MULTIVERSE MECHANICS

Introduction
The ontology
Charge space
Observers and objects
Reciprocity
Number density of object particles
The arcuum force
The particle radius
The mean free path
Derivation of observer's mean arcuum velocity
Rules of arcuum space vs. gravitational space
Derivation of gravity from the strong force
Superposition enhancement factor in arcuum space
Free particle impact on string: momentum transfer, no splitting
Can gross acceleration from a wave split a string?
How worlds split: particle-strings collision
Double-slit experiment; worked examples of the underlying reality
Rest mass energy derives from typical arcuum velocity?
How animals evolved to exploit the multiverse ontology
The roles of other dimensions of arcuum space
Appendix

Introduction

In multiverse mechanics we can show how the quantum probabilities and wave-particle duality emerge from the underlying reality by using simple equations to calculate accelerations, velocities, and distances travelled in a given time. At a fundamental level, particles - even photons - are particles, with a defined position, momentum and spin, all at the same time. The 'problem' is that this fundamental level - the level of a single universe or root universe - is always inaccessible to any observer or apparatus more complex than random free particles that are not part of a string.

Those who deny the existence of additional spatial dimensions and parallel worlds will always be left with weird phenomena that they cannot explain, such as "ghostly action at a distance", wave-particle duality, a quantum-classical dichotomy, "wave functions", faster than light (FTL) signalling, etc., and may postulate bizarre entities or processes such as "pilot waves" or "wave function collapses" in their attempts to do so, which are inevitably doomed to failure.

The ontology

There are ten dimensions in the multiverse mechanics ontology. After the three spatial dimensions of everyday existence, which we term gravitational space, plus time, which together comprises the 4-d space-time of General Relativity, we have four dimensions of arcuum space - the space "of the curves", since objects move through a series of curves or circles within this space.

A quantum probability of an observing particle or apparatus experiencing a hit from an object particle over some specified time is exactly equal to the distance travelled in arcuum space over that time, divided by the mean free path λ of that object particle in the 2-d plane of arcuum space that the subject observer particle will be moving along in a series of curves.

Within two dimensions of arcuum space, object protons have a fixed spacing of ~3.60868 microns. The arcuum spacing S_a is determined by the mass of the object particle M_obj, according to:

         2^9/4 * hbar^5/4 * M_obj^1/2
S_a =  ^{__________________________}
          G^1/4 * c^3/4 * M_p²

...where M_p is the proton mass, and so the neutron spacing is still ~3.61 microns and the electron is ~84.2 nanometres. Consequently, it is around this 3.6 micron range that gravity reverts from an inverse square law to an inverse sixth law. The inverse sixth attenuation is responsible for the more than thirty orders of magnitude difference in strength between gravity and the nuclear forces.

And if we let the three gravitational space dimensions be x, y and z, the four arcuum space dimensions may be a, b, c and d. Two arcuum dimensions, a and b, are very large, but gravity does not 'leak' beyond the 3.6 micron range because most of gravity derives from protons and neutrons and they are spaced at that range within the a, b plane. And the electron spacing is smaller, in proportion to the square root of its mass.

The remaining two arcuum dimensions c and d are compacted, rolled up so that the circumference is ~3.60868 microns, so no 'leakage' is possible there at longer range.

Charge space

The 9th dimension of charge space provides a geometric account of electromagnetism and so unifies it with gravity. The 10th dimension of omniversal space is the space containing an infinity of parallel universes or worlds.

In charge space, an electron will occupy the -1 point, a proton will be at the +1 point, and a neutron is at the zero point. Suppose an electron is moving in some direction in gravitational space, with a proton approaching it and moving in the opposite direction. We can consider the electron as moving along a rail linked to the -1 point in charge space. The electron produces the equivalent of a miniature 'black hole' at its gravitational space coordinates, but at the opposite point in charge space, the -1 point. This is negative space-time curvature, where the total volume of space is lower than it would be in a Euclidean space, and there is attraction. Moreover, the proton does the same in its turn, and so each is attracted to the other.

However, at the same point in both gravitational and charge space, the charged particle produces the equivalent of a miniature 'white hole'. There is positive curvature here, and the total volume of space is higher than for a Euclidean space. Thus, two particles of like charge approaching each other experience repulsion. On the other hand, the neutron is at the zero point in charge space which exhibits no electromagnetic curvature, although there is still a far smaller gravitational curvature caused by mass.

Observers and objects

Given any two particles, we can designate one of them as the "observer", and the other as an object that the observer may interact with. When a particle exists at the same coordinates in 3-d gravitational space and three of the arcuum space dimensions, (and charge space since it's the same particle type,) at the same time, and adjacent points along the remaining arcuum axis correspond to adjacent parallel worlds / universes, they are bound together by the ultimate attractive superforce, which we term the multiversal force. In each world or coordinate in omniversal space where eight of the particle's coordinates are equal and the remaining coordinate's separation is very small, this subject observer particle's motion must exactly track that of its counterparts in the alternate worlds, unless something occurs to cause a divergence within some of the worlds - namely, an interaction, or impingement of an object particle.

And so, the observer or subject is a string or particle-string, which extends across a particular set of points along the a,b plane in arcuum space in alternate worlds or points in the 10th dimension of omniversal space. We designate that particular set of worlds, which is very large but not necessarily infinite, as the multiverse for that particular observer. The observer could be a single particle or a macroscopic body such as a piece of apparatus or an animal brain, comprised of a very large number of these particle-strings, which are attracted to each other in 3-d space by electromagnetism. But the strings themselves are held together by the multiversal force which extends across arcuum space. Gravity and the nuclear forces derive from the multiversal force. Splitting of string(s) occurs when forces attempting to separate sections exceed the multiversal force attracting each particle (at an alternate point in omniversal space) to adjacent co-ordinates in 9-d space.

The particle-strings are comprising of enough points that they can continue splitting over thousands of millions of years, and shorter pieces may recombine into a longer string.

Reciprocity

Object particles can be considered as observers in their own right. However, from the viewpoint of the original subject observer, the object particle will be in a superposition of various positions in gravitational and arcuum space, various momenta, and various spins. The original observer can perform various measurements upon the object particle, but this will only split the observer - and by extension the object particle as perceived by that observer - across a certain basis. This is because we cannot simultaneously measure position and momentum, or x-spin and y-spin.

The object particle becomes a subject observer particle-string when we consider another particular set of parallel universes where that object particle happens to be at matching coordinates of time, 3-d gravitational space, charge space and three of the arcuum space dimensions, c, d and either a or b (when we align the axis along the string). An object apparatus would 'see' a subject as a superposition, with a consensus view only emerging at the classical level.

Thus, there is the multiverse pertaining to the original subject observer, and there is the multiverse associated with the object particle in its own role as observer. The omniverse is the totality of all parallel worlds, truly infinite, and the number of multiverses within the omniverse is larger than the number of points comprising a particle-string.

Number density of object particles

Given the diameters of the subject and object particles, and the arcuum spacing of the object particles, the subject will sweep through a collision rectangle in arcuum space, with one hit on average for each travelling of the mean free path λ. A particular type of object particle will be spaced out across the a,b plane in 4-d arcuum space, and particles of alternate mass could exists at various levels in the c and d dimensions. In the a,b plane, for each square metre there will be a certain number N of object particles, equal to the reciprocal of the spacing S_a squared. That is, 7.67895x10¹⁰ protons, 1.40997x10¹⁴ electrons or ~1.28x10³⁹ photons.

            G^1/2 * c^3/2 * M_p⁴
N =  ^{__________________________}
         2^9/2 * hbar^5/2 * M_obj

The arcuum force

The arcuum force is actually an acceleration resulting from curvature of the arcuum space, as with gravity in 3D space. We can multiply the acceleration by the subject particle mass to find the 'force', but the elegance of Nature's scheme is that varying the acceleration or force does not change the mean arcuum velocity of the subject observer particle-string. The acceleration varies directly with the energy of the object particle in 3D space, but the de Broglie cycle period Pe varies inversely with the object particle energy. Consequently, the subject observer's mean arcuum velocity is only determined by the subject / object combination, which defines the mean free path λ, and |ψ| (where |ψ| is the total modulus), and the phase factor φ, and the rate or flux per second of incoming objects N, which is the incoming power W divided by the energy E in 3D space per object particle.

Since we have defined the rate of incoming object particles as per second, then over one second the subject observer displacement d_a in arcuum space is numerically equal to its mean arcuum velocity v_a, and we end up with:

d_a / λ = R . diameter_subject . |ψ_(x)total|² . φ

So the rate of interactions per second at some point x is just the normalised probability density times the rate of incoming object particles, adjusted for a bin sized at the diameter of the observing subject particle-string. And this is equal to the displacement in arcuum space divided by the mean free path λ between object particles for the subject. Each encounter in arcuum space results in a splitting of part of the observer string, which can then diverge or decohere from the rest of the string that is tracking along in 3D space as having registered no interaction at that instant.

Each contribution from component amplitudes has the effect of a low rise-time force in a particular direction in arcuum space, with the direction then proceeding to sweep around 360 degrees as the de Broglie 'phase' of period h / E clocks through a single cycle, or in other words the object particle travels a distance of one wavelength in 3-d gravitational space. The resultant motion is of oscillation about one axis, and acceleration from zero to a peak and back to zero in the perpendicular axis. Therefore, there is a mean velocity - half the peak along the latter axis - corresponding to the magnitude of the accelerating force a_net times the period Pe, with the direction being 90 degrees off that of the sudden emergence of the force (e.g. as the first photons pass).

Imagine a test particle, subjected to a force that suddenly appears in the 12 o'clock direction, which then continues with a clockwise rotation. Along the x-axis, there is acceleration in the positive direction throughout the first two quarter cycles, and then a countering deceleration over the final quarter cycles. Thus, the test particle accelerates to the right, the east, or the +ve x direction for half a cycle, then decelerates to a standstill, after which the process repeats every cycle, and there is an overall displacement.

Along the y-axis there is merely an oscillation. The first quarter cycle produces acceleration in the +ve y direction; the second quarter has deceleration bringing it to rest. The third quarter cycle produces downward or -ve y acceleration, and the final quarter deceleration brings the test particle back to the original y coordinate.

That's the equivalent of a single slit experiment. Open up the second slit, and there could be a force of equal magnitude but 180° out of phase (all the time, as for a monochromatic light source the frequency or period are identical from each slit's contribution, or amplitude). This corresponds to maximum destructive interference, and the test particle goes nowhere. The difference between path lengths from source to screen, for the two slits, is half a wavelength, or some integer of wavelengths plus half a wavelength.

However, if the phases are equal, which would correspond to the difference in path lengths from source to screen being zero or some integer number of wavelengths, the contributions from each slit reinforce each other and we have constructive interference. The test particle moves off, say, initially in the +ve y direction and ultimately is displaced towards the +ve x direction in the same curve as for one slit, but the total force, size of the curve, or displacement is greater. And when the phase difference is intermediate between 0° and 180°, the curve gets distorted and the total displacement over some time could be greater or smaller according to the cosine law of the phase factor φ.

This is what a quantum "amplitude" actually corresponds to in physical reality. We shall show later some worked examples for a two-slit experiment. The quantum amplitude is a vector quantity with modulus and phase; adding all the amplitudes is equivalent to adding arrows and then squaring the resultant arrow to obtain a probability. Physically, the vector quantity is the magnitude and direction of an apparent 'force' in arcuum space.

However, the arcuum force is not some force that operates by somehow attracting the subject observer particle-string and pulling it 'up' in the +ve y direction in arcuum space. It is equivalent to a gravitational wave moving along the c or d dimensions of arcuum space, caused by a vibrating particle-string, in turn leading to a rotating vector polarisation mode in the a, b plane, perpendicular to the GW's propagation direction. The rotating vector mode is possible since this gravitational wave operates in at least four, rather than three, spatial dimensions.

The particle radius

From:

                   4 * hbar * M_particle
r_particle =  ^{_____________________}
                            c * M_p²

...we get 5.029x10^-44 m for the photon particle radius, 4.5815x10^-19 m for the electron, and 8.4123x10^-16 for the proton radius, whether as an observer or an object, and in both gravitational and arcuum space. We suppose that the photon is a particle with very low mass, say 10^-55 kg. Its velocity is very slightly lower than c, with a blue photon being faster than a red one.

The mean free path

For any permutation of subject and object particle, the mean free path λ for the subject observer to encounter an object particle is dependent on the object particle spacing in arcuum space Sa and the size of the particles according to:

                S_a²
λ = ^{_____________________________________}
        diameter_subject + diameter_object

...which is equal to:

             2^3/2 * hbar^3/2 * M_obj
λ = ^{________________________________________}
         G^1/2 * c^1/2 * M_p² * (M_subj + M_obj)

Or if we let MassRatio = M_obj / M_subj we have:

             2^3/2 * hbar^3/2 * MassRatio
λ = ^{________________________________________}
         G^1/2 * c^1/2 * M_p² * (MassRatio + 1)

...and the mean or effective velocity of the subject observer particle-string through arcuum space v_a is given by:

v_a = R * λ * |ψ_(x)|² * φ * diameter_subject

...where R is the rate or number of incoming object particles per second (e.g., the power output W from the slits in a double-slit experiment divided by the energy E_obj3D in 3D-space of the object photons), |ψ_(x)| is the total modulus of the quantum amplitudes for some point x, and φ is a phase factor between 0 and 1.

The phase factor is:

           |A|² + |B|² + 2 |A| |B| . cos(θ)
φ = ^{____________________________________}
          |A|² + |B|² + 2 |A| |B|

Since we are dealing with the rate per second of incoming object particles, we are interested in the displacement or distance travelled in arcuum space per second. And so, over each second, the subject travels in arcuum space a distance d_a = v_a = R * λ * |ψ_(x)|² * φ * diameter_subject.

Hence d_a / λ = v_a  / λ  = R * |ψ_(x)|² * φ * diameter_subject. This is the rate of incoming object particles per second, adjusted to cover a bin with size equal to the diameter of the subject observing particle, times the probability density, which is the resultant modulus squared, or the total modulus squared times the phase factor.

Derivation of observer's mean arcuum velocity

Now let's explain how we obtain this mean arcuum velocity for the subject observer, from an acceleration due to curvature.

The curvature could be considered as a gravitational wave (GW) from a vibrating object particle-string. The GW propagates along the c or d axes in arcuum space, and perpendicular to this propagation, produces a rotating force vector in the a,b plane. The amplitude of the GW wave is proportional to the energy of the object particle in 3D space, and it has periodicity inversely related to its energy.

However, rather than a GW producing this wave in arcuum space, it is better to think of de Broglie matter waves in arcuum space as the more fundamental phenomena from which GWs emerge at the classical level, rather like gravity emerging from the strong force.

More fundamental is the gross acceleration acting on parts of the subject observer particle-string, those worlds encountering an object particle. This gross acceleration is given by:

                     W * λ² * |ψ_(x)|² * φ * diameter_subj
a_gross = ^{__________________________________________}
                                    hbar x diameter_obj

Since we have the particle size scaling directly with their mass, the diameter_subj / diameter_obj above could be replaced by M_subj / M_obj if desired.

                 8 hbar² * W * |ψ_(x)|² * φ * M_obj * M_subj
a_gross = ^{________________________________________________}
                G * c * M_p⁴ * (M_subj + M_obj)²

And if we let MassRatio = M_obj / M_subj we have:

                 8 hbar² * W * |ψ_(x)|² * φ * MassRatio
a_gross = ^{________________________________________________}
                G * c * M_p⁴ * (MassRatio + 1)²

And the net acceleration acting upon the entire subject observer particle-string is:

a_net = a_gross * diameter_obj / λ

        W * λ * |ψ_(x)|² * φ * diameter_subj
= ^{____________________________________________}
                             hbar

(We do not need to have a_net = a_gross * diameter_obj / (λ + diameter_obj) to allow for cases where λ < diameter_obj, since under the above rules for object spacing and particle size, λ / diameter_obj is at least ~4.6x10¹⁸.)

             2^9/2 * hbar^3/2 * W * |ψ_(x)|² * φ * M_subj * M_obj
a_net = ^{_________________________________________________}
             G^1/2 * c^3/2 * M_p⁴ * (M_subj + M_obj)

Even at the fundamental level of the gross acceleration, for the tiny minority of parallel worlds where the subject string encounters an object particle at some instant, the phase factor still holds up. In those types of universes where it doesn't, any particle-strings would quickly get broken up into free particles, stable atoms would not exist, and there would be no observers of any complexity to ponder ontological questions.

The phase factor persists down to a very small scale, because of how an object particle-string exists in a subset of single universes, root universes, or a multiverse, that is very different to the multiverse of another particle-string, or to a particle-string that we consider to be the subject observer. And so subject and object would perceive each other as a superposition until a measurement is performed.

For Nature, and for life, the advantage of this is that when the phase factor is not equal to one, there isn't an acceleration on part of the string in one direction and on another part of the string in the other direction, which would bend it. The phase factor can cancel out the gross acceleration on smaller lengths of the string, as well as the net acceleration over a longer length.

Take the example of a proton, which we designate as the subject observer particle-string. In each adjacent parallel world in its multiverse, one of its spatial coordinates is changed by the Planck length at most, or even by a shorter length. Arcuum 4d space has some different laws compared to 3d gravitational space. The latter has more restrictions, such as the Planck length or Planck time, and curvature is determined by local matter at the single universe level, with no superpositions allowed. In contrast, in arcuum space, curvature and acceleration are determined by mass at the multiverse level, i.e., by a superposition.

If adjacent worlds in the proton string are apart by only the Planck length instead of the proton diameter, then those worlds comprising a length of the proton string equal to its diameter are a superposition of ~10²⁰ worlds, which means that the force holding the string together is multiplied by an amount that we may term the superposition enhancement factor (SEF), where SEF = diameter(particle) /Δ_a, with Δ_a being the minimum length unit in arcuum space.

And where the path lengths for object particles are such that alternative amplitude contributions are out of phase, there is not one large set of adjacent worlds in the subject observer's multiverse where all contributions give rise to a acceleration or 'force' in one direction in the a,b plane and then another large set of worlds where all contributions produce a force in the other direction. Instead, they are jumbled up into a random superposition, with adjacent out of phase GWs or de Broglie matter waves combining at very small scale, so that the gross acceleration is multiplied by the phase factor even at this scale.

The net acceleration a_net acting on the particle-string is the gross acceleration acting on a very small proportion of the string multiplied by the fraction it is operating on. And this fraction relates to conditions in arcuum space. It is a fixed mark/space ratio for some given combination of subject and object particle. It is the diameter of the object particle divided by the mean free path λ between object particles in a,b as seen by the subject particle. And so as above, we have:

                               diameter_obj
a_net = a_gross * ^{_________________}
                                          λ

        W * λ * |ψ_(x)|² * φ * diameter_subj
= ^{__________________________________________}
                             hbar

Now the mean or effective velocity of the subject observer particle-string through arcuum space v_a is given by:

                     Pe
v_a = a_net * _____
                     2π

...and the period Pe = = h / E_obj3D, and so:

                     hbar
v_a = a_net * _______
                    E_obj3D

The mean arcuum velocity for the subject string derives from a_net and the period Pe of the de Broglie cycle. Fortunately, because the acceleration varies directly with the object's energy in 3D space E_obj3D and the period varies inversely with it, as per Pe = h / E_obj3D, the mean arcuum velocity v_a is independent of the object's energy. And since:

                  W * λ * |ψ_(x)|² * φ * diameter_subj
a_net = ^{__________________________________________}
                               hbar     

                  W * λ * |ψ_(x)|² * φ * diameter_subj
v_a = ^{__________________________________________}
                            E_obj3D

= R * λ * |ψ_(x)|² * φ * diameter_subj

...where as above R is the rate of incoming object particles per second.

Now let's look at how these accelerations or 'forces' acting on the string compare with the 'force' or acceleration holding the string together.

Rules of arcuum space vs. gravitational space

As mentioned above, in the three gravitational space dimensions x, y, z there is the speed of light limit c, the Planck length and Planck time minimum units, and curvature is determined by mass locally at the single or root universe level. Superpositions are not allowed to determine curvature.

On the other hand, in 4D arcuum space, superpositions in adjacent parallel worlds do indeed determine curvature of arcuum space at small scales, and the minimum unit of length may be as low as ~1.233x10^-63m. Based on the adjacent parallel worlds for the particle-string we designate as the subject, this string exists as a superposition of these minimum units of length, rather than being in a line with a separation equal to its particle diameter. Because of the superposition, the curvature, acceleration or 'force' holding the string together is the strongest force in a multiverse, and the string can only be broken by impact with another string.

The ratio of the subject particle's diameter to the minimum length Δ_a in arcuum space is the number of worlds comprising the superposition along a length of the string equal to its particle diameter, and this ratio is the superposition enhancement factor (SEF), the ratio of the acceleration or curvature with superposition enhancement compared to the base value if there were no enhancement. It is the factor of how the mass has been effectively multiplied.

For example, for a proton subject observer particle-string, its diameter is ~1.682x10^-15m. Even if the minimum arcuum length is no smaller than the Planck length, ~1.616x10³⁵m, the SEF in this case is ~10²⁰.

Derivation of gravity from the strong force

Here's how gravity derives from the strong force, and how we get a minimum length Δ_a of ~1.233x10^-63m, and why the proton object spacing is 3.608685671x10^-6m.

For the strong force, at the proton radius 8.412356402x10^-16m, we take a value of 2 x hbar x c = 6.323053543x10^-26 N.m². Now these units assume an inverse square law all the way down from astronomical levels, but in fact gravity reverts from an inverse square law to an inverse sixth law at the transition point R₁ = 3.608685671x10^-6m, which is the proton spacing in at least the two arcuum space dimensions a and b, with c and d probably being compacted to the size of R₁. And so, for some separation r, the acceleration a is given by:

a(r) = -G * M * (1/r² + R₁⁴/r⁶)

At very short range, where r << R₁, the 1/r² term becomes negligible in relation to the other and the force follows an inverse sixth law. At long range where r >> R₁, the R₁⁴/r⁶ term becomes negligible, and the force is the familiar inverse square law of gravity. And at the R₁ transition point of 3.608685671x10^-6m both terms are equal and we anticipate gravity is at twice the strength of the inverse square law prediction.

We suppose that the maximum acceleration occurs where r is the particle radius, and at closer range it attenuates in a linear law (roughly like gravity inside the Earth's volume), so that at r = 0.1 of the proton radius the acceleration is -5.341875306x10³⁰ m/s², one-tenth of that at the proton radius, as per a(r) = -G * M * R₁⁴/r⁶.

Superposition enhancement factor in arcuum space

Now taking the average spacing between galaxies as ~5 million light years, then the ratio between the galaxy spacing and the Planck length is 4.73026x10²²m / 1.616x10^-35m ~ 2.927x10⁵⁷. Let the proton spacing in arcuum space of 3.608685671x10^-6m be analogous to galaxy spacing, and then we obtain 1.233x10^-63m as a minimum unit of length in arcuum space.

Let a particle-string be a superposition of points that are 1.233x10^-63m apart in arcuum space. Each alternate point corresponds to an alternate parallel world in omniversal space. Over the proton diameter of 1.68247128x10^-15m there are 1.3645x10⁴⁸ of these Δ_a of ~1.233x10^-63m that fit. This gives the superposition enhancement factor of 1.3645x10⁴⁸, the amount by which the acceleration due to the proton mass is multiplied by, due to the superposition in arcuum space.

In gravitational space with no superposition, the acceleration at the proton radius is -5.341875306x10³¹ m/s², as given by a(r) = -G * M * R₁⁴/r⁶. But in arcuum space, after allowing for the superposition enhancement factor of 1.3645x10⁴⁸, the acceleration is -7.289x10⁷⁹ m/s².

Free particle impact on string: momentum transfer, no splitting

There are probably free object particles moving around that are not part of a string. Unless the speed of light limit does not apply in arcuum space, such free particles are not powerful enough to split a string, and will cause the impacted part of the string to vibrate at a frequency determined by the acceleration or 'force' holding the string together and the radius of the subject particle.

Simulations demonstrate the effect of a free particle impacting one of the points comprising a subject observer particle-string. For the acceleration regime, we suppose maximum acceleration at the subject radius, and this would attenuate in an inverse 6th law beyond the radius, until reverting to an inverse square law beyond 3.608685671x10^-6m. At separations shorter than the radius, we suppose that the acceleration decreases linearly with displacement s / radius r, as gravity would decrease for an object within the Earth's volume as the object got closer to the centre of gravity.

For velocities below a certain limit, the point will oscillate, with the maximum displacement directly related to the impact velocity. The point only escapes from the rest of its string if the impact velocity is so high in relation to the restoring acceleration that the displacement exceeds the radius. Under the acceleration regime as described, the oscillation frequency ν was found to be:

ν = 1/(2π) * SQRT(a/radius)

Even at the Planck length minimum unit in arcuum space, and the smaller SEF 1 value for superposition enhancement factor, a proton subject observer particle-string could cope with an impacting free proton particle at 2x10¹⁸ m/s so that the subject particle point moved off from its string at the same initial velocity. The maximum displacement was found to be ~7.77x10^-16m, still inside the radius limit, and at simulated time increments around 10^-40s, the particle point would continue to vibrate with no signs of any escape or splitting.

Under the stronger restoring acceleration regime of SEF 2, the proton string could handle impacts of 2x10³² m/s without escape or splitting.

Even at the smaller SEF 1, an electron subject observer particle-string could withstand an impacting electron free object particle at 10²³ m/s without splitting. And so, for free particle impacts, the arcuum minimum unit need not be smaller than the Planck length unless faster-than-light speeds are permitted.

If the minimum unit is the Planck length, then the proton oscillation frequency is 4.092x10³² Hz and the electron is 5.911x10⁴⁰ Hz.

At the 1.233x10^-63m value for Δ_a the proton oscillation frequency is 4.685x10⁴⁶ Hz and the electron is 6.768x10⁵⁴ Hz.

If we take 10⁵⁵kg as the proton mass, then its radius is 5.029x10^-44m, so the minimum length unit is < L_Planck, so the minimum SEF value is greater than SEF 1.

Can gross acceleration from a wave split a string?

Any sub-light speed impacts from free object particles would be quite unable to knock out a point on a string. However, the gross accelerations from the GWs or de Broglie matter waves can be very large, and some degree of superposition enhancement factor is needed, so that these waves merely guide the string rather than split it.

If we take the weaker restoring acceleration regime SEF 1 for a proton string, with the Planck length the minimum arcuum space unit, then we have -5.5609x10⁵¹ m/s² to hold points on the string together.

From:

                   W * λ² * |ψ_(x)|² * φ * M_subj
a_gross = ^{_____________________________________}
                                    hbar x M_obj

       8 hbar² * M_obj * W * |ψ_(x)|² * φ * M_subj
= ^{________________________________________________}
      G * c * M_p⁴ * (M_subj + M_obj)²

...if we take the weaker restoring acceleration regime SEF 1 for a string, with the Planck length the minimum unit, then we have -5.5609x10⁵¹ m/s² to hold points on the string together. In the case of proton subject / proton object, this value is reached when the power of the incoming object particles is ~10GW, and with total moduli of 2 and phase factor of 1, i.e., maximum constructive interference if possible under such conditions. In other words, the incoming energy per second would be equivalent to more than two tons of TNT!

Other combinations of electron / proton / neutron subject and object require greater energies to defeat the restoring acceleration and split the string.

And so, there is ample Superposition Enhancement Factor to hold particle-strings together when faced with high energy de Broglie waves or GWs, and the result of this is motion rather than splitting of subject observer particle-strings.

How worlds split: particle-strings collision

In contrast, when a particle-string hits a particle-string, all of the points comprising the diameter are hit almost simultaneously by the other particle-string. And the curvatures or accelerations from each one holding the string together are of opposite sign, so will tend to annul each other.

Splitting of strings can occur both at the quantum level (e.g. detection of a photon) or at the classical level (e.g. a Schrödinger's Cat-type experiment as the human observes the status of a macroscopic object after a quantum event has been amplified to the classical level).

The rate of object particle hits is directly related to the proportion of the observer particle-string (within the one-dimensional multiversal or omniversal space - the space that can be considered to contain all the parallel root universes, each of which corresponds to a particular point in multiversal space) that splits apart from the remainder per unit time, and this rate of multiversal splitting is directly related to the observed rate of interactions.

Double-slit experiment; worked examples of the underlying reality

We suppose the source is a helium-neon (He-Ne) laser that produces red photons of wavelength 632.8nm, the energy is 1.959 eV = 3.139x10^-19 J, and the period is 2.111x10^-15s. Taking the case of electron subject observer particle-string and photon object, the mean free path λ in the a,b plane of arcuum space is 8.4969x10^-22m.

The power output from the slits is 10mW, and so we have 0.01 / 3.139x10^-19 = 3.186x10¹⁶ photons per second from the slits. With the shortest length from slits to screen L at 2m, the distance d between slits is 6.328 μm, the slit width a is 2.531 μm, and we are considering a line along the screen x = 0 to 1m, then the main central peak is at 0.5m, the first null point is at 0.4m, the next, smaller, peak is at 0.3m, the next null point is at 0.2m, and symmetrical in the other direction.

Under the far-field approximation, the normalised probability density (m^-1) at some point x is:

      [ sin(2π(x - 0.5))          ]²
4 x [ ^{____________________} ]  x cos²(5π(x - 0.5))
      [     2π(x - 0.5)              ]

Integrated over -50 to 50, the definite integral is ~0.999, or over 0 to 1 it is ~0.902. So some 90% of the photons hit the screen between 0 and 1m, and around 0.1% make it to more than 50m along.

To find the flux rate n(x), the actual number of photons arriving per second in some one-micron bin on x, we change the 4 in the above formula to 0.04/3.139x10^-13. Integrated over -50 to 50m, this gives ~3.182x10¹⁰, so adjusting back to metre units it is very nearly 3.186x10¹⁶ photons/second.

The general formula is:

n(x) = (W/E) * |ψ_total(x)|² * Δx

...with Δx the bin size.

The far-field approximation seems to give some rather idealised results, where the null points occur at exactly 0.4m, 0.2m, etc..

In the QBasic implementation in the appendix, rather than treating a slit as a point, 1,000 points per slit are integrated, the contributions from each slit are summed, and the probability density computed. When the slits were treated as a point source, the diffraction envelope had too little attenuation over distance. For some specified point on x, the rate of photons expected to arrive per second in an electron-diameter-sized bin (9.163024974x10^-19m) is computed, and this can be compared and shown to match the rate of interactions calculated in the arcuum velocity program.

To find the normalisation factor NF, all contributions from each points for each slit, and points along x from -50 to 50 were integrated, and the trapezoid rule employed. When set for 1, the maximum was nearly 4 at ~3.8797.

In the double-slit program, enter 0.5m for x, and it calculates 0.1132530401717373 photons/bin/s. The moduli |A| and |B| are equal to 15 figures at ~0.9848, and the phase difference is 0°. The phase factor is 1.

Going over to the arcuum velocity program, select 7 for the option electron subject, photon object, enter 3.139D-19 for the object particle energy, 0.01 for the object particle wattage, .9848524317784662 for |A|, .9848524317784666 for |B| and 0° for the phase difference (as displayed in the double-slit program). It displays 0.1132530401816548 for the fraction distance travelled (in arcuum space for the subject observer particle-string) divided by the mean free path λ in arcuum space, so matches to the 10-figure accuracy of the fundamental constants.

In this case there is a gross acceleration of ~2.419x10¹⁵ m/s² acting on parts of the observer string, from:

                   8 hbar² * M_obj * W * |ψ_(x)|² * φ * M_subj
a_gross = ^{________________________________________________}
                       G * c * M_p⁴ * (M_subj + M_obj)²

The probability density |ψ_(x)|² is 3.879737249 and the phase factor is 1. We have 10^-55 kg for the photon (object particle) mass, and so after plugging in the constants we obtain the ~2.419x10¹⁵ m/s² gross acceleration.

The net acceleration is the gross acceleration times the fraction of the observer particle-string it acts on, which is the photon object diameter of 1.005888572x10^-43m under our assumptions divided by the mean free path λ of 8.496918536x10^-22m, which gives the net acceleration of 2.864352599x10^-7 m/s².

For the mean arcuum velocity of the subject string, we multiply the net acceleration by the period Pe = 2.1108856801x10^-15s / 2π, to get 9.623018564x10^-23 m/s. The arcuum displacement over 1 second is numerically the same, and we divide that by the mean free path λ of 8.496918536x10^-22m to get the 0.1132530402 expected rate of photons arriving in the electron diameter-sized bin per second.

Take another example, say x = 0.47m. When this is entered into the double-slit program we immediately see that the rate of arrival of photons per electron diameter per second is reduced to 0.08884613459. The B-slit is slightly further away, and we have |A| = 0.9789791264 and |B| = 0.9789766532. Both are reduced, and there is now a clear trend of |B| < |A|. The phase difference is shown as 53.99392602°, and the phase factor is down to 0.7939355068.

We input the same initial values into the arcuum velocity program, so that with the same electron / photon combination, and the same object particle energy and power, the rate of photons coming out of the slits is unchanged. Then enter in the new values for |A|, |B|, and the phase difference.

The total modulus squared is down from (.9848524318 + .9848524318)² = 3.879737250 to (.9789791264 + .9789766532)² = 3.833590835, so that's the diffraction envelope down by a factor of 0.9881057886. Rather more significant - and fascinating, is how the phase factor has declined from 1 to 0.7939355068. Thus, the overall reduction is 0.7844922700. And this leads to the same reduction in gross acceleration, net acceleration, mean arcuum velocity, arcuum displacement per second, arcuum displacement per second as a fraction of the mean free path λ, and the rate of photon encounters for an electron at x = 0.47m compared to 0.5m.

The matter waves in arcuum space generated by photons from slit A are slightly reduced in amplitude, as are those generated by the 'B' photons. But now these rotating force vectors in the a,b arcuum plane are 53.99392602° out of phase with each other, so that at an instant where one of them exerts an accelerating force along one direction the other exerts the force 53.99392602° out of alignment.

In the far-field approximation the first null points are at exactly 0.4m and 0.6m. With the supposedly more precise calculation the best null point occurs at x = 0.399874765m. Enter this into the double-slit program and we get 1.830569759x10^-12 photons/electron diameter-bin/second. |A| is 0.9207563862, |B| is 0.9207484672, |A| has a phase of 44.54690730947053°, |B| is 224.5469070659117°, and the phase difference is 179.9999997564412°.

When this is inputted to the arcuum velocity program,  the gross acceleration is now down to 39109.03453 m/s², the net acceleration is 4.629835006x10^-18 m/s², the mean arcuum velocity is 1.555429601x10^-33 m/s, and the arcuum displacement per second divided by the mean free path λ is 1.83058089x10-12, which matches the value from the double-slit program to nearly seven figures.

In another variation, suppose we keep the ratio W / E the same, so that the photons emerge from the slits at the same rate, but we double the energy and halve the wavelength. Thus, the power emerging also has to double to 0.02W. Now the doubling of power leads to a doubling of gross and net accelerating forces. But the doubling of energy per photon leads to a doubling of frequency and a halving of the period, and so the mean arcuum velocity and rate of interactions remains the same as before.

Now let's suppose we were able to make the slits so much narrower and closer together to allow for much shorter wavelength protons coming from the slits, and a proton observer is at x = 0.5m. Suppose the energy per proton is the same as before at 3.139x10^-19 J, and the power output from the slits remains at 0.01W, so the rate of particles per second remains the same, although the wavelength is now down to 2.045x10^-11m.

If the apparatus could be set up as in the photon case, above, so that we had |A| = 0.9848524317784662, |B| = 0.9848524317784666 and the phase difference = 0°, we input this into the arcuum velocity program, under option 4, proton subject + proton object. The period Pe is unchanged at 2.111x10^-15s. But now the gross acceleration is much higher at 5.510196x10³⁹ m/s², the net acceleration is up to 2.395489x10²¹ m/s², the mean arcuum velocity is way higher at 804783.6 m/s, and the mean free path λ is up to 3870.084m.

Thus, each second, the distance travelled is 207.9498725 times λ, and 207.9498725 is the expected rate of interactions per second for a proton diameter-sized bin. Compare with the 0.1132530401717373 photons/bin/s above, and the difference is the ratio of the proton diameter to electron diameter, or proton mass : electron mass of 1836.15.

Now input the same |A| = 0.9848524317784662, |B| = 0.9848524317784666 and the phase difference = 0°, with the observer changed to an electron, so we use option 2, electron subject + electron object. The period is the same, gross acceleration is down to 1.199072x10³⁷ m/s², the net acceleration is down to 2.607828x10¹⁸ m/s², the mean arcuum velocity is down to 876.1205 m/s, and the mean free path λ is up to 7735.956m. Displacement in one second / λ is 0.1132530402, which makes the expected rate of interactions equal to the photon case above.

Rest mass energy derives from typical arcuum velocity?

For simplification, if we run the arcuum velocity program and set object energy E = 1J, object power W = 1W, |A| = |B| = 1, θ = 0°, then go through the nine permutations, we have:

1 Electron subject, electron object: mean v_a (m/s) = 1.418467261e-14
2 Electron subject, proton object: mean v_a = 2.835390321e-14
3 Proton subject, electron object: mean v_a = 2.835390321e-14
4 Proton subject, proton object: mean v_a = 2.604522454e-11
5 Photon subject, electron object: mean v_a = 3.114299070e-39
6 Photon subject, proton object: mean v_a = 3.114299070e-39
7 Electron subject, photon object: mean v_a = 3.114299070e-39
8 Proton subject, photon object: mean v_a = 3.114299070e-39
9 Photon subject, photon object: mean v_a = 1.557149535e-39

Take the rms velocity for the three cases of electron object, and we get 1.830435981e-14 m/s. Similarly, we have rms velocity for proton object = 1.503724413e-11 m/s, and rms for photon object = 2.697062109e-39 m/s.

Now divide by the rest mass, and we have rms for electron / electron mass = 2.009396067e16. rms for proton / proton mass = 8.990223013e15, rms for photon / photon mass = 2.697062109e16. The maximum difference is only a factor of three.

Given that the arcuum spacing is related to the square root of the rest mass, it is reasonable to suppose that typical arcuum velocities would be proportional to the arcuum spacing. Then this mean velocity squared gives the rest mass energy, and so the total energy is the sum of two components; the square of the typical arcuum velocity for some particle type, or the kinetic energy in arcuum space, and the kinetic energy in 3D gravitational space.

Fundamentally, the rest mass energy derives from the size of the particle. As the particle size increases, the acceleration due to curvature of arcuum space at some given distance increases. If the disturbance is sufficiently large, due to a very large number of particles, the matter wave becomes a measurable gravity wave in 3D-space.

How animals evolved to exploit the multiverse ontology

Experiments by Libet in the early 1980s showed that changes in a readiness potential (RP) in the brain apparently preceded a conscious decision to perform a voluntary movement by several hundred milliseconds. However, a 2023 study at the HSE Institute for Cognitive Neuroscience showed that the changes in RP were apparently not linked to the conscious decisions to make a movement, since the latter would occur at different points in time, whereas the former would tend to occur at around the same time in the experiment.

In 2013 a research group led by Bandyopadhyay found confirmation of certain resonances, e.g. around 8.9MHz, in the microtubules in brain neurons, where this normally insulating material became very high conductance, almost approaching quantum conductance. And the conductance increased with length and width of the microtubule, suggesting quantum mechanisms at body temperature.

A predator that is able to make a random, unexpected change in movement, such as a large cat stalking and making the sudden decision to charge, will have an advantage over its prey. That is, until the prey equalises by evolving to have a similar randomised decision-making capacity, so that it can flee first.

In the Libet experiments, the subjects made the decision to perform a movement under their own free will. However, at the start of the experiment the experimenter and subject exist in a multiverse where the subject - or a very near duplicate! - will go on to perform the movement at all possible times, and it is only when the experimenter finds the subject is moving, or has moved, at some particular time, that the superposition is broken for the experimenter. Meanwhile, if a subject makes the decision to move at time t, then they will carry on as that continuer of their identity in a subset of their original multiverse, in which the readiness potential preceded the voluntary action by hundreds of milliseconds as required.

Consciousness always takes such a path that personal identity is maintained as closely as possible, from one instant to the next. We never find that we have suddenly become another individual. Personal identity is based on beliefs, memories, values, intentions, idiosyncrasies, etc., which includes a conscious decision to move an elbow or press a button at some time. If we are running an experiment where we plan to push a button at some time t between 0 and 30 seconds, and we decide at the moment to push the button at 12 seconds, then it always works every single time. We never see our finger move at 6 seconds, before we intended; nor do we ever find that we are paralyzed at 12 seconds, only to watch our finger hit the button unexpectedly at 23 seconds, for example.

In the case of the HSE experiments, the subjects made their individual decisions to move at various random times, but the experimenters came to expect to see the changes in RP at a particular time. The experimenters ended up in a part of their multiverse consistent with their own expectations, but most of the time, they were not seeing the true "continuer" of a subject, only the near-duplicate whose only difference was that the RPs changed at the 'wrong' time.

The roles of other dimensions of arcuum space

Much of the action in arcuum space takes place in the two-dimensional plane a, b. The "spacing", the motion of the subject observer particle-string, and the propagation of the matter waves. The four arcuum dimensions bring about an inverse sixth law force attenuation at short range that can account for the vast difference in the strength of the nuclear and gravitational forces. And they offer the prospect of cheap decentralised energy sources such as cold fusion - which is anathema to those who want to monopolise energy sources.

The nanometre spacing in two arcuum dimensions a, b, confines gravity from leaking at greater range along those dimensions, and the other two c, d, are compacted. The c, d could allow a framework for particles of different mass to reside at different levels, but their full function is unknown. Given that it is in the a, b, plane where the subject observer moves in a series of arcs, then the c and d axes might be better classed as mass space, or spin space, or momentum space.

Appendix

Qbasic, to demonstrate double-slit experiment

pi# = 3.141592653589793#
L# = 2#: lambda# = 6.328D-7
k# = 2# * pi# / lambda#
d# = 6.328D-6 ' Distance between slits
a# = 2.531D-6 ' Slit width
N = 1000 ' points per slit
xa# = 0.5# - d# / 2# ' Slit A centre
xb# = 0.5# + d# / 2# ' Slit B centre
NF# = 550293.032813455 ' Normalisation factor for integral (psi^2) - 1 over [-50, 50]
W# = 0.01# 'Power output from slits
E# = 3.139D-19 'Energy per photon

10 Input "Enter x (m): "; x#
da# = a# / N ' Step per point

' Initialise real/imag parts
a_real_tot# = 0#
a_imag_tot# = 0#
b_real_tot# = 0#
b_imag_tot# = 0#
real_tot# = 0#
imag_total = 0#

' Slit A integration
For j = 1 To N
y# = xa# - a# / 2# + (j - 0.5#) * da# ' Point in slit
r# = Sqr(L# ^ 2 + (x# - y#) ^ 2)
amp# = NF# / Sqr(r#)
phase# = k# * r#
a_real_tot# = a_real_tot# + amp# * Cos(phase#)
a_imag_tot# = a_imag_tot# + amp# * Sin(phase#)
Next j

' Multiply by da# (integration weight)
a_real_adj# = a_real_tot# * da#
a_imag_adj# = a_imag_tot# * da#
a_modulus# = Sqr(a_real_adj# ^ 2# + a_imag_adj# ^ 2)
real# = a_real_adj#: imag# = a_imag_adj#
GoSub 500
a_theta_deg# = 180# * theta# / pi#

' Slit B integration
For j = 1 To N
y# = xb# - a# / 2# + (j - 0.5#) * da# ' Point in slit
r# = Sqr(L# ^ 2 + (x# - y#) ^ 2)
amp# = NF# / Sqr(r#)
phase# = k# * r#
b_real_tot# = b_real_tot# + amp# * Cos(phase#)
b_imag_tot# = b_imag_tot# + amp# * Sin(phase#)
Next j

' Multiply by da# (integration weight)
b_real_adj# = b_real_tot# * da#
b_imag_adj# = b_imag_tot# * da#
b_modulus# = Sqr(b_real_adj# ^ 2# + b_imag_adj# ^ 2)
real# = b_real_adj#: imag# = b_imag_adj#
GoSub 500
b_theta_deg# = 180# * theta# / pi#
phase_diff# = Abs(b_theta_deg# - a_theta_deg#)

real_tot# = a_real_tot# + b_real_tot#
imag_tot# = a_imag_tot# + b_imag_tot#

' Multiply by da# (integration weight)
real_tot# = real_tot# * da#
imag_tot# = imag_tot# * da#

' Probability density
psi_sq# = real_tot# ^ 2 + imag_tot# ^ 2
photon_rate# = (W# / E#) * 9.163024974D-19 * psi_sq# ' Photons/second in electron-diameter bin

Print "Photons/bin/s = "; photon_rate#
Print "|A| = "; a_modulus#; "phase (deg) ="; a_theta_deg#
Print "|B| = "; b_modulus#; "phase (deg) ="; b_theta_deg#
Print "Phase diff. (deg) ="; phase_diff#
res_modulus# = Sqr(a_modulus# ^ 2# + b_modulus# ^ 2# + 2# * a_modulus# * b_modulus# * Cos(pi# * phase_diff# / 180#))
Print "|A + B| ="; res_modulus#
Print "|A + B| ^ 2 ="; res_modulus# ^ 2#
Print "Psi squared ="; psi_sq#
Print "|A + B| ^ 2 / Psi ^ 2 ="; res_modulus# ^ 2# / psi_sq#
Print "Psi squared / (|A| + |B|) squared = phase factor thi"; psi_sq# / (a_modulus# + b_modulus#) ^ 2#

GoTo 10
500 If real# = 0 And imag# > 0 Then theta# = 0
If real# > 0 And imag# > 0 Then theta# = Atn(Abs(real#) / Abs(imag#))
If real# > 0 And imag# = 0 Then theta# = pi# / 2
If real# > 0 And imag# < 0 Then theta# = pi# / 2# + Atn(Abs(imag#) / Abs(real#))
If real# = 0 And imag# < 0 Then theta# = pi#
If real# < 0 And imag# < 0 Then theta# = pi# + Atn(Abs(real#) / Abs(imag#))
If real# < 0 And imag# = 0 Then theta# = pi# * 1.5
If real# < 0 And imag# > 0 Then theta# = pi# * 1.5# + Atn(Abs(imag#) / Abs(real#))
Return
 

QBasic, calculates arcuum spacing, mean free path, acceleration, velocity, rate of interactions, etc..

Print: Print
g# = .000000000066743#: c# = 299792458#: pi# = 3.141592653589793#
hbar# = 1.0545718176D-34: mp# = 1.67262192595D-27: me# = 9.1093837139D-31
mn# = 1.67492750056D-27: h# = 6.62607015D-34: epzero# = 8.8541878188D-12
alpha# = .0072973525643#: e# = 1.602176634D-19: mph# = 1D-55

protonrad# = 4# * hbar# / (c# * mp#)
protonspacing# = protonrad# * (2# * hbar# * c# / (g# * mp# ^ 2)) ^ .25#
electronrad# = 4# * hbar# * me# / (c# * mp# ^ 2#)
electronspacing# = electronrad# * (2# * hbar# * c# / (g# * me# ^ 2)) ^ .25#
photonrad# = 4# * hbar# * mph# / (c# * mp# ^ 2#)
photonspacing# = photonrad# * (2# * hbar# * c# / (g# * mph# ^ 2)) ^ .25#

'  Find mean free path
'  Electron subject, electron object
lambda1# = electronspacing# ^ 2# / (4# * electronrad#)
'  Electron subject, proton object
lambda2# = protonspacing# ^ 2# / (2# * electronrad# + 2# * protonrad#)
'  Proton subject, electron object
lambda3# = electronspacing# ^ 2# / (2# * protonrad# + 2 * electronrad#)
'  Proton subject, proton object
lambda4# = protonspacing# ^ 2# / (4# * protonrad#)
'  Photon subject, electron object
lambda5# = electronspacing# ^ 2# / (2# * photonrad# + 2# * electronrad#)
'  Photon subject, proton object
lambda6# = protonspacing# ^ 2# / (2# * photonrad# + 2# * protonrad#)
'  Electron subject, photon object
lambda7# = photonspacing# ^ 2# / (2# * electronrad# + 2# * photonrad#)
'  Proton subject, photon object
lambda8# = photonspacing# ^ 2# / (2# * protonrad# + 2# * photonrad#)
'  Photon subject, photon object
lambda9# = photonspacing# ^ 2# / (4# * photonrad#)

50 Print "Enter 1 for electron subj + electron obj, 2 for electron subj + proton obj,"
Print " 3 for proton subj + electron obj, 4 for proton subj + proton obj,"
Print "5 for photon subj + electron obj, 6 for photon subj + proton obj,"
Print "7 for electron subj + photon obj, 8 for proton subj + photon obj,"
Input "9 for photon subj + photon obj, or 10 to see the menu again"; in
If in = 1 Then msubj# = me#: mobj# = me#: srs# = electronrad#: sro# = electronrad#: spacing# = electronspacing#: lambda# = lambda1#
If in = 2 Then msubj# = me#: mobj# = mp#: srs# = electronrad#: sro# = protonrad#: spacing# = protonspacing#: lambda# = lambda2#
If in = 3 Then msubj# = mp#: mobj# = me#: srs# = protonrad#: sro# = electronrad#: spacing# = electronspacing#: lambda# = lambda3#
If in = 4 Then msubj# = mp#: mobj# = mp#: srs# = protonrad#: sro# = protonrad#: spacing# = protonspacing#: lambda# = lambda4#
If in = 5 Then msubj# = mph#: mobj# = me#: srs# = photonrad#: sro# = electronrad#: spacing# = electronspacing#: lambda# = lambda5#
If in = 6 Then msubj# = mph#: mobj# = mp#: srs# = photonrad#: sro# = protonrad#: spacing# = protonspacing#: lambda# = lambda6#
If in = 7 Then msubj# = me#: mobj# = mph#: srs# = electronrad#: sro# = photonrad#: spacing# = photonspacing#: lambda# = lambda7#
If in = 8 Then msubj# = mp#: mobj# = mph#: srs# = protonrad#: sro# = photonrad#: spacing# = photonspacing#: lambda# = lambda8#
If in = 9 Then msubj# = mph#: mobj# = mph#: srs# = photonrad#: sro# = photonrad#: spacing# = photonspacing#: lambda# = lambda9#
If in = 10 Then GoTo 50
If in < 1 Or in > 10 Then Print "Try again": GoTo 50

Input "Enter object particle energy (J) in grav. space"; eobj#
Input "Enter object particle wattage (W) in grav. space"; wobj#
R# = wobj# / eobj#
' Input "Enter delta x for subject observer (m)"; delta_x#
delta_x# = 2 * srs#
Input "Enter moduli |A|, |B|, theta (deg)"; psia#, psib#, theta#

Print "Object particle arcuum spacing (m) ="; spacing#
Print "Mean free path (m) ="; lambda#
period# = h# / eobj#
Print "Period (s) ="; period#
Print "Object particle radius (m) ="; sro#

psi# = psia# + psib#
phinum# = psia# ^ 2# + psib# ^ 2# + 2# * psia# * psib# * Cos(pi# * theta# / 180#)
phidenom# = psia# ^ 2# + psib# ^ 2# + 2# * psia# * psib#
phi# = phinum# / phidenom#
anet# = eobj# * lambda# * R# * psi# ^ 2# * phi# * 2# * srs# / hbar#
agross# = eobj# * lambda# ^ 2# * R# * psi# ^ 2# * phi# * msubj# / (hbar# * mobj#)
aforce# = msubj# * anet#
Print "Phi ="; phi#
Print "Arcumm force (N) ="; aforce#

'  Find effective average arcuum velocity of subject observer
va# = anet# * period# / (2# * pi#)
Print "Effective mean arcuum velocity (m/s) of subject ="; va#
da# = va#
N# = g# ^ .5# * c# ^ 1.5# * mp# ^ 4# / (2# ^ 4.5# * hbar# ^ 2.5# * mobj#)
dp# = period# * va#

Print "Distance travelled (m) in arcuum space over 1 second ="; da#
Print "Distance travelled / mean free path lambda ="; da# / lambda#
Print "Cf. R * phi x psi squared * delta_x = rate of interaction/sec"; R# * psi# ^ 2 * phi# * delta_x#
Print "Distance travelled (m) in arcuum space in one period ="; dp#
Print "Net acceleration (m/s^2) ="; anet#
Print "Gross acceleration (m/s^2) ="; agross#
Print "No. of object particles per m^2 of arcuum space ="; N#
Print: GoTo 50
 

Revised August 18, 2025