How to obtain a mass of a graviton. Does our formulation lead to Undecidability, Uncomputability, and Unpredictability issues ? What are the implications of such Issues ? by andrew beckwith

It seems to me there are various problematic aspects with the ideas discussed here.

For one, it has long been known that theories of a massive graviton suffered from serious pathologies, including a Boulware-Deser ghost and a discontinuity with general relativity in the limit where the graviton mass goes to zero.

Nowadays when considering such a thing one is drawn to rely on specific schemes that manage evade those problems such as de Rham-Gabadadze-Tolley model or bi-metric gravity theories ( i.e. theories with two spacetime metrics). In any event, all those proposals are based on specific action functionals which differ substantially from the standard Einstein Hilbert action with a cosmological term, as used in eq. ( 1) and eq. ( 2) in the present work. In fact nowhere do we find any hint of what the "new action principle of the massive gravity" under consideration here is supposed to be.

On another hand, and on a different aspect I am also quite puzzled by the following statement:

"I also argue that this limit (i.e. a question concerning the link between experimental results and the actual number of inflationary e- folds) and is a physics counter part to the Godel incompleteness axioms, i.e. where in [14] the emphasis is upon the incompleteness of axiomatic logic, which Godel stated doomed Hilberts dream of a fully axiomatic treatment of physics [15] ."

The point is of course that as far as I know Hilbert never dreamt of a fully axiomatic treatment of physics ( which in contrast with math requires complex interpretative discussions involving ontological as well as epistemic issues). Hilbert certainly dreamt of a fully axiomatic treatment of mathematics and that dream was shattered by Gödel's famous results.

Dear Andrew,

I am not a fan of bosons as fundamental force particles (except for Higgs), and can provide alternative suggestions for photons, gluons, and W/Z bosons. Nor am I a believer in gravitons, as I have formulated my own 'action at a distance' theory of gravity using strings of what I suppose are Higgs particles, although I call them ginn (or aether particles). Because I have a working particle theory I decided to do a back of the envelope calculation of their (string) gram equivalent mass and got a number 10-34 g which is some 28 orders greater than the 10-62 g you mentioned for the graviton.

Regards,

Lockie Cresswell

Hilbert's plan might have worked...

Had there been a detailed knowledge in his time of fundamental mathematical objects like E8 or the Mandelbrot Set. Now we have a vast array of knowledge about specific attributes that was lacking in that time. We could only guess that something like the Monster group existed at first, but now we know a lot about it. This kind of knowledge will over time provide a linkage that evades Gödel. Once discovered; these objects reveal fundamental patterns in Math itself. We might not guess at their form, but once seen it can be grasped and used as a pivot point.

All the Best,

Jonathan

Hi all, this discussion is very interesting, but If I can, we arrive still about a very important philosophical problem , what must we consider even if that can converge like philosophy. The strings consider that all comes from fields with the 1D main field at this Cosmicscale connected with 1D strings at this planck scale and so after we create the 11D with the different geometrical algebras, and so we have these gravitons wich can converge with the supergravity, the Mtheory and branes. But if the main philosophical origin is not correct, so all the geneality also is not correct. Like you know I consider particles coded and 3D spheres and 3 main systems of finite series , one for the space and two fuels, photons and a cold Dark matter, but I have the same problem, I cannot affirm or prove but we are all persuaded lol of course, in all case it exists maybe a kind of convergence with the 3D spheres in motions and oscillations with these fields, maybe even a kind of conjecture probably with Poincare and Thurston. But it is really the main philosophical origin of our geometries, topologies, matters, properties and fields the real problem. Maybe these strings are a kind of fashion and that it was the only one theory taken into account, but observe well the generality of this universe, we have probably pure 3D spheres coded at all scales, if the particles are 3D spheres, so we understand why the universe is a pure 3D and all the Chemistry, biology, mineralogy, it is like a foundamental for me this 3D and the rotationg oscillating 3d Spheres. Of course I must prove , but it is not easy due to limitations in technology and knowledges. I like this E8 also for its geometry and beauty , it can be relevant to insiert these finite series of 3D spheres instead of points or strings at my humble opinion and like said Jonathan we can utilise these relevant Clifford algebras for the rankings. I know that it is difficult to change a philosophical line of reasoning because we are all persuaded and we know also that our Community is the most vanitious Community on this Earth probably lol, me too I am not perfect and I am persuaded but with humility it could be well to see the convergences and conjectures between fields, Waves, particles , like a deeper analysis of this wave particle duality in fact.

An other point that I have remarked to conclude also is that this evolution seems essential at all scales, it is the meaning of my theory of spherisation, the optimisation evolution of the universal sphere or future sphere, this evolution seems important, the biology evolves and the consciousness also even, but I ask me how we must consider this evolution at this quantum scale because it seems that we have stable series and others no, maybe this quantum scale is also under an evolution but how, where and why , it is the question.

Friendly

Professor Beckwith,

I think perhaps you need to be told the vDVZ discontinuity in Daniel Sudarsky's comment is not a subjective issue, but one of hard Maths. Basically; it arises because giving a graviton mass means it has 5 polarization states instead of 2 (0, ±1,±2). It turns out the spin-0 modes are more strongly-coupled than one would like, creating a divergence from the predictions of Relativity - called vDVZ discontinuity (where Zakharov is the Z).

This arises in ALL cases where the graviton is similar to Fierz-Pauli, even when the zero mode approaches zero mass (starting from a massive state), but there are exceptions. Using a KK-based theory; you are working on an island where vDVZ might be avoided. But you would still need to prove that or forge a firm connection to one of those exceptions. In my work, as in DGP gravity; the portion of the universe containing 0-mode (Higgs-like) gravitons is trapped behind a fold in a brace - effectively at infinite distance. And bigravity lets you renormalize.

But there are other roads to analytic completion without complications. You can find an example here:

No vDVZ Discontinuity in Non-Fierz-Pauli Theories

More later,

Jonathan

Whoops...

Should be; "fold in a brane" spell check must have 'fixed' it.

JJD

Johnathan I am well aware of the issue in terms of massive gravity. This is precisely why I tried an approach to a limiting value of graviton mass using a relationship to 5 dimensional cosmology, akin to earlier Kaluza klein Models. I will say more about this later

Hi , there are the same problems. If we take this approach of van Dam-Veltman-Zakharov (vDVZ) discontinuity with a Minkowski space, it seems to arise in (anti) de Sitter space. But the problem is the act to consider only this GR and the photons like I told and the philosophy correlated with branes and modes, that cannot quantify this quantum gravitation.The real problem is the tensors and this relativistic prisons and the strings , you can utilise all what you want like maths with the modes, frequences, branes, the ADS CFT correspondance or others, that will not change, because the problem is that it lacks a main new thing to superimpose. The massless limit and the massive graviton propagator are for me fake Tools and reasonings. We retrun about this main philosophical problem.It is mainly due to consider this minkowski space time , the GR and the photons like the only one piece of puzzle and these fields like main essence. Think beyond the box to reach this quantum gravitation, consider thei universal balance between cold and heat and this cold dar matter encoded in nuclei and sort the fields also. Regards

Thanks for chiming in here Steve...

You are correct, in at least some of what you say. The view with tensors is limiting in the same way a square lattice is. People working in that framework imagine the grid implies reality is grid-like, but it is another form of the 'blind men and the elephant' problem, with the characteristics of tensors being the blindness. Nobody sees enough of the picture to capture the whole elephant, that way.

Jonathan

lol, Thanks also. I just explain my points of vue to give some food for thoughts humbly, I search like you and all answers, whaht I find important is to Think a Little differently that these fields like origin of our reality, I have remarked that the strings are a kind of fashion and now the majority focus on this theory like a foundamental and they create so pertitions mathematical to explain our fields and unknowns, but they forget to consider these particles coded like main essence, I cannot affirm of course the main origin physical and philosophical like all, I just discuss but it seems really for me that these coded particles are the main piece of puzzle and this 3D also. This 3D seems logic at all scales, the Chemistry, the biology, the cosmology are in 3D , so probably that the quantum scale also. I have explained this superfluid gravitational aether for the space, the main codes and the two fuels made of these finite series of 3D spheres having the same finite number than our cosmological finite series of spheres, and when they merge they create this physicality and their geometries, topologies,matters and fields, I beleive that these strings can converge because they are in motions , rotations and oscillations also, it is this conjecture between these coded 3D primordial spheres and these fields, branes, strings wihc intrigue me a lot. I have remarked an important point about the philosophy of strings , they don t take into account the evolution, these 3D spheres seem a better explaination for this evolution. You know Jonathan I don t want to be a problem for the thinkers, searchers, I just share ideas, I am not here to destroy the strings or to be vanitious or irritate, I just search answers. I agree with you , we know so few still, we need to encircle so many things and unknowns, we must accept our limitations and try to explain these unknowns, it is a big difficult puzzle all this, take care, I like how you Think, friendly.

I study the Clifford algebras and Bott periodicty for these spheres and I try to find a conjecture unifying the two different philosophical interpretations about this main origin of our universe, my 3D coded spheres or the fields, it exists probably something there to unify, not easy I must say.

the periodicity in the homotopy groups of classical groups, which proved to be of foundational significance for much further research, there is convergence with the K theory but I am interested to converge with the 3D coded spheres like primoridal essence as well as the stable homotopy groups of spheres. The quaternionic symplectic group becomes interesting for the homomorphism from the homotopy groups of orthogonal groups to stable homotopy groups of spheres, now in inserting the good number for these finite primordial coded series of 3D spheres, that can become very relevant with the Clifford algebras. This poincare conjecture also becomes relevant and an intrinsic Ricci flow more the lie groups, derivatives and algebras, and the topological and euclidian spaces, an universal partions exists in logic with these motions of 3D spheres, their rotations and oscillations more the 3 main finite series thjat I have explained, one for the main space, this gravitational aether and the two others, the fuels.

I have remarked an other relevance Jonathan , The Hopf fibrations on 2D surfaces of My 3D spheres permit to rank a lot of quasiparticles under excitations, these finite primordial finite series of 3D spheres more these hopf fibrations on their surfaces can permit to rank and discover many quasiparticles. The phonons, polarons,magnons,plasmons, excitons, are just a small part of all these rankings.

The rankings with the Hopf fibration son 2D surfaces, more the motions rotations of these 3D finite series, one for the space, and the two fuels can show us an universal partition if it is well utilised, see these relevances for the ranking of all these 3D spheres with the angles of rotations, sense of rotations permiting to balance and di fferenciate this negentropy and entropy with the cold and heat, the photons and this cold dark matter encoded also, in fact we can rank many things, the particles, the fields and quasiparticles with the volumes of these finite primordial series having the same finite number than our cosmological finite serie of spheres ,more the fact that this space disappears with the gravitation space aether, the main codes and the two fuels. We can rank the motions, the volumes, the 2D surfaces with these hopf fibrations, the densities due to synchro, sortings, superimposings, the moments, orbital and spinal rotations, the mass, this and that, in fact the combinations are infinite.