Registered: May 2005
Sorry for the pause. I had to put together required links and explanations.
(C) 2005 Ivan V. Krasnyj (draft)
I call the concept "Simulational Metaphysics" because it deals with incognizable fundamental structure of matter and would provide means for carrying out virtual computational experiments, replacing real physical experiments, thus, eliminating the observer’s intervention effects. We shall not use conventional forces and fields’ notions here. They looks to be not appropriate for the Plank’ scale microcosm, though being useful in macrocosm. Instead, the holistic approach is suggested. I expect that the model objects, represented by ensembles of elements would show emergent behavior, peculiar to all real world phenomena. It seems, that a few basic principles put to the concept, bring our logical reasoning to single possible solution at each stage of the model development. I’ll try to explain this point of view below.
THE F.C.C. LATTICE
I start with the only postulate of Euclidean quantum discrete space-time existence. Albeit, this may be considered as direct conclusion of the quantum theory. If the space is stated being discrete, the next conclusion would assume existing of a space-filling polyhedron for the volume quantum. http://mathworld.wolfram.com/Space-...Polyhedron.html
There are few space-filling polyhedrons. We’ll choose the rhombic dodecahedron. http://mathworld.wolfram.com/RhombicDodecahedron.html
Rhombic dodecahedra form Voronoy-Delaunay (Vigner-Zeits) cells for the f.c.c. lattice. In 1611 the Johannes Kepler stated that no packing could be denser than that of the face-centered cubic (f.c.c.) lattice arrangement. It took mathematicians some 400 years to prove him right. Thomas Hales announced successful proof, in 1998.
The densest f.c.c. lattice would provide the “least action” principle maintained in physics. Besides, the rhombic dodecahedron has the largest number of symmetries among space-filling polyhedra.
LORENTS-INVARIANT STATIONARY ETHER
To avoid giving effect to mystical long-range action in the model, next step would be the luminiferous ether concept revival. Some people prefer to call it "physical vacuum", but the old-fashioned term suits better, because it naturally explains the model elements behavior. The model will utilize undeservedly missed by theorists Lorents-invariant stationary ether concept. For the case studies on the issue see: “On the possibility of invariant rest and relative motion properties combination, based on the new model of space with minimal length.” V.V.Korukhov, O.V.Sharypov, (Novosibirsk, 1995, in Russian)
Irrelative of some moot points, like planckeons properties and their oscillatory motion as well as mixed discrete-continuous model of space, the article thoroughly examines the stationary ether concept (which is the only point of my interest here). Non-archimedian arithmetic and space geometry problems bound to the discrete space-time model are also being focused. Authors state, that “It would be methodologically correct to treat light speed invariance phenomenon as the corollary of invariantly resting ether existence. At the same time the model should permit relative motion of substantial inertial observers.”
If the invariant minimal length existence condition will be introduced to the Special Relativity, that would mean an introduction of the equivalent for the upper speed limit of the object. According to the SR, the length of the object alongside its velocity vector would tend to the invariant minimal length magnitude. [See formulae (1) in the article] There would be two peculiar strictly Lorents-invariant values Vmax=0 and Vmax=C. The Vmax=0 condition concerns Lorents-invariantly resting objects. This means, that no any inertial frame exists, where an object of fundamental length would be observed in motion. Hence, the hypothetic media, consisting of elements with basic length, would cinematically stay in rest. Perturbations propagation velocity for this kind of media also should conform to Lorents-invariance. The speed of light, according to the SR postulates, exactly meets the requirements.
Another point concerns absolute reference frame existence, which one could hardly elude when dealing with lattice models. Physical aspects of the absolute frame existence we’ll discuss later.
ISOTACHY, KEKINEMA AND RENOVATION PROPERTIES
The investigation of discrete space-time concept has been initiated by the ancient philosophers. Aristotle in his Physics 6.2 http://classics.mit.edu/Aristotle/physics.6.vi.html examines the discrete motion mechanics and discusses famous Zeno paradoxes. He states, that there’s no way to accept different or mixed nature of space and time. Both should be postulated discrete or both continuous. Sextus Empiricus (in Adversus Mathematicos) first introduces equal velocities statement, - isotachy for discrete space-time motion. Ancient atomists Lukreci and Epikuri also stood for this statement. To render in modern way, this means that in discrete space-time concept the only possible motion velocity is r/t = const, where r and t are indivisible length and time magnitudes.
A.N.Vyaltsev in his basic work “Discrete Space-Time” (Moscow , “Nauka” publishers, 1965, in Russian) states that any theory, basing on discrete space-time concept should necessarily include properties of isotachy, kekinema (accomplished motion, where it’s phases are nonobservable in principle) and renovation (successive disappearance and rebirth of a particle).
V.V. Korukhov in “Fundamental constants and space-time structure”
(Novosibirsk, 2002, in Russian) in Ch. 3.2 states, that no any theoretical models of discrete space, implementing at the same time isotachy, kekinema and renovation properties are known so far.
DISCRETE AND CONTINUOUS NOTIONS (remark)
One should understand that as applied to discrete space-time model, we sometimes still need to use continuous space notions. We can not use linear and plane continuous geometry elements, like polyhedron’s edges and facets together with volume quanta directly in discrete space. The discrete space contains only a set of voxels and nothing more. In case we need to examine spatial and plane objects at once, one should assume a projection of these objects as well as objects of other dimensions to continuous space model.
The fifth postulate of Euclid has no avail in discrete space. It’s possible to drop more than one perpendicular to discrete line from a point outside. (Zoubov, V., "Walter Catton, Gerard d¼don et Nicolas Bonet," Physics, vol. 1 (1959), pp. 261-278). Discrete space requires special means of the discrete geometry to describe its objects relations.
Let’s have a look to how do we treat time in the model. Discrete time goes by strokes, corresponding to indivisible intervals. Each stroke of time includes a set of simple events in the whole model space. Any simple event constitutes a shift of mobile ether portion to one of the adjacent vacant cells. All simple events in one stroke of time occur synchronous. Synchronism in the model is caused by the postulate of quantum space and time. The space and time quanta presumably have Planck units’ size. The only speed possible for the shifts is r/t = const = C. I do not leave out possibility, that to keep the observed speed of light magnitude, we’ll have to increase the speed of ether shifts in the model, and consequently, r/t ratio. This may require because of the polylinear routes of perturbations propagation, as well as their group nature, discussed below. The final solution may be found in computational modeling results.
THE SLIDER GAME TYPE MOTION
I consider "empty" space voxels everywhere are being filled with the ether contact interaction media. Ether here is not an object of matter, but just an entity. I mean, if ether already occupies a voxel, it couldn't disappear to nowhere. To implement motion phenomenon in quantum discrete space, we need a mechanism, providing conservation of the ether portion, participating in elementary motion. The discrete space does not permit ether portions to “move apart” to let other portions to pass through. I could imagine the only one way appropriate for the task; - voxel contents interchange between the ether and neighboring vacant voxels. This is a way we play slider game (or "15"-game). So, if the ether is a medium, normally filling voxels, corresponding to empty space, what does the vacant voxel represent in this model? - Yes, indeed, the vacant voxels are basic elements of matter! As we’ll discuss later, elementary particles, and other real world phenomena, are expected to be represented by ensembles of basic elements.
Evolving the model, I try to hold to equal possibility principle. This means, that any model elements inequality needs to have a reason. Particularly, if there’s no specific reason for a given cell either to contain ether, or to be vacant, the model should permit element to switch between both states. Currently we have two possible properties for voxel state, - “ether filled” and “vacant”. To provide global equal possibility of the cell contents, let's assign ether portion a natural property to aspire for shifting to neighboring vacant voxels. To perform shift, ether portion should gain mobility, provided by a set of neighboring vacant voxels.
It would be useful to note here, that in context of the kekinema and renovation properties, the ether portion shifts in the model should be perceived in discrete space as their disappearance at the beginning of time stroke and subsequent rebirth in adjacent voxel at the end of time stroke.
HOW CAN WE PLAY A SLIDER GAME, -
THE 3D-SPACE IS NOT A PLANE?
One should notice that trivial plane slider game differs from the 3D version on the f.c.c lattice. Square shaped dibs in plane let one of four neighbors to shift to the vacant cell. For example, if we'll look at the slider game with hexagonal dibs in plane, we'll see two dibs, able to shift to two vacant cells. (We need at least two neighboring adjacent vacant cells to provide mobility for any hexagonal dib.) In the 3D slider game there would be two basic cases, where the rhombic dodecahedron gains mobility. First, when it borders three vacant voxels, adjacent to its three-facet vertex. And second, when it borders five vacant voxels, adjacent to its four-facet vertex. The other voxel configurations should be considered as mixed basic cases.
In the first case we’ll have only one mobile ether portion, able to shift to one of the three vacancies (due to the f.c.c. lattice constraint). Which direction would it choose? There should be an algorithm, responsible for the shift direction choice in this case. Let’s call it “Sensorium Dei” (SD) algorithm and get back to the question later.
In the second case the empty voxels configuration will provide five mobile ether portions at once, able to shift to one of the five vacancies. The ether portions couldn’t contend for occupying the vacant cells because they are separated by empty voxels, thus wouldn’t interact in previous time stroke. It would be reasonable to accept another property for the model, - to permit accumulation of several ether portions in one voxel at the end of time stroke. It doesn’t matter how can we keep them inside one voxel, - by 4D-space stacking, jamming, direction specific volume reservation, or else. The macrocosm notions are not appropriate for the case. We should just consider that there may be up to six levels of the excess states possible in the model. Though each rhombic dodecahedron has twelve neighbors, the polyhedron shape and the f.c.c. lattice constraint wouldn’t let more than six ether portions at once (in one time stroke) to accumulate in one voxel. To be specific, let’s consider that excesses accumulate in one voxel by means of the 4D-space stacking. Only one excess ether portion of the upper level at once could gain mobility in a single time stroke.
In reality the number of excess levels may decrease substantially due to availability of the GOE (Garden Of Eden) combinations. Hence, besides vacancies we’ve got excesses (up to six levels). Let’s call vacancies and excesses in the model by term “dislocations”. The dislocations notion would be useful for initial combinations set up in order to keep equal number of vacancies and excesses and follow up equal possibilities principle. It would be reasonable to believe of the excesses behavior should be symmetrical to that of the vacancies. The difference regards the SD-algorithm application discussed below.
THE “SENSORIUM DEI” ALGORITHM
In real world any specific particle motion is defined by spatial disposition of surrounding particles. This concerns any fields and forces in physics. The rule has been taken for our model too. Continuous approach gives no any limitations for the motion direction choice. In our case a wonderful confinement feature of the f.c.c. lattice, allows ether portion in each simple event to choose exactly one of the three, or five possible shift directions for the mobile ether portion in basic cases. We need to define rules for the direction choice.
Let’s have a look at the particular mobile ether portion, adjacent to three vacancies. The lattice constraint will permit it to slide to one of the vacant voxels. In other words, just imagine that the mobile ether portion “falls in” one of the vacancies. The choice between directions would depend upon the infinitesimal advantage of one of the three directions, comparing to others. The advantage should be estimated, basing on equal possibilities principle (equal possibility of any voxel to change its contents). To analyze possible shift directions, we’ll take in account only neighboring voxels, constituting adjacent ether filled layers, which form directed multilayer tetrahedron (composed of rhombic dodecahedra cells) with the mobile ether portion in its vertex and the nearest vacancy (or vacancies) in its foot.
It’s not appropriate to speak of the voxcels “pressure” in Planck’s microcosm to make the direction choice, but we need to estimate a formal criterion for the task. The position of nearest vacancies would define layer thickness for the continuously infilled neighboring voxels, bordering each of the three facets of the rhombic dodecahedron, opposite to the adjacent vacancies. We need not calculate the layers thickness all over, as we are estimating only the shift direction advantage. That should be just a comparative choice, triggered by the nearest vacancy, or vacancies, no matter of how far is the triggering vacancy from the mobile ether portion. “Size doesn’t matter”… :) We just need to choose at the nearest vacancy around, which side of the tetrahedron leaning against the three facets of mobile ether portion “weights more”. In case the first nearest vacancy lies strictly between the two residual sides of the tetrahedron, and we need to choose between them, we’ll look for the next vacancy further on until we’ll find an advantage.
Vacancies are shielding any interaction. This is a major principle for the model. In some extreme cases it may happen that the SD-algorithm wouldn’t find any direction advantages due to shielded layers equality, like Buridan’s donkey. Well, let it “miss the move”. Most likely these situations belong to GOE combinations. Anyway, in the next time stroke the shield will be destroyed.
In case of five neighboring vacancies, adjacent to four-facet vertex, the difference is that we’ll have a square pyramid shaped set of voxels to choose one of five shift directions for the mobile ether portion in the center. The other four mobile ether portions shifts will conform to the three vacancies cases.
The model would necessarily provide composite configurations of basic cases with multiple shift directions choice. The SD-algorithm task is to compare all possible shift directions in this case.
As regards excesses behavior, to gain mobility and provide shifting, they would also require to group in a three- or five-voxcel basic sets, adjacent to mobile ether portion. In this case it would be suitable not to consider that ether portion “falls in” one of the excess voxels, but conversely, the strongest (defined by the SD-algorithm) excess is being “pushed out” to mobile ether portion cell. Besides, for multilevel excesses we’ll have no “contents interchange” between voxels. The upper level ether portion shift should be considered just as excess level decrease for the strongest excess in the set.
THE SYNERGETIC COORDINATS AND WRAPAROUND UNIVERSE
To implement the proposed f.c.c. lattice motion algorithm one needs a suitable indexing system. The Synergetics Coordinates, invented by R. Buckminster Fuller would suit the task.
The model space could be divided to four “tetrants”(space segments adjoining to tetrahedron’s facets), defining positive index values range for each coordinate axle. Each voxel position will be defined by a four signed integers, providing control summing.
The proposed SD-algorithm would reach model space borders. In order to bypass this obstacle and maybe to guess the Universe topology, we’ll accept that it really has the 3d-torus topology. In fact, if we’ll pack voxels around the central rhombic dodecahedron, the multilayer set would constitute cuboctahedron (a cube with cut-out vertices).
This polyhedron does not belong to space-filling polyhedra. To let it tile space, we need to complete it with missing vertices in order to get cube. To wrap around our universe we’ll paste three pairs of opposite cube facets to each other. It is clear concerns indexation looping in software.
The real size of the model would depend upon computational facilities availability.
Some possible candidates are here:
The Blue Gene/L supercomputer:
The QCDSP and QCDOC computers:
ENSEMBLES OF DISLOCATIONS
Now let’s look around the whole picture. The mobile vacant voxels would tend to scatter from each other to the side of ether filled “empty” space. The mobile excesses will rush after them.
To gain mobility ether portion needs at least three neighboring adjacent dislocations (vacancies or excesses). That wouldn’t be enough to move out from the initial place. The ether portion would cycle between four voxels. This doesn’t mean that the ensemble motion is impossible. We just need more dislocations for the task. Complex ensembles of dislocations would reveal mobility of the set. They would show specific grouping and emergent properties.
MICROCOSM OBJECTS CORRESPONDENCE
We can presume that the ensembles, showing cyclic motion without advancement on the lattice, would correspond to fermions. The number of dislocations in the ensemble seems to present equivalent of mass. Vacancies and excesses would correspond to positive and negative charges (or vice versa). The bosons ensembles would naturally perform advancement on the lattice.
Another kind of ensembles will not gain independent existence and would reveal its properties, being attached to other particle ensembles. This kind of ensembles presumably constitutes portions of energy. The ensemble of energy could be repartitioned between particles in elastic scattering, or used as construction material for other particles creation in non-elastic scattering and weak interactions.
The proposed concept leaves no chance for direct experimental ether existence discovery. Instead, the absolute space existence could be estimated in experiments (discussed below).
Energy as well as objects of matter would occupy volume in space. This should result in additional particles interaction cross-sections increasing. The phenomenon of cross-sections increase together with particles energy rise, really exists, but there may present data scattering due to absolute particle impulse magnitude neglect. One should consider the observer’s reference frame absolute speed and corrections for the additional kinetic energy of each particle, referenced to absolute space lattice.
Earth based observers should take in account continuous change of the absolute speed of their reference frame due to Earth axle rotation, Earth-Moon barycenter orbiting, Earth around Sun orbiting and the Sun system barycenter motion in absolute space. The Earth based observer absolute speed corrections can be easily calculated basing on the observer’s coordinates and Earth ephemeris as well as Sun system barycenter speed estimations relative to cosmic microwave background radiation or from other sources for ex.: http://redshift.vif.com/JournalFile...DF/V03N2MON.PDF
It would be useful to take in account current absolute speed of the observer’s reference frame to introduce corrections for the particles interaction cross-sections in nuclear physics experiments.
The proposed model conforms to deterministic principles. But what regarding fortuity? Our planet rushes through space, covering some 400 kilometers per second. According to the concept, the empty space is being ether filled. The equal possibility principle assumes that there’s no reason to consider voxels of space being in the same state. Thus, we are justified to consider equally possible existence of single stationary dislocations (vacancies and excesses) anywhere in space. This kind of objects exists outside of time, as they do not perform simple events (shifts). The mobile dislocations would participate in particles and energy ensembles, but stationary would not. They will happen upon moving particles, and trigger such events as radioactive decay radiation. The Universe in whole is being determinate, but in particular case we don’t know what we’ll meet on the road… I guess, we can even govern radioactive decay activity. We need just slow down, or stop in absolute space to see the effect… It may not be as evident as complete decay stop. The spectrum lines activity may shift, or new lines would appear.
The conjecture of stationary dislocations availability in space may provide another explanation for the red shift and cosmic microwave background radiation phenomena. Photons and other particles would interact with the dislocations on their way in Universe and undergo a special kind of scattering. In case of successful computational testing of the assumptions, these kinds of objects may help for substantial revision of the available cosmological models.
Different nature of the ether dislocations may help to explain matter to antimatter asymmetry. Vacancies though being dual to excesses, do not provide interaction and shield SD-algorithm long-range action, because contain empty space. The same property, providing a kind of inequality between positive and negative charges, may cause gravity effects in the model.
Another explanation may be suggested for the two-slit experiment results. How the electron (photon) does know if the slot is closed? – Easy. It uses the SD-algorithm for its motion direction choice. That would provide an alternative explanation for the particle-wave duality notion.
Basing on the model mechanics, we could suggest the EPR-paradox and Bell’s inequality explanation. Let’s shed some light to non-locality mechanics in the model. First, we’ll emphasize that there would be two types of the model objects mutual influence, - “contact interaction” and “bounded behavior”. The first one happens when the particle’s ensembles exchange their basic elements in direct contact, no matter of the element’s membership in energy or mass ensemble. This kind of mutual influence is limited to light speed propagation (or rather to the assigned simple events speed). The second is caused by the SD-algorithm implementation and provides momentary action just in the next time stroke. Any particular mobile ether portion shift to neighboring voxel momentarily (in the next time stroke) affects other mobile ether portions direction choice if it is being located in their active region. In addition, it would be useful to note, that the SD-algorithm implementation complies with Mach principle.
How do we deal with Heisenberg uncertainty principle? In our model, it concerns ensembles of basic elements (dislocations), but not basic elements itself. Uncertainty of the ensemble position/speed is being substituted by uncertainty of the element’s membership in ensemble. This means that in some cases for the discrete space-time model we’ll be unable to distinguish between membership of the element in ensemble of particle, or its attached energy ensemble. This does not prohibit us to know exact element’s position and speed (shift direction). Besides, according to Heisenberg, observer’s intervention is required to get information. The examined SD-algorithm mechanism shows, that any observer’s intervention would break the process under review, but the proposed approach, suggesting virtual model wouldn’t.
- Shnoll effect tests for correlation with calculated observer’s speed in absolute space.
(Collimated 241-Am sources and detectors in vacuum at guided platform.)
- Particles interaction cross-sections results enhancement by corrections for the reference frame absolute speed (based on already observed data). Additional testing time, direction and observatory location information required.
- Space tests for alpha-decay spectra dependency on the observatory absolute speed.
Ivan V. Krasnyj
P.S. To train space imagination, I've compiled some compositions of rhombic dodecahedra in 3d Studio Max 7.0. I could post them here if required.
Nature plays a slider game with rhombic dodecahedra.
Last edited by IvanKrasnyj on 05-29-2005 at 11:08 PM
Report this post to a moderator | IP: Logged