Topological Quantum Gravity

[Jeltz]

For what it is worth, here is my ToE! based entirely on a very few simple geometrical premises. I started down from the basic truths in general relativity and quantum mechanics, and up from some basic axioms of topology theory, and met at a point that (at least to me) makes a lot of sense for a unification theory. As such my work is more in the nature of a paradigm shift than a new theory of physics.

The quantum wave function is expressed directly and completely as the transverse distortion in a simply connected closed 4 complex dimension manifold. The surrounding manifold accommodates the folding of the wave function by distorting in exactly the way predicted by general relativity. Both effects are the direct result of a single local topological constraint acting at all points on the manifold. Mass/energy may therefore be more properly expressed as a geometrical property of the manifold (the amount of folding required to form the wave function for the particle of interest)

In Lagrange nomenclature the topological constraint is (delta psi) squared = zero, stating that the Euclidean distance between any two neighbouring points in the 4C manifold is zero. It is my contention that the entirety of physics is derivable from this constraint.

It is a quite remarkable fact that in higher dimensions (including this proposed 4C manifold) two neighbouring points do not have to be congruent to meet this constraint. It is also interesting to note the similarity of the relative vectors inherent in this equation with the root vector system of the E8 Lie group.

This paradigm shift may be used to explain cosmological observations of inflation, dark energy and dark matter without resorting to new physics. The cosmological constant is a natural result of the manifold having to be closed (the universe by definition having no boundary requires this to be so). Closure requires curvature, and curvature is energy, so the cosmological constant results quite naturally from the act of closing the manifold. Entropy and degrees of freedom available in the manifold take on primary roles in explaining entanglement and the collapse of the wave function at macroscopic scales.

This theory shows that both quantum mechanics and general relativity are essentially complete and exact theories that taken together are an exact solution to the topological constraint outlined above. Planck's constant (fine structure constant in Stoney units) relates the amount of folding in the manifold (the wave function) to the distortion in the surrounding manifold required to accommodate the folding. It is therefore a calculable geometric property of the manifold and the constraint. Particles are stable folded patterns (wave functions) in the manifold. Rest masses of stable particles therefore will be calculable geometric properties of the manifold and the constraint.

I do not believe that there remain any numerical constants in the standard model or outstanding cosmological observations not explained at least in principle above.

Full details at http://jonkers.net.au/funstuff/funstuff.aspx

[Mikal]

Hi Jeltz….thanks for a very fine read and congrats on your hard work and what must have taken some pretty fine and concentrated thought to figure out.

Now I cannot add any scientific discussion here because I am just learning this science stuff…smiles…! However I am impressed that you use words like ‘hyperspace.’ I tend to think the 4th dimension is ‘hyperspace’ and that yes there are higher dimensions. I also like your 8 fold paradigm you presented.

Now I wanted to know if you could comment on this. I have been studying the theory of Stuart Hameroff & Roger Penrose, a physicist and anetheologist who study consciousness and developed a theory as to consciousness concerns the microtublules inside cell structure.
Hameroff stated that “the state of unconsciousness during anathesia is due to immobility of the electron and states of superconsciousness may be related to the speed of the electron in mobility in the microtubules.”

This is supposed to have something to do with changing quaternian scalar potential.

In relation to this would you have any comments on electron mobility where you could enable me to better understand this and all this science talk. This is just an initial question and I will go on reading your theory....

Regards Mikal

[austintorn@aol.com]

Very refreshing TOE.


DeltaPsiSquared = 0

Could be a cousin to my Balance of Nothing Theory.


Each M-surface in this manifold could in fact be identical to that defined as flat Space-time in the special theory of relativity except that it must also be slightly curved to close the manifold rather than being flat. This is required because the universe (by definition the totality of all there is) can therefore have no boundary conditions.

There is perhaps only space and curved space(gravity and energy-mass greatly curved in time), time being the difference in space (which is, more or less, energy).


It follows that the energy of the photon must be a calculable property of the photons wave function, and the only property this wave function can have is a geometric shape.

I will soon be examining the shape of a photon in my ‘Amending Immaterial “Science” thread.


Two hyper-spheres in this manifold may also be observed consisting of the co-ordinates of the four real dimensions and the four imaginary dimensions (the ++++ and ---- hyper-spheres respectively). These two hyper-spheres have some special characteristics. The topological constraint and the connectivity of the manifold allow the four real dimensions to expand or contract at the same rate as each other provided only that the four imaginary dimensions contract or expand at the negative of this same rate. It also imposes the requirement that all three of the like-sign dimensions on each M-surface must expand or contract at the same rate (i.e. be isotropic to each other in just those three dimensions.)

I was thinking of the 4-D hypersphere having two 3-D halves of opposite polarity (charge) which, of course, nullifies 4-D Totality in the overview (the Balance of Nothing).


It is proposed that one node of the harmonic resonance of the entire manifold is a hyper-sphere of congruent co-ordinate points (the big bang), the other hyper-sphere completing the manifold at this time being a point of maximum expansion. The two parts of the manifold each oscillate between these extremes over a period of several tens of billions of years.

Indeed, here had to be something before the Big Bang.


Finally it has always puzzled me why the probability concepts inherent and necessary in quantum mechanics led to the conclusion that energy can spontaneously appear and disappear from the quantum vacuum. Fortunately we can now maintain the probability concepts inherent in the wave function while not having to discard our long-held belief in the absolute conservation of energy at all places and times that lies at the heart of the laws of thermodynamics.

Only if in canceling anti/matter pairs emanating, perhaps.


The very act of defining a closed manifold (one with no boundaries) introduces a gentle curvature in the manifold. This curvature represents energy (by definition since it is after all a bending of the manifold).

The 4-D hyper-construct must be finite, this being the one and only one boundary condition; 3-D space would be the infinite “surface” of the finite 4-D construct.


Great thoughts, Jeltz. Welcome to Toequest.

[Jeltz]

Mikal, I think you will find I do not use the word "hyperspace" anywhere. I do make reference to hyperspheres that have a very specific mathematical definition. I have no knowledge or opinion on the Hameroff/Penrose conjecture. In general if a sentence cannot be de-constructed and comprehended by a personal of normal intelligence then I find it suspect (and no I do not claim immunity for my writings). IMHO It is an open question as to whether consciousness is inherently a quantum process or an emergent property of a system with the right kind of complexity (much as the periodic table is an emergent property of quantum theory). I suspect the latter but time will tell. The question will become clearer soon as there are at least three ways I can think of by which an artificial consciousness might be created within the next 50 years. If consciousness is inherently quantum in nature, these techniques should fail to produce results. My bet is that one or more WILL produce results, but that is opinion not fact.

[Jeltz]

austintorn@aol.com, the only construct required is the manifold which is built from mathematical points. There are no "add on" properties such as mass or functions such as the quantum wave function (these are all geometrical properties of the points in the manifold). In this sense it is not "Nothing". Particles and potential energy are a geometric property of how points in the manifold fold relative to each other. Because the manifold can start from a uniformly smooth state this implies the manifold starts with a potential that I say is due to the axioms used to construct it (in particular the axiom of closure which results directly from the topological axiom of every point in the manifold having exactly the same number of nearest neighbours). However the universe does sum to zero in the sense that every point maintains zero Euclidian distance from its nearest neighbours in all possible allowed configurations of the manifold.

[Mikal]

Mikal, I think you will find I do not use the word "hyperspace" anywhere. I do make reference to hyperspheres that have a very specific mathematical definition. I have no knowledge or opinion on the Hameroff/Penrose conjecture. In general if a sentence cannot be de-constructed and comprehended by a personal of normal intelligence then I find it suspect (and no I do not claim immunity for my writings). IMHO It is an open question as to whether consciousness is inherently a quantum process or an emergent property of a system with the right kind of complexity (much as the periodic table is an emergent property of quantum theory). I suspect the latter but time will tell. The question will become clearer soon as there are at least three ways I can think of by which an artificial consciousness might be created within the next 50 years. If consciousness is inherently quantum in nature, these techniques should fail to produce results. My bet is that one or more WILL produce results, but that is opinion not fact.

Hi Jeltz….apologies for word usage and I do stand corrected however I do think we are talking about the same thing through two words. Words on Toequest can get dicey…lol..
Thank you for answering my question!

I did enjoy reading your theory and will continue to follow the link or your posts here concerning your theory as I do see you are in progress with this.

Regards Mikal

[austintorn@aol.com]

Some ideas on quantum consciousness from Hammerhoff and others…

http://www.toequest.com/forum/consci...explained.html

[austintorn@aol.com]

I will look into "points"; I have some good leads.

[Bogie]

Hi Jeltz, welcome to the "Your TOE Theory" forum. Your TOE is good.

You started with the best departure points from what you accept as the basic truths, i.e. in theories where there is a lot of consensus among those in the scientific community. And you start from what I call the bottom up too, i.e. your own preferred views which you see as axiomatic. You combine the two into an overview of your ToE which I am pretty much untrained to comprehend but there are those here who will engage you on your views.

Anyway, I'll look over your links and see if there are any questions I can ask that might allow me to benefit from your views.

[Jeltz]

Bogie, Yes exactly. There is very little debate about mechanisms by which the quantum wave function (which most people accept carries the mass/energy of a particle) can cause the stress/energy tensor in general relativity (which most people concede is what deforms space-time to form a gravitational field). I propose a mechanism by which it might happen. It just makes sense to me that if you locally fold up a manifold to form a wave function, that the surrounding manifold must distort to accommodate this folding and it is not difficult to imagine that the wave function is quantum in nature, and the accommodation to its folding could and should fit that described by general relativity. How the manifold folds is dictated by the topological constraint (delta psi) squared equals zero. I did not pick this constraint out of thin air. It is compatible with the definition of space-time of special relativity, and I have numerically shown that limited solutions to the constraint are compatible with Dirac's quantum wave function. And finally it is derivable by logic from basic topological axioms. This paradigm shift is actually a very serious attempt to advance the understanding of physics in sufficient detail to being disprovable if it is incorrect. Too often I see proposals in this forum that are either internally inconsistent or not expressed in sufficient detail to be open to serious scientific criticism. I am under no illusions that I might be wrong and welcome serious scientific debate on the issue. But what if I am right......(warm fuzzy feelings to follow!)