_{1}

^{*}

We look at, starting with Shankar’s treatment of the partition function, inserting in the data of the modified Heisenberg uncertainty principle as to give a role to the inflaton in the formation of a partition of the universe. The end result will be, even with the existence of a multiverse, i.e. simultaneous universes, uniform physical laws throughout the multiple universes.

We review the modification of the Penrose cyclic conformal cosmology paradigm given in [

Modification of the HUP and included in our representation of the inflaton, in the partition function will then lead to, after we are including in the results from [

On the contrary, the supposition is given by Susskind and others, [^{100} universes, with only say 10^{6} of them surviving due to sufficiently “robust” cosmological values, for stable physical law. The end result is that what we would have instead is a “multiverse” which is dynamic and stable over time. And so we review our present modification of the Penrose cyclic conformal cosmology model to take into account multiple universes.

That there are no fewer than N universes undergoing Penrose “infinite expansion” [^{7} - 10^{8} bits of information per partition function in the set

However, there is non-uniqueness of information put into each partition function

Each of

Claim 1:

For N number of universes, with each

Claim 2:

What is done in Claim 1 and Claim 2 is to come up with a protocol as to how a multi dimensional representation of black hole physics enables continual mixing of spacetime largely as a way to avoid the Anthropic principle, as to a preferred set of initial conditions. How can a graviton with a wavelength 10^{−}^{4} the size of the universe interact with a Kere black hole, spatially. Embedding the BH in a multiverse setting may be the only way out.

Claim 1 is particularly important. The idea here is to use what is known as CCC cosmology, which can be thought of as the following.

First. Have a big bang (initial expansion) for the universe. After redshift z = 10, a billion years ago, SMBH formation starts. Matter-energy is vacuumed up by the SMBHs, which at a much later date than today (present era) gather up all the matter-energy of the universe and recycles it in a cyclic conformal translation, as follows, namely

c_{1} is, here a constant. Then we have that for consistency in our presentation that the main methodology in the Penrose proposal has been shown in Equation (6) where we are evaluating a change in the metric

Penrose’s suggestion has been to utilize the following [

The infall into cosmic black hopes has been the main mechanism which the author asserts would be useful for the recycling apparent in Equation (8) above with the caveat that

Equation (9) is to be generalized, as given by a weighing averaging as given by Equation (3). where the averaging is collated over perhaps thousands of universes, call that number N, with an ergotic mixing of all these universes, with the ergodic mixing represented by Equation (3) to generalize Equation (9) from cycle to cycle.

We will, afterwards, do the particulars of the partition function. But before that, we will do the “mixing” of inputs into the Partition function of the Universe, i.e. an elaboration on Equation (3) above. To do this, first, look at the following, from [

Birkhoff’s Ergodic mixing theorem:

Let

Then for

In the end, we need to have a way to present how the bona fides of Equation (9) can be established, and the averaging of both Equation (10) and Equation (4) above need to be put to a consistent general treatment for an invariant

To do this, we also refer to the generalized treatment of, from [

Having said, that, the remaining constraint is to come up with a suitably averaged value of the Partition function in the above work. Our averaging eventually will have to be reconciled with the Birkhoff Ergodic Mixing theorem.

We begin with what is given in Shankar’s treatment of the partition function of [

Using, for Pre Planckian space-time the approximation of [

Approximate using Beckwith’s treatment of the HUP, in Pre Planckian space-time [

Put in now the value of the inflaton given by Padmanbhan, [

Put in the value for the inflaton as given in Equation (15) into the partition function of Equation (14)

Then using Shankar, [

Then by use of Equation (11) we obtain

This is the baseline of the constraint which will make Planck’s constant, a constant per universe creation cycle. As given by Equation (9). i.e. Equation (9) is confirmed by Equation (18). We will next then go to how this ties into Equation (10) above, via use of averaging is affecting the choice of the inputs into Equation (18) above. Doing this will allow investigation as to how to falsify the Birkhoff Ergodic mixing theorem as mentioned next.

To do this, we specifically look at the wavelength, namely, applying [

i.e. the averaging by the Burkhoff theorem implies that there is a critical invariance. And this invariance should be linked, then, to the diameter of a nonsingular bounce point. A nonsingular bounce, i.e., beginning of an expansion of a new universe is the main point of [

We will try to show, in a later date that these are invariant per cycle, but the upshot is that if there is a natural fit, as to Equation (19) and if

In a word this demolishes the program of the cosmic landscape of string theory [

If this is confirmed, experimentally, it will do much to reduce what has been at times a post modern fragmentation of basic physics inquiry and to have physics, with a uniform set of laws, regardless of whether there were many worlds, or just one, in terms of one universe, or many universes, and as well as allow investigation of the information theory approach of [

This work is supported in part by National Nature Science Foundation of China grant No. 11375279.

Beckwith, A.W. (2016) Examination of a Multiple Universe Version of the Partition Function of the Universe, Based upon Penrose’s Cyclic Con- formal Cosmology. Leading to Uniform Values of h (Planck’s Constant) and Invariant Physical Laws in Each Universe of the “Multiverse”. Journal of High Energy Physics, Gravitation and Cosmology, 2, 571-580. http://dx.doi.org/10.4236/jhepgc.2016.24049

The following formulation is to highlight how entropy generation blends in with quantum mechanics, and how the breakdown of some of the assumptions used in Lee’s paper coincide with the growth of degrees of freedom. What is crucial to Lee’s formulation, is Rindler geometry, not the curved space formulation of initial universe conditions. First of all, [

“Considering all these recent developments, it is plausible that quantum mechanics and gravity has information as a common ingredient, and information is the key to explain the strange connection between two. If gravity and Newton mechanics can be derived by considering information at Rindler horizons, it is natural to think quantum mechanics might have a similar origin. In this paper, along this line, it is suggested that quantum field theory (QFT) and quantum mechanics can be obtained from information theory applied to causal (Rindler) horizons, and that quantum randomness arises from information blocking by the horizons.”

To start this we look at the Rindler partition function, as by [

As stated by Lee [

where

If we do a rescale

The example given by (Lee, 2010) is that there is a Hamiltonian for which

Here, V is a potential, and

Here, the

Now, for the above situation, the following are equivalent.

1)

2) QFT formation is equivalent to purely information based statistical treatment suggested in this paper.

3) QM emerges from information theory emerging from Rindler co-ordinate.

Lee also forms a Euclidian version for the following partition function, if

There exist analytic continuation of

Important Claim: The following are equivalent.

1)

2)

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