Friday, August 24, 2018

Unification of quantum mechanics and relativity in a four-dimensional universe

Laniekea galaxy cluster in black (Picture credit, Tully et al, 2014)

Laniekea or "immeasurable heaven" in Hawaiian is the name of our home galaxy cluster. Understanding our place we must consider the cosmos the smallest and the largest scales. String theory applies to the fundamental forces and particles. However, relativity offers the global structure of space. In a stringy model, micro-dimensions are separated by an information-blocking horizon, where discrete particle vibrations form standing waves and entanglement entails inverse transformations of micro- and macro-dimensions (space). Entanglement forms opposite, yet complementary points, satisfying conservation principles. When complementary sister particles undergo interaction, the wave function collapses and reformulates information and the field curvature. This way, the field curvature, and the particle wave function evolve together.

Because local particle interaction either contracts or expands space, over large scales, it formulates polar regions. Regions with expanded micro-dimensions accumulate pressure, which is experienced as gravity, whereas regions with greater macro-dimensional volume expand. According to Landauer’s principle, information accumulation within micro-dimensions enhances temperature, whereas the expansion of macro-dimensional space cools down. Thus, micro-dimensions form black holes. The model offers an intuitive view of quantum mechanics and eliminates discrepancies with relativity; it also correlates well with the latest cosmological data. This stable and unified alignment of the universe satisfies Mach’s principle and Occam’s razor.

Postulates of the model:

1. Particles (wave function) form closed strings of three complex dimensions (i.e., micro-dimensions). 

2. Any arbitrarily small sample of the universe can be divided into micro-dimensions (particle) and surrounding space (macro-dimensions)

3. The closed strings are embedded within constant field curvature space. 

4. Entanglement changes the wave function’s frequency, satisfying quantum mechanics. 

5. GR dictates that interaction correspondingly modifies the field curvature.

6. Energy/information transfer between micro and macro-dimensions engenders their orthogonality: space represents the here and now, whereas the wave function is non-local and independent of time. 

Consequences of the postulates: 

1. The loop of micro-dimensions represents the velocity of the particle, whereas macro dimensions correspond to its position, leading to the Heisenberg uncertainty principle. 

2. The frequencies of the wave-function are exclusive to specific spatial curvature, i.e., age.

3. Entangled particles produce spooky action at a distance. 

4. The model satisfies the AdS/CFT correspondence

5. It satisfies the holographic principle

6. Interaction requires mirror symmetry between the complex wave function (micro-dimensions) and the action (Hamiltonian)

7. The model explains that the micro-dimensions exist as a wave, but interaction brings forth their particle nature. (It gives an elegant explanation to the Bell's theorem, the delayed choice quantum eraser, and others)

8. Entanglement produces curvature variations (geometry) of the gravity field and creates the experience of dark energy and dark matter. 

9. The stepwise increase of micro-dimensional frequencies corresponds to the age of particles and formulates a time progression of space. 

10. Aging uses up the macro-dimensions; dimensional loss in the high entropy black holes formulates information firewalls. 

11. Landauer’s principle shows that information accumulation corresponds to heat, whereas erasing information cools temperature. 

12. The principle of static time necessitates that erasing information produces contrasting dimensionality change to black holes. Expanding macro-dimensions increase in dimensionality: cosmic voids might harbor four-dimensional white holes, which expand space.

13. The near Euclidean regions of the universe are three dimensional, gravity is an extremely weak force here, which permits low entropy instability.

14. The large value of vacuum energy expands space into the fourth dimensions, thus eliminating the cosmological problem. 



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