It was found that acceleration of two bodies toward each other depended on a higher bit density between the two bodies than in other directions around the bodies. Further, attraction of two bodies conventionally described as gravity required a minimum bit density in the space between the bodies.
Discussion of these results suggests that space-time curvature, such as postulated in the General Theory of Relativity by Einstein is not required to explain gravity or other related observations, and indeed, probably does not even exist in the absence of data requiring it.
Perhaps to appreciate the BM basis for gravity, vacuum definitions might be reviewed. A perfect vacuum is conventionally defined as a volume without any particles such as ions or atoms, while a partial vacuum is a very low pressure volume with most particles removed.
In BM, the conventional perfect vacuum is in fact filled with a substantial number of binary units called bits of two types: mites and lites , perhaps at a level of some ten percent of maximum bit density. Indeed, this agrees with a number of theorists who have postulated that the perfect vacuum contains something -- virtual particles, dark matter or energy, electromagnetic (EM) fields, etc. Thus, it is necessary to describe the vacuum in further detail in order to fully explain physical phenomena .
In BM, an absolute vacuum is defined as zero bit density in a spatial volume. Given the strong tendency of the vacuum to absorb incoming energy, one might suspect that an absolute vacuum does not exist, even in deep outer space, which is usually characterized as a partial or near perfect vacuum in conventional terminology.
The present pilot experiment measures the distance between the center of bits of two bodies in an absolute vacuum, where the center of bits is analogical to the center of mass. As bit energy emerges from the two objects, the bit density between them would naturally be greater than in any other direction. The research question, then, is do the two objects move and if so, in what direction?
The BM simulator (Hotspot 1.23) was used to create two objects separated by 6 spots (12d in BM distance units) with a bit density per volume of 0.5 or 0.4 in an otherwise absolute vacuum. The spot loci and bit type masks were both set to 255 (all). The simulated space cubes were 40x40x40 or 48x48x48 spots. In all cases, the bodies were separated by 6 spots of absolute vacuum in the initial states.
In the 40 spot dimension spaces, the bodies were set in ranges for [X (-14,13), Y (-14,-4) and Z (-14, 13)] for one and [X (-14,13), Y (3,13) and Z (-14, 13)] for the other. For the 48 spot dimension data, the ranges for each of the two objects were [X (-18,17), Y (-18,-4) and Z (-18, 17)] and [X (-18,17), Y (3,17) and Z (-18, 17)]. Thus, the two objects were identical except for their position on the Y-axis.
The distance of the centers of bits of the bodies was tabulated as the average position of all bits at or above the zero center of the space (Y = 0) minus the average for bits below the center of the simulated volume on the Y-axis (R2Bot-R2Top column in the simulator .csv output file). Also, the standard deviations in each of the X, Y and Z dimensions for the entire volume were computed (sd1, sd2 and sd3 columns in the .csv output file).
Fig. 1 shows the inter-body distance in units of BM distance d over time (simulator Ticks) for a 40x40x40 spot volume with an initial bit density of 0.5 for each body.
The rate of change in inter-body distance appears to have several discernible phases. First, motion rate from Tick 11 (the peak) to Tick 15 is less than the rate between Tick 15 and Tick 22. That is, the hypothesized acceleration due to "gravity" increases over Ticks 11 to 22. From Tick 22 to Tick 43 (the lowest distance), the rate of motion decreases, as if a repulsive force between the objects opposes the apparent attractive force between the bodies.
After a short delay of 4 (X and Z) and 5 (Y) Ticks, all three measures of dispersion decrease rapidly, to low points at 22 Ticks (X and Z) and at 23 Ticks (Y). Next, up to about Tick 60, the two control deviations indicated rapid bit dispersion after which the deviations slowly decline toward an eventual stable level beyond Tick 200 (not shown; see Fig. 1).
Meanwhile, the experimental Y deviations displayed a more complex pattern of time development. There was dispersion (increase in the Y standard deviation) up to Tick 39, after which it appeared to be opposed by the overall decrease in inter-body distance (Figs. 1 and 2). Similar to the inter-body distance measure (Fig. 1), the Y deviation oscillated as a more stable inter-body distance was attained in later Ticks.
Comparing the initial and final states, the control dimensions (X and Z) started with about the same standard deviations and ended with increased deviations, indicating significant bit dispersion. In contrast, the experimental Y values started with a greater standard deviation due to the initial state specified. However, compared to the X and Z controls, the Y deviation measure moved in the opposite direction, namely, Y dispersion decreased over time, in apparent agreement with the inter-body distance results (Fig. 1).
Several variations in the experimental protocol may help clarify the foregoing results.
1. Change in Body Mass. In a 48x48x48 spot dimension space, the size (total number of bits) of each object was increased using [X (-18,17), Y (-18,-4) and Z (-18, 17)] and [X (-18,17), Y (3,17) and Z (-18, 17)] (Methods), but with the same randomized bit density of 0.5 in each body, and the same inter-body distance of 6 absolute vacuum spots.
2. Initial Object Bit Density. Reducing the initial bit density of the two bodies from 0.5 to 0.4 in a 40x spot dimension simulation resulted in an exactly 11 Tick delay before reduced inter-body distance began. However, with this reduced initial energy (temperature) of the objects, the first low point in inter-body distance occurred a bit later (Tick 51 versus Tick 43) and there was very little overshoot and "bounce back" with respect to the final steady state.
This pilot study used initial states of two bodies with high energy density (0.4 or 0.5 per spatial volume) in an absolute vacuum. Much of the energy in these objects was expected to disperse rapidly into the vacuum. In this process, the bit density in the surrounding vacuum would increase and increase even more in the vacuum space between the two bodies. Would this difference result in repulsion, attraction or no effect between the two objects? A major result is the reported decrease in inter-body distance of the respective center of bits along the Y-axis perpendicular to the thin 6 spot wide space between the two objects.
Several high-lights in the data may relate to gravitational effects.
1. Objects with different mass (number of bits) achieve maximum inter-body distance decrease in the same time, as seen comparing the Tick 11 to Tick 43 intervals for the 40x and 48x simulations. This result suggests a similarity to gravity as commonly understood, namely that objects of different mass are accelerated at the same rate.
2. Object temperature may affect gravitational effects as seen in the minor differences comparing the cooler, less dense 0.4 initial bit density with the hotter, more dense 0.5 bit density. Whether this is a new BM result remains to be seen, pending more detailed experiments. The author is not aware of any systematic work where surface temperature of a object has been considered as a factor in gravitational force. But work by Hawking and others regarding black hole surface temperature  may be relevant even if space-time curvature theoretical underpinnings may require a rather complete rewrite.
3. The time development of the X, Y and Z standard deviation components, each based on all bits in the simulated volume (Fig. 3), may help explain the observed inter-body distance decrease in the Y dimension. The initial rapid deviation decline was probably due to loss of bits from the periphery of the simulated volume. The subsequent increase in the standard deviations, most pronounced in the control X and Z directions, likely tracked the continued dispersion into surrounding space of the high energy (bit density) from the initial state within the two bodies. The final slower decline in the deviations toward a more stable level some hundreds of ticks later was associated with the later phases of the cooling of the two bodies, concluded by bit patterns within the objects displaying zero bit motion due to inertia (I column in ouput file) or heat content (S and V columns tabulating bit motion due to scalar and vector forces).
In sum, the initial and final values of the deviations may be the most relevant, where the control values (X and Z) increased and the experimental dimension (Y) decreased, indeed, falling into the range of the control values.
4. Do gravity-like effects occur within bodies? The lepton and baryon bit cycles   tend to capture and hold bits, a phenomenon which might be expected to concentrate bits in spatial volumes. In turn, this mechanism may be responsible for apparent attraction of material within bodies which could be attributed to a supposed gravity force. Indeed, these considerations initially suggested to the author that gravity was merely a by-product of the BM laws already postulated.
5. Absolute vacuum disabled putative gravitational attraction. If not a mere artifact in this pilot study, this may be a new BM prediction. The first 11 Ticks of the simulations, where no significant change in inter-body distance was observed, were occupied with filling the vacuum around and between the two objects. Note that in conventional terminology, this filling of the absolute vacuum with bits emerging from the two bodies may be classified as a perfect vacuum insofar as it continued to contain no "particles". But in the present experiments, it is clear that gravitational effects (or at least the attraction measured) did not commence with an absolute vacuum between the objects. Instead, the vacuum must be filled to a definite extent, at which time an apparent "force" attracting the objects to each other may be observed.
Perhaps needless to say, the apparent anti-gravity effect of a thin layer of absolute or near absolute vacuum is a possibly significant result which obviously suggests flight based in whole or part on a conceptually rather simple anti-gravity technology.
6. Another consideration supporting a gravitational interpretation of the reported reduction in inter-body distance is the relatively weak strength of the implied force, compared with the electromagnetic and strong bit operations. Consider the following approximation.
In the 40x spot cube with each object initialized at 0.5 density per volume unit (Fig. 1), the total number of bits in the simulation (Total column in .csv output file) started at about 69,000 dropping to about 59,000 after 200 Ticks, as bits exited the simulated space. The mid-point at 64,000 bits will suffice for a rough calculation.
In 33 simulator Ticks (11 to 43) or 132 BM ticks (33 x 4 sub-ticks, one for each bit operation), net bit motion reduced inter-body distance by 1.76 BM distance units. Hence, an estimate of the apparent strength of this effect, in units of motion of one bit over one BM distance unit per BM time unit (tick), is 1.76/(64000 x 132) or about 2 x 10-7. Compared to the scalar, vector and strong bit operations, where one bit moves one unit of distance in one tick, the suspected gravitational effect reported above might be some 10 million times weaker, as a rough approximation. At least, this comparison agrees with the widely accepted notion that gravitational effects are substantially weaker than electromagnetic or strong forces.
The present data should be regarded as very preliminary, but may point in the right direction on the subject of gravity. In agreement with BM, Einstein reportedly rejected gravity as a fundamental force. However, he favored curvature of space-time, which probably is not necessary to explain any of the phenomena that it is purported to predict. Each of these items requires specific study. By jettisoning curved space-time, its associated problematic singularities are also discarded. At present, BM does not discard the notion that its fundamental constants for distance d and time t might vary. On the other hand, there is no evidence that they do vary.
In spite of the decidedly unusual initial states used (high bit density surrounded by absolute vacuum), it is plausible that the purported gravity effects reported in this study in a very small spatial volume may occur at much larger distance scales as seen in objects falling to earth and of course among astronomical objects. Regardless of the scale, the principle mechanism would appear to remain the same, namely that the vacuum between any pair of objects is more dense than in any other direction from each object.
The present results may pertain to the Casimir effect , since the initial states used were similar to two plates very close to each other.
Finally, if gravity is not a fundamental force, then the laws of BM may be in place as a valid grand unification in theoretical physics.
 Keene, J. J. "Binary mechanics" J. Bin. Mech. July, 2010.
 Keene, J. J. "Vacuum thresholds" J. Bin. Mech. March, 2011.
 Wikipedia. "Black hole" April, 2011.
 Keene, J. J. "Physical interpretation of binary mechanical space" J. Bin. Mech. February, 2011.
 Keene, J. J. "The central baryon bit cycle" J. Bin. Mech. March, 2011.
 Wikipedia. "Casimir effect" April, 2011.
© 2011 James J Keene