First update: november 2002
Last update: oktober 2004

Form Interpretation Theory

(in search of the perfect FIT)

This project is a search for a theory that for the time being is called FIT. Most of what you can read here is NOT considered belonging to the common body of knowledge of physics. In a way much of it is how I think it should be.

FIT seeks to describe nature and why we see it the way we do. It does so by means of a two level model.

On the first level (Space Structure and Space Form) FIT describes what nature consists of and how it works. Summarising there is only space. It has a form and this form can change.

On the second level (Space Form Interpretation) FIT describes how nature can be interpreted. The second level relates the first level to the different perspectives that can be chosen to describe and measure the phenomena we experience.

The first layer establishes unity and coherence. The second layer establishes reduction, distinction and the particle view.

FIT wants to be a foundation in the search for the inner form of the structures we perceive in our experiments. The theory will hopefully give us (among other things) new understanding of the possibilities and limitations of the perspectives we choose.

Space Structure
Space Form
Space Form Interpretation
More Speculations
Some More Philosophy
The Project
Some Definitions
Some More Pictures
Some Literature

FIT, level 1:

Space Structure

From the philosophy that the understanding of the physics of nature should be based on a minimal set of simple and beautiful laws from which all can be deduced, five laws are proposed, one law for the main object and four others to establish its attributes.

On the object

On its attributes

Explanatory notes:

Illustration 1: From a three dimensional cubic grid the 3D form of one sheet (a deformed Euclidic plane) is projected on screen. Here is a film (rotating GIF 1.4Mb) that shows how a pseudo particle can be interpreted to come into existence and disappear again. (See also illustration 2 for the 3D picture and film).

Space Form

The form of space and its deformations can in principle be described with mathematics through bijective maps that abide by the laws. In simple words: every point in space gets assigned a new position and keeps the same neighbours. This new position is expressed in three real numbers. Space can be twisted and turned into any form within the rules. To describe the twists and turns of the form of space with numbers we can use a 3 x 3 matrix. Each of the nine positions in the matrix is a real valued function of the three euclidic coordinates and of global time which is ticking with a constant rate (one can speculate on possible fluctuations in the global time rate but personally I find this premature). So in a sense one could say that 9 space dimensions and one time dimension are necessary to describe the behaviour of the form of space.

Obviously this deformation matrix is incredibly complex as it describes the changes of the form of the whole universe over time. No use trying to find it. We can however try to describe local pieces of space and their behaviour over time. We can even try to give names to special kinds of deformations (on different space scales) that seem to be localised and start classifying them. As part of the connection between the first level of FIT and the second level (space form interpretation) hopefully we can find isomorphisms between the classification of these local deformations of space and our standard model of particle physics and models of other unifying mechanisms such as string theory. That is my personal hope and belief of course.

Illustration 2: A three dimensional deformed cubic grid is projected on screen. Here is a film (rotating GIF 2Mb) that shows how a pseudo particle can be interpreted to come to existence and disappear again.

To facilitate the mathematical interfacing from level one to level two, we can also describe deformed space and its behaviour in time with a vectorfield and a (standard) wave equation. The vectorfield describes the displacements from the original places of the points in Euclidean space and the wave equation describes the behaviour of the vectorfield in time. It is very tempting to call this vectorfield the universal vectorfield. From it other field descriptions may be deduced through maps that will have to be developed. The local properties of space are hidden in the wave equation. So you cannot ask the wave equation WHY space behaves the way it does but it can answer you HOW it will behave.

In the language of mathematics the electromagnetic interpretation of deformed space would (an intuitive direction of investigation) sound something like:

Describe deformed space with the notion of a 4-dimensional Riemannian manifold M. One dimension to represent time and three for space. The time dimension is not deformable, just a straight line. (at least as a first order approximation).

The form of M is described with the use of a section of the tangent vectorbundle (TM) on M in the usual differential geometrical sense. This vectorbundle describes all of the possible deformations of space. The particular form M can be described by a (tangent) vectorfield that is deduced with the use of the concept of derivation in the usual sense. The behavior of this vectorfield can be interpreted in different ways, according to the specific content.

For an electromagnetic interpretation we use the exterior differential d and the cotangent vectorbundle T*M. This will bring us to a 4x4 skew-symmetric tensor. Compare this to the well known field strength tensor and dual field strength tensor from relativistic electrodynamics. One could imagine this to be a fruitfull link and possibility for (computer)experiment to make visible the behavior of electromagnetism as derived from the change of form of the three space dimensions.

FIT, level 2:

Space Form Interpretation

To be able to understand what kind of universe we live in we use our senses, our measuring instruments and brains, producing mathematics and words to relate to reality through theories. Commonly acknowledged theories today (ways of looking at nature) are quantum mechanics, relativity theory and statistical physics. On the edge of physics we have theories like string theory and loop-quantum-gravity that are very promising. In this section an intuitive effort is made to relate these theories to FIT.

  1. From form to quantum mechanics

    To come from a global picture of one form representing the universe to a quantum mechanical interpretation the following is suggested.

    A local form (a simplified universe with for instance only one particle in it) is to be given a name, for instance electron. In FIT an electron is a deformed (infinite) volume of space, deformed with a special kind of symmetry. Each point in space is represented by 6 numbers. 3 for its place in Euclidic space and 3 for its new place at a particular moment. We now make a projection of these 6 real coordinates onto a space with 5 real coordinates. Each point in 3D space gets assigned a number-pair (representing a complex number). This collection of numbers gets a system name (i.e. electron) and it represents the (probabilistic) behaviour of the system in its environment over time. In more regular words: the particle is represented as a point-particle with a wave function, or if you will: the subsystem is now a wave function with a name. The projection is the process of distinguishing a system and assigning it a wave function in space. (see for instance {Tribble} on the physicist’s use of QM). By making the projection (seeing particles) and as such losing information exact predictability of the behaviour of space turns into probability of behaviour of particles.

    Some comments on the measuring process:

    Objects are:

    • the measuring system (M.S.)

    • the primary system (P.S.)

    • the measurement (M.S.- P.S. interaction)

    • the measuring system projection (M.S. wave function)

    • the primary system projection (P.S. wave function)

    The global form is considered to be a superposition of two forms, the forms of the measurement system and of the primary system. This virtual separation between forms is done by just building the measurement apparatus (and its ability to distinguish between certain states by operating the apparatus). The description of the apparatus in QM consists of a state vector and is calculated from the global form of M.S. by a projection operator. Obviously this operator is very complex and for the time being beyond our grasp.

    At the same time the primary system is found from another projection. This projection operator reduces the global form of P.S. to the primary state vector as we know it in QM. In these two projection operators lies all our interpretation knowledge. They imply how we order space into subspaces (read i.e. particles) and their relative relations (read i.e. fields). In other words, what do we consider the system under investigation to be and what do we consider the investigating system to be.

    Illustration 3: From a three dimensional cubic grid the 3D form of one sheet (a deformed Euclidic plane) is projected on screen. Here is a film (rotating GIF 600Kb) that shows how a flat wave is bouncing against a wall (blue line) with two slits in it. The continuing interference pattern becomes visible and also the effect of a pseudo black hole behind the wall. In the film different slit-distances are made visible. The two red lines are visualising two screens at different distances from the wall as in the classic two slit experiment.

    Illustration 4: Here is an impression (rotating GIF 1.5Mb) of a projection of space. Only those places in space with enough deformation are coloured yellow. The space between the two blue lines can be interpreted as a cavity with 4 holes in it. The holes in the left blue line generate energy. The two holes in the right blue line emit energy. Sort of an impression of particles existing for a brief period ("quantum foam") and interacting with a screen, creating an interference pattern.

  2. From form to relativity theory

    To come from one form representing the universe to the interpretation of relativity theory we can imagine the following.

    Complex subforms like stars, consisting of subforms called particles represent masses in space. The space in between the particles is deformed or stretched and waving just as it is in FIT and influences the movement of the subforms. In fact it is one and the same form but once you start classifying, once you make distinctions and subdivide, you have to start giving names to the different objects (and their attributes such as mass) and their relations (forces or stretched space).

    When going from a global picture to a local picture with different objects and their relations it also becomes necessary to introduce a second type of time to measure relative change in space. This is the kind of time we are familiar with and we use in relativity theory. The global time is visible in what we call the speed of light. Space deformations like photons travel with a speed that directly relates to the stiffness of space.

    Illustration 5: From a three dimensional cubic grid the 3D form of one sheet (a deformed Euclidic plane) is projected on screen. Here is a film (rotating GIF 1.9Mb) that shows how a pseudo flat gravitation wave encounters a pseudo black hole.

  3. From form to string theory

    To me it is very informative to create these (discretised elastic 3D) spaces in the computer. To create a deformation one can take a point or a line of points or a two dimensional membrane of points or a volume of points and start moving and distorting it in space. This will obviously influence all the rest of space. Coupling FIT to string theory would in my opinion be established by finding the right strings that manipulate their surroundings so the environment looks like a particle we know and recognize from the behaviour we can measure with our measuring devices. In a way we go from a global 3 x 3 matrix (that represents the new form of space) to a local 3 x 3 matrix to describe a particle. Again we go from a global picture of one-ness to a discrete picture in which we see strings that interact.

  4. From form to loop-quantum-gravity (LQG)

    For me it would be very interesting to hear what loop-quantum-gravity physicists, who would momentarily adopt FIT for the sake of argument, would say if they tried to compare the concepts of LQG to the assumptions of FIT. I would not be surprised if FIT could shed light and suggest modifications on some of the assumptions that still cause difficulties in LQG. Specifically the result that space may be discretised seems to me to be a snake biting its own tail resulting from the discretised world of quantum mechanics. Combining GR and QM without an intermediate, I would imagine, has to have the result of either a discretised space (knot states as quanta of space if you fit GR to QM) or a disappearance of the particle view (if you fit QM to GR in a theory that would maybe be called gravitational quantum mechanics). Furthermore I suspect that in a discretised space, the law of conservation of energy will slightly fluctuate and will only hold in the limit where discrete becomes continuous. I would be very interested to hear if any of such calculations exist. In my own grid, which by its very nature is discrete, what I consider to be the analog of energy is stabel but fluctuates just a bit. Fluctuations depend on the relative deformation of the grid. Only locally infinitely small deformations result in zero fluctuation. I need a continuum to uphold the law of energy conservation on all scales (which for some reason I would prefer from an aesthetic point of view).

  5. The speed of light and Planck’s constant

    Let's assume the assumptions are right and its a given that there is only space, that we are made of distorted space. Then we should be able to explain where the most important constants, that we know in physics, come from.

    My suspicions:

More speculations

Prediction 1:

True unification of our physics theories can only be established when we completely leave our instinctive urge for seeing and modelling particle-like structures separated from their environment
A discrete approximation of a continuus phenomenon will be accurate to any desirable degree but it will never produce a continuum. Therefore our theories, if on a discrete basis, will be approximations, occasionally giving rise to infinities.

Prediction 2:

Describing the universe locally will ultimately consist of describing the internal continuous structure of the set of locally defined Forms (particles) that are relevant to form a discrete interpretation (picture) of our world and the relations those local Forms can have with their environment. This can be done statistically as well as deterministically, depending on the scope of the pieces of space that are under consideration and the knowledge about their internal structure.

One hopes to be able to show concepts like attraction and repulsion depending on the shapes of the deformations, twisting, denting, antisymmetries and symmetries in local spaces. Speculate for instance on two point-mirror symmetric twisted particles when the orientation of the mirroring is opposite (+ and -). A natural relaxation in the tension of the fabric may occur when the deformations get closer. The reverse may happen when the space deformations are the same (+ and +).

The 4 known forces will come from the interpretation of the form. Gravity more or less being the simplest force, born out of the cumulative stretch from all deformations of space The other three forces (electromagnetism, weak and strong interactions) being born from more complex interpretations of the interactions of deformations. When interpreting on smaller and smaller scales one is tempted to anticipate more forces through interactions among finer and finer local structures. These new forces (particles) will be the unifying mechanism for our old forces. Speaking of gravity there will be no visible opposite of stretch because small pieces of space that are compressed will be part of the internal structure of elementary particles and exotic structures like black holes. In the local deformations of spaces one should find symmetries that can be interpreted as spin and charge.

Some More Philosophy

An implication is that if you are willing to describe nature with the eyes of FIT, the interpretation of the axioms is relatively simple (as in general relativity theory) but the mathematics will be dazzling. This as opposed to quantum mechanics in which the interpretation is dazzling.

When one starts to distinguish between objects, if there is no direct contact between these objects one could argue that there must be something in between, space. If there seems to be nothing in between but still the objects are not touching that space is normally called a vacuum or empty space. In quantum mechanics we need the concept of quantum foam to describe the weird things that seem to happen in empty space. In FIT all of space is constantly moving and the matter in which it moves will determine if and how some local piece of space can be experienced. Do we give it a name and consider it an object or is it empty space for the time being?

FIT embraces more topological restrictions on space than for instance string theory. Holes, knots and extra dimensions are in my opinion not objects you would want to use in explanations for the structure of objects unless you are quite sure that you need them for explaining real or thought experiments. Questions and speculations may arise unless it is clear that you choose those objects within a broader frame that already puts a hold on these speculations. The assumption that all places in space are equal should not be compromised too easily. Personally I am very suspicious of anything in a theory that allows for stuff like time travel, parallel universes or infinite mass densities located in points.

So many different creatures, so many different perspectives and interpretations. It would be nice if the assembly of theories that explains the behaviour of the universe would fundamentally reflect the concepts of interpretation and perspective. I hope the universe is one whole thing, one unity, and that, to explain it locally, the theory has to be one of interpretations and perspectives. Wouldn't it be nice if the whole concept of I is ultimately not applicable?


The project

This project is driven by the following intuïtions:

The basic assumption and hope for this research is that it is possible to design a useful theory, named FIT (Form Interpretation Theory), containing a set of assumptions and descriptions to describe the most basic laws of the physics of nature. To me it is worth attempting to find the words and formulas to describe the world as I seem to understand and picture it, attempting to do so with the scientific method and in a harmonic relationship with current knowledge and the people from the scientific community. I will continue to search until either I (or hopefully we) succeed or until someone shows me that it is of no use. It is a search for a minimum set of assumptions from which all others can be put in the right perspective. This set should be based on simple, beautiful and logical choices. It should be able to show how present models (like Relativity Theory, Quantum Mechanics and String Theory) work within its framework, preferably as specialised perspectives on and interpretations of reality. The theory and models should obviously be presentable to other physicists for evaluation.

Results should be:


Some definitions (an initial proposal)

Energynumerical quantity related to the deformations of space (an attribute of a form)
FormThe description of deformed space. The specification of the position of every point in space.
Form Interpretation TheoryA theory (consisting of two layers, the Form Layer and the Interpretation Layer) that seeks to explain the inner mechanisms of nature
GlobalCovering the whole of space
Internal structureLocal form of space inside a specified object
InterpretationThe process of assigning meaning (objectnames and attributes, discriminating parts of space from their environment) to the local deformations of space. Technically it is a mathematical analyses of a Form
LocalA part of space
Local form(also subfrom) (principally global) deformation of space representing a locality (particle, string, knot, ...)
ObjectAs in the dictionary or improvising: something useful to distinguish which has at least one attribute. Examples: a Form, a particle, a field, space, time, a force, a wave
Particleas usual or: the interpretation of a piece of space that is assigned specific attributes and interacts with its environment.
Time global (level 1)A measure of change, an attribute of space which is directly related to the stiffness of space and the speed of light as we know it.
Time local (level 2)A measure of change, related to interpreted form changes


Some more pictures

Illustration 6: In this picture an experiment is illustrated with two pseudo particles with radii of 10 units. Two types of particles (mirror-images) are simulated. The experiment brings the two pseudo particles in the same space at different distances from eachother. The total length of the grid is then calculated, defining an analog for the energy in the deformed grid. With equal particles the least energy occured at a distance of 2 times the nucleus radius. With mirror particles the potential dip (suggesting the most stable configuration) occured at a distance between the nuclei of 5 units (half a nucleus radius). The colourful pictures are a close-up of the hart of both stable configurations.

Illustration 7: Here is a part of distorted space (top and side view using a zonal harmonic) to represent a pseudo electron around a proton in a certain excited state. (Maybe one day it will move through space. Remember these images are just to get a feel and impression. The space deformations do not (yet?) exhibit any attributes that can be recognised as for instance spin or charge)


Some Literature

Abelson, H.,diSessa, A. (1980)Turtle geometry, MIT Press, ISBN 0-2-62-01063-1
Bottger, Harald (1983)Principles of the theory of lattice dynamics, Physik-Verlag, ISBN 3-87664-064-4
Bredon, Glen E. (1993)Topology and geometry, Springer-Verlag, ISBN 0-387-97926-3
Brillouin, Leon (1946)Wave propagation in periodic structures, McGraw-Hill
Brillouin, Leon (1960)Wave propagation and group velocity, Academic Press
Feynman, Richard P. (1963)Lectures on physics, Addison-Wesley, ISBN 0-201-02010-6-H
Greene Brian (1999)The elegant universe, Norton & Company, ISBN Dutch version 90-295-2199-6
Gilat, Gideon (ed., 1976)Methods in computational physics vol. 15, vibrational properties of solids, ISBN 0-12-460815-9
Hill, Francis S. (1990)Computer Graphics, Macmillan Publishing Company, ISBN 0-02-946185-5
Junich, Klaus (2001)Vector Analysis, Springer-Verlag, ISBN 0-387-98649-9
Lee, John M. (1997)Riemannian manifolds, Springer-Verlag, ISBN 0-387-98322-8
Lee, John M. (2000)Introduction to smooth manifolds, Springer-Verlag, ISBN 0-387-95495-3
Marathe, K.B., Martucci, G. (1992)Studies in mathematical physics vol. 5, The mathematical foundations of Gauge theories, Elsevier Science Publishers, ISBN 0-444-89708-9
Munkres, James R. (2000, 1975)Topology, Prentice Hall, ISBN 0-13-181629-2
Reissland, J.A. (1973)The physics of phonons, Wiley & sons, ISBN 0-471-71585-9
Schroeder, Daniel V. (2000)An introduction to Thermal Physics, Addison Wesley Longman, ISBN 0-201-38027-7
Silsbee, Robert H., Drager, Jorg (1997)Simulations for solid state physics, Cambridge Univ. Press, ISBN 0-521-59911-3
Schroeder, Daniel V. (2000)Thermal physics, Addison Wesley Longman, ISBN 0-201-38027-7
Stoll, Manfred (2001)Introduction to Real Analyses, Addison Wesley Longman, ISBN 0-321-04625-0
Thompson, B., Bruckner, J. and A. (2001)Elementary Real Analyses, Prentice Hall, ISBN 0-13-019075-6
Tribble, Alan C. (1996)Princeton guide to advanced Physics, Princeton Univ. Press, ISBN 0-691-02670-X
Tsvelik, Alexei M. (1995)Quantum Field Theory in condensed matter physics, Cambridge Univ.Pr. ISBN 0-521-45467-0
Watt, Alan (1989)Three-dimensional computer graphics, Addison-Wesley Publishing Company, ISBN 0-201-15442-0