Schrodinger's cat <<==>> Universe ????

[Turambar]

-edit-

No idea why that isn't working.

[cecilia]

Turambar wrote:


-edit-

No idea why that isn't working.

it's an imageshack thing. they don''t allow hotlinking

use something like http://tinypic.com/

[Turambar]

cecilia wrote:
it's an imageshack thing. they don''t allow hotlinking

Damn not having my own webspace anymore. Wonder why they provide forum code then...

[metalman]

[Dandy]

blobrana wrote:

Hum,
yeah, most string theorists  already thought that the E8 x E8` gauge group / Heterotic string would be able to  describe  all the particles and forces that we see (this is the simplest model to include all the  forces including gravity and  known particles).  

As I previously stated, I'm currently digging into Heim Theory.

The following quote from the AIAA (2006-4608LetterExtndVersionRevisedSept.pdf) compares String Theory, Gauge Theory and Extended Heim Theory:

Spacetime of Higher Spatial Dimensions: String Theory

Novel physics most likely comes from a unified theory. Over the last five decades many attempts have been made. No successful theory has emerged so far. One of the most
prominent recent theories is String theory which uses ideas from Kaluza and Klein.

The theory by Kaluza and Klein (1921, 1926) already introduced a fourth spatial dimension
to account for electromagnetism. There is nothing in Einstein's theory to forbid the introduction of additional coordinates.

According to string theory, electrons are not point particles, but are vibrations of a string, whose length is at the Planck scale, some 10-35 m. Strings are one-dimensional
entities.

Sounding these strings they can turn into other particles, for instance, the electron can turn into a neutrino, or into any of the known subatomic particles.

String theory leads to a unification of the four fundamental interactions, but requires more spatial dimensions.

However, because of the discrete nature of spacetime there seems to be no need for string theory, which replaces point particles by strings, but requires hitherto unobserved additional spatial dimensions.


Gauge Theory as Spacetime with Internal Dimensions

However, there is a fundamental difference compared to the concept of spacetime with internal dimensions, in that strings are objects in spacetime, while in this section a geometrization concept is employed that explains all particles as geometric objects constructed from spacetime itself.

There exists another concept, coming from the idea that elementary particles have additional degrees of freedom in some kind of internal space.

Therefore, the concept of physical space as the combination of spacetime and internal space is introduced. This marriage of 4-dimensional spacetime with internal space is called fiber bundle space mathematically.

In the following the term physical space will be used for this combination, since all the fundamental forces of physics will be described in this space. These internal degrees of freedom can then be connected with the dynamical motion in spacetime. This is the geometrical structure utilized in gauge theory.

The dimension of the internal space and its symmetries determine the physics that is possible. In order to have a unified field theory the proper internal space has to be constructed that encompasses all interactions of physics.

In the next section, GR is equipped with an 8-dimensional internal space, termed Heim space. Once this internal space is set up, all physical interactions are fixed. There is only one single selection rule for building internal subspaces that have physical meaning, see below.
It turns out that six fundamental physical interactions should exist.


Special Gauge Theory: Extended Heim Theory

In EHT a set of 8 additional coordinates is introduced, but contrary to String theory, the theory postulates an internal space with 8 dimensions that governs physical events in
our spacetime (actually a curved 4D manifold M).The crucial point lies in the construction of the internal space that should come from basic physical assumptions, which must be generally acceptable. In EHT, an 8-dimensional space is constructed, termed Heim space, H8 that is missing in General Relativity.

In other words, GR does not possess any internal space, and thus has a very limited geometrical structure, namely that of pure spacetime. Because of this limitation, GR cannot
describe the fundamental forces in physics and consequently has to be extended.

The extension as done in EHT, lies in the introduction of the internal space H8. EHT reduces to GR when this internal space is omitted.

The metric tensor, as used in GR, has purely geometrical means that is of immaterial character only, and does not represent any physics.

Consequently, the Einsteinian Geometrization Principle (EGP) is equating the Einstein curvature tensor, constructed from the metric tensor, with the stress tensor, representing
energy distribution.

Stated in simple terms: matter curves spacetime.

In this way, the metric tensor field has become a physical object whose behavior is governed by an action principle, like that of other physical entities.

According to the quantization principle, the minimal length in the space part of H8 is the Planck length. Applying the geometrization rule of the GODQ principle, see next paragraph, Planck mass and Planck time are converted into length units leading to two additional lengths constants
lpm = h /mpc and lpt = ctp
that have the same numerical value as lp but define two additional different length scales, relating lengths with time units as well as length with mass units.

The introduction of basic physical units is in contradiction to classical physics that allows infinite divisibility. As a consequence, measurements in classical physics are impossible, since units cannot be defined.

Consequently, Nature could not provide any elemental building blocks to construct higher organized structures, which is inconsistent with observation.

Thus the quantization principle is fundamental for the existence of physical objects. Therefore the three Planck length units as defined above must occur in the structure of both spacetime and internal space H8.

In spacetime length unit lp is the basic unit for the spatial coordinates and lpt measures the time coordinate. In order to connect geometry with physical entities, in the internal symmetry space coordinates xi i are measured in units of lpm. Hence all lengths in H8 are represented by multiples of 1/mp, and therefore internal coordinates xi i with i = 1,...,8 are denoted as energy coordinates. In other words, the concept of energy coordinate ensures that an inverse length is representing a physical mass. Since length values are quantized, the same holds for physical mass. In this regard the connection of geometry with physical objects has been established, but, in order to achieve this goal, the quantization principle had to be introduced ab initio. In contrast to Einstein, EHT is based on the following four simple and general principles, termed the GODQ principle of Nature7.

1. Geometrization principle for all physical interactions,
2. Optimization (Nature employs an extremum principle),
3. Dualization (duality, symmetry) principle (Nature dualizes or is asymmetric, bits),
4. Quantization principle (Nature uses integers only, discrete quantities).

From the duality principle, the existence of additional internal symmetries in Nature is deduced, and thus a higher dimensional internal symmetry space should exist, termed Heim space H8, which will now be determined.

In GR there exists a four dimensional spacetime, comprising three spatial coordinates, x1, x2, x3 with positive signature (+) and the time coordinate x4 with negative signature (-). It should be remembered that the Lorentzian metric of R4 (actually spacetime is a manifold M) has three spatial (+ signature) and one time-like coordinate (- signature)8.

The plus and minus signs refer to the local Minkowski metric (diagonal metric tensor, see Eq. (1)). Therefore, the squared proper time interval is taken to be positive if the separation of two events is less than their spatial distance divided by c.

Hence a general coordinate system in a spacetime manifold M (locally R4) comprises the curvilinear coordinates eta µ with µ = 1,..,4 and eta = eta µ € M where eta denotes an element (point) of M.

The set of 8 internal coordinates is determined by utilizing the GODQ principle introduced above. The three internal spatial coordinates xi 1 ,xi 2 ,xi 3 are associated with Planck length lpm, the internal time coordinate xi 4 with lpt.

The other four coordinates are introduced to describe the degree of organization and information exchange as observed in Nature.

To this end, the second law of thermodynamics is considered, which predicts the increase of entropy. Although negative entropies are possible, they cannot account for the high degree of organization prevailing in Nature.

The second law of thermodynamics says something about the direction of a process, but will not lead to highly organized structures by itself. Everywhere in Nature, however, highly organized structures can be found like galaxies, solar systems, planets, plants etc., which, according to the duality principle, have to be introduced into a unified theory.

We are referring to the article of P.W. Anderson: "More is Different" [28]. It simply says that the ability to reduce everything to its basic constituents and fundamental laws
does not imply the ability to start from these laws and reconstruct the phenomena, i.e., the Universe.

In that sense, these coordinates express some kind of a collective behavior, which is reflected by the entelechial and aeonic coordinates, see below. A description of Nature that only provides a route to decay or to lower organizational structures is in contradiction to observation.

Therefore, an additional, internal (negative signature -) coordinate, termed entelechial coordinate,  xi 5 , is introduced.

The entelechial dimension can be interpreted as a measure of the quality of time varying organizational structure (inverse or dual to entropy). It should be mentioned that all other additional internal coordinates have negative signature, too.

When the Universe was set into motion, it followed a path marked by a state of great order. Therefore, to reflect this generic behavior in Nature, the aeonic dimension, xi 6 , is introduced that is interpreted as a steering coordinate toward a dynamically stable state. On the other hand, the entropy principle is firmly established in physics, for instance in ß-decay.

Entropy is directly connected to probability, which in turn is related to information. Therefore, two additional coordinates xi 7 , xi 8 are needed, which are complementary to the
organizational coordinates, to reflect this behavior of Nature, termed information coordinates that are describing information waves.

Finally, a connection from geometry (space and time) to physics (mass) has to be established. Since space and time coordinates are associated with Planck length scales (see above), they provide the connection between geometry and mass via the Compton wave length and thus are present in H8.

In summary, internal coordinates xi i with i=1, ..., 4 denote spatial and temporal coordinates, xi i with i=5,6 denote entelechial and aeonic coordinates, and xi i with i=7,8 denote two information coordinates in H8, mandating four sets of types of coordinates. With the introduction of a set of four different types of coordinates, the space of fundamental symmetries of internal space H8 has been fixed.

The theoretical framework is provided in Sec. 5, where a set of metric subtensors is constructed, each of them describing a physical interaction or particle.

Thus the connection between physical space and physics (symmetries) is established in exactly the way as foreseen by Einstein. Physical space is responsible for all physical interactions.

However, in order to reach this objective, spacetime had to be complemented by internal space
H8. This is the novel aspect in EHT, which otherwise is based on the well known concept of gauge theory.

Once the internal space with its sets of coordinates has been determined,
everything else is fixed because Eq. 2 is nothing but the direct extension of GR provided with an internal space.

It should be noted that a dimensional law can be derived that does not permit the construction of, for instance, a space H7. Heim space, H8 , comprises four subspaces, denoted as R3, T1, S2, and I2.

Fig. (7) shows the set of metric-subspaces that can be constructed, where each admissible metric subtensor is denoted as hermetry form.

The word hermetry is a combination of hermeneutics and geometry that is, a hermetry form stands for the physical meaning of geometry. Each hermetry form has a direct physical meaning, for details see refs. [13], [29].

blobrana wrote:

The real discovery is the `pattern` that emerged that  seems to  describe groups or families of certain   particles and related forces. The difficult part was that `pattern` is best viewed in 8 dimensional space so it wasn't  easy to first see  that structure.  But  now that it is found we an make  predictions how  certain particles are related to other known/unknown particles.

How do you view a pattern in 8 dimensional space?
My eyes can only see events in the 4 dimensional space-time...

 :-?  :-?  :-?

[meega]

cecilia wrote:

Turambar wrote:


-edit-

No idea why that isn't working.

it's an imageshack thing. they don''t allow hotlinking

use something like http://tinypic.com/

Yes they do.

[orange]

IIRC, I was told at school that "measurement" is any interaction between quantum and classical system. That dark matter is interacting with everything, so how come this is problem?

[Dandy]

KThunder wrote:

when you get into m-theory, multiple universes,
...
32 dimensions etc.
...

A "law of dimensions" can be derived from the "law of tensor formulation for empty spectra of metric structure stages".  

If p denotes the number of dimensions of an already known reference space, then this space could as a subspace be part of an superior space, whose "number of dimensions" can be labeled with n.

If in a space Sp with p >= 0 a system of differential equations of the kind of spacetimely structure equations is valid, then the Sp is a subspace of Sn, provided that the by 1 reduced square number of n - 1 becomes identical with the sextuple of the 3 combinations to the class p.

Formal this interrelationship of the "numbers of dimensions" is expressed with
( n - 1 )² = p ( p - 1 )( p - 2 ),
whereas it indeed has to be considered that "numbers of dimensions" of reference spaces Sp or Sn always have to be positive, integral numbers.

Thus such a "hyperspace" does NOT exist for every p-dimensional space.

Immediately it becomes clear that a positive branch n = 2 and a negative branch n = 0 arise from p = 0, p = 1 and p = 2. Point, curve and area are consequently mappable onto an area or point. For p = 2 the negative branch does not apply, because "numbers of dimensions" only can be positive, integral numbers. For p = 3 or p = 5 no Sn is existent, because n is no integral number, what is equally valid for p = 7 up to p = 13.

If we appoint p = 4 for the empiric spacetime, we get an hyperspace S6 with n = 6, which includes the spacetime as subspace.

Finally with p = 6 a hyperspace S12 becomes possible because of n = 12. The hyperspace S6 is energetically determined by the eigenvalue spectra and therefor has been labeled as <>.

In S6 there has to be an energy density tensor of 6th order where 12 of its 36 components are always 0. In the S12 however there indeed are volumes defined but no energies, so that the energy density tensor of 6th order appears to be <> into the S12.

An analysis of the hyperspace coordinates shows that only the coordinates of the physical space S3 really count, while all other coordinates like the lighttime are imaginary; else there would neither be stable orbits of gravitating masses in the macro scale nor stable ground states for atomic electron sheaths in the micro scale.

This circumstance is the mathematical result, if one arranges Newton's version of the law of gravitation and the quantum physically law of the electrical interdependencies between atomic nucleus and electron sheath for more than three real dimensions.

In the macro scale all real "numbers of dimensions" > 4 result in logarithmical spirals as "gravitational orbits", while just for four such dimensions an orbit is possible, which yet becomes a logarithmical spiral (because of its irrationality) by least disturbances.

The stable Kepler orbits, which are the only ones to allow stable macro scale systems, result only for three real dimensions [plus "time" as a fourth, imaginary dimension].



Translated from:
Burkhard Heim: Informatorische Zusammenfassung von "Elementarstrukturen der Materie" Vol. 1 & 2, pages 18-19