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

Hi Andy,

Nice Essay,congrats.

You know that I strongly appreciate your previous works on massive gravitons, early universe and quantum gravity. This Essay seems to be an interesting summarizing of your ideas on the above cited issues with some interesting speculation on Unpredictability. Eq. (5) is intriguing. Do you think that this can mean that it exists a third massive gravity wave polarization arising from the cosmological constant? This is also endorsed by the issue that the final addendum of yours Eqs. (4) and (5) is nether else than the cosmological Ricci scalar! I will think about these two interesting points. I am also honored that you cited my MPLA paper in ref [12], thank you very much.

My global judgement is that you wrote a remarkable Essay which deserves a high score that I am going to give you. Good luck in the contest!

Cheers, Ch.

Hi Dr Beckwith,

I liked your general essay trying to unify this inflation, cosmology and this quantum gravitation. Congratulations.

Personally I have reached it and I work about the mathemtical formalisation, I renormalize this puzzle and I have quantized it in all humility,I have thought beyond the box if I can say.

My main approach was to consider a Before this inflation in fact simply with new paramters to superimpose, I have made the same for this standard model in superimposing a new logic encoded .

I beleive that all is made of particles in a kind of gravitational aether sent from the central cosmological sphere, it is there that something codes and transforms the E in matters for me.

And so I have considered 3 main E8 and finite series of 3D spheres instead of points or strings. I have a specific serie primordial for these series, the same number than our cosmological finite series of spheres in fact and oddly we see the Dirac large number appearing.

So in resume I consider so that all is made of particles coded and so we have not a 1D main Cosmic field and strings at this planck scale , but Particles. That respect also the Waves particles duality.

See so now my general reasoning with these 3 E8 , we have one main E8 for the space vacuum with these finite series of 3D coded spheres playing between the zero absolute and the planck temperature, a Little bit if I said that this central cosmological sphere is a super matter and after distributes and codes the finite series of spheres where the space disappears when we apply a specific serie, take a central biggest sphere and after apply the primes for example, so we put smaller around and we continue, the number two becomes relevant for the two other E8 considered like fuels, one for the photons and one for the cold dark matter. So when these 3 E8 fuse, they create our geometries, topologies , properties of matters.

I have considered for this the Ricci flow, the Hamilton Ricci flow but like codes inside these series instead to consider the fields from external causes. I have considered also an assymetric Ricci flow to explain the unique things, the lie derivatives, the lie groups, the poincare conjecture,mthe topological and euclidian spaces and other mathematical Tools.

So for this quantum gravitation, I have considered the cold DM encoded also in nuclei , and series of quantum BHs and main codes farer than our nuclear forces, so I have simply changed the disatances and mass to respect the newtonian mechanics and surprise, I reach this quantum gravitation.

The problem was for me that the thinkers have only considered the photons like main essence and have also considered that all was made of fields. But my reasoning seems for me more logic because the particles are more foundamental, we cannot have fields without particles in motions rotations oscillations in contact with the Environments made also of particles, so we can have particles without fields without these motions but not the opposite, that proves that all is made of particles in a kind of superfluid considering this aether, vacuum , space.

Cosmologically speaking I work about my theory of spherisation, an optimisation evolution of the universal sphere or future sphere with these 3D quantum and cosmological spheres, I beleive strongly that even if we have evidences for this BB and the CMB, it is just a step but we have a deeper logic at this inflation and Before, this central cosmological sphere intrigues me a lot, it is there that this maybe infinite eternal consciousness transforms the E in matters and create and sends the main codes with these series of Spheres and these 3 E8 to rank the properties of matters and E.

The evolution is an important point is my theory, it is the meaning of the spherisation, I don t tell that all will be spherical but just that the universe is in optimisation.

Philosophically speaking it seems logic for me all this. I have really doubts that this universe has only created photons and that we had an infinite heat Before this physicality and that this universe oscillates with the strings these photons to create our reality, Witten abd Einstein have created a kind of prison for me and the thinkers now cannot go deeper and Think beyond the box.The Energy outside so for me is a thing that we cannot define and is not an infinite heat, it is different.

It seems odd, the strings have some relevances for the rankings of fields in maths but that is all, they are not foundamental for me simply. the D branes, the ADSCFT correspondance, the dualites, T , S or the Mtheory or this or that are Beautiful maths but all is false if these strings are not our foundamental mathematical and physical objects simply and the same for the correlated philosophy with this 1D Cosmic field.

"Note that the Standard Model of Particle physics has scores of experimental inputs. It is a dazzling success in many ways but we are finding it extremely tough going to develop further beyond that model. We may have a similar situation with respect to massive gravity and its purported linkage to inflation ..."

How might the massive graviton hypothesis be compatible with Lestone's theory of virtual cross-sections?

Those who are interested in the hypothesis of a massive graviton might want to study the following:

Bachas, Constantin, and Ioannis Lavdas. "Massive Anti-de Sitter gravity from string theory." Journal of High Energy Physics 2018, no. 11 (2018): 3.

arXiv preprint, 2018

I say that Milgrom is the Kepler of contemporary cosmology -- on the basis of overwhelming empirical evidence. Banik and Kroupa have recently suggested a rather decisive (but difficult) test of (non-relativistic) MOND.

Banik, Indranil, and Pavel Kroupa. "Directly testing gravity with Proxima Centauri." Monthly Notices of the Royal Astronomical Society 487, no. 2 (2019): 1653-1661.

arXiv preprint, 2019

Hello Mr Knight,

I can understand , but if these strings are false , so the gravitons cannot be the answer because they come from the strings. All seems a question of philosophy about the origin of our physicality and these foundamental mathematical and physical objects at this planck scale. We can tell all what we want , the gravitons don t permit to renormalize and quantize this quantum gravitation, see my reasoning above , it seems more logic when we consider main codes farer and that we change the distances and mass considering that our actual standard model is just emergent. We must Think beyond the box to reach it at my humble opinion,Regards

lol oops sorry I confound the name Mr Brown, I am sorry, I cannot change , regards

Dear Andrew Beckwith,

I always enjoy your essays and papers, most of which I have read, but I generally fail to understand them satisfactorily.

I keep several of your papers handy on gravitomagnetism, as I believe that this is where we most overlap. As you know, the linearized equations are based, not on mass flow, but on mass flow density, and the beautiful thing about 60 efolds is that flow density is as big as you want it to be!

I see the gravitational field as a super fluid, in the manner of Volovik (The Universe in a Helium Droplet) and Kerson Huang (A Superfluid Universe). I believe that turbulence in a superfluid can shrink to a vortex, hence electrons and quarks. Those vortices that fail to go toroidal become solitons, probably neutrinos. I am unsure how these traveling gravitational waves differ from 'gravitons'.

Of course, the LHC, expected a quark gas from nucleus-nucleus collisions but found a perfect fluid (as I had predicted) and the energy densities in this little corner of the universe should behave as I state above. When people get tired enough with the stasis of the Standard Model, there is a whole new theory waiting to be explored.

In any case, I only deal with the easy problems, and I hope you will enjoy my current essay: Deciding on the nature of time and space.

My warmest regards,

Edwin Eugene Klingman

These gravitons cannot answer because the philosophy considering that all is made of fields like in the theory of strings don t consider the evolution and a kind of infinite consciousness creating this physicality, there is a problem philosophical, we are probably inside a physicality made of coded particles.

Hi sorry to both of you, the strings and witen and Einstein have really created a prison, the thinkers cannot consider a deeper logic now and the majority try to explain our unknowns only with the photonic electromagnetism ....it is odd generally, see well the problem considering the evolution and the philosophy and ontology about the strings like if something that we cannot define oscillated the fields, waves to create this physicality. Why so this thing beyond our understanding don t stop with an instantaneous oscillations and resonances the human stupidities ? you see well that we have a general prpoblem with the strings-...

Hi Professor Beckwith, I have just considered Before this physicality a kind of inifnite eternal consciousness , en energy that we cannot define, I understand that the sciences Community is divided and that the others consider that we cone from a mathematical accident like if we had an infinite heat Before this physicality and the probabilities and statistics so have created a physicality. But for me it is odd we need a kind of creator of codes and transformations matters energy. What I find relevant is that all our best past thinkers like Newton, Tesla, Einstein, Borh, Heisenberg,Maxwell, Galilei, Euler, Fermi, Lie ,Cantor, Godel and so more had understood that something codes and exists beyong our understanding, for me humbly we cannot understand generally this physicality in evolution without this paramter but it is just my opinionb of course, we cannot prove our philosophy in fact but it seems so evident generally, Einstein said that God does not play at Dices, we can consider this parameter in respecting the pure determinism like a God Of Spinoza, best regards

A thing important Dr Beckwith is that it is difficult I recognize to convice the thinkers about our own philosophies, in general we cannot change the philosophy of persons because lol we are all persuaded and that we have encoded our informations and conclusions. But frankly when I see this generality of our physicality, how is it possible that all this universe comes from nothing or a mathematical accident? it seems anti deterministic considering the main causes and informations, this universe is a system in evolution and complexification made of particles and fields, Waves creating geometries, topologies, matters and correlated properties, it d be very odd to consider that we come from nothing. Of course all this is philosophical and ontological but maybe it is simply easier to understand this physicality about these transformations matters E with this parameter coding , I have thought a lot about this , why we are and why this thing have created this physicality ? maybe simply this energy was alone , it is very simplistic of course but maybe we create an incredible thing simply evolving towards an unification of something. But we cannot prove nor me nor the others persons seeing differently, all what we can is just to encircle with our limitations this physicality with determinism in tryiong to complete with rationalism and logic our laws, axions, equations, it is a kind of wisdom maybe to recognize this and humility.

ps I accept and respect all the others philosophies of course , we cannot affirm in fact and can share ideas , extrapolations

Hi Andrew, Interesting essay. The major violation of the maths percentage didn't matter as measured in absolute terms it passed! But your limited text did get your propositions across well.

I certainly agree a good marriage of experimental data with theory built from on sound logic is the ONLY way ahead, and often forgot. But is that not a problem when logic itself is beset by paradox? I suggest how that can be overcome in my own essay, with improved foundations.

I confess I'm no fan of 'gravitons'. Are they not just a dubiously founded theoretical 'placeholder' substitute for a better derivation of 'action-at-a-distance'? Again I suggest a more consistent option, and using your own methods!

I agree your excellent analysis that using the approach you outline does mean the limitations you identify are, in terms of advancing understanding; "all we can do" and "the best we can hope for" and certainly that we need a "fundamental re-think" of how we relate data and thoeretical models, using "robust experimental platforms" to avoid, or rather; escape from current! ..dead ends.

But do you not think the data is there when we chose to search? I did and found it! much buried in massive sets, but lets just take the peculiar CMB anisotropies. Will not a theory producing those as well as more familiar data be 'a priori' likely to be correct? That's what I've done but ignored or dismissed in our current belief based system! Nice you seem to agree that needs changing but how is it done?

I think you'll like my essay, though an entirely different approach and theoretical construct to yours. I'll be interested in your comments.

Luckily content isn't a scoring criteria so that won't affect me scoring yours well.

Best of luck in the contest.

Peter

Andrew,

Your answer was exquisitely clear:

"This essay is focused upon the idea that certain inputs into physical models cannot be LOGICALLY deduced but have to be used to get connections to the actual physics. It is an old argument which is a repose to Hilbert who really believed that physics could be made purely axiomatic , with logic thereby removing the need for experiment. Godel pretty much destroyed that argument, on the part of Hilbert, and I am raising it again as to the issue of the graviton itself and e folds of inflation."

That is a much deeper goal than is apparent in the equations themselves. I certainly agree with you, and toast your smoking of Hilbert.

Edwin Eugene Klingman

Dear Andrew,

I am very happy to see you continuing your program to apply Klauder's enhanced quantization in an original way. Very interesting and topical your connection between the e-folds and Gödel's incompleteness theorem. I wish you good luck with the contest!

Cheers,

Cristi

Your paper is interesting, and it would be curious if the mass of the graviton were related in some ways to the entropy and maybe efolds of the inflationary cosmos. Of course detecting the mass of a graviton m_g ≈ 10^{-62}g is a daunting proposition. I think the putative mass of the photon in a Proca equation is bounded below 10^{-80}g at this point. The QED field is relatively strong interacting, so these measurements can be made with some degree of precision. If I recall these involve measurements of the geomagnetic field and of late the Jovian magnetic field. An analogous measurement would have to involve the Lense-Thirring or frame dragging effect.

I am not sure where the mass of the graviton comes from. I tend to like conformal gravitation, and if the graviton has mass this would break conformal symmetry. So, there must be some mechanism whereby the graviton gets its mass. There would be some process, such as a Ginsburg-Landau mechanism, where the graviton would acquire mass. However, as with such processes this would imply the absorption of a Goldstone boson in the field. Hence there could in fact be a spectrum of massive gravitons. Such things do occur in N = 4 and 8 supergravity, where there is the breaking of symmetry and the occurrence of massive gravity. The breaking of E8 symmetry with the 8 principal weights for gravitons gives a Zamolodchikov spectrum. Of course, there is a little problem in that this spectrum is near the Planck scale. However, that might be rectified if there is some STU duality between two copies of E8 in the heterotic E8Г--E8. In some sort of S-dual setting between two sets of masses m_g and m'_g, m_gm'_g = constant. The large massive gravitons are dual to the tiny massed gravitons.

That is a speculation of course. I suppose that was why I give your paper a 9 and not a 10. The occurrence of a graviton mass involves some serious implications for quantum gravitation. I suppose this is a missing gap that seemed problematic. However, overall your paper is interesting, and it would be curious if there is some connection between graviton mass and the initial entropy of the universe.

Cheers LC

This is a bit abstruse Andy...

However I'm somewhat familiar with your research program and sources. So I'll begin by explaining first that you are working in a framework where the graviton is minimally-massive. That is; it has a vanishingly small mass, but this contributes to things like cosmic expansion and the reheating phase where by assuming the graviton has mass, you can explain the missing piece of the universe normally attributed to dark energy and dark matter. I should also mention that this work ties in to Jack Ng's infinite quantum statistics, and employs Klauder's enhanced quantization as a kind of CFT.

It is brilliant to connect the graviton's mass in this case to uncertainty. But the way you connect it back to the organizers' questions is tenuous. You do not clearly explain how the one regime connects back to the other, although to me it is fairly clear. The reader would need familiarity with your prior work, or to be conversant in minimally massive gravity, to grasp some of your points. So you get a high grade from me but not full credit. I hope these comments will help you or your readers to clarify some of the issues.

Is there something more you can add here, to help us connect the dots?

All the Best,

Jonathan