A compact topological model which relates displacement and rotation isotropically leads to diverging geodesics. A volume of points which individually follow these geodesics becomes expanded during the transport.
The volume expansion red shifts electromagnetic energy transported with the volume. Receiving the enlarged volume after a long transport leads to the impression of a time dilatation.
What is the impact of this volume expansion on particles or matter transported along cosmic distances? Is there a loss of kinetic energy? Does this mean that a very weak static gravitational potential exists, which extracts energy from movements over cosmic distances?
Attachment: Description of the model
The model relates an orientation O=(x/R, y/R, z/R) to a point P=(x,y,z) and also relates a rotation vector V=(dx/R,dy/R,dz/R) to a displacement D=(dx,dy,dz).The axes of the rotation operation is perpendicular to the orientation O and the rotation vector V. R is in the range of about 14 billion light years.
The model has the following properties:
The coupling properties of the three axis rotation operations cause the divergence of the geodetic lines. The rotation operation takes place in an image space. A displacement operation in the native space includes a transformation to the image space, a rotation and a back transformation. The Quaternion formalism allows finding the diverging properties of the geodesics in a straight forward way.
The foundation you establish for your model seems to me very close to the assumed foundation of QFT with its underlying neutral energy field, From my understanding, it also relies on motion to explain the existence of kinetic energy, although I see this more easily with your model than with QFT.
How would you describe the difference between the foundation of you model and that of QFT?
Quantum field theory considers Lagrange densities of real physical fields. The proposed model only considers geometry and includes the assumption that diverging geodesics have a physical impact.
I feel the same as yours professor!
But I still knows that the effect of red shift is more seen when the density of Dark energy falls more than -1, then I strongly feel that a Big Crunch may happen!
In that scenario may answer your question. Sorry If I am wrong.
Hi Anand,
sorry, but I miss any relation between dark energy and the possible existence of an isotropic static gravitational potential. The static nature of the model excludes the possibility of a big crunch.
I don't believe you get a static potential, but possibly a dynamic one in near equilibrium with localized exceptions. Gravity potential is one of the proposed components of the ZPE, off set by other potentials to get a small cosmological constant, gravity potential depleted near an event horizon, but nearly constant in much of space. Then we argue about how much energy is there. It is the microscopic implication of your large scale geometry.
Hi Jerry,
all the tems "dynamic potential", "near equilibrium", "localized exceptions", "zero point energy", "event horizon" seem to be from another world as a geometry with isotropically diverging geodesics.
Hi Graham Peter Michael,
do you have a more specific description of the geometric toroid view and of the expansion to vortex you mention?
Hi Graham Peter Michael
Thank you for the concrete description of the geometry you are proposing. The toroid structure is indeed a candidate geometry for a finite universe. Do you see a way how it can be transformed to become isotropic?
Hi Graham Peter Michael
You asked for an explanation of the isometric view of the geometry of our universe.
Einsteins cosmological priciple requires a homogenous and isotropic geometry. Because of a missing explanation for the red shift, all currently accepted geometries are non isotropic, expanding and potentially infinite.
It is obvious, that a finite geometry cannot be flat and therefor cannot have parallel geodesics like an Eulerian geometry. Therefor with numerical methods I begin checking possible isotropic geometries for diverging geodesics and hope to get help from experienced mathematicians or ambitious researchers. The idea is, that diverging geodesics lead to an expansion of transported volumes, which would explain the red shift.
I hope that this explanation is understandable though it contains differential geometry concepts. And I don't think it is worth considering solutions not conformable to the cosmological principle, which means that isotropy is strictly required.
Hi Graham Peter Michael
What do you mean with with your statement "Neither word implies the other is true"?
What kind of truth are you missing?
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