Merging holography and conformal cyclic cosmology by Penrose: is it somewhat meaningful at all?

[Tommolo]

Penrose's Conformal Cyclic Cosmology and Bousso Holographic Bound-compresso.pdfPenrose's Conformal Cyclic Cosmology and Bousso Holographic Bound-compresso.pdfHi there! How are you all?

I would like to share with you my highly speculative working paper about a phylosophical interpretation of holography that could be seen as a goofy way to merge holography model with Conformal Cyclic Cosmology via Raphael Bousso's Holographic bound on entropy. I am not at all convinced that the Weyl curvature could be an useful tool to determine entropy at the end of life of an universe or at the beginning of another one, or even inside a black hole. I try to use Bousso instead.

 

Here it goes the abstract, for those interested:

Quote

We suggest in this work a modest yet quite speculative idea: what if the Ω field in the Penrose Conformal Cyclic Cosmology (CCC) is noth that necessary after all? Maybe there are other ways around the problem without having to deal with the Weyl Curvature Hypothesis (WCH). The work is divided into five part. In part one we speculate about the meaning of the growing entropy, and the flowing of time towards states of less knowability of the given adiabatic system. We suggest that maybe another kind of approach is more useful than the one proposed by Penrose in his works, focused on the WCH. Maybe an holographic approach can give new, interesting insigth on the nature of time and the growing of entropy. We will use in this case a specific definition of “holography”: not as a bidimensional encoding of a volumetric image but as a volumetric display on an interior free space of projections of information encoding from the boundary. A way to visualize this is through the free space volumetric display based on the photophoretic-trap projections, where images are projected onto small particles floating inside an enclosed volume. We will take then a small detour in part two considering the physical meaning of the dimensionality of time, using non-conventional approaches like inductive dimension, Lebesgue covering dimension and Minkowski-Bouligand dimension to understand better the nature of time. We will be back to the holographic approach considering the flowing of time as foliations at spatial infinity. In part three we propose a speculative model to understant the behaviour of the connected coherent holographic sheets at spatial infinity in order to produce time-like behaviour. The flowing of time -we speculate- could eventually emerge as the surface of the holographic sheet encoding every qubit of our universe gets asymptotically closer and closer to the shell of this bulk that we call “the universe”. In part four we will delve more into the proposals of Penrose's CCC and we suggest that the same holographic approach can lead towards the new concepts of the Bousso Holographic Bound, which is a generalization of the Bekenstein Bound. With this interesting tool, and under some highly speculative assumptions, we suggest, we could rule out another (according our view) unnecessary element of the CCC theory: the Ω field. We propose that the smooth conformal transition between the high-entropy universe of the former aeon and a new, low entropy universe in a new aeon can be obtained with the help of the Bousso holographic bound. In part five we will discuss the hypotesys about how could an asymptotically Minkowskian foliation at spatial infinity could map onto a positively curved surface at the boundary at null infinity using a de Sitter transformation applied at spatial infinity. From the boundary, a de Sitter outward geometry would likely produce a universe like ours

Here's the link to download the working paper: 

https://www.academia.edu/115137536/Penroses_Conformal_Cyclic_Cosmology_and_Bousso_Holographic_Bound

Thanks for your opinion! 🙂

Thomas

Edited February 21 by Tommolo

[Tommolo]

The idea, in a nutshell, is that in Penrose's Conformal Cyclic Cosmology there is a huge proble with entropy from an universe to the other, so that the following aeon the new universe would have just very deteriorated energy and extremely high entropy. It would be a short-lived aeon.

So Penrose add an omega term which arises later in the history of the universe and cleans off entropy, letting the new universe have a very low "Weyl curvature tensor" at the beginning of the aeon. The problem here is that this omega field is an ad hoc terms added without proper justification. But if we adopt an holographic approach and we mix with a proper conformal rescaling, then we could dare to say that the Planck lenght itself vary through aeons, and it would help us using a tool like Bousso's Entropy Bound.

So the conformal rescaling would also extend to the Planck lenght itself: the former aeon's maximum dimension becomes the new aeon's minimum distance (the "new" Planck lenght).

This applies too with black holes "singularity", where new "conformal baby universes" may grow and thrive with their own disconnected metrics completely unseen from outside. 

In order to do so, I try to implement a kind of holography (sort of...) based onto a new, conformally rescalable definition of time as a foliation of hypersurfaces getting closer and closer to the boundary projecting onto the bulk. Yes, it's a radical holographic interpretation, as I don't need mass inside the bulk and I conjecture a really de Sitter group dominated bulk. A theatrical scenario, in a sense.

Can anyone see the maths and the formalization of my idea? Are there errors or things to correct?

[Tommolo]

This is the abstract, just in case 🙂