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From 4th to 3rd dimension degree - problematic issues,V-VI


Mass as property - once again ?

How is the property of Mass deduced from pure dimensions, geometries and motions, according to our very elementary model through steps 4 → 3 → pole 3a (or 3b) ?

1. We have the views from earlier files that
- mass is a degree of complexity in structure,
- represents enclosed centers, in opposition to the excluded   center,
- is a property that (to a great extent - ?- or totally) lies in binding energy,
- implies a step in the "substantiation" of lower d-degrees towards higher levels,
- is closely related to Gravitation, regarded as a force, a vector field,
- represents the dense "pole" of the physical quantity Density when polarized,
  and inward Direction, referring to our first identification of physical quantities.

2. Mass from radiation or vector fields?
According to suggestions in our elementary model, mass should be a property not defined as such before d-degree 3 is polarized and mass constitutes one "pole" or partial structure of d-degree 2 in relation to Vacant Space, d-degree 2 suggested as representing the property Charge.

                 3b ---------2 ------------ 3a:

Hence, we should expect some close relation to the concept of Charge already in the concept of Mass. And in terms of fields also to the electromagnetic field (EM).

From the other point of view, from the 0/00-end of the dimension chain, Mass could include 2 (or 2,5) d-degrees of motion built-in, (of built-in Time if we want to express it that way), or of "velocity" as a concept for d-degree steps.

Physicists want to think of the first Universe after Big Bang as "radiation - obviously of EM-type, this then in some way transformed to protons and electrons with mass.
   According to our model, this should be only half the history: Some kind of 3-dimensional structure out of vector fields should be "meeting" in step 3-2 and included in the creation of matter with protons representing most of the mass.

3. A Higgs' branch and a Coulomb branch:
In connection with the search for "Higgs particle" in later years which should carry the Mass property, one meets the words about "a Higgs' branch" and "a Coulomb branch", as if the properties Mass and Charge was about a ramification. In our model this should imply the perpendicular reading of the dimension chain - as polarizations 5 → 4+1, 5→ 3+2:

(A little more about Higgs' particle below.)

4. From bosons as "superpositions" to fermions with Mass:
The derivation of Mass from fields is in accordance with most physicists' theories: mass as tied up vector fields, locked kinetic energy or the like.
   In our model Mass is assumed as a property stepwise defined through 2-3 polarizations, i. e. through d-degree steps 5→4→3→(3a — 3b).

Bosons, the quanta of vector fields, usually described as massless as the photon, can have any mass whatsoever according to another formulation. We remember the interpretation of "superpositions" in quantum mechanics. In our model Mass is not yet defined in d-degree 4, first in d-degree step 3-2, as a certain quality of the energy, a certain structure in our view here. It's possible then to see the bosons as superpositions, representing higher d-degrees, the level where the outcome may be "mass - no mass" in lower degree.
   In our first postulates we have assumed the definition that higher d-degrees represent the binding force in relation to next lower degree. This seems illustrated in the relation bosons -- mass particles (fermions).
   The assumption is that bosons in some way develop into fermions with defined masses through polarization, giving increased complexity - revealed in the spin.

In spite of these general views, the vector boson W+/- of the "electroweak force" is attributed a defined mass. Here we have the property of Charge involved too, in our model assumed as not defined until d-degree 2 or step 2→1. We have interpreted the electromagnetic force (EM), related to Charge, as a force in step 3-2 in relation to other forces in a the dimension chain of forces and obviously it's already involved in W+/-.
   Hence, the fact that the Mass property - complementary to Vacant space - also is defined, should be natural. (Also the 3rd vector boson Z° is attributed a mass.)


5. Does Mass include a component from the complementary pole 4b?
Several suggestions in other files imply in our model that Mass as a property not only should be regarded as some transformation of "pole 4a", the inward directed vector fields, but also include a factor from the complementary vector field of outward Acceleration. So the suggested figure on MEGA-fields, the aspect on protons as "grandchildren" of the Gravitation force, so the suggested interpretation of quarks. To this comes the general view on Mass as a question about growing complexity.

How in that case identify it?
A general aspect in our model is to see development as a stepwise building-in of the surrounding as "00-pole" into centers defined as 0-poles. The simplest and most obvious suggestion is naturally that the outward directed (divergent) vector field in d-degree 4 becomes part of the structure, locked into the web of Mass by the inward directed one.
   Gravitation is in certain contexts attributed a negative energy, and the real, positive energy in Mass could then in some sense be attributed this built-in divergent field, on the higher level representing a positive energy of expanding Vacant Space. If so, not only matter but also the property of Mass should break down in the centers of black wholes, if Gravitation becomes the totally dominating force.
   Another application, with a viewpoint from the other end of the dimension chain, could be the aspect on Mass as braking of motion, negative acceleration, one form of built-in energy (in relation to Charge as built-in velocity) ? Compare Time as built into Space in a "4-dimensional Space".


6. About Complex numbers:
Concerning the charged W+/- and building in of the complementary poles in paragraphs above: The charge of the vector boson W+/- is said to depend on complex numbers which make the difference between plus and minus.
   Suppose we have a coordinate system and write a square in the 3rd quadrant, with sides along the negative axes of x and y: both x- and y-sides = -1. This surface exists totally in the negative domain that we could read as inwards. The surface is said to be positive according to the mathematical rules used hitherto, which seem to have a limited validity; minus times minus = plus. (Why so?) To take the square root out of this negative, 2-dimensional surface to get its side, is said to be impossible (imaginary), therefore the "complex numbers". Hence, these numbers seem related to the 2nd d-degree (presumed as representing Charge) taken in the wrong direction, outwards.
   We have inversions around the unit number 1, inwards towards zero, 0.
   We have negative numbers on the other side of zero 0, as linear inward directions (towards a built-in negative infinity).
   The complex numbers could be seen as forming a 3rd realm of the inner world?


7. M-fields and Mass:
The Magnetic force, not very appreciated as such, in its own right, depends, it's said, totally on the rotation of electrons.
   In the file about Mass and Matter was pointed to the relation found in some research between the proton being proportional to the M-field squared (and the electron proportional to the E-field squared.). And the main mass of the atom is concentrated to the protons (and neutrons). This seems to indicate a connection of Gravitation and Mass with M-fields.
   If M-fields are interpretable as results of rotation of electrons, then one could guess that Mass could be dependent on some "pre-rotation" structure, i. e. a circular one, as in our first geometrical suggestions. Rotation as motion attributed to d-degree 3, a transformation of still one d-degree through step 4→3.


8. Higgs' particle:
This assumed particle should be responsible for the property Mass and it should be the "carrier" or quanta of a new field.
   Expressed in those terms, perhaps only misleading (a single field representing Mass?), it sounds incompatible with the model here and the view on Mass as a result of increased complexity and relations between fields.
   It's said about this field that its angle towards other (vector boson) fields is another and that the strength of the force doesn't reach zero. We may compare with assumed angle steps in our model and the roughly suggested geometry: radial versus circular, in d-degree 3. A circular field doesn't reach zero, the 0-pole. It could be expressed as a "center displacement", one of the general views on development in our model. (Mass as two steps of "strangeness"?)

Center displacements
:

(A logical consequence of this view in our model should be that gravitational centers are more fundamental - or precede - mass centers.)

Then there is the presumption that Higgs' particle represents a new field. If so, this obviously contradicts views in our (certainly much more elementary!) model in which the inwards directed vector field of pole 4a (Gravitation) transforms through an angle step to a circular one in d-degree 3.
   It's easy to say that we, in order to get a 3-dimensional "web" for Mass, need something representing three coordinate axes*, not only two, but the 4th d-degree in our model is all-directed. In any case, the different fields or forces of the standard model should be derivable or viewed as transformable into one another for a satisfactory model to arise.
   A perhaps related question: Should we imagine a phase displacement involved in the relation between G-and A-fields towards Mass, comparable with the phase displacement between E and M in electromagnetic waves?

* A simple aspect on growing complexity - as transubstantiation of a warp to a web and this further to a 3-dimensional one - is the operation of multiplication, multiplication of three variables as along 3 crossing coordinate axes: x times y times z. Cf. 3 polarization steps from 5→4 → 3 →(3a — 3b).
    3a — 3b as Mass — Vacant Space, "outer poles" (or partial structures) of d-degree 2.
   Multiplication as an operator? The quarks in a proton are attributed masses around 5-10 MeV. 10 x 10 x 10 = 1000, roughly the magnitude of the proton mass or half of it.

These annotations about Higg's field were written some years ago, Now, February 2014, the theory is regarded as proved, the "Higg's boson found.
A new file about this theory is added here.


9. Substantiation through "Colliding Singularities"
- and Interference:
Such views on the question about the Mass property are aspects from the other end of the dimension chain in terms of our model, from lower d-degrees toward higher ones.
   Or in the perpendicular view on the dimension chain the polarization 5 → 4 + 1.
   In the Dual field theory is suggested that Mass could be created through "colliding singularities". Oddly enough it sounds like a suggestion in the booklets behind this site, not presented here, that substantiation towards higher levels and matter could occur through the meeting between "haploid" dimension chains from the 0-pole (outward directions).
   (Compare the psychological development of the 4-dimensional"I" of a child to a saturated Self and a 3-dimensional "personality" through meeting "confirmation" from others.)
   The theory seems also to include efforts "blowing up" such "singularities", creating some shell geometries (representing Charge or what?): Compare cell balls developing to blastulas in embryology!

Are such ideas possible to unite with the theories about angled vector fields ?

Interference between waves could be described as one kind of substantiation through colliding of similar entities. We have assumed linear, longitudinal waves in d-degree 4 (file Motions). They represent a polarization of the property Density (assumed as first physical concept in d-degree step 5→4) into maxima and minima. In d-degree step 2←1 inwards, L-waves could take the curved form similar to sea waves. (Step 2←1 inwards is connected with the step 4→3 outwards according to the model.)
   When such L-waves, forming an angle, interfere with amplified maxima, what happens? We could perhaps associate to the braking of what is called Monster waves in the see, said to have been explained by some development of Schrödinger's wave functions?
   What should in a 4→3-dimensional form correspond to a braking Monster wave, stealing energy from its neighbors? The sun and its planets?


Step 4 → 3 in terms of Forces

1. Gravitation as a unique force:
It's said that Gravitation is a unique force, not possible to simulate or connect with the other "forces". One suggestion here is that the problem partly depends on the fact that the complementary "FA-force" - identified here with the universal constant A, has been neglected as a force. Yet it has been described as "some form of inner pressure" in opposition to Gravitation as "an outer pressure".

Another reason for regarding Gravitation as unique could be the mix in definition of "forces" which seems to exist from the viewpoints in our model:
   Gravitation (and the complementary FA-force) may represent forces in the sense of built-in higher d-degree, a binding force, while the other forces the physicists identify concerns the outer connection between the complementary partial structures of the lower d-degree, their "interaction", with quanta as "carriers".
   Hence, the problems or unique character of Gravitation may be about definitions and differentiation between concepts as Fields or Forces and Interaction (carriers).

2."ga"-quanta of a double-directed field?
If the "FA-force" is recognized as such, the old differentiation between "purely aggregating forces", FG and strong interaction, and polarized forces (the electromagnetic one and weak interaction, may be misleading. In terms of "carriers" it may be wrong to look for "a graviton", instead a "ga"-quanta of connected fields - perhaps closely related to the "Higgs particle"? - in the same way as the photon represents the carrier of an EM-field (the electromagnetic one)?
   Perhaps such "ga-quanta" makes up the interaction (or the binding force) between E- and M-components in the photons? If so, with a phase displacement (180°?) analogous to the displacement of 90° between E and M in EM-waves. 180° in L-waves, "density waves".

In terms of waves, could we perhaps find "ga-quanta" as halves of the photon? Remembering Hawking's description of the spin relation?
   A connected question: May we imagine that colliding photons could result in gravitons or "ga-quanta"? (One kind of a "dual field theory"!) The locked light in "black holes" responsible for the strong gravitation?


3. About negative and positive energy:
Gravitation is said to have negative energy in a certain sense: energy is required to counterbalance gravitation. A positive energy of "the universal constant A" (or FA) is revealed in expanding Universe. Compare the description of the universal constant A as a kind of inner pressure in opposition to gravitation as a kind of outer pressure.
   Perhaps it's possible to interpret this "negative energy" of gravitation in 3rd d-degree as analogous to the opposition in atomic shells between the potential energy in amplitudes and the kinetic energy as in frequency? Geometrically of the complementary type circular versus radial. There we could find a "positive energy" in the separation of shells and orbitals.

What Einstein interpreted as "gravitational radiation" through contraction of celestial masses, seems to correspond to the transformation of energy from high amplitudes of excited electrons, through jumps inwards, into energy of frequency type in outward radiation.

In the literature one meets the expression "the potential energy of magnetic fields". If magnetic fields may be regarded as "potential", this could point to the connection we have assumed in this model between gravitation and magnetic fields?


4. Mass as result of inversions of fields or of acceleration?
In the file about Mass and Matter we have mentioned the possibility to interpret Mass in terms of inverted Acceleration, of negative acceleration in that case. This in the same way as we have presumed that Charge would be a property definable in terms of braking of motion, negative velocity. With Velocity suggested as expression for steps between dimension degrees, it seems natural that the analysis also could be carried out in terms of fields in different d-degrees.
   We have Gravitation as a form of inward directed acceleration (Acc),
   One form of inward direction = inversions to the realities between 0 and 1. (Negative or positive.)
   If G is proportional to or equivalent with - Acc, and Mass proportional to 1/- Acc, so we get M proportional to 1/G.

There is a formula (from Newton) were we have Gravitation in inverted form, 1/G2. It expresses how celestial bodies are forced to move in orbitals, i.e. rotate.(McGraw & Hill Encyclopedia). An "inverse-square gravitational field of force requires a body to move in an orbital that is a circle, ellipse, parabola, or hyperbola"
   Without pretending any deeper insight in the mathematics, it could be said that the formula points to a factor of inversion in what we have described as the d-degree step 43, leading to external rotation, even if it here doesn't concern rotation around the own axis of a celestial body.

What is called "quaternions" are hypercomplex numbers representing points in a 4-dimensional space. They are used in studies of rotation of objects about their own axes. Here 3 of 4 factors in such a number q are imaginary, i2 = j2 = k2 = ijk = -1. Its conjugate (a -bi - cj - dj) is the same as the inverse quaternion 1/q when referring to a unit number 1 as the axis. (Wikipedia.) Again it seems that we in this advanced mathematics could find support for the idea of inversions connected with d-degree step 4→3. Here applied to vector fields.


5. Is it possible to physically identify a unity of G and A?
It doesn't seem so. This central question about the suggested scheme in our model remains. How identify the unpolarized, "superposed" states in d-degrees 4, 3, 2, assumed as binding forces in relation to the polarized states: divergent — convergent vector fields, Mass — Vacant Space, charges (+) — (-) ?
   There is only geometries - or interaction through quanta of fields, the motional aspect of which in our model may be regarded as debranched in the d-degree steps and thus a testimony of an internal relationship ?
   One aspect could possibly be to look for an "E0-line" between E = +mc2 and E = -mc2, where we can imagine that the polarization between FG and FA on a basic level has occurred? We could imagine such E0-points or -lines as more or less mysterious entrance doors to the higher dimension degree, this one as a "superposition" in quantum mechanical terms?

There are density waves in macrocosm, (which Bengt Lindblad suggested as explanation for spiral galaxies), one expression for the relation Mass — Vacant Space. We could identify the orbitals of the stars in the galaxy as such "E0-lines", the motions not demanding any energy in Newton's terms.
   We could regard the distribution of electrons in shells around heavier atoms as similar "density waves" (with Schrödinger's wave functions) on another level. Perhaps connected is the notable fact (?) that the rotation of electrons about the nucleus doesn't produce any photons.
   Could the potential barrier in the atom, separating nucleus (+) from e-shells (-) in some sense represent an "E0-line" in its shape itself ? Connected with the "tunnel effect" when alpha particles sometimes slip through the barrier without the usually necessary energy?


6. Complementary "poles" versus similar units:
It's necessary to distinguish between on one hand relations between complementary "poles" as Mass --- Vacant Space (or +/- E = mc2) or protons — electrons and on the other hand relations between similar units as Mass — Mass, p — p, q — q, e — e.
   Interactions between similar units (most elementary quanta) are evidently that which is identified as "forces" in the Standard model, but not primarily in our model.

The assumption in our model implies a "binding force" and a "polarizing force" together defining the complementary relation Mass ---Vacant space, or E= +/- mc2,
   In relation to the Standard model it may seem as only a suggested, vague formulation, departing from the Whole, without content, however real this polarization is.
   But a binding force between protons and electrons in atoms is difficult to deny, and it was earlier identified as the electromagnetic force. The relation p — e includes both attraction and repulsion moments. (The same seems to be valid for electron pairs of opposite, complementary spin.)

Among celestial bodies (the relation between similar units as Mass 1— Mass 2) there is both the separation, interpretable as result of a polarizing, separating force, and attraction, as a binding force between the separated masses, so in solar systems and galaxies.
   (Why don't all the masses in a galaxy or solar system contract to one? There is G and the factor 1/G2 in the formula above for the orbitals of the bound masses.)
   Hence, it would (only?) be possible to recognize the "unpolarized " state of higher d-degree which was looked for above, (a superposition of two forces), as manifesting itself in this very relation, - on a new level.

Assume that interaction between similar units shall be regarded as a superposed level, versus a dimension chain with relations between complementary "poles" (or partial structures):
   Then, one aspect in terms of our elementary model, would be the "pole exchange" occurring in the last step. In d-degree 0/00, the degree of Motions, "motions from each other" are derived from first 0-pole and outward direction, but define an anticenter, a 00'-pole for inward direction on next higher level. "Motions toward each other", derived from primary 00-pole, likewise define a secondary 0'-pole, a center for outward direction.
   On this second level G and A, Gravitation and outward Acceleration should appear with reversed roles: Gravitation acting as a binding force, Acceleration outwards as the separating, polarizing one. The opposition to first proposed identifications of "poles" 4a — 4b.
   (The same may be said about the relations between protons and electrons versus p-p-relations (or between quarks) and e — e-relations.)


7. Gravitation as a pushing or pulling force:
How should we after all understand Gravitation as an "attractive force"? Is the "attraction" in reality a pulling force, emanating from a center, a 0-pole, not a pushing one from outside as the 00-pole, a pressure inwards?
   The first case seems to agree with identifications here on the elementary level, Gravitation as an inward directed vector field. Compare the description by a physicist of Gravitation as "a kind of pressure from outside", versus FA as a kind if pressure from inside.
   On the second level, with Gravitation appearing as a binding force, it should emanate from the 0-pole, a center in the conceptual structure here. Hence with the character of a pulling force? If so, it should be connected with the gravitational center rather than the Mass center of each atom or celestial cloud or body?

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© Åsa Wohlin:
Universe in 5 dimensions - as a model of Zero.
A conceptual structure suggested for interpretations in different sciences.
Free to distribute if the source is mentioned.
Texts are mostly extractions from a booklet series, made publicly available in year 2000.