Using Klauder’s Enhanced Quantization to set a bound to the Cosmological constant, in Pre Planckian space- as a way to ascertain the most important fundamental physics question. by Andrew Beckwith

Andrew,

OK, it's not the type of essay a 'speed read' can penetrate from any distance away.(I do that for 3x the essay number first order evaluation). But on second reading, after Kaluder's I got in, and I found it a world full of wonders, nicely put together, though I'd have liked a little more English and less symbolism!

Novel, original, interesting and informative and fundamental it was, so that's a good score sorted.

As far as the derivation. As you may have seen I've mainly followed the older traditions after Zwicky, Rees, Smoot and Lahav of 'observational' rather than theoretical cosmology so I can't much comment. I'm familiar with the singularity and cosmological constant matters (see my recent linked in post re Sandage 2006 etc) but as you may have seen have derived a real physical cyclic ontology overcoming both. There may be some link but it wasn't clear to me. If you can see one do advise! or if you see flaws in mine do point them out.

I also have no issue with the 'space/time bubble concept, indeed I invoke it at all scales from sub Plankian up! so was interested in another view. I think all approaches are valid and none of my unfamiliarity with yours of course affects scoring so I'm pleased to give it due reward, hold on tight..

Very Best

Peter

dammit, logged me out! At least it's not punctiuated with 'n's and no gaps as mine are at present!

P

... there is no need for a bounce (cyclic in radius and time) when you have ralpha'/R. The universe is cyclic in mass and time.

Andrew wanted me to post something I wrote on my essay blog area. This concerns a difficulty I see with Klauder's quantization. I do this with some trepidation I must confess, for I have noticed that when I point to a problem with some claimed physics this results in down votes.

Here is the problem with Klauder's idea. I have to use parentheses for langle and rangle or bra-ket stuff because this system snags up on those. If we have quantum states П€(p,r,t) = (П€(t)|p,r) then the operators bf p and bf r (bf before letter stands for operators) act on the wave function

bf pbf rП€(p,r,t) = (П€(t) bf |pbf r|p,r) = (П€(t)| bf pr|p,r) = pr(П€(t)|p,r)

and similarly I can write

bf rbf pП€(p,r,t) = (П€(t)| bf rbf p|p,r) = (П€(t)| bf rp|p,r) =rp(П€(t)|p,r)

where r and p are just eigenvalues or numbers and so rp = pr. We can then conclude [bf p, bf r] = 0, which is a big oopsie. I hinted at this problem and he responded in a way that was a bit testy. There is a problem with pointing out a possible error in somebody's paper in that they can one-bomb you.

Klauder maintains we can have a position and momentum representation of QM simultaneously. This is generally not admitted. In your paper you use the Schrödinger equation i∂ψ/∂t =Hψ to get under "langle rangle" pdq - Hdt in the classical setting. This turns out to be alright in general.

Quantum mechanics has only one representation at once. Either one has the position or momentum configurations. This hearkens back to the Heisenberg uncertainty principle. The operators used in a representation act on the variables of that representation. Unfortunately Klauder is trying to do QM in incommensurate variables or operators.

Cheers LC

Andrew,

I agree that certainly the cosmological constant is a fundamental metric... and very constant.

I have read somewhat about the severe difficulties in computing it from theory, so I appreciate that you are searching out and testing new methods.

To be sure, I am not expert in this aspect. But to my thinking it would help a lot if GR theorists treated the temporal curvature as an imaginary quantity. That certainly eliminates the cosmological coincidence problem... so perhaps both problems resolve together?

Anyway, I am sure that there is more "what" to that which is "fundamental". For certain one must account for quantum algebra.

More to the point, our universe is merely the sum of its particles. So for the respective formulae to be consistent, both must have the SAME form!

Given that, and my assertion of a foundational formula, I'd suggest that you also read Sabine Hossenfelder's paper. It discusses some of the issues you responded to in Sec 6 at length.

Wayne

Dear Andrew,

Thank you very much for reading and for commenting the ideas from my essay.

You wrote "I would like it very much if you reviewed and commented on my essay, December 21, using this analogy to rate and review why I used John Klauders enhanced quantization. Awaiting your reply. i.e. this is a very relevant insight."

You seem to approach inflation and the problem of the cosmological constant using Klauder's quantization to obtain a bound on the cosmological constant. You seem to get this by equating Klauder's action and that of Padmabhan for inflation. You derive from this a bounce to avoid the cosmic singularity in pre-Plankian regime. I'm happy for your result on what you consider to be "THE outstanding problem and question of physics today", congratulations! I say this as a humble spectator of inflation and Klauder quantization, not being actively involved in either, so I don't know how useful my comments are to you, but I hope they help. I hope you'll get more relevant comments from Klauder himself. Success with your work and the contest!

Best regards,

Cristi

Wayne, you mean T-duality provides the bounce. That is quite possible.

Hello Mr Beckwith,

What a wonderful general essay.I loved how you take the problem of this quantum gravitationa and how you link with the pre planckian era and this inflation.One of my favorite.I asked me if you have already thought about the spherical coordinates and the lagrange euler method and also in considering the motions orbital and spinal.In all case your essay is relevant, I am wishing you all the best in this contest.

Best Regards

Hello Mr Beckwith,

Thanks for sharing.It seems a good road to better understand this inflation and this gravitation. I asked me if the gravitons which are bosons can be considered for this quantum weakest force.The problemm seems that they are bosons and that if this QG is not baryonic, so these gravitons are not the answer.This dark matter intrigues me a lot, I prefer to consider it instead of considering the MOND of Milgrom.Your works are relevant Mr Beckwith, a real pleasure to read these lines of reasoning, general.

Best Regards

Thanks for sharing, all this is very relevant,best regards ,