Transition from the quantum mechanics (QM) wave function to the binary mechanics (BM) bit function is inevitable. The wave function wrongly assumes that physical events at multiple points occur at a single point and events may occur at points in space and time that do not exist, due to belief that space and time are continuous rather than quantized. The wave function also fails to adequately represent physical events in the network of concurrent and countercurrent spot unit components of the BM spot cube spatial lattice. Historically, technologies that work have been generally adopted even before underlying physics is fully understood. The "follow the money" rule leads directly to exponential increase in BM technology usage, which improves spatial and temporal resolution by multiple orders of magnitude (Fig. 1), required for continuing progress in industries working at increasingly microscopic "nanotechnology" scales, attracting both physicists and capital investment.
The 1994 "Binary mechanics" paper, first published in 2010 [1], noted intrinsic limitations of the QM wave function:
"... differences in the state vectors -- the binary mechanical bit function and the quantum mechanical wave function, pinpoint why quantum mechanical formalism cannot, in principle, provide exact results. Namely, it assumes that bits at different physical locations are positioned at one point. This defect remains even if quantum mechanical calculations are conducted at the same fine scale of binary mechanics.With the need for increased accuracy and resolution as multiple commercial industries probe more microscopic levels of fineness to meet their design and engineering goals, use of the BM bit function in applications avoids major sources of error in the QM wave function.
This oversimplification intrinsic to the quantum mechanical wave function limits the accuracy of calculations at reduced distances and time durations. It also leads to qualitative paradoxes and discrepancies with experimental observation, similar in nature to those found when classical mechanics is applied at an atomic scale."
Binary mechanical calculations of physical quantities are, in principle, exact. Therefore, the precision of calculations is limited only by the degree of precision, available at the time, of measurements used to set the primary constants of binary mechanics (aka the Keene scale) [2] [3]. The intrinsic limitations of the wave function may be easily remedied by using the bit function.
As presented previously [4], the QM wave function may misrepresent position in continuous (real number) coordinates (Fig. 2, top right) which are only an approximation of actual positions where only integer coordinates are allowed with BM spatial quantization (Fig. 2, top left). How bad is this QM defect? QM calculation results may indicate motion when there was none (Fig. 2, second row) or may overestimate (Fig. 2, third row) or underestimate (Fig. 2, bottom) motion distance.
Fig. 3 shows similar results for time quantization [4]. The QM wave function may misrepresent time in continuous (real number) coordinates (Fig. 3, top right) which are only an approximation of actual time where only integer multiples are allowed with BM temporal quantization (Fig. 3, top left). QM calculation results may indicate time difference when there was none (Fig. 3, second row) or may overestimate (Fig. 3, third row) or underestimate (Fig. 3, bottom) time differences.
QM infinitesimal operators are quite simply the wrong math when position and time may have only integer values in the BM quantized frame of space and time. Thus, at the BM fineness level, QM predictions may be distorted or outright incorrect. A specific example of this limitation of QM formalism was reported previously [5]. As a consequence, success of QM formalism at the atomic level is becoming more difficult to duplicate at the elementary particle and nuclear physics levels.
QM Fails to Quantize Energy
Max Planck reportedly hoped to quantize energy. This goal was not achieved. However, his milestone contribution defined his Planck action constant h which is the product of energy x time, in units of Joules seconds. BM completes this story defining energy quantization with its eq. 1 [6] (Fig. 4, upper, from [2]).
QM Failure to Quantize
The foregoing commentary may highlight key weaknesses of QM formalism. Meanwhile, the BM postulates of full quantization provided a basis to discover the Keene scale values, which map directly to SI units of measurement used in science: energy in kg (convertible to Joules or eV), length in meters and time in seconds. Without the BM postulates, the Keene scale was not known to exist, much less what its values are. In short, full quantization replaces the long held assumption that energy, space and time are continuous.
QM Fails to Define Motion
BM system state eqs. 1-6 are thought to define an absolute reference frame, which is required to determine if motion has occurred or not. The Schrödinger and Dirac equations strive to define motion in a particular reference frame. However, without an absolute reference frame, it may not be fully clear if apparent motion is physically real or only a result of the choice of reference frame.
This QM defect has a dire consequence, namely QM formalism does not pin down if an object motion actually happened physically. Hence, QM cannot even begin to address the question of the mechanism of motion. Physics is supposed to be about how things work. The author encourages physicists to have more curiosity.
For example, Newtonian and QM physics are happy to describe motion and leave the question of how things move -- the mechanism of motion -- for another day. In contrast, biologists were not content to simply describe the motion of a cockroach across the grid on a chess board -- its velocity, acceleration, etc. They wanted to know mechanisms. Thus, the sliding filaments of contractile protiens were discovered, the energy source described and further, the neural networks coordinating the muscle contractions.
Since BM defines an absolute reference frame, motion can be studied and its mechanism revealed [7].
Pauli Spin Matix Reveal
The Pauli spin matrix set appears in both the Schrödinger and Dirac time development equations. These QM equations have produced excellent results, say, for electron behavior. Physics literature presents a variety of somewhat cryptic explanations of why use of these matrices works to produce results as predicted.
Physicists generally agree that rotation of a matrix used in an equation does not alter the "underlying physics". Former MIT student James S. Hughes showed that rotation of the Pauli spin matrices produced the eight vertices of a cube, which subsequent work by the author mapped to eight elementary particles (Table 1 in [1] [2]). That is, the Pauli spin matrices may be specifying a cubic lattice of these cubic structures, called "spot cubes" (Fig. 4, lower left).
In sum, with rotation of the Pauli spin matrices, two views are permitted and revealed: (1) the original unrotated version and its collection of cryptic explanations or (2) the rotated version defining the eight vertices of a cube leading to the BM model of space as a cubic lattice of spot cubes. In outdated QM, the time development equations might wrongly portray complex interactions among the eight BM elementary particles represented in the spot cube as the behavior of a single particle type, such as the electron.
If this is true, the bottom line is that QM is simply unable to represent correctly events at the BM level of microscopic fineness. This possible QM fail is a major limitation for continued usage of QM formalism in commercial applications. In contrast, BM formalism (eqs. 1-17 in [2]) provides an unprecedented means to achieve substantially greater accuracy and resolution in commercial design and engineering tasks (Fig. 1).
Incomplete QM Wave Function
QM formalism asserts the so-called uncertainty principle as a purported fundamental property of physical systems. In BM, this QM principle is known as the "dumb universe theory", namely that the universe is dumb, not the theoretical physicists. One result is that the wave function describes only half of the story -- object position or object momentum, not both simultaneously. With this self-imposed limitation, the wave function is now obsolete since the advent of the BM bit function which demonstrably represents both object position and momentum simultaneously at any quantized time T, where T is the Keene scale primary constant.
Discussion
Does the Dog Bark? This article outlines a tsunami of bad news for QM and its wave function. With the limitations and defects briefly listed, the reader might wonder why QM formalism is used at all some fifteen years after the first principles of BM were introduced [1].
What Works Best? Historically, technologies that work have been generally adopted even before underlying physics is fully understood and before all debates among physicists have been resolved. For example, electron microsocpy provides useful images of atomic configurations. Its practical real-world utility stimulates its widespread usage, although QM theoreticians continue to discuss what the electron actually is, its size, shape and composition. Likewise, one might expect increasing and considerable demand for quantum technology advances based on BM first principles, while physicists continue to discuss and explore fundamental questions and the scientific merit.
Licensed For Physics? BM technology advances may be licensed to users and packaged as a collection of software tools including the time-development engine, setup of initial states for any physical system, capture of "frame-by-frame" state changes for analysis and many more.
For example, consider a cesium 133 atom "clock" where a single tick cycle occurs in approximately 1.09E-10 seconds (1/9,192,631,770). With the present quantum technology advances, this interval amounts to about 3.8E+13 frames documenting the exact sequence of events in a cesium 133 clock cycle during which an electron is thought to transition between hyperfine energy states. Investigators can study what actually occurs much like film or video may be examined "frame-by-frame" to view and learn details of the events recorded.
And there is another, perhaps even greater payday available with BM technology. Once key events are better understood as described above, factors changing clock rate may be studied such as temperature, pressure, energy density and altitude comparing clocks in orbit or on earth. This is just one example of how BM technology might produce both practical and scientific advances.
At present, a selection of BM software tools are freely available in the hotspot.zip file here: Binary Mechanics Lab Simulator.
Play For The Win The "follow the money" rule may lead directly to exponential increase in BM technology usage, which improves spatial and temporal resolution by multiple orders of magnitude (Fig. 1), required for continuing progress in industries working at increasingly microscopic "nanotechnology" scales, attracting both physicists and capital investment. To be competitive, BM technology may be a required resource at academic physics departments and US national labs, in addition to numerous commercial enterprises.
References
[1] Keene, J. J. "Binary mechanics" JBinMech July, 2010.
[2] Keene, J. J. "Binary mechanics postulates" JBinMech November, 2020.
[3] Keene, J. J. "How to derive the primary and secondary physical constants" JBinMech March, 2025.
[4] Keene, J. J. "Quantization asymmetry" JBinMech May, 2016.
[5] Keene, J. J. "Intrinsic electron magnetic moment derivation" JBinMech February, 2015.
[6] Keene, J. J. "Binary mechanics equations" JBinMech March, 2025.
[7] Keene, J. J. "Law of motion based on mechanism of motion" JBinMech March, 2025.
© 2025 James J Keene
