NTuft

I have failed to understand your point. I suppose I was working with a group of quadratic surds, and then looking at fields in terms of physics. Still doubt anything I derived is correctly done. I'll leave off on further developments, and only refer to the work by Reg. Cahill for dynamical space and process physics as a better derivation alternative to GR than Suchard as a correction. That invalidates part of the premise, being that Cahill extends a flat space, but that seems like a fine way to wrap it up.

I have read over this I would infer that Bourbaki does not agree with Godel's incompleteness theorem, and I have read previously that some other contemporary luminaries of his were also not convinced by the theorem. Very interesting. I also assume you mean the Erlangen program? I will have to read up on the history of Klein and Hilbert in that context. On the two examples, unless + b = - b is some special property you're defining, yes it is hard to escape 2 b = 0. However b =/ 0 should then be sufficient to qualify the contradiction? In terms of entropy, a concept I find exceedingly difficult, I would phrase it to be "possible degrees of freedom" for a particular thing under consideration. Energy in a system or a chemical tending towards lowest equilibrium value I do not think necessarily goes against the tendency towards increased entropy: a molecule in a ground state of excitation still has the availability to be excited to other entropic forms. I might even go so far as to say an energetic system that is excited may have less entropy than the one in a lower state, but I don't understand entropy well enough, and I'm not sure the excited state necessarily precludes the other degrees of freedom towards to the ground state or is active to reduce/increase entropy. I think physics is trying to do that, too, don't you? In order to make the scheme explanatory I would agree there are some extreme conceptual difficulties.

I agree Mathematics is indispensible to Physics in its descriptions. I do not think that the approach to their topics seperately should be construed as antithetical. I think this comes from the conception that mathematics in its development has not always needed to correlate its constructions with any tangible reality, whereas physics is concerned with precisely trying to describe what can be observed as reality. However, I think there have been many times where mathematical developments that seemingy had no physical reality came to be found to be useful in descriptions of the natural sciences. Perhaps you're saying that mathematics is more akin to logic in requiring self consistent axioms, whereas physics has to account for contradictory (i.e. not necessarily self consistent) phenomena? I do not necessarily agree that mathematics is or would like to be axiom based, but rather that it is constrained under axiomatic sets in some formulations (like physics is in some of its specific formulations) to maintain self-consistency, remain coherent and logical and thus create a system that can express ideas with mathematical rigor. I do not think that setting axioms (mathematics) vs. establishing principles (physics) can be said to be truly antithetical approaches.

That is to say, I am paraphrasing what I've read without re-checking everything. I think the idea is that quantum gravity as an emergent phenomenon can explain gravity writ large. What is going on with the electric field lines at the event horizon of a black hole? Or out from the theoretical white hole? GR reduces to Newtonian gravity when you remove the equivalence of inertial to relativistic masses? Magnetic fields can be induced by current flowing. Is there a reliance for G.R.'s explanation of gravity to have the existence of magnetic monopoles, or what were you alluding to? Or if you would explain what you know about monopoles vs. dipoles and how that's relevant I would appreciate it. If magnetic field lines are induced to run along the geodesics of curved spacetime I do think that looks like gravity.

I am spit-balling. I have been reading The World Treasury of Physics, Astronomy, and Mathematics, Ed.: T. Ferriss, Fwd by: C. Fadiman: 1991. From Wheeler, we read that Einstein's idea for G.R. was to get rid of gravity in order to re-claim it. Rather than direct force attraction between gravitational masses, relativistic masses were under a sort of tension along a curved, complexified time and space. There he was combining the ideas from Riemann on closed or open spaces and geometries, and Mach on acceleration being reference-frame dependent. However, I think there is a need to assign a cosmological constant to explain the expansion of the universe. I think that this is a close or replaceable corollary with the uneven repulsive>attractive force interaction pairs or triplicates postulated by Suchard. From S. Weinberg, we learn that early on in cosmological expansion there is little neutron-proton material, and the interactions are: *antineutrino plus Proton yields positron plus Neutron (and vice versa) *neutrino plus Neutron yields Electron plus Proton (and vice versa) and that since we have been experiencing expansion, cooling to 3 degrees Kelvin, and a preponderance of increasingly quantized photons(see also G. Maitres) that've absorbed heat energy relative to the neutrinos the wavelengths of which have bounded out as inverse to the temperature which has decreased orders of magnitude. So we have the standard model, with the excitations of particles (silly strings) and the ideas of creation and annihilation? And what about nucleation -- Maitres posits that the nucleus is contiguous protons even through heavy elements! What do you think? A proton-neutron disparity develops to the order of 86:14, IIRC, and the masscharge of a neutron is significantly greater than a proton; and the thermodynamics of cooling dictate the matter-antimatter component of the energy in preponderance over the nuclear particles. **Edit** I got off track. So, whereas G.R. gravitation needs magnetic point charges as I rephrase your postulate, the theory of quantum gravity would use gravitons -- conceivable as a string with seperated charges inducing self-interactions akin to Newtonian gravity + universal expansion or Relativistic Gravity with cosmological constant. I don't know about quantizing gravity with gravitons -- but I think that that will have to be experimentally verified. As for quantizing time with chronons, I don't think that can be quantified but would have to be qualified obligatorily by the equations' or measurements' makers. I think we need Galois' Group Theories, Algebra Geometry Trigonometry? I'd bet I'm doing a Gish gallop, so I'll refrain from the usual reference manual quote. studiot, what do you think of the footing for algebraic quadratic roots as being four part? Negative roots having two compositions as do positive roots. Also, I'd say what you cite as a contradiction will show up in the unit's definitions.

Classic and alternative definitions for mathematical fields, wrt axioms, constructive mathematics: Sure, it is word salad. I don't know how to account for that other nucleon, how massive it is, how massive the proton is, what the equivalency is between mass, charge, and energy; how any conservation or interconversion should be. As I mentioned with the Suchard paper, it is possible that potential energy can be stored in an accelerating frame. The connection is that what is taken as universal gravitational attraction, dependent on both mass and distance, could be accounted for by a potential (although I'd call it kinetic) energy. That there could be long-distance weak attraction, and singularity type situations accounted for by charges, instead of mass at close distance overpowering other forces? Word salad. I will suppose you've read the whole discussion. If you think that the question of how to define certain square root mathematical objects does not have implications following along the lines I've gone to discuss here, please continue to probe. I think there is sense, and I've noted your advice. What of the issue of the magnetic monopole and dipole? I do not see any need for magnetic point charges here. All I want is induced magnetic field lines to try and describe gravity. Do you think the magnetic monopole is a sure bet, as most others seem to think?

Foundations of the Quaternion Quantum Mechanics "

Foundations of the Quaternion Quantum Mechanics https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7766457/

Not that I actually know that. Here is an attached paper as .pdf: Surprises with Logarithm Potential by Debnarayan Jana Dept. of Physics, University College of Science and Technology 92 A P C Road, Kolkata -700 009 W.B. E-mail:djphy@caluniv.ac.in 12 pages on logarithmic potential energy, independent of mass Surprises with Logarithm Potential by Debnarayan Jana Dept. of Physics, University College of Science and Technology 92 A P C Road, Kolkata -700 009 W.B. E-mail djphy@caluniv.ac.in.pdf

Mass charge equivalence, e.g. equating limit momentum to charge of proton, or other nucleon. An algebraic field of quadratic irrationals could map to a unit space of the reals via Minkowski's ?(x) function or an alteration thereof? The field in physics as I best understand it wants electric and magnetic lines and geodesics for motions described as geometric spatial translations of algebraic equations, or types of algebraic function equations? Path-over-steps: summations to account for all indeterminate paths leading to the point where the measurement is found to be made. I haven't finished reading it.

I read @J.Merrill's "question" to be a declarative statement, and something about the syntax and formulation were so offensive to my thinking I don't think I even registered a question. I may re-read the original question. The "graph", with pictures, of time vs. mass or whatever it was was there, too. And apparently the presentation of this was a school project. As to your proposition, I'm uncertain about the arrow of time or what breakdown process you're describing. I do think we are able to describe spacetime mathematically and are doing the mathematical operation you mention to interpret measurements of spacetime. Thanks to all for the discussion here.

Comments: issues with source credibility of Suchard paper, gravity v. magnetism wrt force directions, monopole v. dipole. From Appendix B: The paper is pointing at a need for experimentation, and it isn't a few buzzwords: it is a geometric derivation of the geodesics we take as the gravity field, and it is positing that a further development of the Standard Model may be elementary particles splitting into positive and negative halves generating self-interactions. These are things that I was positing and so why I posted the paper. The paper was produced with some specific interests tied to industry, and so other than credibility you did not have anything to address to it other than magnetic monopoles vs. magnetic dipoles? I am not positing anything about magnetic monopoles, but yes of course more explanation on magnetism is obviously warranted. Chronons are not Vaknin's theory of 30 years ago. I don't think the paper is really based on Vaknin's theory. They are quantizing time, and I haven't finished the Royal Society paper and I shouldn't have posted it as a distraction. But, the author there is developing a Hamiltonian while treating time through coarse graining. Off on a tangent, of course. I did explain I thought that, "why an only attractive force is the same as one that is both attractive and repulsive", was covered by the unequal actions of positive charges acting on neutral charges and negative charges acting on neutral charges as well as on each other was the reason for apparent normal gravity observations of small masses at a distance. And how massive charges could be accounted for as storage in a moving field. I sense the pressing issue of the monopole, but I'm not there yet. I think I repeatedly addressed your issue with source credibility on the Suchard paper. All I intended to address wrt magnetism was field lines and then equating those with the current description of long-distance gravitational action. I have gathered that you are a constructivist in mathematics? For number theory I thought we'd established that: set of numbers from infinity (we take it that prime numbers exist; excuse platonism) numbers can be multiplied by themselves 4x multiplication gives number squared adding squared numbers can define integers The number theory is touching on imaginary numbers, looking to make them a set. This then results in addressing other things. The name of the thread has two parts.

Fiber or other artifact. Microfilaria in urine at magnifcations, but it doesn't have a macro helminth head afaik like 100x10. Stain it?

To use a number theory incorporating a set of values for i that can assign spatial dimension or vector quantities to z = a + bi, 3 part quaternion: a + bi + cj + dk, 7 part octonion, 15-16 part sedenion. Perhaps the real number component could now be related to time instead? To get from number theory to uft.

From what I understand the paper is a formal derivation of a tensor that would match the force of gravity as a weak potential energy stored in a constantly accelerating frame. It treats time differently than in the spacetime conjunction of G.R. This can be an alternate explanation of general relativity, as Einstein formulated the idea of the gravity field as being indistinguishable to an observer under a uniform acceleration. There is an argument developed that electric and magnetic fields and forces arising from charge seperation creates self-interactions that can explain the four fundamentals forces, and I conjecture that the magnetic field lines are a background curvature along lines of net gravitational potential energy (but also potentially massively repulsive) that is equatable to the gravity field of general relativity as currently formulated.

From the prior cited article on Octonions from QuantaMagazine: From the introduction to the paper by Suchard:

1 2 3 4

As a graph. Any masses, extension, self re-inforcing electromagnetics?

@swansont, I drink I'm not going to look it up. Comments on the math here? How can we make half roots equal cosh(x) for hyperbolic Pythagorean theorem sinh(x) cosh(x) We take cosh^2 (x) − sinh^2 (x) = 1 and extend the complex plane to 4 quadrants by negative real access and "negative imaginary" 3rd and 4th quadrant access as positive square roots of primes. More legitimate complex plane by tetrapartite roots. ++ -- +- -+

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Au contraire, what is juxtaposed is an imaginary component for the time-dimension, which throws that sign before the multiplication (which should be quantized), thus making it opposite sign from the spatial dimensions. Minkowski space is 1-D: taken as a Pseudo-Euclidian (slightly bent) map of spacetime, no? It is not quite yet hyperbolic, but more like elliptic -- you're not presuming it's a flat rectangle, are you?? Elliptic I'd call positive cosmological constant, equatable to Gaussian curvature >0. Towards spherical or de Sitter at 1. Reflecting through the origin to generate a hyperbolic -1 Gaussian curvature with an elliptic asymptote we have hyperbolic geometry, a la Lobachevsky-Bolyai. Dieing early, sounds like W.K. Clifford and N.H. Abel, etc. We on Fire1. 1Pascal 3,4,5 ray spallation. Tear the roof off this mo**erf**ker2. 2Banks

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Borax Potassium Iodide Check mixture for explosion beforehand. Borax: possible oxidant SSKI: possible oxidant Mixture should be ... effective against fungus. Mix borax into warm/hot water, add SSKI. SSKI: 1g Potassium Iodide + 1 mL distilled water + = 1g/dry wt. + 1g/mL = 100g + 100mL : salt + solvent = saturated solution Borax ... Sodium Borate Heptahydride. Anti-Fungal. 4tsp. + 4tsp. boiling water for mirror injection treatment, assuming you can succuss (shake) meter after injection.

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What I am proposing is electric field lines that do not form a barrier of an asymptote between charges, but rather extend to infinity as they pass into another dimension. Upon extension of 1-D mass charge to 2-D we have curvature to space having moved into time. The paper from the Royal Society publication I cited has "coarse granulation" of time co-ordinate to account for Time Reversal symmetry violation in making the quantum Hamiltonian. From the prior paper on geometrization accounting for a tensor of stress-energy-momentum given acceleration, we are equating general relativity as it is formulated as either a pervasive gravity field upon inertial masses = gravitational masses to a uniformly accelerated frame, from which it is indistinguishable. The paper's author produces the tensor that would emerge from charge seperation, accounting possibly for weak, stong, and electro -+ "gravitic|magnetic" -- 4 charge!~seperation force phenomena -- in the context of a constant positive cosmological constant (de Sitter space, which is equatable or equally explainable in Anti-de Sitter space of constant negative curvature for the cosmological constant). The Royal Society paper demonstrates a problem with the quantum treatment of time. The chronon paper treats time as theoretical quantiziation issue wherein frame of measurement when made and frame of measurement being assumed cannot necessarily be correlated, as far as I get it, and so we must quantize time to have differential physics equations for description given conditions; the explanation is a uniformly accelerated universe with self-interactions from charge seperation accounting for gravitic forces: both a stronger gravitic force and a weaker anti-gravitic force if I understand it (net gravity on geodesic lines of least energetic falling). The Royal Society paper proposes a different mechanism for Hamiltonian (time evolution Energy description) formulation due to violation or accord with Time reversal symmetry (I think it is saying that the normal quantum interpretation implies time evolution, an Arrow of Time, but what they find necessitates a Symmetric Arrow of Time). Please read the Chronon paper through, and account for what the geometer is deriving as an equivalency to the stress-energy-tensor, and how this could have implications for an alternate basis for G.R.. Examine the electric field lines collapsing. Instead, let them run off to a point off the graph (or into an asymptote on a 2-D hyperbolic map); electric charge seperation and resulting 3-D spin and 4-D momentum generation induces self-referential forces of inductance, and magnetic field inductance, which magnetic field lines are malleable as lines of force, as demonstrated in the plasma furnace. See Alfven waves.