximum of 6 bits -- 3 mites and 3 lites. Upon arrival at the destination electron spot (Z1 in Fig. 1), the additional arriving bit might well boost its energy above the particle threshold, which may be 2 or 3 bits for a one spot particle such as the electron. In short, for a particle to move, all of its bits need not move from location A to location B. Rather, motion of perhaps only one bit might suffice to accomplish an apparent particle motion.

This reckoning of the underlying mechanisms of electron motion may have significant implications. For example, in classical physics, mass and acceleration (force) is thought to involve the motion of a whole object, whereas the above treatment opens the door to an entirely different approach, namely that part of a particle may move causing the particle to cease to exist (drop below particle threshold) at the source location A (electron spot X1, Y1, Z3 in Fig. 1) while another particle may commence to exist at the destination location B (electron spot X1, Y1, Z1 in Fig. 1).

What does particle existence mean? Concretely, one might suppose a particle object exists if it is directly detectable by our senses or instruments. This sort of operational definition of a particle as opposed to a single BM bit is consistent with the supposed mechanisms of particle event detectors, namely that a particle is inferred based on energy transfer from its motion to the detector device. And, of course, the ability of investigators to imagine particles that cannot be so directly observed is also worthy of mention, which makes the whole game of science very interesting.

**Homework Assignment**

The VUSF bit operations order was used in this article. Work out the maximum quantized velocities if the USVF bit operations order is used.

**References**

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

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

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

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

[5] Keene, J. J. "Captives in a binary mechanical universe" J. Bin. Mech. March, 2011.

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

© 2011 James J Keene