Geometry
Physical Laws
Octonionic
No quantum physics.
Electromagnetic fields
dominate.
Pre-quantum to
quantum transition
Unknown geometry.
Transition from
octonionic to standard.
Semiclassical derivation
of Planck's constant is
possible. Quantum
physics emerges.
Standard
Quantum field theory
and general relativity
apply. Inflation occurs.
1. The document discusses the behavior of initial singularities in a single repeating universe versus a multiverse. It argues that in a single repeating universe, an initial singularity with Rinitial → 0 may be possible without violating general relativity.
2. In a multi
Original scientific paper on which September 3&9 presentations by Chongquing University's Dr. Andrew Beckwith is based, and published within the July 2011 edition of the Journal of Modern Physics. (Scientific Research Publishing)
First part of abstract, i.e. part I•
Detailing Coherent, Minimum Uncertainty States of Gravitons, g , y , as Semi Classical Components of Gravity Waves, and How Squeezed States Affect Upper Limits to Graviton Mass /•
“We present what is relevant to squeezed states of initial space time and how that affects both the composition of relic GW and also gravitons. A side ii f li GW, d l i id issue to consider is if gravitons can be configured as semi classical “particles”, which is akin to the Pilot particles model of Quantum Mechanics as embedded in a larger non linear “deterministic” background.” g g -Dr. Andrew Beckwith, Chongquing University, PRC
Links:
G999 Conference, Philadelphia, PA http://ggg999.org/
San Marino Workshop on Astrophysics and Cosmology For Matter and Antimatter, in San Marino, N. Italy.
http://www.workshops-hadronic-mechanics.org/
Slideshare: http://t.co/vEv2ci5
WordPress: http://asimov52.wordpress.com/2011/09/03/dr-andrew-beckwith-%E2%80%9Cdetailing-coherent-minimum-uncertainty-states-of-gravitons-g-y-as-semi-classical-components-of-gravity-waves-and-how-squeezed-states-affect-upper-limits-to-gravito/
Detailing Coherent, Minimum Uncertainty States of Gravitons, as Semi Classical Components of Gravity Waves, and How Squeezed States Affect Upper Limits to Graviton Mass /• We present what is relevant to squeezed states of initial space time and how that affects both the composition of relic GW and also gravitons. A side issue to consider is if gravitons can be configured as semi classical “particles”, which is akin to the Pilot particles model of Quantum Mechanics as embedded in a larger non linear “deterministic” background.
First Presented Saturday, September 3, 2011 at the G999 Conference, Philadelphia, PA http://ggg999.org/
Next Presentation : Friday, September 9, SAN MARINO WORKSHOP ON ASTROPHYSICS AND COSMOLOGY
FOR MATTER AND ANTIMATTER
http://www.workshops-hadronic-mechanics.org/
San Marino, N. Italy
Discussion: The Nature of Semi-classical Nature of Gravity Reviewed; And Can We Use a Graviton Entanglement Version of the EPR System to Answer if The Graviton is Classical or Quantum in Origin?
Publisher’s note: Dr. Beckwith: I am honored that you have seen fit to acknowledge me in your presentations of today, September 3, 2011 at the G999 Conference in Philadelphia, and Friday, September 9, at the San Marino Workshop on Astrophysics and Cosmology For Matter and Antimatter, in San Marino, N. Italy.
In my view, these are rather extraordinary postulations, especially the probability of extra-universal black hole gravitational origins, along with expansion beyond Hawking of Quantum Wave theory and the “quantizing” of gravity. The latter may very well lead to a thorough reexamination of our concept of space and time, and that the latter might not be so unidirectional afterall. The potential is breathtaking, as it represents steps forward in proving the existence of subspace, the possibility of concomitant multi-universiality and 5D dimensionality of black holes.
Can time manipulation and Biefeld-Brown suggested electro-gravitics as a spacecraft propulsive methodology be far behind? I think not…
Detailing Coherent, Minimum Uncertainty States of Gravitons, as Semi Classical Components of Gravity Waves, and How Squeezed States Affect Upper Limits to Graviton Mass /• We present what is relevant to squeezed states of initial space time and how that affects both the composition of relic GW and also gravitons. A side issue to consider is if gravitons can be configured as semi classical “particles”, which is akin to the Pilot particles model of Quantum Mechanics as embedded in a larger non linear “deterministic” background.
First Presented Saturday, September 3, 2011 at the G999 Conference, Philadelphia, PA http://ggg999.org/
Next Presentation : Friday, September 9, SAN MARINO WORKSHOP ON ASTROPHYSICS AND COSMOLOGY
FOR MATTER AND ANTIMATTER
http://www.workshops-hadronic-mechanics.org/
San Marino, N. Italy
Discussion: The Nature of Semi-classical Nature of Gravity Reviewed; And Can We Use a Graviton Entanglement Version of the EPR System to Answer if The Graviton is Classical or Quantum in Origin?
Publisher’s note: Dr. Beckwith: I am honored that you have seen fit to acknowledge me in your presentations of today, September 3, 2011 at the G999 Conference in Philadelphia, and Friday, September 9, at the San Marino Workshop on Astrophysics and Cosmology For Matter and Antimatter, in San Marino, N. Italy.
In my view, these are rather extraordinary postulations, especially the probability of extra-universal black hole gravitational origins, along with expansion beyond Hawking of Quantum Wave theory and the “quantizing” of gravity. The latter may very well lead to a thorough reexamination of our concept of space and time, and that the latter might not be so unidirectional afterall. The potential is breathtaking, as it represents steps forward in proving the existence of subspace, the possibility of concomitant multi-universiality and 5D dimensionality of black holes.
Can time manipulation and Biefeld-Brown suggested electro-gravitics as a spacecraft propulsive methodology be far behind? I think not…
Slideshare-LinkedIn-eMOTION! REPORTS.com Exclusive Academic Paper Presentatio...GLOBAL HEAVYLIFT HOLDINGS
A.Beckwith1 Chongqing University, Department of Physics Chongqing, PRC, 400044
E-mail: abeckwith@uh.edu
Abstract. We ask if there is always entanglement entropy in the universe. We find the resolution by work from Muller and Lousto, as to entanglement entropy 2 2 .3 H entropy r S a . We present entanglement entropy in the early universe with a steadily shrinking scale factor, due to work from Muller and Lousto , and show that there are consequences due to initial entangled entropy for a time dependent horizon radius in cosmology, with for flat space conditions r(H)=conformal time. In the case of a curved, but not flat space version of entropy, we look at vacuum energy as proportional to the inverse of scale factor squared times the inverse of initial entropy, effectively when there is no initial time except with H r in line with the conformal time being almost zero. . The consequences for this initial entropy being entangled are elaborated in this manuscript. No matter how small the initial radial length gets, then for initial cosmological entropy if it is entanglement entropy, it will not go to zero.
Understanding the experimental and mathematical derivation of Heisenberg's Uncertainty Principle. Simple application for estimating single degree of freedom particle in a potential free environment is also discussed.
Original scientific paper on which September 3&9 presentations by Chongquing University's Dr. Andrew Beckwith is based, and published within the July 2011 edition of the Journal of Modern Physics. (Scientific Research Publishing)
First part of abstract, i.e. part I•
Detailing Coherent, Minimum Uncertainty States of Gravitons, g , y , as Semi Classical Components of Gravity Waves, and How Squeezed States Affect Upper Limits to Graviton Mass /•
“We present what is relevant to squeezed states of initial space time and how that affects both the composition of relic GW and also gravitons. A side ii f li GW, d l i id issue to consider is if gravitons can be configured as semi classical “particles”, which is akin to the Pilot particles model of Quantum Mechanics as embedded in a larger non linear “deterministic” background.” g g -Dr. Andrew Beckwith, Chongquing University, PRC
Links:
G999 Conference, Philadelphia, PA http://ggg999.org/
San Marino Workshop on Astrophysics and Cosmology For Matter and Antimatter, in San Marino, N. Italy.
http://www.workshops-hadronic-mechanics.org/
Slideshare: http://t.co/vEv2ci5
WordPress: http://asimov52.wordpress.com/2011/09/03/dr-andrew-beckwith-%E2%80%9Cdetailing-coherent-minimum-uncertainty-states-of-gravitons-g-y-as-semi-classical-components-of-gravity-waves-and-how-squeezed-states-affect-upper-limits-to-gravito/
Detailing Coherent, Minimum Uncertainty States of Gravitons, as Semi Classical Components of Gravity Waves, and How Squeezed States Affect Upper Limits to Graviton Mass /• We present what is relevant to squeezed states of initial space time and how that affects both the composition of relic GW and also gravitons. A side issue to consider is if gravitons can be configured as semi classical “particles”, which is akin to the Pilot particles model of Quantum Mechanics as embedded in a larger non linear “deterministic” background.
First Presented Saturday, September 3, 2011 at the G999 Conference, Philadelphia, PA http://ggg999.org/
Next Presentation : Friday, September 9, SAN MARINO WORKSHOP ON ASTROPHYSICS AND COSMOLOGY
FOR MATTER AND ANTIMATTER
http://www.workshops-hadronic-mechanics.org/
San Marino, N. Italy
Discussion: The Nature of Semi-classical Nature of Gravity Reviewed; And Can We Use a Graviton Entanglement Version of the EPR System to Answer if The Graviton is Classical or Quantum in Origin?
Publisher’s note: Dr. Beckwith: I am honored that you have seen fit to acknowledge me in your presentations of today, September 3, 2011 at the G999 Conference in Philadelphia, and Friday, September 9, at the San Marino Workshop on Astrophysics and Cosmology For Matter and Antimatter, in San Marino, N. Italy.
In my view, these are rather extraordinary postulations, especially the probability of extra-universal black hole gravitational origins, along with expansion beyond Hawking of Quantum Wave theory and the “quantizing” of gravity. The latter may very well lead to a thorough reexamination of our concept of space and time, and that the latter might not be so unidirectional afterall. The potential is breathtaking, as it represents steps forward in proving the existence of subspace, the possibility of concomitant multi-universiality and 5D dimensionality of black holes.
Can time manipulation and Biefeld-Brown suggested electro-gravitics as a spacecraft propulsive methodology be far behind? I think not…
Detailing Coherent, Minimum Uncertainty States of Gravitons, as Semi Classical Components of Gravity Waves, and How Squeezed States Affect Upper Limits to Graviton Mass /• We present what is relevant to squeezed states of initial space time and how that affects both the composition of relic GW and also gravitons. A side issue to consider is if gravitons can be configured as semi classical “particles”, which is akin to the Pilot particles model of Quantum Mechanics as embedded in a larger non linear “deterministic” background.
First Presented Saturday, September 3, 2011 at the G999 Conference, Philadelphia, PA http://ggg999.org/
Next Presentation : Friday, September 9, SAN MARINO WORKSHOP ON ASTROPHYSICS AND COSMOLOGY
FOR MATTER AND ANTIMATTER
http://www.workshops-hadronic-mechanics.org/
San Marino, N. Italy
Discussion: The Nature of Semi-classical Nature of Gravity Reviewed; And Can We Use a Graviton Entanglement Version of the EPR System to Answer if The Graviton is Classical or Quantum in Origin?
Publisher’s note: Dr. Beckwith: I am honored that you have seen fit to acknowledge me in your presentations of today, September 3, 2011 at the G999 Conference in Philadelphia, and Friday, September 9, at the San Marino Workshop on Astrophysics and Cosmology For Matter and Antimatter, in San Marino, N. Italy.
In my view, these are rather extraordinary postulations, especially the probability of extra-universal black hole gravitational origins, along with expansion beyond Hawking of Quantum Wave theory and the “quantizing” of gravity. The latter may very well lead to a thorough reexamination of our concept of space and time, and that the latter might not be so unidirectional afterall. The potential is breathtaking, as it represents steps forward in proving the existence of subspace, the possibility of concomitant multi-universiality and 5D dimensionality of black holes.
Can time manipulation and Biefeld-Brown suggested electro-gravitics as a spacecraft propulsive methodology be far behind? I think not…
Slideshare-LinkedIn-eMOTION! REPORTS.com Exclusive Academic Paper Presentatio...GLOBAL HEAVYLIFT HOLDINGS
A.Beckwith1 Chongqing University, Department of Physics Chongqing, PRC, 400044
E-mail: abeckwith@uh.edu
Abstract. We ask if there is always entanglement entropy in the universe. We find the resolution by work from Muller and Lousto, as to entanglement entropy 2 2 .3 H entropy r S a . We present entanglement entropy in the early universe with a steadily shrinking scale factor, due to work from Muller and Lousto , and show that there are consequences due to initial entangled entropy for a time dependent horizon radius in cosmology, with for flat space conditions r(H)=conformal time. In the case of a curved, but not flat space version of entropy, we look at vacuum energy as proportional to the inverse of scale factor squared times the inverse of initial entropy, effectively when there is no initial time except with H r in line with the conformal time being almost zero. . The consequences for this initial entropy being entangled are elaborated in this manuscript. No matter how small the initial radial length gets, then for initial cosmological entropy if it is entanglement entropy, it will not go to zero.
Understanding the experimental and mathematical derivation of Heisenberg's Uncertainty Principle. Simple application for estimating single degree of freedom particle in a potential free environment is also discussed.
Fundamental principle of information to-energy conversion.Fausto Intilla
Abstract. - The equivalence of 1 bit of information to entropy was given by Landauer in 1961 as kln2, k the Boltzmann constant. Erasing information implies heat dissipation and the energy of 1 bit would then be (the
Landauer´s limit) kT ln 2, T being the ambient temperature. From a quantum-cosmological point of view the minimum quantum of energy in the universe corresponds today to a temperature of 10^-29 ºK, probably forming a cosmic background of a Bose condensate [1]. Then, the bit with minimum energy today in the Universe is a quantum of energy 10^-45 ergs, with an equivalent mass of 10^-66 g. Low temperature implies low energy per bit and, of course, this is the way for faster and less energy dissipating computing devices. Our conjecture is this: the possibility of a future access to the CBBC (a coupling/channeling?) would mean a huge
jump in the performance of these devices.
Here is just a basic demonstration of my first educational platform TeachAdemic's classes! Here you can only find 6 topics with description but in the course we are covering almost every part of physics of 11th and 12th grade
hf=mc^2 ? Let's try to discover it (WWW.OLOSCIENCE.COM)Fausto Intilla
Both electromagnetic radiation and fundamental particles when interpreted
as waves fit the Planck-Einstein relation, E = hf. The universality of this
relation as proposed by de Broglie suggests that electromagnetism and
fundamental particles are compositionally and functionally related
elements. In this usage, the interpretation is that frequency is a intrinsic
property of all fundamental wave or particle quanta, regardless of their
inertial or non-inertial motion. By this analysis, intrinsic wave-particle
frequency is a non-dimensional motion, and is independent of other
motion except in the relativistic sense. The relativistic relations, mass =
mo/ (1 - v2/c2), length = lo(1 - v2/c2), time = to/ (1 - v2/c2), and
frequency = fo (1 - v2/c2), can each be derived from the single generalized
relativistic expression, hf/mc2 = 1/(1 - v2/c2). This generalized expression
defines the relativistic wave property common to both electromagnetic
photons and fundamental material particles. The concept of mass-energy is
related to the frequency property of the fundamental wave-particle. The
equivalence of mass-energy suggests that mass and energy can be defined
by the same principle. Therefore, mass or energy of all fundamental
quanta can be defined mathematically using the Planck-Einstein relation
(E = hf) or descriptively as the mass-energy equivalence of wave-particle
frequency.
As we are all aware,therecent discovery of the Higgs boson has revealed a highly massive particle, the value of which lies between 125and 126.5 GeV/c2.. According to the basic concepts of Quantum Mechanics, and in full compliance with the Uncertainty Principle and Yukawa intuitions, we were able to calculate the maximum limit of the Higgs boson‟s field of action. From the calculations show that the Higgs boson presents a range of action really very small, namely 9.8828∙10-16[cm], that is slightly smaller than 10-15[cm]. This value is justified by the considerable mass that the Higgs bosonacquires, in perfect agreement with the Uncertainty Principle.
Implication of Nernst's Heat Theorem and Its application to deduce III law of thermodynamics and Determination of absolute entropies of perfectly crystalline solids using III law of thermodynamics
Fundamental principle of information to-energy conversion.Fausto Intilla
Abstract. - The equivalence of 1 bit of information to entropy was given by Landauer in 1961 as kln2, k the Boltzmann constant. Erasing information implies heat dissipation and the energy of 1 bit would then be (the
Landauer´s limit) kT ln 2, T being the ambient temperature. From a quantum-cosmological point of view the minimum quantum of energy in the universe corresponds today to a temperature of 10^-29 ºK, probably forming a cosmic background of a Bose condensate [1]. Then, the bit with minimum energy today in the Universe is a quantum of energy 10^-45 ergs, with an equivalent mass of 10^-66 g. Low temperature implies low energy per bit and, of course, this is the way for faster and less energy dissipating computing devices. Our conjecture is this: the possibility of a future access to the CBBC (a coupling/channeling?) would mean a huge
jump in the performance of these devices.
Here is just a basic demonstration of my first educational platform TeachAdemic's classes! Here you can only find 6 topics with description but in the course we are covering almost every part of physics of 11th and 12th grade
hf=mc^2 ? Let's try to discover it (WWW.OLOSCIENCE.COM)Fausto Intilla
Both electromagnetic radiation and fundamental particles when interpreted
as waves fit the Planck-Einstein relation, E = hf. The universality of this
relation as proposed by de Broglie suggests that electromagnetism and
fundamental particles are compositionally and functionally related
elements. In this usage, the interpretation is that frequency is a intrinsic
property of all fundamental wave or particle quanta, regardless of their
inertial or non-inertial motion. By this analysis, intrinsic wave-particle
frequency is a non-dimensional motion, and is independent of other
motion except in the relativistic sense. The relativistic relations, mass =
mo/ (1 - v2/c2), length = lo(1 - v2/c2), time = to/ (1 - v2/c2), and
frequency = fo (1 - v2/c2), can each be derived from the single generalized
relativistic expression, hf/mc2 = 1/(1 - v2/c2). This generalized expression
defines the relativistic wave property common to both electromagnetic
photons and fundamental material particles. The concept of mass-energy is
related to the frequency property of the fundamental wave-particle. The
equivalence of mass-energy suggests that mass and energy can be defined
by the same principle. Therefore, mass or energy of all fundamental
quanta can be defined mathematically using the Planck-Einstein relation
(E = hf) or descriptively as the mass-energy equivalence of wave-particle
frequency.
As we are all aware,therecent discovery of the Higgs boson has revealed a highly massive particle, the value of which lies between 125and 126.5 GeV/c2.. According to the basic concepts of Quantum Mechanics, and in full compliance with the Uncertainty Principle and Yukawa intuitions, we were able to calculate the maximum limit of the Higgs boson‟s field of action. From the calculations show that the Higgs boson presents a range of action really very small, namely 9.8828∙10-16[cm], that is slightly smaller than 10-15[cm]. This value is justified by the considerable mass that the Higgs bosonacquires, in perfect agreement with the Uncertainty Principle.
Implication of Nernst's Heat Theorem and Its application to deduce III law of thermodynamics and Determination of absolute entropies of perfectly crystalline solids using III law of thermodynamics
MASSIVE PHOTON HYPOTHESIS OPENS DOORS TO NEW FIELDS OF RESEARCHijrap
Mass, an inherent property of matter, is calculated directly for the photon particle from the very classical
principles of the kinetic theory of gases. It is not an end result with no perspective nor other outcome.
Quite the opposite, a single ponderable tiny photon frees the mind of old ways of thinking and opens up
new paths to a broad field of investigation where the very large can then be described and explained by the
very small. This reality of a non-zero mass suddenly shows up in the interpretation of many experiments
which become clear and simple to comprehend. Besides, that same key particle has the potential to unlock
and solve some long lasting major observational issues or enigmas. All this converges upon its
acknowledgement and acceptance.
In this paper, the underlying principles about the theory of relativity are briefly introduced and reviewed. The mathematical prerequisite needed for the understanding of general relativity and of Einstein field equations are discussed. Concepts such as the principle of least action will be included and its explanation using the Lagrange equations will be given. Where possible, the mathematical details and rigorous analysis of the subject has been given in order to ensure a more precise and thorough understanding of the theory of relativity. A brief mathematical analysis of how to derive the Einstein’s field’s equations from the Einstein-Hilbert action and the Schwarzschild solution was also given.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
Fi ck law
Diffusion: random walk of an ensemble of particles from region of high “concentration” to region of small “concentration”.
Flow is proportional to the negative gradient of the “concentration”.
Nuclear Decay - A Mathematical PerspectiveErik Faust
Radioactivity as a phenomenon is often misunderstood: if one says ‘Radioactive’, most people will think about disastrous electrical plants, dangerous bombs and other forms of life-threatening details. In my native Germany, members of the Green party have been campaigning for a decade to put an end to nuclear energy. Only few think of the useful aspects of this unique actuality, although radiotherapy is most promising of tools in the fight against cancer, and radioactive dating allows us to identify the age of any historical item. But even fewer people see radioactivity as the natural process that it actually is: A spontaneous mechanism, in which one nucleus decays into another. As an aspiring Physicist and Engineer, Radioactivity is one my favourite topics in the realm of science. I am fascinated at how we are able to predict exactly how many Nuclei will decay in a certain amount of time, but not say for certain which Nuclei exactly will do so.
Chongqing University's Beckwith Paper Posits a Challenge to Dysonian Assertio...GLOBAL HEAVYLIFT HOLDINGS
"According to Dr. Andrew Beckwith, renowned Astrophysicist Freeman Dyson asserted that Gravitons were undetectable via an analysis of infinite space; I.e., the analysis of the infinite distances involved, were to invalidate any chance of working with experimentation based upon the assumption of infinite distances, of propagation and of where the relevant physics interactions occurred. I believe Dr. Beckwith is correct in saying he has turned this analysis on its head by making reference to a small cavity based regime of probability analysis, as it relates to GW production by a Tokamak, which changes the probability of detection from 0 to 100%, by use of the same probability calculations Dyson used in his document. Dr. Beckwith substantively contends all of Dyson's suppositions are based upon infinite spatial geometry and Dyson did not once examine the physics of what would occur with a device based physics generator of gravitational waves." - Myron D. Stokes, Research Assistant
Beckwith Paper Posits a Challenge to Dysonian Assertions As to Non-viability ...GLOBAL HEAVYLIFT HOLDINGS
"According to Dr. Andrew Beckwith, renowned Astrophysicist Freeman Dyson asserted that Gravitons were undetectable via an analysis of infinite space; I.e., the analysis of the infinite distances involved, were to invalidate any chance of working with experimentation based upon the assumption of infinite distances, of propagation and of where the relevant physics interactions occurred. I believe Dr. Beckwith is correct in saying he has turned this analysis on its head by making reference to a small cavity based regime of probability analysis, as it relates to GW production by a Tokamak, which changes the probability of detection from 0 to 100%, by use of the same probability calculations Dyson used in his document. Dr. Beckwith substantively contends all of Dyson's suppositions are based upon infinite spatial geometry and Dyson did not once examine the physics of what would occur with a device based physics generator of gravitational waves." - Myron D. Stokes, Research Assistant
Review of Tokamak Physics As a Way to Construct a Device Optimal For Graviton...GLOBAL HEAVYLIFT HOLDINGS
Abstract: - Review of arguments in refutation of Dyson’s alleged prohibition against use of device physics as to determining if Gravitons can be determined to exist is followed up by use of a hot Plasma within a Tokamak in a re do of the amplitude of alleged Gravitational waves. This overlaps with gravitons,and we follow up with an analysis of the pertinent form of Gravitons, i.e. do we have massless or massive gravitons. In addition we also obtain GW of amplitude as low as five meters above the Tokamak center such low strain values are extremely close to brane world GW, and strain values in early universe cosmology. This is after our device analysis.Using Grischuk and Sachin (1975) amplitude for the GW generation due to plasma in a toroid, we generalize this result for Tokamak physics. We obtain evidence for strain values up to in a Tokamak center. These values are an order of magnitude sufficient to allow for possible detection of gravitational waves. The critical breakthrough is in utilizing a burning plasma drift current, which relies upon a thermal contribution to an electric field. Such low strain values are extremely close to brane world GW, and strain values in early universe cosmology.We conclude with statements as to comparing our basic results with those of Yan-Gang Miao, Ying-Jie Zhao as to their generalized HUP which gives support to the suppositionsgiven in our comparison of the character of gravitons which are initially at the start of inflation versus those of our present era, as measured by the Tokamak.
Infinite Energy, Space Travel... Would this be the greatest Discovery of our ...GLOBAL HEAVYLIFT HOLDINGS
"This might be the greatest discovery of our time. The Holy Grail of almost infinite energy production, and propulsion through the universe using the fabric of nature. I am telling this story as it was told to me.
In 2013, an international incident was created by the intent of a government to violate a treaty to share scientific information with another. The scientists and their work had to be extracted before the scientists were assassinated and their work used as strategic advantage to who knows what purposes.
Just a couple of hours more and the scientists would have been killed and the discovery would be in the hands of only one country, and may not for the most noble of purposes." - Francisco Lopez
Infinite Energy, Space Travel... Would this be the greatest Discovery of our ...GLOBAL HEAVYLIFT HOLDINGS
"This might be the greatest discovery of our time. The Holy Grail of almost infinite energy production, and propulsion through the universe using the fabric of nature. I am telling this story as it was told to me.
In 2013, an international incident was created by the intent of a government to violate a treaty to share scientific information with another. The scientists and their work had to be extracted before the scientists were assassinated and their work used as strategic advantage to who knows what purposes.
Just a couple of hours more and the scientists would have been killed and the discovery would be in the hands of only one country, and may not for the most noble of purposes." - Francisco Lopez
Possible Ripple in LIGO MIT NSF Announcement of Gravitational Wave "Ripples i...GLOBAL HEAVYLIFT HOLDINGS
Possible Ripple in LIGO MIT NSF Announcement of Gravitational Wave "Ripples in Einsteinian Space-Time" Detection Suggested by Astrophysicist Dr. Andrew W. Beckwith, Chongqing University Department of Physics, PRC
Chongqing, Peoples Republic of China 2/12/16 1238 EST, +5 GMT -The author has viewed extensively the LIGO paper in PRD and finds that it is a very good beginning. However several caveats are in order.
a. If or not gravity waves can be composed of Gravitons is a non-trivial matter and in spite of Freeman Dyson's statement as to the impossibility of finding Gravitons, the author has reviewed Dyson's arguments as to the Gertshenshtein process effect and probability and found that these arguments most heavily fall upon more than kilometer long interferometer geometry and the light years of propagation given in Dyson's paper.
http://publications.ias.edu/sites/default/files/poincare2012.pdf
"An American Walkabout": Book Narrative by Myron D. Stokes, Automotive/Aerosp...GLOBAL HEAVYLIFT HOLDINGS
Some of The Best Things in Life are Indeed Free... And Breathtaking....
Rancho Cucamonga, CA June, 2015 - After the death of my wife Deadra on September 12, 2012 in St. Augustine, I decided rather than settling into the new reality of spousal loss and the experiential constant of relatives/friends expressing sympathy - much needed of course - I would accept the "down under" wisdom of fictional character "Crocodile Dundee" and go "walkabout": Covering almost 250,000 miles with the help of GM, FCA Chrysler & Ford PR colleagues.
The writing technique deployed here is quasi-poetic using sonnet variation architecture of millenia old origins, and derives from an understanding of how the brain processes sensory data in a continuous stream. Arguably, humans will happily absorb any volume of verbiage as long as there is observable continuity, flow and logic regardless of the seeming complexity of terminologies, phraseologies and references utilized therein...
Contact data for publisher inquiry: 248-825-2489 (new) email: globalheavyliftholdings@ymail.com
"An American Walkabout": Book In Development Narrative - Myron D. Stokes, A...GLOBAL HEAVYLIFT HOLDINGS
Some of The Best Things in Life are Indeed Free... And Breathtaking....
Rancho Cucamonga, CA June, 2015 - After the death of my wife Deadra in September 2012, I decided rather than settling into the new reality of spousal loss and the experiential constant of relatives/friends expressing sympathy - much needed of course - I would accept the "down under" wisdom of fictional character "Crocodile Dundee" and go "walkabout": Covering almost 250,000 miles with the help of GM, FCA Chrysler & Ford PR colleagues.
The writing technique deployed here is quasi-poetic using sonnet variation architecture of millenia old origins, and derives from an understanding of how the brain processes sensory data in a continuous stream. Arguably, humans will happily absorb any volume of verbiage as long as there is observable continuity, flow and logic regardless of the seeming complexity of terminologies, phraseologies and references utilized therein...
Book In Development Narrative: "An American Walkabout" Myron D. Stokes, Auto...GLOBAL HEAVYLIFT HOLDINGS
Some of The Best Things in Life are Indeed Free... And Breathtaking....
Rancho Cucamonga, CA June, 2015 - After the death of my wife Deadra in September 2012, I decided rather than settling into the new reality of spousal loss and the experiential constant of relatives/friends expressing sympathy - much needed of course - I would accept the "down under" wisdom of fictional character "Crocodile Dundee" and go "walkabout": Covering almost 250,000 miles with the help of GM, FCA Chrysler & Ford PR colleagues.
The writing technique deployed here is quasi-poetic using sonnet variation architecture of millenia old origins, and derives from an understanding of how the brain processes sensory data in a continuous stream. Arguably, humans will happily absorb any volume of verbiage as long as there is observable continuity, flow and logic regardless of the seeming complexity of terminologies, phraseologies and references utilized therein...
Rancho Cucamonga, CA June, 2015 - After the death of my wife Deadra in September 2012, I decided rather than settling into the new reality of spousal loss and the experiential constant of relatives/friends expressing sympathy - much needed of course - I would accept the "down under" wisdom of fictional character "Crocodile Dundee" and go "walkabout": Covering almost 250,000 miles with the help of GM, FCA Chrysler & Ford PR colleagues.
The writing technique deployed here is quasi-poetic using sonnet variation architecture of millenia old origins, and derives from an understanding of how the brain processes sensory data in a continuous stream. Arguably, humans will happily absorb any volume of verbiage as long as there is observable continuity, flow and logic regardless of the seeming complexity of terminologies, phraseologies and references utilized therein...
GM RECALL DAMAGE CONTROL: STOKES/DOUGLAS PROPOSED FULL PAGE AD IN RESPONSE TO...GLOBAL HEAVYLIFT HOLDINGS
In light of the ever worsening GM crisis relative to a faulty ignition switch on Chevy Cobalt and Saturn Ion, amongst other models in the product line-up, "Car Concerns" Radio Show with Host Harry Douglas and Monday Morning Co-Host Myron D. Stokes, presented on today's show a proposed full page ad designed to address a state of affairs epitomizing Public Relations and Corporate Reputational disaster. GM has to now look past the catastrophe and rebuild their relationship with customers and their stakeholders. We wish them well
33014 Show re GM Recall: http://archives.warpradio.com/ltrn/CarConcerns/033109.mp3
FOR HUMANITY: (V4) A BREAKTHROUGH IN TOKAMAK APPLIED PHYSICS GRAVITATIONAL WA...GLOBAL HEAVYLIFT HOLDINGS
To whom it may concern: (Note: Abbreviated acknowledgement narrative by Dr. Andrew W. Beckwith )
The author, Dr. Andrew Beckwith, authorizes Myron D. Stokes, Publisher, eMOTION! REPORTS.com, a legacy automotive/aerospace research and analysis site and Managing Director, Global HeavyLift Holdings, Inc., a Defense Logistics Agency listed Federal Contractor, as to the dissemination of the following Tokamak applied physics notes for Gravitational wave generation, as his acting manager of public release of the aforementioned document. The information within will be peer reviewed , but the basic technology is intended for humankind as far as fundamental physics advancement world wide.
The notes, within, were created by Dr. Beckwith, in the Keyuan Hotel in room 1205, in Chongqing, PRC, as part of a joint USA-PRC endeavor as to GW physics; the notes are correctly identified by Gary Stephenson , as a civilian employee of the US air force, as pertinent to " Higher drift current during fusion burning" as an enabler of high GW amplitudes, of the order of h ~ 10^-25 to 10^-26 which are candidates for testing of GW direct identification technology incurrent development in both PRC and in America. The notes were also written up as of November 4 to November 12, in an eight day period, in room 1205 of the Keyuan hotel as of Chongqing University under the auspices of Chongqing University department of physics, in work which was enabled by the hospitality of Chongqing University which took unusually comprehensive steps as to the proper circumstances for the creation of this work so cited by the Author.
The following individuals should be thanked as far as their discussions and input as to formation of the "Higher drift current during fusion burning" which is crucial to the development of this material.
a. Dr. Fangyu Li, whose interest in Tokamak physics never flagged, as to its utilization. He informed the author during a stay from November 2 to November 13 of his partnership with a Tokamak fusion laboratory as of Hefei, PRC, which would serve as a test bed of GW amplitudes. His physics questions were timelyand very important during the 12 days of stay in Chongqing University.
b. Dr. Fan, Chief scientific administrator of Chongqing University wrote in administrative authorization of Dr. Beckwith's visit to Chongqing University and also as part of a 40 year friendship with Dr. Li, accompanied Dr. Li to the Tokamak fusion laboratory as of Hefei, PRC, which the author saw in photographs as to the facility, and the chief engineering officer who runs the Hefei Tokamak facility
The above written statement should be part of a slide share release of this basic information as set up by Myron D. Stokes, of Global Heavylift Holdings corporation without further delay.
Andrew Beckwith, PhD, written in Setauket, New York, as of 6 PM, November 16 ( November 17, PRC time, Chongqing), 2013
FOR HUMANITY: A BREAKTHROUGH IN TOKAMAK APPLIED PHYSICS GRAVITATIONAL WAVE GE...GLOBAL HEAVYLIFT HOLDINGS
To whom it may concern: (Note: Abbreviated acknowledgement narrative by Dr. Andrew W. Beckwith )
The author, Dr. Andrew Beckwith, authorizes Myron D. Stokes, Publisher, eMOTION! REPORTS.com, a legacy automotive/aerospace research and analysis site and Managing Director, Global HeavyLift Holdings, Inc., a Defense Logistics Agency listed Federal Contractor, as to the dissemination of the following Tokamak applied physics notes for Gravitational wave generation, as his acting manager of public release of the aforementioned document. The information within will be peer reviewed , but the basic technology is intended for humankind as far as fundamental physics advancement world wide.
The notes, within, were created by Dr. Beckwith, in the Keyuan Hotel in room 1205, in Chongqing, PRC, as part of a joint USA-PRC endeavor as to GW physics; the notes are correctly identified by Gary Stephenson , as a civilian employee of the US air force, as pertinent to " Higher drift current during fusion burning" as an enabler of high GW amplitudes, of the order of h ~ 10^-25 to 10^-26 which are candidates for testing of GW direct identification technology incurrent development in both PRC and in America. The notes were also written up as of November 4 to November 12, in an eight day period, in room 1205 of the Keyuan hotel as of Chongqing University under the auspices of Chongqing University department of physics, in work which was enabled by the hospitality of Chongqing University which took unusually comprehensive steps as to the proper circumstances for the creation of this work so cited by the Author.
The following individuals should be thanked as far as their discussions and input as to formation of the "Higher drift current during fusion burning" which is crucial to the development of this material.
a. Dr. Fangyu Li, whose interest in Tokamak physics never flagged, as to its utilization. He informed the author during a stay from November 2 to November 13 of his partnership with a Tokamak fusion laboratory as of Hefei, PRC, which would serve as a test bed of GW amplitudes. His physics questions were timelyand very important during the 12 days of stay in Chongqing University.
b. Dr. Fan, Chief scientific administrator of Chongqing University wrote in administrative authorization of Dr. Beckwith's visit to Chongqing University and also as part of a 40 year friendship with Dr. Li, accompanied Dr. Li to the Tokamak fusion laboratory as of Hefei, PRC, which the author saw in photographs as to the facility, and the chief engineering officer who runs the Hefei Tokamak facility
The above written statement should be part of a slide share release of this basic information as set up by Myron D. Stokes, of Global Heavylift Holdings corporation without further delay.
Andrew Beckwith, PhD, written in Setauket, New York, as of 6 PM, November 16 ( November 17, PRC time, Chongqing), 2013
DEFENSE AT&L 2004: TRANSFORMATIONAL RECAPITALIZATION: RETHINKING US AIR FORCE...GLOBAL HEAVYLIFT HOLDINGS
“Budgetary constraints, with due respect, exist only in the minds of those in the public and private sector who are at best disingenuous in their claims of continuing attempts to rein in spending. A true and viable solution exists that will forever change Department of Defense acquisition processes, and it’s designated Transformational Recapitalization,” says Myron D. Stokes, Managing Director, Global HeavyLift Holdings, Inc a Defense Logistics Agency (DLA) list contractor..
“As described by national security strategist Dr. Sheila R. Ronis, Director, MBA/MSSL Programs and Associate Professor, Management, Walsh College, in a November 2004 Defense AT&L analysis “Transformational Recapitalization: Rethinking USAF Procurement Philosophies”, it is a financial management approach that is Einsteinian in its simplicity:
(Excerpt from Defense AT&L November/December 2004)
How the Strategy Works
“‘To illustrate, let’s apply this strategy to a fictitious Air Force need for a fleet of 300 aircraft. Instead of producing them at a very efficient rate of 75 per year for four years, produce them at a reasonably efficient rate of 20 per year for 15 years. Every four or five years, incorporate a technology spiral upgrade to new aircraft coming off the production line; however, do not retrofit existing aircraft. Near the end of the 15-year production, begin selling the oldest, less capable aircraft while they still have at least half their useful life remaining. Then, instead of closing the production line, continue producing new aircraft to replace those sold.
“‘Theoretically, the production line can continue indefinitely until either technology or requirements drive the need to produce an entirely new platform or when demand for the used aircraft dries up.
“‘Although the unit price of each aircraft may be slightly higher, the lower production rate combined with used aircraft sales revenue should decrease overall cash flow and provide much-needed stability to the budget and our industrial base. In addition, this strategy not only facilitates spiral development, but also ensures that the U.S. military flies the most capable aircraft while avoiding maintenance and operating costs for aging aircraft.
“‘For the 10-year-old (now 15) C-17, now is the time to start selling older less capable craft and continue production of new ones for the Air Force. As the last major aircraft production line in southern California, it would be devastating to lose that industrial capacity in 2008 (now 2011) when the 180th (216th approx.) aircraft is finished. Reducing the rate to 12 per year and selling off older inventory would not only allow the production line to continue for another 10 years, but applying the resale value and avoiding upgrade modifications would significantly reduce the cost of increasing the capacity of the fleet.
2013 Dodge Challenger R/T at L'Auberge de Sedona: A Blending of Technological...GLOBAL HEAVYLIFT HOLDINGS
Sedona, AZ, 15 December, 2012 - Ten years ago, as Reuters photographer John Hillery and myself rounded a curve on Arizona Service Route 89 in a pre-production and completely revamped 2002 Ford Explorer, we came face-to-face with at least a 2 ton boulder blocking the roadway. There was no place to go; going around on the left would have placed us perilously close to the road edge and an estimated 1,000 ft. drop. Going to the right was out of the question.
The only choice was to stop, hopefully, in time.
We had four things working to our advantage: 1. Anti-lock braking (ABS) 2. New for Explorer anti-dive geometry 3. Lighter weight. and 4. Driving skills (John’s) presumed adequate. Thankfully, all these aspects combined to stop us just a hairsbreadth from this massive boulder which would have made short work of our vehicle - and perhaps us - had we impacted it.
Fast forward to 15 December, 2012, again headed to Sedona, this time for lunch at the renowned and highly recommended by my driving companion, L'Auberge de Sedona Resort and its Restaurant on Oak Creek.
RON HOWARD’S UNIVERSAL PICTURES MOVIE "RUSH" CHRONICLING THE RIVALRY BETWEEN ...GLOBAL HEAVYLIFT HOLDINGS
Argonne National Labs Providing Technological Assistance For World's First 36 Hour "Green" Racing Event Targeted For 2015; Projections Show That CO2 Footprint of 30 Cars Averaging 200mph For 36 Hours is Significantly Lower Than The Boston Marathon; Proposed Race Track City Will Utilize Advanced Building Materials, DOE Developed Alternative Energy Processes and Arcosanti derived Soleri Arcology Architecture... Hunt is On For Energy Company Title Sponsor - Involvement of Clean Cities (Arizona) Coalition Demonstrates Seriousness of Environmental Sustainability Objectives
RON HOWARD’S UNIVERSAL PICTURES MOVIE "RUSH" CHRONICLING THE RIVALRY BETWEEN ...GLOBAL HEAVYLIFT HOLDINGS
Argonne National Laboratory Providing Technological Assistance For World's First 36 Hour "Green" Racing Event Targeted For 2015; Projections Show That CO2 Footprint of 30 Cars Averaging 200mph For 36 Hours is Significantly Lower Than The Boston Marathon; Proposed Race Track City Will Utilize Advanced Building Materials, DOE Developed Alternative Energy Processes and Arcosanti derived Soleri Arcology Architecture... Hunt is On For Energy Company Title Sponsor - Involvement of Clean Cities (Arizona) Coalition Demonstrates Seriousness of Environmental Sustainability Objectives
The Problem:
September 11, 2001 proved the High-rise rescue operational inadequacies of municipally based fire/rescue services. It is imperative that this problem is quickly addressed using both existing and proposed technologies and methods.
A Solution:
IN-S.E.R.T. is a dedicated emergency response unit operated as an extension of The United States Coast Guard (USCG) F.E.M.A. and existing fire/rescue departments in any major city. Team members will have at their disposal a range of fire/rescue and fire suppression technologies designed to facilitate High-rise rescue operations. The potential flexibility of IN-S.E.R.T makes it a template for a broad spectrum of emergency responses not limited to High-rise rescue. Therefore, it has value beyond that immediately observable.
Technology, Equipment, Methods:
Specially trained personnel will benefit from the decades old expertise of the acclaimed “Smoke Jumpers” of the Western/Pacific Northwestern United States and Red Adair’s legendary pyro-containment methodologies. Additionally, they will benefit from newly developed Victim Extraction At Altitude (VEAA)techniques.
“We are now at a cusp of human history,” notes Beckwith, “equivalent to the discovery of fire, hundreds of thousands of years ago, and for a very unexpected reason. For the first time in human history, we are at the point where an analysis of false to true vacuum transitions, the entire nexus of symmetry breaking and the formation of mass in the early universe is enabling scientists and technologists the foundations of space time geometry. This could lead to within 50 years to developing appropriate technology for star travel and to genuine space ship ventures to the neighboring solar systems. At stake is to understand what closer to the idea of an interstellar ram jet, similar to Bussard ram jet with tweaking will work.” - Dr. Andrew W. Beckwith, Chongqing University Department of Physics, Chongqing, Peoples Republic of China
HIGGS-BOSON - eMOTION! REPORTS PRESS RELEASE FOR JULY 10, 2012 - THE REAL “M...GLOBAL HEAVYLIFT HOLDINGS
“We are now at a cusp of human history,” notes Beckwith, “equivalent to the discovery of fire, hundreds of thousands of years ago, and for a very unexpected reason. For the first time in human history, we are at the point where an analysis of false to true vacuum transitions, the entire nexus of symmetry breaking and the formation of mass in the early universe is enabling scientists and technologists the foundations of space time geometry. This could lead to within 50 years to developing appropriate technology for star travel and to genuine space ship ventures to the neighboring solar systems. At stake is to understand what closer to the idea of an interstellar ram jet, similar to Bussard ram jet with tweaking will work.
What Does the PARKTRONIC Inoperative, See Owner's Manual Message Mean for You...Autohaus Service and Sales
Learn what "PARKTRONIC Inoperative, See Owner's Manual" means for your Mercedes-Benz. This message indicates a malfunction in the parking assistance system, potentially due to sensor issues or electrical faults. Prompt attention is crucial to ensure safety and functionality. Follow steps outlined for diagnosis and repair in the owner's manual.
Comprehensive program for Agricultural Finance, the Automotive Sector, and Empowerment . We will define the full scope and provide a detailed two-week plan for identifying strategic partners in each area within Limpopo, including target areas.:
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• Scope: Provide support solutions to enhance agricultural productivity and sustainability.
• Target Areas: Polokwane, Tzaneen, Thohoyandou, Makhado, and Giyani.
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• Scope: Develop collaborations with automotive service providers to improve service quality and business operations.
• Target Areas: Polokwane, Lephalale, Mokopane, Phalaborwa, and Bela-Bela.
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We will also prioritize Industrial Economic Zone areas and their priorities.
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3. Sectors : Agriculture ( primary and secondary) and Automative
Women and Youth are encouraged to apply even if you don't fall in those sectors.
Symptoms like intermittent starting and key recognition errors signal potential problems with your Mercedes’ EIS. Use diagnostic steps like error code checks and spare key tests. Professional diagnosis and solutions like EIS replacement ensure safe driving. Consult a qualified technician for accurate diagnosis and repair.
In this presentation, we have discussed a very important feature of BMW X5 cars… the Comfort Access. Things that can significantly limit its functionality. And things that you can try to restore the functionality of such a convenient feature of your vehicle.
Fleet management these days is next to impossible without connected vehicle solutions. Why? Well, fleet trackers and accompanying connected vehicle management solutions tend to offer quite a few hard-to-ignore benefits to fleet managers and businesses alike. Let’s check them out!
"Trans Failsafe Prog" on your BMW X5 indicates potential transmission issues requiring immediate action. This safety feature activates in response to abnormalities like low fluid levels, leaks, faulty sensors, electrical or mechanical failures, and overheating.
What Exactly Is The Common Rail Direct Injection System & How Does It WorkMotor Cars International
Learn about Common Rail Direct Injection (CRDi) - the revolutionary technology that has made diesel engines more efficient. Explore its workings, advantages like enhanced fuel efficiency and increased power output, along with drawbacks such as complexity and higher initial cost. Compare CRDi with traditional diesel engines and discover why it's the preferred choice for modern engines.
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5 Warning Signs Your BMW's Intelligent Battery Sensor Needs AttentionBertini's German Motors
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Core technology of Hyundai Motor Group's EV platform 'E-GMP'Hyundai Motor Group
What’s the force behind Hyundai Motor Group's EV performance and quality?
Maximized driving performance and quick charging time through high-density battery pack and fast charging technology and applicable to various vehicle types!
Discover more about Hyundai Motor Group’s EV platform ‘E-GMP’!
Things to remember while upgrading the brakes of your carjennifermiller8137
Upgrading the brakes of your car? Keep these things in mind before doing so. Additionally, start using an OBD 2 GPS tracker so that you never miss a vehicle maintenance appointment. On top of this, a car GPS tracker will also let you master good driving habits that will let you increase the operational life of your car’s brakes.
Things to remember while upgrading the brakes of your car
STARGATE! Precursor Formulations to Artificial Wormholes: Dr. Andrew Beckwith, Astrophysicist, Chongqing University, PRC
1. COSMIC INITIAL SINGULARITIES IN A SINGLE
REPEATING UNIVERSE AS OPPOSED TO THEIR BEHAVIOR
IN A MULTIVERSE
Andrew Beckwith
Chongqing University Department of Physics;
E mail: abeckwith@uh.edu
Chongqing, PRC, 400044
Abstract
When initial radius of the universe in four dimensions and there is only ONE repeating universe then
Rinitial → 0 or gets very close to zero if Stoica actually derived Einstein equations in a formalism which
remove in four dimensions the big bang singularity pathology. So then the reason for Planck length no
longer holds. This assumes a repeating single universe. We present entanglement entropy in the early
universe with a shrinking scale factor, due to Muller and Lousto , and show that there are consequences
2
due to initial entanged S Entropy = .3rH a 2 for a time dependent horizon radius rH in cosmology, with
(flat space conditions) rH = η for conformal time . Even if the 3 dimensional spatial length goes
to zero. This construction preserves a minimum non zero Λ vacuum energy, and in doing so keep
the bits, for computational bits cosmological evolution even if in four dimensions we have
Rinitial → 0 . We also find that in the case of a multiverse, that such considerations will not hold
and that cosmic singularities have a different characteristic in the multiverse setting than in the
single universe repeated over and over again. i.e. using an argument borrowed and modified
from Kauffman, the multiverse will not mandate ‘perfect’ singularities. The existence of a
multiverse may allow for non zero singularities in lieu with the Kauffman argument cited at the
end of the document, plus the lower pre big bang temperatures which may allow for the survivial
of gravitons just before the onset of the cosmological expansion phase, if a multiverse exists
embedding our present universe.
Keywords: Fjortoft theorem, thermodynamic potential, matter creation, vacuum energy
non pathological singularity affecting Einstein equations,planck length.Braneworlds.
2. 1. Introduction
We first examine what is to be expected in the four dimensional case as to what happens if
there is a single repeating universe. In such a situation, one can employ the following argument
as to a singularity with the aforementioned behavior as given below. First before doing it, we
investigate via simple arguments involving scaling arguments for the Friedman equations what to
expect in the case that the cosmological “constant” is indeed a constant or has a temperature
dependence as T to the beta power, according to formalism developed by Park et.al. [1]. In doing
so, a case can be made using the Weinberg argument [2] that if there is a high initial background
“viscosity” ( for graviton propagation) there is a high initial temperature. This high temperature
would be consistent with the modus operandi of a single repeating universe, done again and
again. To make the point of this, we also can refer to the Penrose CCC [3] hypothesis as yet
another way to delineate this same repeating universe, with black holes in four dimensions. I.e.
in the case of the single repeating universe, one may use the Stoica convention [4] as to non
pathological singularities, or a near singularity at the beginning of space-time.
The situation changes if we have a multiverse. Here, the behavior of viscosity changes
fundamentally in terms of its contribution to temperature, and this in turn has manifest
implications as to possible advoidance of singularities in initial space time. To set the frame
work for doing this, we will generalize the Penrose CCC hypothesis [3] in a way presented by
the author in San Marino, Italy, and other places. First now, let us look at the single repeating
universe case and comment upon it.
The final part will be a summary in section 13 below which states a generalized treatment
as to how the singularity is avoided in the multiverse with reccomendations as to future research
in section 14.
2. If there is a Single repeating universe, what can we expect in terms of entropy and
Singularies ? Case written below.
This first part of the article is to investigate what happens physically if there is a non
pathological singularity in terms of Einstein’s equations at the start of space-time if there is a
single repeating universe. This eliminates the necessity of having then put in the Planck length
since then ther would be no reason to have a minimum non zero length. The reasons for such a
proposal come from [4] by Stoica who may have removed the reason for the development of
Planck’s length as a minimum safety net to remove what appears to be unadvoidable pathologies
at the start of applying the Einstein equations at a space-time singularity, and are commented
upon in this article. ρ ~ H 2 / G ⇔ H ≈ a −1 in particular is remarked upon. This is a counter part
to Fjortoft theorem in Appendix I below. The idea is that entanglement entropy will help
generate bits, due to the presence of a vacuum energy, as derived at the end of the article, and the
presence of a vacuum energy non zero value, is necessary for comsological evolution. Before we
get to that creation of what is a necessary creation of vacuum energy conditions we refer to
constructions leading to extremely pathological problems which [4] could lead to minus the
presence of initial non zero vacuum energy. [5]also adds more elaboration on this.
3. Note a change in entropy formula given by Lee [6] about the inter relationship between energy,
entropy and temperature as given by
m ⋅ c 2 = ∆E = TU ⋅ ∆S =
⋅a
⋅ ∆S
2π ⋅ c ⋅ k B
(1)
Lee’s formula is crucial for what we will bring up in the latter part of this document.
Namely that changes in initial energy could effectively vanish if [4]is right, i.e. Stoica removing
the non pathological nature of a big bang singularity. That is, unless entanglement entropy is
used.
If the mass m, i.e. for gravitons is set by acceleration (of the net universe) and a change in
c2
enthropy ∆S ~ 1038 between the electroweak regime and the final entropy value of, if a ≅
for
∆x
acceleration is used, so then we obtain
SToday ~ 1088
(2)
Then we are really forced to look at Eq. (1) as a paring between gravitons (today) and
gravitinos (electro weak) in the sense of preservation of information.
Having said this note by extention ρ ~ H 2 / G ⇔ H ≈ a −1 . As ρ changes due to ρ ~ H 2 / G
1
and Rinitial ~ Ng < lPlanck , t hen a is also altered i.e. goes to zero..
#
What will determine the answer to this question is if ∆Einitial goes to zero if Rinitial → 0 which
happens if there is no minimum distance mandated to avoid the pathology of singularity behavior
at the heart of the Einstein equations. In doing this, we avoid using the energy E → 0+ situation,
i.e. of vanishing initial space-time energy, and instead refer to a nonzero energy, with
∆Einitial instead vanishing. In particular, the Entanglement entropy concept as presented by Muller
and Lousto [7] is presented toward the end of this manuscript as a partial resolution of some of
the pathologies brought up in this article before the entanglement entropy section. No matter how
small the length gets, S entropy if it is entanglement entropy, will not go to zero. The requirement is
that the smallest length of time, t, rescaled, does not go to zero. This preserves a minimum non
zero Λ vacuum energy, and in doing so keep non zero amounts of initial bits, for computational
bits cosmological evolution even if Rinitial → 0
Before doing that, we review Ng [8] and his quantum foam hypothesis to give conceptual
underpinnings as to why we later even review the implications of entanglement.entropy. I.e. the
concept of bits and computations is brought up because of applying energy uncertainty, as given
by [8] and the Margolis theorem appears to indicate that the universe could not possibly evolve if
[8] is applied, in a 4 dimensional closed universe. This bottle neck as indicated by Ng’s [8]
formalism is even more striking in the author’s end of article proof of the necessity of using
4. entanglement entropy in lieu of the conclusion involving entanglement entropy, which can be
non zero, even if Rinitial → 0 provided therre is a minimum non zero time length.
3
Review of Ng, [8] with comments.
First of all, Ng [8] refers to the Margolus-Levitin theorem with the rate of operations
Mc 2 l
⋅ . Ng wishes to avoid black-hole formation
< E ⇒ # operations < E × time =
c
lc 2
. This last step is not important to our view point, but we refer to it to keep
⇒M ≤
G
fidelity to what Ng brought up in his presentation. Later on, Ng refers to the
2
# operations ≤ ( RH lP ) ~ 10123 with RH the Hubble radius. Next Ng refers to the
# bits ∝ [ # operations ] . Each bit energy is 1/ RH with RH ~ lP ⋅10123/2
3/4
The key point as seen by Ng [8] and the author is in
E l
# bits ~ ⋅
c
Mc 2 l
≈
⋅
c
3/4
3/4
(3)
Assuming that the initial energy E of the universe is not set equal to zero, which the
author views as impossible, the above equation says that the number of available bits
1
goes down dramatically if one sets Rinitial ~ Ng < lPlanck ? Also Ng writes entropy S as
#
proportional to a particle count via N.
S ~ N ≅ [ RH / lP ]
2
(4)
We rescale RH to be
RH
rescale
~
lNg
#
⋅10123/2
(5)
The upshot is that the entropy, in terms of the number of available particles drops
dramatically if # becomes larger.
1
Ng < lPlanck grows smaller, as # becomes larger
#
a. The initial entropy drops
b. The nunber of bits initially available also drops.
So, as Rinitial ~
The limiting case of Eq.(4) and Eq. (5) in a closed universe, with no higher dimensional
embedding is that both would almost vanish, i.e. appear to go to zero if # becomes very much
larger. The question we have to ask is would the number of bits in computational evolution
actually vanish?
5. 4.
Does it make sense to talk of vacuum energy if Rinitial ≠ 0 is changed to Rinitial → 0 ?
Only answerable straightforwardly if an embedding superstructure is assigned.
Otherwise difficult. Unless one is using entanglement entropy which is non zero even
if Rinitial → 0
We summarize what may be the high lights of this inquiry leading to the present paper as
follows.
4a. One could have the situation if Rinitial → 0 of an infinite point mass, if there is an
initial nonzero energy in the case of four dimensions and no higher dimensional
embedding even if [4] goes through verbatim. The author sees this as unlikely. The
infinite point mass construction is verbatim if one assumes a closed universe, with no
embedding superstructure and no entanglement entropy. Note this appears to nullify the
parallel brane world construction used by Durrer [9] .The author, in lieu of the
manuscript sees no reason as to what would perturb this infinite point structure, so as to
be able to enter in a big bang era. In such a situation, one would not have vacuum energy
unless entanglement entropy were used. That is unless one has a non zero entanglement
entropy [7] present even if Rinitial → 0 . See [10]for a smilar argument.
4b. The most problematic scenario. Rinitial → 0 and no initial cosmological energy. I.e.
this in a 4 dimensional closed universe. Then there would be no vacuum energy at
all.initially. A literal completely empty initial state, which is not held to be viable by
Volovik [7].
4c. If additional dimensions are involved in beginning cosmology, than just 4 dimensions
will lead to physics which may give credence to other senarios. One scenario being the
authors speculation as to initial degrees of freedom reaching up to 1000, and the nature
of a phase transition from essentially very low degrees of freedom, to over 1000 as
speculated by the author in 2010 [12].
4d. What the author would be particularly interested in knowing would be if actual
semiclassical reasoning could be used to get to an initial prequantum cosmological state.
This would be akin to using [13], but even more to the point, using [14] and[15], with
both these last references relevant to forming Planck’s constant from electromagnetic
wave equations. The author points to the enormous Electromagnetic fields in the
electroweak era as perhaps being part of the background necessary for such a
semiclassical derivation, plus a possible Octonionic space-time regime, as before
inflation flattens space-time, as forming a boundary condition for such constructions to
occur [16]
The relevant template for examinging such questions is given in the following table 1 as printed
below.
6. 4e. The meaning of Octonionic geometry prior to the introduction of quantum physics
presupposes a form of embedding geometry and in many ways is similar to Penrose’s
cyclic conformal cosmology speculation.:
4f. It is striking how a semiclassical argument can be used to construct Table 1 below. In
particular, we look at how Planck’s constant is derived, as in the electroweak regime of
space-time, for a total derivative [14] ,[15]
Ey =
∂Ay
∂t
= ω ⋅ A′ (ω ⋅ ( t − x ) )
y
(6)
Similarly [10],[11]
Bz =
−
∂Ay
∂x
= ⋅ A′ (ω ⋅ ( t − x ) )
ω y
(7)
The A field so given would be part of the Maxwell's equations given by [9] as, when
represents a D’Albertain operator, that in a vacuum, one would have for an A field [14], [15]
[ ]A=0
[]
(8)
And for a scalar field φ
[ ]φ = 0
(9)
Following this line of thought we then would have an energy density given by, if ε 0 is the early
universe permeability [14]
η=
ε0
2
2
⋅ ( E y + Bz2 ) = ω 2 ⋅ ε 0 ⋅ A′ 2 (ω ⋅ ( t − x ) )
y
(10)
We integrate Eq. (10) over a specified E and M boundary, so that, then we can write the
following condition namely [14], [15] .
− x ) dydz
∫∫∫η d ( t=
ωε o ∫∫∫ A′2 (ω ⋅ ( t − x ) )d ( t − x ) dydz
y
(11)
(11) would be integrated over the boundary regime from the transition from the Octonionic
regime of space time, to the non Octonionic regime, assuming an abrupt transition occurs, and
we can write, the volume integral as representing [14] ,[15]
Egravitational −energy = ⋅ ω
(12)
Then by applying [14], [15] we get formed by semiclassical reasons In semi classical
reasoning similar to [13]
( t ) (Constant value)
→
Apply − Machs − Re lations
(13)
7. The question we can ask, is that can we have a prequantum regime commencing for Eq.
1
Eq.(11) and Eq (12) for if Rinitial ~ Ng < lPlanck ? And a closed 4 dimensional universe? If so,
#
then what is the necessary geometrial regime of space-time so that the integration performed in
(11) can commence properly? Also, what can we say about the formation of Eq. (12) above, as a
number, # gets larger and larger, effectively leading to. Also,with an Octonionic geometry
regime which is a pre quantum state.[16]
TABLE 1
.Time Interval
Dynamical consequences Does QM/WdW apply?
Just before Electroweak Form from early E & NO
era
M fields, and use
Maxwell's
Equations
with
necessary
to
implement
boundary
conditions created from
change from Octonionic
geometry to flat space
Electro-Weak Era
kept constant due to YES
Machian relations
Post Electro-Weak Era kept constant due to YES
to today
Machian relations
Wave
function
of
Universe
In so many words, the formation period for is our pre-quantum regime. This table 1 could
even hold if Rinitial → 0 but that the 4 dimensional space-time exhibiting such behavior is
embedded in a higher dimensional template. That due to Rinitial → 0 not removing entanglement
entropy as is discussed near the end of this article.
5. If Rinitial → 0 then if there is an isolated, closed universe, there is a disaster unless
one uses entanglement entropy.
One does not have initial entropy, and the number of bits initially disappears. That is if
one is not using entanglement entropy, as will be examined at the end of this article.
Abandoning the idea of a completely empty universe, this unperturbed point of matter-energy
appears to be a recipede for a static point with no perturbation, as may be the end result of
applying Fjortoft theorem [17] to the thermodynamic potential as given in [18], i.e. the non
definitive anwer for fufillment of criteria of instability by applying Fjortoft’s theorem [17] to the
potential [18]leading to no instability as given by the potential given in [18] may lead to a point
of space-time with no change, i.e. a singular point with ‘infinite’ mass which does not change at
all. This issue will be reviewed in [19] a different procedure, i.e. a so called nonsingular universe
8. construction. To get there we will first of all review an issue leading up to implimentation of
[19].
6. Can an alternative to a minimum length be put in? Consider the example of Planck
time as the minimal component, not Planck length.
From J. Dickau, [20] the following was given to the author, as a counter point to
Rinitial → 0 leading to a disaster.
“If we examine the Mandelbrot Set along the Real axis, it informs us about behaviors that
also pertain in the Quaternion and Octonic case-because the real axis is invariant over the
number types. If numbers larger than .25 are squared and summed recursively ( i.e. –z = z^2 +c )
the result will blow up, but numbers below this threshold never get to infinity, no matter how
many times they are iterated. But once space-like dimensions are added-i.e. an imaginary
compoent- the equation blows up exponentially, faser than when iterated“
Dickau concludes:
“Anyhow there may be a minimum (space-time length) involved but it is probably in
the time direction”.
This is a counter pose to the idea of minimum length, looking at a beginning situation
with a crucial parameter Rinitial even if the initial time step is “put in by hand”. First of all,
look at [7], if E is M, due to setting c = 1, then
∆Einitial ≈ 4πρ ( Rinitial ) ∆Rinitial
2
(14)
Everything depends upon the parameter Rinitial which can go to zero. We have to look at
what Eq. (14) tells us, even if we have an initial time step for which time is initially
indeterminate, as given by a redoing of Mitra’s g 00 formula Eq. [10] which we put in to establish
the indeterminacy of the initial time step if quantum processes hold.
−2
g 00
= exp
→
0
ρ + p=
0
1 + ( ρ ( t ) / p (t ) )
(15)
What Dickau [20] is promoting is, that the Mandelbrot set, if applicable to early universe
1
geometry, that what the author wrote, with Rinitial ~ Ng < lPlanck small − value
→
# ≠∞
#
potentially going to zero, is less important than a minimum time length. The instability issue is
reviewed in Appendix II. for those who are interested in the author’s views as to lack proof of
instability. It uses [18] which the author views as THE reference as far as thermodynamic
potentials and the early universe.
7. Muller and Lousto Early universe entanglement entropy, and its implications.
Solving the spatial length issue, provided a minimum time step is preserved in the
cosmos, in line with Dickau’s suggestion.
9. We look at [7]
2
S Entropy = .3rH a 2 for a time dependent horizon radius rH in cosmology
(16)
Eq. (16) above was shown by the author to be fully equivalent to
2
= .3rH a 2 ~
S Entropy
.3
Λ
exp −t ⋅
2
a
3
(17)
i.e.
a2
Λ
−t
~ ln e ⋅ S entropy
3
.3
(18)
So, then one has
3 a2
Λ ≈ 2 ⋅ ln e ⋅ S entropy
t .3
2
(19)
No matter how small the length gets, S entropy if it is entanglement entropy, will not go to zero.
The requirement is that the smallest length of time, t, re scaled does not go to zero. This
preserves a minimum non zero Λ vacuum energy, and in doing so keep the non zero initial bits,
for computational bits contributions to evolving space time behavior even if Rinitial → 0
8. Reviewing a suggestion as to how to quantify the shrinkage of the scale factor and
its connections with entanglement entropy.
We are given by [19] if there is a non singular universe, a template as to how to evaluate
scale factor a against time scaled over Planck time, with the following results.
8π
a6 2 ⋅ a3
t
+
=
⋅
6
3
3 t Planck
Two time and scale factor values in tandem particularly stand out. Namely,
ascale
a~
≡ 1.344 ⇔ t ∝ t Planck ~ 5.4 ×10−44 sec
−25
aPlanck ~ 10
ln e a +
(20)
(21)
Also
a~
ascale
≡ .7414 ⇔ t ∝ 0+
−25
aPlanck ~ 10
(22)
The main thing we can take from this, is to look at the inter-relationship of how to pin down an
actual initial Hubble “constant” expansion parameter, where we look at:
10. ln e (1.813)
t Planck
=
=
1.813 exp( H Planck ⋅ t Planck ) ⇔ H Planck
(23)
2
3 a2
Recall that Λ ≈ 2 ⋅ ln e ⋅ S entropy , which is predicated upon , if the time is close to Planck
t .3
time the initial maximal density of
ρ Planck ~ 5.2 ×1096 kg / m3
(24)
And length given by
Length= lPlanck ~ 1.6 ×10−35 meters
( Planck )
(25)
So (24) is implying that the amount of matter in a region of space ( lPlanck ) is initially about
3
ρinitial ~ 2 ×10−10 Kg ~ 2 ×10−7 grams
(26)
Using 1 GeV/c2 = 1.783×10−27 kg means that (26) above is
ρinitial ~ 2 ×10−10 Kg ~ 2 ×10−7 grams ~ 10+17 GeV
(26a)
Then if
10
+17
3 a2
GeV ~ Λ ≈ 2 ⋅ ln e ⋅ S entropy
t .3
2
(27)
It will lead to
a2
(28)
10+17 GeV ×10−70 sec 2 ~ ln e ⋅ S entropy
.3
Then, to first order, one is looking at Initial entropy to get a non zero but definite vacuum
energy as leading to an entanglement entropy of about ( just before the electro weak regime)
(29)
S entropy ~ 1/ a 2 ~ 1020 − 1040
9. Reviewing the geometry for embedding Eq. (29) above.
.
In line with Stoica [4] shrinking the minimum length and referring to both Eq.(29) and
Eq.(27), the idea is to use a surface area treatment as to getting the initial entropy values as given
in Eq. (29). To do so, the author looks at the following diagram:
11. Figure 1, from [9]
Brane world dynamics in the case of a single, repeating universe, as opposed to a multiverse.
Now for a review of Figure 1 above. The two branes given at yb and ys refer to the two Brane
world states, especially in line with [24], [25]. The first one, namely yb is the brane where our
physical universe lives in, and is embedded in. If one uses this construction, with higher
dimensions than just 4 dimensions, then it is possible to have a single point in 4 dimensional
space as a starting point to a tangential sheet which is part of an embedding in more than 4
dimensions. Along the lines of having a 4 dimensional cusp with its valley (lowest) point in a
more than 4 dimensional tangential surface. The second brane is about 10−30 centimeters away
from the brane our physical world lives in, and moves closer to our own brane in the future,
leading to a slapping of the two branes together about a trillion years ahead in our future
[24],[25]. The geometry we are referring to with regards to embedding is in the first brane yb . [9]
uses this geometry to have graviton production which the author has used to model Dark Energy
[21]
10. 1st Conclusion when looking at ONE repeating universe. Making computational bits,
via (19).
As stated by Ng [8]. the idea would be to have to give imputs into (3) i.e.
3/4
Mc 2 l
E l
(3)
⋅
# bits ~ ⋅ ≈
c
c
Here in this case, even if the spatial contribution, due to [4] goes to zero, the idea would be to
have the time length non zero so as to have a space-time version of l non zero. . This would
3/4
2
3 a2
also be in tandem with calling E, in (3) as proportional to Λ ≈ 2 ⋅ ln e ⋅ S entropy , where
t .3
if the time is Planck time, in minimum value, and S entropy ~ 1/ a 2 ~ 1020 − 1040 in value, one
would have before the electro-weak an input into E, which would require an entropy
(entanglement)
12. What remains to be seen is, if there is a geometric sheet in more than 4 dimensions, allowing
2
3 a2
for non zero time, as argued for Λ ≈ 2 ⋅ ln e ⋅ S entropy , even if the spatial componet
t .3
goes to zero, according to [4]. We suggest an update as to what was written by Lloyd [26]
I = S total / k B ln 2 = [# operations ]
3/ 4
[
= ρ ⋅ c5 ⋅ t 4
]
3/ 4
(30)
when [27]
ρ ≡ T 00 ~ Λ vacuum−energy
(31)
While doing this, a good thing to do, would be to keep in mind the four dimensional version
of vacuum energy as given by Park, [1] namely
Λ 4−dim ≈ c 2 ⋅ T β
(32)
As well as the transition given by a combination of [1] , with [28], Barvinskey et. al.
[
2
Λ 4−dim ∝ c 2 ⋅ T graviton − production → 360 ⋅ m P << c 2 ⋅ T ≈ 10 32 K
]
(33)
Quantifying the above, and giving it experimental proof, via detector technology may allow us
to investigate an old suggestion by the author as to four dimension and five dimensional vacuum
energy which was given for small time values t ≈ δ 1 ⋅ t P , 0 < δ 1 ≤ 1 and for temperatures sharply
lower than T ≈ 1012 Kelvin , Beckwith [22] , where for a positive integer n
Λ 4−dim
1
−1 ≈
Λ 5−dim
n
(34)
In particular, the author is interested in investigating if the following is true, i.e.
Look at an argument provided by Padmanabhan [29] and [30] , leading to the observed
cosmological
constant
value
suggested
by
Park
[1].
Assume
that
~
l P ~ 10 −33 cm Quantum → N α ⋅ l P , but that when we make this substitution that
−Gravity −threshold
~
1 ≤ N α ≤ 10 2 [30]
ρVAC ~
~ l
Λ observed
~ ρUV ⋅ ρ IR
8πG
−4
Planck
⋅l
−4
H
~l
−2
Planck
⋅H
(35)
2
observed
i.e. looking at if
2
∆ρ ≈ a dark energy density ~ H observed G
Now to make it more interesting:
(36)
13. 2
2
We can replace Λ observed , H observed by Λ initial , H initial . In addition we may look at inputs from the
initial value of the Hubble parameter to get the necessary e folding needed for inflation,
according to
E − foldings = H initial ⋅ t
−t
End of inf beginning
⇒ H initial ≥ 10 39 − 10 43
of inf
≡ N ≥ 100
(37)
Leading to
a(End − of − inf ) a(Beginning − of − inf ) ≡ exp(N )
[
(38)
]
If we set Λ initial ~ c1 ⋅ T ~ 10 32 Kelvin implying a very large initial cosmological constant value,
we get in line with what Park suggested for times much less than the Planck interval of time at
the instant of nucleation of a vacuum state
[
]
Λ initial ~ 10156 ⋅ 8πG ≈ huge number
(39)
.Question. Do we always have this value of Eq.(39)? At the onset of Inflation? When we are not
3
that far away from a volume of space characterized by l P , or at most 100 or so times larger ?
Contemporary big bang theories imply this. I.e. a very high level of thermal energy. We need to
ask if this is something which could be transferred from a prior universe, i.e. could there be a pop
up nucleation effect , i.e. emergent space time? This question is what should be investigated
throughly. Appendix III and Appendix IV give suggestions which the author has thought of
which may contribute to, if anything, models of how instantons from a prior universe may be
transmitted to our present universe, i.e. Appendix V which is based in part on what Wesson
formulated as to five dimensional universe constructions, and instantons [33]. The very
interesting topic of vacuum fluctuations in such space-time has also been reviewed briefly in
Appendix VI, and Appendix VII
11. What if we have a multiverse? Argue then that the above methodology should be
modified. I.e. consider the following scaling of quantities from the Friedman
equation.
Using the formalism given in Peacock [34], page 80 we can make the following scaling
argument which will prove useful as to the divergence of the multiverse case, and how there is
no longer a convenient singularity to refer to, via Stoica [4] or anyone else
Peacock, has it that one can write as follows, namely for a scale factor, with a0
14. infinitesimally small and representing the intial scale factor in pre Planckian space time
(40)
= a0 exp H ⋅ t
a (t )
Here, the main evolving factor to consider is, Peacock [34] , page 80 with Λ cos −const from Eq. (32)
above. If so then we have to look at one datum which will be important. Mainly, how the
temperature changes.
`
`
Λ cos −const ⋅ c 2
(41)
H=
3
If the term beta in the coefficient of temperature, T , is zero, we have merely the Einstein vanilla
Cosmological constant . If the term beta in the coefficient of temperature, T, is not zero, then we
should take a good look at what is done in Weinberg [ 2] where there is a concerted effort to mix
in background viscosity =. But first take note of the Grischuck [35] expression as to GW
frequency in the hign end, with Temperature approaching Planck Tempure values, with behavior
due to space-time temperature dependence as given by:” M = mass of ‘universe’ initially, and R
= radius of initial dimensions, with Planck temperature values giving for a single universe, and
four dimensions
T
f Peak ≈ (10−3 Hz ) ⋅
~ 1010 Hz
TeV
(42)
90 km
≈
⋅
M solar − mass
R
Then in doing this, we will also consider the case where the temperature is low, which we claim
is due to a multiverse, and this will be leading to, for ultra low initial temperatures, for the “pre
big bang, namely if there is a multiverse having
M
T
−18
−10
f Peak ≈ (10−3 Hz ) ⋅
~ 10 − 10 Hz
TeV
(43)
Furthermore, we can write from Page 163 of Penrose [3] , that, if N ~ S (entropy) as given by Ng
[8] for a regular single repeating universe structure, that we will have, for a cyclical universe the
following power law relationship. Note that in Eq. (44) the abbreviation of F.T. stands for field
theory.
Λ Today [vacuum − energy ]
c3
~ 6
≡ N −6
≈ 10−120 times{FT calculated version of Vacuum energy} (44)
value −Today
N G
6
~ 1/ Sinitially
15. I.e that the cosmological constant is set by the initial release of, maybe, gravitons. i.e. and also
note that if one does this that one is able to state that initially low entropy will lead to a tendency,
later to a scaled cosmological constant which is todays value.
The question in reaching Eq (44) is , if entropy is commensurate with graviton production as
brought up by both Beckwith [21] and Giovannini [36] that then one is looking at thermally
induced GW production which may indeed impact the cosmological constant. The question to
ask is the following reasonable? I.e. as given by Giovannini [36]
SGraviton −Today ' s.era ∝ V ∫
1011 Hertz
10−19 Hertz
r ( v ) ⋅v 2 dv
3
H1
90
≅ (1030 ) ⋅
∝ 10
M Planck −mass
~ (difference of 1011 to 10−19 Hertz )3
(45)
If Eq. (45) is defensible as to entropy growth, and gravitons play a role, then the initial
temperature may be affected by modeling Gravitons as a particle in a viscous fluid, see Weinberg
[2] page 592 with Planck time as of the order of magnitude of a mean free time of collisions of
Gravitons in a formation plasma as an imperfect fluid
15 1 η
T ~ ⋅ ⋅
4 a t Plank
β
β /4
15 1
η
∝ ⋅ ⋅
4 a τ graviton
β /4
(46)
Using this Eq.(46), if the viscosity drops, the temperature drops as well. We posit that this will
then have immediate consequenes for the problem of a multiverse versus a single universe
12. Penrose Comology supposition and its tie in to temperature and viscosity as used in
Eq. (46)
From Penrose, [3] page 130, we have
=
E 8π ⋅ T + Λ ⋅ g
E = source for gravitational field
T = mass energy density
(47)
g = gravitational metric
Λ =vacuum energy, rescaled as follows
g g = Ω 2 g
→ˆ
ccc
(48)
The single universe CCC has, then, when black holes ( up to a million of them) take in space
time from an expanding universe, a ‘reverse’ conformal re set which Penrose [ 3] sets as
16. Ω Ω −1
→
CCC
(49)
This re set, would tend toward a huge viscosity, as for Eq. (46) with a very large initial
temperature.
The question is, what would happen to this equation, and temperature if there is a multiverse. I.e
the viscosity would drop, and that would lead to low initial pre big bang temperatures, i.e. see the
following
dΩ
dΩ
SAME
→
2
Ω −1
→Ω
CCC
Ω −1
Ω2 − 1
=
Π
(50)
This will be generalized in the case of a multi verse as follow . Eq (47) is not really altered, but
Eq (49) will have a multi verse interpretation, i.e. for the four dimensional ‘domain’ universes
we will call Ω j
n[ number − of − ' universes ']
1
Ωinput − new−cycle
⋅
Ω j
∑
n[number − of − ' universes ']
=1
j
Then, there will be a new mapping, of
Ω j [ ' our − universe '] ( Ωinput − new−cycle )
→
−1
(51)
(52)
This would, then go to a modification of the Penrose mapping in Eq.(50) to read as
d Ω j
d Ω j
→ SAME
−1
Ω [ ' our −universe '] ( Ωinput −new−cycle )
→
j
Ω j − 1
Ω j 2 − 1
2
(53)
Eq.(53) with Eq.(52) are in reality a motivation of Ergodic mixing , i.e. a way to have continual
re sets of the initial data, for the purpose of having the same initial conditions again and again,
i.e. this is a way of a re set of Planck’s constant, and of the fine structure constant without the
annoyance of the anthropic principle.
The governing principle behind it would be the Ergodic theorem, i.e. see Dye[39] , as an
averaging process again and again. In doing so, Eq. (52) and Eq.(53) would through mixing lead
to the same re set again and again, but with one major different consequence than in the single
repeating universe case, i.e there would be a low temperature pre big bang, using Eq. (43),
instead of Eq. (42). This would be a way of having a very different answer as to the character of
early universe GW generation, with the multiverse having very low GW frequency, even before
red shifting of GW, instead of the high frequency GW predicted by Eq. (42). Next then, we will
examine the consequences of the initial starting point of the multiverse recycled starting point.
Note the multiverse would likely entail an initially low viscosity, which says low temperature.
13. Re examining the question of a ‘near singularity’ in a multiverse
We follow the recent work of Steven Kenneth Kauffmann [40], which sets an upper bound to
concentrations of energy, in terms of how he formulated the following equation put in below as
17. Eq. (54). Eq. (54) specifies an inter-relationship between an initial radius R for an expanding
universe, and a “gravitationally based energy” expression we will call TG ( r ) which lead to a lower
bound to the radius of the universe at the start of the Universe’s initial expansion, with
manipulations. The term TG ( r ) is defined via Eq.(55) afterwards.We start off with Kauffmann’s
expression [40]
c4
R ⋅
G
≥
TG ( r + r ′′ ) d 3 r ′′
∫
(54)
r ′′ ≤ R
Kauffmann calls
c4
G
a “Planck force” which is relevant due to the fact we will employ Eq. (54)
at the initial instant of the universe, in the Planckian regime of space-time. Also, we make full
use of setting for small r, the following:
TG ( r + r ′′ ) ≈ TG
0
( r ) ⋅ const ~ V (r ) ~ mGraviton ⋅ nInitial −entropy ⋅ c 2
(55)
I.e. what we are doing is to make the expression in the integrand proportional to information
leaked by a past universe into our present universe, with Ng [8] style quantum infinite statistics
use of
nInitial −entropy ~ SGraviton −count −entropy
(56)
Then Eq. (54) will lead to
c4
R ⋅ ≥ ∫ TG ( r + r ′′ ) d 3 r ′′ ≈ const ⋅ mGraviton ⋅ nInitial −entropy ~ SGraviton −count −entropy
G r ′′ ≤ R
c4
⇒ R ⋅
G
≥ const ⋅ mGraviton ⋅ nInitial −entropy ~ SGraviton −count −entropy
(57)
−1
c4
⇒ R ≥ ⋅ const ⋅ mGraviton ⋅ nInitial −entropy ~ SGraviton −count −entropy
G
Here, nInitial −entropy ~ SGraviton −count −entropy ~ 105 , mGraviton ~ 10−62 grams , and we set Plank length as:
Planck length = lPlanck = 1.616199 × 10-35 meters
where we set lPlanck = G with R ~ lPlanck ⋅ 10α , and α > 0 . Typically R ~ lPlanck ⋅ 10α is about
3
c
103 ⋅ lPlanck
at
the outset, when the universe is the most compact. The value of const is chosen based on
common assumptions about contributions from all sources of early universe entropy, and will be
more rigorously defined in a later paper
We argue that the above methodology, giving a non zero initial starting point is made especially
tendable if one is using a low temperature start, allowing for the existence of prior recycling
universes gravitons to play a role, i.e. that in the single universe repeated again and again, there
would be real issues as to the survival of the graviton allowing for the conclusion as to Eq. (57).
18. 14. Fork the road. Nonzero radii of start of inflation may be linkable to low
temperature pre universe due to multiverse. How to confirm it ?
The author’s supposition and argument as to the results of Eq. (57) which would be key to
identifying if a zero point starting point to inflation were mandatory is akin to the question of
could gravity and gravitons exist prior to inflation. If there is a multiverse, i.e. repeatedly, as
mentioned in section 12, then the answer is likely yes. Hence, Eq. (57) would indicate that a
‘perfect’ singularity is not mandatory. The problem though is that then likely initial relic GW
would then be enormously long, ie as given in Eq. (43) above. This independent of red shifting.
If one has ultra high gravity waves as created at the big bang, then it is likely that a
singularity is mandatory. We also then have referred to Stoica’s work as to how this could be
squeezed down below the Planck length limit, but itself would not be pathological for the reasons
stated above.I.e. confirmation of the two alternatives likely hinges upon determination if ultra
high GW are indeed part of the pre inflation to inflationary universe’s signal heritage.
Note that Figure 1 above is pertinent to a single, repeating universe. The author knows of no
viable counter part to Figure 1 in the case of a multiverse. Hence, as for higher dimensions, the
author, in lieu of his generalization of the Penrose cosmology conjecture [3] has referenced
Appendix V below which is really akin to the material given in Wesson [33] as to Appendix
VIII below, as to a different geometry than Braneworlds as to the multiverse hypothesis.
Suitable inquiry should be in terms of if Braneworlds as of Figure 1 can suitably be modified for
the multiverse. The author doubts this is possible. I.e. if low GW are confirmed as to relic
conditions for our particular universe, then if we choose the multiverse, disternment of if Figure
1 has a real generalization to the multiverse hypothesis is mandatory. The author believes that
this will be futile.
Note also, if a single repeating universe is confirmed via relic HFGW, then Figure 1 is
probably legitimate and brane world ‘vibrations’ may be necessary for HFGW. If so, then one
can as an intellectual inquiry inquire if the generalization to Appendix VIII is then really
necessary.
Acknowledgements
The author particularly appreciates the Mandelbrot example given to him by J. Dickau as a
legitimate research inquiry question which he will pursue in future work. The author also thanks
his late father, and Dr. Xi Yang of Brookhaven national laboratory as to imbuing him with the
necessary curiosity and physics questions which much later on lead to the singularity issues in
this document being investigated. Part of this presentation was also in lectures to Graduate
Physics Students in Chongqing University, in November 2013.
References
[1]D. H. Park, H. Kim, and S. Tamarayan, “Nonvanishing Cosmological Constant of Flat Universe in
Brane world Scenarios,” Phys.Lett. B535 (2002) pp. 5-10
[2] S Weinberg, Gravitation and Cosmology, principles and applications of the general theory of
relativity, Wiley, 1972, San Francisco, USA.
[3] R. Penrose, Cycles of Time , The Bodley Head, 2010, London, UK
[4] Cristi Stoica, “Beyond the FRWL Big Bang Singularity”, http://arxiv.org/pdf/1203.1819.pdf
19. [5].A.W. Beckwith, “Is Quantum Mechanics Involved at the Start of Cosmological Evolution? Does a
Machian Relationship Between Gravitons and Gravitinos Answer This Question? ”,
http://vixra.org/abs/1206.0023
[6] Jae-Weon Lee, “On the Origin of Entropic Gravity and Inertia”, http://arxiv.org/abs/1003.4464;
Foundations of physics, Volume 42, 2012
[7] R. Muller, a C. Lousto, “ Entanglement entropy in curved space-times with event horizons”, arXIV grqc/9504049 v1, 28 april, 1995
[8] Y.J. Ng, Entropy 10(4), pp441-461 (2008);
Y.J. Ng and H. van Dam, FoundPhys30, pp795–805 (2000);
Y.J. Ng, “Quantum Foam and Dark Energy”, in the conference International work shop on the Dark Side
of the Universe, http://ctp.bue.edu.eg/workshops/Talks/Monday/QuntumFoamAndDarkEnergy.pdf
[9] R. Durrer et.al., “Dynamical Casmir effect for gravitons in Bouncing Braneworlds”, 2009,
http://theory.physics.unige.ch/~durrer/papers/casimir.pdf;
Earlier version
http://www.scribd.com/doc/79001898/Ruth-Durrer-and-Marcus-Ruser-The-dynamical-Casimir-effect-inbraneworlds ;
Version put into PRD
Marcus Ruser, Ruth Durrer, “Dynamical Casimir effect for gravitons in bouncing braneworlds”,
http://arxiv.org/abs/0704.0790;
Phys.Rev.D76:104014,2007
[10] Abhas Mitra, “Why the Big Bang Model Cannot Describe the Observed Universe having Pressure
and Radiation”,Journal of Modern Physics 2011,2,1436-1442 ( published online December 2011)
[11]G.E. Volovik, “Vacuum Energy: Myths and Realities”, arXIV: gr-qc/0604062 v2, April 16, 2006
[12] A. Beckwith, “How to use the cosmological Schwinger principle for energy flux, entropy, and
"atoms of space–time" to create a thermodynamic space–time and multiverse”,
http://iopscience.iop.org/1742-6596/306/1/012064, in “5th International Workshop DICE2010: SpaceTime-Matter – Current Issues in Quantum Mechanics and Beyond”, T. Elze ed.
http://iopscience.iop.org/1742-6596/306/1;jsessionid=A05372A78C18D970BF35F40A9A863B51.c2
[13]M. Gryzinski, “Classical theory of Electronic and Ionic Inelastic Collisions”Phys Rev Vol. 115, no2,
July 15, 1959, pp 374-383
[14]U. Bruchholz; “Derivation of Planck’s constant from Maxwell’s Electrodynamics”, Progress in
Physics, V4, October 2009, page 67; http://www.ptep-online.com/index_files/2009/PP-19-07.PDF
[15] U. Bruzchholz, “Key notes on a geometric theory of fields”, Progress in Physics, 2009, v.2, 107–113.
[16] A. Beckwith, "Octonionic Gravity Formation, Its Connections to Micro Physics," Open Journal of
Microphysics, Vol1 No1, 2011, pp13-18
[17]J. Pringle and A. King; Astrophysical Flows, Cambridge University Press, New York, 2007
[18] Thanu Padmanabhan 2011 J. Phys.: Conf. Ser. 306 01200;”Lessons from Classical Gravity about the
Quantum structure of space-time”, DICE 2010, editor T. Elze, http://iopscience.iop.org/17426596/306/1/012001
[15][19] C. Gao, “ A Model of Nonsingular Unvierse”, Entropy 2012, 14, 1296-1305.
[16] [20] J. Dickau, private communication to the author as to Minimum space-time ‘length’ provided as
of August 7, 2012.
[21] A. Beckwith, “Identifying a Kaluza Klein Treatment of a Graviton Permitting a deceleration
parameter Q (Z) as an Alternative to Standard DE”, Journal of Cosmology, 2011, Vol. 13
http://journalofcosmology.com/BeckwithGraviton.pdf
[18] [22]Sumati Surya, “In Search Of A Covariant Quantum Measure”, From DICE 2010, with Elze as
editor , i.e. http://iopscience.iop.org/1742-6596/306/1/012018
[19][23] A. W.Beckwith, “Identifying a Kaluza Klein Treatment of a Graviton Permitting a deceleration
parameter Q (Z) as an Alternative to Standard DE”, Journal of Cosmology, 2011, Vol. 13
http://journalofcosmology.com/BeckwithGraviton.pdf
[24]J. Koury, P.J. Steinhardt,N. Turkok, PRL92, 031302(2004),hep-th/0307132
20. [25] J. Koury, P.J. Steinhardt,N. Turkok, PRL91, 161301(2003),astro-ph/0302012
[26]S. Lloyd , “Computational capacity of the universe”, Phys. Rev. Lett. 88, 237901 (2002)
[27] A.W. Beckwith “Symmetries in evolving spacetime from prior to present unverses”, arXIV mathph/0501028 (2007)
[28] A. Barvinsky,A. Kamenschick,A.,Yu, “ Thermodynamics from Nothing: Limiting the
Cosmological Constant Landscape, Phy Rev D 74 121502 (Rapid communications)
[29] T. Padmanabhan, An Invitation to Astro physics, World Scientific Publishing Co. Pte. Ltd,
Singapore, 2006
[30]T. Padmanabhan. “Understanding Our Universe: Current Status and Open Issues” , in
100 Years of Relativity Space-Time Structure: Einstein and Beyond, edited by A. Ashtekar,World Press
Scientific, Singapore, 2005
[31]L. Crowell, Quantum Fluctuations of Space-Time , World Scientific Series in Contemporary
Chemical Physics, Vol 25, World Scientific, PTE, LTD, 2005, Singapore
[32]
Lecture
notes
taken
at
IGC
conference,
http://www.gravity.psu.edu/igc/conf_files/program_complete.pdf
with respect to the Penrose presentation, “ Conformal Cyclic cosmology, Dark Matter, and Black Hole
Evaporation”, plus questions asked of the lecturer in the aftermath of that presentation
[33]P. Wesson, P., Space-Time-Matter, Modern Kaluza Klein Theory, World Scientific, Singapore,
Republic of Singapore, 1999
[34] J. Peacock, Cosmological Physics, Cambridge University Press, 2002
[35] L. Grischuck, personal communication to the Author, at the John Wheeler school of astrophysics, in
Erice Italy, 2006
[36] M. Giovannini A primer on the Physics of the Cosmic Microwave Background, World Scientific
Publishing, Singapore, Republic of Singapore, 2008
[37]C. Misner, K. Thorne, K., and J. Wheeler., Gravitation , W.H. Freeman, and Company, San
Francisco, USA, 1973
[38] D. Samtleben , S. Staggs, S., B.Winstein., “The Cosmic Microwave Background for Pedestrians: A
Review for Particle and Nuclear Physicists”, Annu..Rev . Nucl. Part. Sci. 2007, 57, pp. 245-83
[39] H. Dye, “on the Ergodic mixing theorem”, http://www.ams.org/journals/tran/1965-118-00/S00029947-1965-0174705-8/S0002-9947-1965-0174705-8.pdf
[40] . S. Kauffman, “ A Self Gravitational Upper bound On Localized Energy Including that of Virtual
Particles and Quantum Fields, which Yield a Passable Dark Energy Density Estimate”,
http://arxiv.org/abs/1212.0426
Appendix I. Fjortoft theorem:
A necessary condition for instability is that if z∗ is a point in spacetime for which
d 2U
= 0 for any given potential U , then there must be some value z0 in the range z1 < z0 < z2
dz 2
such that
d 2U
dz 2
⋅ [U ( z0 ) − U ( z∗ ) ] < 0
(1)
z0
For the proof, see [17] and also consider that the main discussion is to find instability in a
physical system which will be described by a given potential U . Next, we will construct in the
boundary of the EW era, a way to come up with an optimal description for U
21. Appendix II. Constructing an appropriate potential for using Fjortoft theorem in
cosmology for the early universe cannot be done. We show why
To do this, we will look at Padamanabhan [18]and his construction of (in Dice 2010) of
thermodynamic potentials he used to have another construction of the Einstein GR equations. To
start, Padamanabhan [18]wrote
ab
If Pcd is a so called Lovelock entropy tensor, and Tab a stress energy tensor
cd
U (η a ) =−4 ⋅ Pab ∇ cη a ∇ dη b + Tabη aη b + λ ( x ) g abη aη b
= U gravity (η a ) + U matter (η a ) + λ ( x ) g abη aη b
(1)
cd
⇔ U matter (η a ) = abη aη b ;U gravity (η a ) =−4 ⋅ Pab ∇ cη a ∇ dη b
T
We now will look at
U matter (η a ) = Tabη aη b
;
U gravity (η ) =−4 ⋅ P ∇ cη ∇ dη
a
cd
ab
a
(2)
b
So happens that in terms of looking at the partial derivative of the top (1) equation, we are
looking at
∂ 2U
= Taa + λ ( x ) g aa
2
∂ (η a )
(3)
Thus, we then will be looking at if there is a specified η∗a for which the following holds.
2
∂ U =x ) g aa ∗
Taa + λ (
∂ (η a )2
η0a
cd
a
b
b
−4 ⋅ Pab ( ∇ cη0 ∇ dη0 − ∇ cη∗a ∇ dη∗ ) +
a b
b
a b
b
Tab ⋅ η0η0 − η∗aη∗ + λ ( x ) g ab ⋅ η0η0 − η∗aη∗
<0
(4)
η∗a for which (4) holds.
Therefore, we say there is no official point of instability of η∗a due to (3). The Lagrangian
structure of what can be built up by the potentials given in (3) with respect to η∗a mean that we
cannot expect an inflection point with respect to a 2nd derivative of a potential system. Such an
inflection point designating a speed up of acceleration due to DE exists a billion years ago
[19][23] . Also note that the reason for the failure for (4) to be congruent to Fjoroft’s theorem is
due to
What this is saying is that there is no unique point, using this
2
∂ U = + λ ( x ) g aa ≠ 0, for∀η∗a choices
Taa
∂ (η a )2
(5)
22. Appendix III, Details as to forming Crowell’s time dependent Wheeler De Witt equation, and its
links to Worm holes
This will be to show some things about the worm hole we assert the instanton traverses en route
to our present universe. From Crowell [31]
1 ∂ 2Ψ
1 ∂Ψ
(1)
−
+ 2⋅
+ rR (3 ) Ψ = rηφ − rφ ⋅ Ψ
2
ηr ∂r
ηr ∂r
This has when we do it φ ≈ cos(ω ⋅ t ) , and frequently R (3 ) ≈ constant, so then we can consider
(
∞
[
φ ≅ ∫ dω a(ω ) ⋅ e ikϖ x − a + (ω ) ⋅ e −ikϖ x
µ
)
µ
]
(2)
0
In order to do this, we can write out the following with regards to the solutions to Eqn (1) put up
above.
4
t
C1 = η 2 ⋅ 4 ⋅ π ⋅ 5 ⋅ J 1 (ω ⋅ r ) + 5 ⋅ sin (ω ⋅ r ) + (ω ⋅ r ) ⋅ cos(ω ⋅ r )
ω
2ω
15
6
+ 5 cos(ω ⋅ r ) − 5 Si (ω ⋅ r )
ω
(3)
ω
And
3
6
(4)
⋅ (1 − cos(ω ⋅ r )) − 4e −ω ⋅r + 4 ⋅ Ci (ω ⋅ r )
4
2 ⋅ω
ω
x
x
sin ( x ′)
cos( x ′)
This is where Si (ω ⋅ r ) and Ci (ω ⋅ r ) refer to integrals of the form ∫
dx ′ and ∫
dx ′ .
x′
x′
−∞
−∞
It so happens that this is for forming the wave functional permitting an instanton forming , while
we next should consider if or not the instanton so farmed is stable under evolution of space time
leading up to inflation. We argue here that we are forming an instanton whose thermal energy is
focused into a wave functional which is in the throat of the worm hole up to a thermal
discontinuity barrier at the onset , and beginning of the inflationary era.
C2 =
Appendix IV: The D’Albembertain operation in an equation of
motion for emergent scalar fields
We begin with the D’Albertain operator as part of an equation of motion for an emergent scalar
field. We refer to the Penrose potential ( with an initial assumption of Euclidian flat space for
computational simplicity) to account for, in a high temperature regime an emergent non zero
value for the scalar field φ due to a zero effective mass, at high temperatures. [32]
When the mass approaches far lower values, it, a non zero scalar field re appears.
.7 0
Leading to φ T →2Kelvin → ε + ≈ 0 + as a vanishingly small contribution to cosmological evolution
23. Let us now begin to initiate how to model the Penrose quintessence scalar field evolution
equation. To begin, look at the flat space version of the evolution equation
φ − ∇ 2φ +
∂V
=0
∂φ
(1)
This is, in the Friedman – Walker metric using the following as a potential system to work with,
namely:
~
1
ℜ
a
V (φ ) ~ − ⋅ M (T ) + φ 2 + φ 4 ≡
6
4
2
(2)
~
1
κ 2 a 4
− ⋅ M (T ) + 2 φ + φ
4
6a (t )
2
This is pre supposing κ ≡ ±1,0 , that one is picking a curvature signature which is compatible
with an open universe.
That means κ = −1,0 as possibilities. So we will look at the κ = −1,0 values . We begin with.
∂V
φ − ∇ 2φ +
=0⇒
∂φ
κ
1
φ 2 = ~ ⋅ c12 − α 2 + 2 + M (T )
a
6a (t )
(3)
⇔ φ ≡ e −α ⋅r exp(c1t )
We find the following as far as basic phenomenology, namely
κ
1
φ 2 = ~ ⋅ c12 − α 2 + 2 + (M (T ) ≈ ε + )
a
6a (t )
M (T → 0 →φ 2 ≠ 0
~ high )
(4)
1
κ
φ 2 = ~ ⋅ c12 − α 2 + 2 + (M (T ) ≠ ε + )
a
6a (t )
M (T ≠ 0 →φ 2 ≈ 0
~ Low)
(5)
The difference is due to the behavior of M (T ) . We use M (T ) ~ axion mass ma (T ) in
asymptotic limits with
ma (T ) ≅ 0.1 ⋅m a (T = 0 ) ⋅ (Λ QCD / T )3.7
(6).
24. Interesting speculation. Does there exist a five dimensional
version of an instanton in the worm hole transition regime?
Appendix V
We will attempt to build the contribution as to a Reissner-Nordstrom metric embedded in a five dimensional spacetime metric , and see if this satisfied . i.e. .look at (1) below This allows us to determine, using of the RisessnerNordstrom metric as given, by Kip Thorne, Wheeler, and Misner [37], for an added cosmological ‘constant’ Λ and
‘charge’ Q . This will be shown to lead to [33]
[
]
M g (r ) = ∫ T00 − (T12 + 2 ⋅ T22 ) ⋅ − g 4 dV3
r3
Λ
r2
≈ π ⋅ c12 ⋅ − 2 M ⋅
+ Q ⋅ r − ⋅ r5 +
2
15
3
Λ
4π ⋅ c1 ⋅ r 2 − 8 ⋅ M ⋅ r − ⋅ r 4 δ → ε + ≈ 0
r→
3
(1)
To do this, we start off with the following space time line metric in five dimensions. This is a
modification of Wesson’s book [33]
2 Φ (r )dt 2
e
dS5 − dim = [exp(i π 2)] ⋅ 2 Λ (r ) 2
~
2
2
+ e
dr + R dΩ
µ
2
+ (−1) ⋅ e dl
(2)
We claim that what is in the { } brackets is just the Reissner-Nordstrom line metric in four
dimensional space. The parameters in the { } bracket are linked to the Reissner-Nordstrom
metric via
2M Q 2
e 2 Φ ( r ) = 1 −
+ 2
r
r
(3)
And
e
And this is assuming that
~
2 Λ (r )
2M Q 2
= 1 −
+ 2
r
r
−1
(4)
R ~ r as well as using µ ≈ c 1 ⋅r with a maximum value topped off
by a Planck’s length value due to µ Maximum ≈ c 1 ⋅rMaximum ~ l P ≡ 10 −35 cm . So being the case, we
get the following stress tensor values
25.
2 M 2Q 2Λr 2
2
− 3 −
2
Λ 2 c1 c1 c1 r 2
− 1 2M Q
0
3
r
T0 = ⋅ 1 −
+ 2 − r ⋅
+ + ⋅
r
r
3 4
4 2M Q 2 Λ 2
r
8π
1−
+ 2 − r
r
3
r
2 M 2Q 2Λr 2
− 3 −
Λ 2 c1 c1 r 2
− 1 2M Q
3
r
T11 = ⋅ 1 −
r ⋅
+ 2 −
+ ⋅
r
3 r
4 2M Q 2 Λ 2
r
8π
1−
+ 2 − r
r
3
r
(5)
2
(6)
2 M 2Q 2Λr 2
2
− 3 −
2
Λ 2 c1 c1 c1 r 2
− 1 2M Q
2
3
3 (7)
r
T2 = T3 = ⋅ 1 −
+ 2 − r ⋅
+ + ⋅
r
3 4
2 2M Q 2 Λ 2
r
r
8π
1−
+ 2 − r
r
3
r
Furthermore, we get the following determinant value
2M Q 2 Λ 2
− g 4 = 1 −
+ 2 − r
r
3
r
(8)
All these together lead to Eq. (1) being satisfied. Let us now see how this same geometry
contributes to a worm hole bridge and a solution as to forming the instanton flux wave functional
between a prior to a present universe. The Reissner-Nordstrom metric permits us to have a
radiation dominated ‘matter’ solution whose matter ‘contribution’ drops off rapidly as the spatial
component of geometry goes to zero. This is in tandem with radiation pressure and density
falling off rapidly, as we leave the center of such a purported soliton/ instanton. This is
extremely useful because it ties in with the notion of fractional branes contributing to entropy
calculations. In fact it is useful to state that these two notions dove tail with each other quite
closely. The only difference is that the construction above does not in itself lend to the
complexity of what we would observe, which is in itself a multiple – joined net work of charge
centers and of shifting geometry.
Appendix VI. Basic physics of achieving minimum precision
in CMBR power spectra measurements
Begin first of all looking at
This leads to consider what to do with
∆T
≡ ∑ almYl ,m (θ , φ )
T
l ,m
(1)
26. C l = al ,m
2
(2)
Samtleben et al [38] consider then what the experimental variance in this power spectrum, to
the tune of an achievable precision given by
∆C l
=
Cl
2
⋅
2l + 1
4π ⋅ (∆Texp )
2 2
f sky ⋅ e l σ b
2
1
f sky
+
Cl
⋅
(3)
f sky is the fraction of the sky covered in the measurement , and ∆Texp is a measurement of the
total experimental sensitivity of the apparatus used. Also σ b is the width of a beam , while we
have a minimum value of l min ≈ (1 ∆Θ ) which is one over the fluctuation of the angular extent of
the experimental survey.
I.e. contributions to C l uncertainty from sample variance is equal to contributions to
uncertainty from noise. The end result is
( [
4π ⋅ f sky = C l ⋅ exp − l 2σ 2
]) (∆T )
2
Cl
(4)
Appendix VII. Vacuum fluctuations which may occur : Cosmological
perturbation theory and tensor fluctuations (Gravity waves)
Durrer [9] reviews how to interpret C l in the region where we have 2 < l < 100 , roughly in the
region of the Sachs-Wolf contributions due to gravity waves. We begin first of all by looking at
an initial perturbation , using a scalar field treatment of the ‘ Bardeen potential’ Ψ This can lead
us to put up, if H i is the initial value of the Hubble expansion parameter
H
k Ψ ≅ i
MP
3
2
2
(1)
And
Ψ
2
n
⋅ k 3 = A 2 k n −1 ⋅ η 0 −1
(2)
Here we are interpreting A = amplitude of metric perturbations at horizon scale, and we set
k = 1 / η 0 , where η is the conformal time, according to dt ≡ adη = physical time, where we have
a as the scale factor.Then for 2 < l < 100 , and − 3 < n < 3 , and a pure power law given by
27. H (k ,η = 1 / k )
2
−
⋅ k 3 = AT2 k nT ⋅ η 0 nT
(3)
We get for tensor fluctuation, i.e. gravity waves,, and a scale invariant spectrum with nT = 0
(T )
Cl
2
AT
1
≈
⋅
(l + 3) ⋅ (l − 2) 15π
(4)
Apppendix VIII. Toward a 5 dimensional geometry which may be pertinent to the five
dimensional multiverse hypothesis: From Wesson [33] .
3
=
dS52− Dim l 2 dt 2 − ∑ exp i (ω ⋅ t + k j x j ) ⋅ dx j − L2 dl 2
j =1
(
)
(1)
Here in this setting, L is the length of the dimension in 5 dim. The other ‘lengths’ are from 4D
contained dimension in the line element in 5D. j=1,2,3 corresponds to x,y,z , while t is for the
time. Furthermore, we also have that the five dimensional cosmological ‘constant’ is negative
Λ 5− D
3⋅ω 2
= 2
−
4l
(2)
Whereas we also have
3⋅ω 2
8π T00 = −
4
(3)
3ω
⋅ exp i ⋅ (ω ⋅ t + k j x j )
4
= = radius of curvature 0
R 12 l 2 L2
→
L →∞
8π T jj
=
2
3⋅ω
8π p = =2
−8πρ
4l
(4)
(5)
2
(6)