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**David Brown**: *on* 7/3/18 at 12:26pm UTC, wrote Consider this hypothesis: The empirical successes of MOND are the first...

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FQXi FORUM

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TOPIC: Is Milgrom’s MOdified Newtonian Dynamics (MOND) fundamental for philosophy, science, and the physical interpretation of string theory? by David Brown [refresh]

TOPIC: Is Milgrom’s MOdified Newtonian Dynamics (MOND) fundamental for philosophy, science, and the physical interpretation of string theory? by David Brown [refresh]

This essay raises questions concerning what is fundamental in physics. There is a brief discussion of Milgrom’s MOdified Newtonian Mechanics with two possible interpretations: one possible interpretation in terms of string theory with the finite nature hypothesis and another possible interpretation in terms of string theory with the infinite nature hypothesis.

David Brown has an M.A. in mathematics from Princeton University and was for a number of years a computer programmer.

The electromagnetic effects of axions (1-spheres with virtual cross sections) and leptons (2-spheres with virtual cross sections) might suggest that some form of electromagnetic uncertainty might be approximated by (axion mass)/(electron mass).

Can the proton charge radius puzzle be resolved in terms of electromagnetic effects from axions?

Proton radius puzzle,...

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Can the proton charge radius puzzle be resolved in terms of electromagnetic effects from axions?

Proton radius puzzle,...

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Beck gives the estimate 110±2 micro-electron-volts for the axion rest mess (putting c = 1).

Beck, Christian. "Axion mass estimates from resonant Josephson junctions." Physics of the Dark Universe 7 (2015): 6-11. arXiv preprint

1.10±.02 * 10^-4 eV is a more precise estimate than 1.2 ± 1.0 * 10^-4 eV and Beck arrived at his estimate by alternate routes of reasoning and evidence.

Beck, Christian. "Axion mass estimates from resonant Josephson junctions." Physics of the Dark Universe 7 (2015): 6-11. arXiv preprint

1.10±.02 * 10^-4 eV is a more precise estimate than 1.2 ± 1.0 * 10^-4 eV and Beck arrived at his estimate by alternate routes of reasoning and evidence.

Can MOND explain existence of Blue shifted Galaxies? What are the other fundamental issues it addresses?

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post approved

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"Are there any galaxies that have blue-shift?", physicslink.com

Category: MOND, Triton Station blog, S. McGaugh

Category: MOND, Triton Station blog, S. McGaugh

Hi David Brown

Your references are nice Dear David Brown….…..….. very nice idea…. I highly appreciate your essay and hope you please spend some of the valuable time on Dynamic Universe Model also and give your some of the valuable & esteemed guidance

** Some of the Main foundational points of Dynamic Universe Model :**

-No Isotropy

-No Homogeneity

-No...

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Your references are nice Dear David Brown….…..….. very nice idea…. I highly appreciate your essay and hope you please spend some of the valuable time on Dynamic Universe Model also and give your some of the valuable & esteemed guidance

-No Isotropy

-No Homogeneity

-No...

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post approved

David, you have brought together a lot of interesting topics in your essay to address the question of what is fundamental. I think it is the first time I have seen IUT theory connected to physics.

I am particularly glad that you have looked at the question of whether the digital philosophy of finite nature is correct. If nature is described by some finite structure then how big does that structure have to be?

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I am particularly glad that you have looked at the question of whether the digital philosophy of finite nature is correct. If nature is described by some finite structure then how big does that structure have to be?

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"If nature is described by some finite structure then how big does that structure have to be?" The preceding is a crucially important question — unfortunately, at this stage, my only answer is an extremely crude, wild guess. Let us assume that classical information reduces to quantum information reduces to Fredkin-Wolfram information. How much classical information is there in the observable universe? How many cubic millimeters might there be in the observable universe? According to Wikipedia, one plausible estimate for the number of the cubic millimeters in the observable universe might be 3.57 * 10^89

Observable universe (Size), Wikipedia

If nature can be described by Wolfram's cosmological automation, then how many bits of Fredkin-Wolfram information might be involved in the complete description of Wolfram's cosmological automaton? Let us define googol = 10^100, googolplex = 10^(googol), googolplexplex=10^(googolplex). As a wild guess, it seems to me that the number of bit of classical information in the observable universe might be at the googol level, the number of bits of quantum information in each particular universe in the multiverse might be at the googolplex level, and the number of bits of Fredkin-Wolfram information needed to describe the hypothetical finite structure of the multiverse might be at the googolplexplex level. In order to accurately describe Wolfram's cosmological automation, 4 steps might be necessary: (1) Write down 4 or 5 simples rules that completely describe Wolfram's automaton. (2) Using the 4 or 5 simple rules, derive empirically satisfactory approximations to quantum field theory and general relativity theory. (3) Make new predictions using Wolfram's automation. (4) Empirically verify the new predictions. Can this be done? I don't know.

Observable universe (Size), Wikipedia

If nature can be described by Wolfram's cosmological automation, then how many bits of Fredkin-Wolfram information might be involved in the complete description of Wolfram's cosmological automaton? Let us define googol = 10^100, googolplex = 10^(googol), googolplexplex=10^(googolplex). As a wild guess, it seems to me that the number of bit of classical information in the observable universe might be at the googol level, the number of bits of quantum information in each particular universe in the multiverse might be at the googolplex level, and the number of bits of Fredkin-Wolfram information needed to describe the hypothetical finite structure of the multiverse might be at the googolplexplex level. In order to accurately describe Wolfram's cosmological automation, 4 steps might be necessary: (1) Write down 4 or 5 simples rules that completely describe Wolfram's automaton. (2) Using the 4 or 5 simple rules, derive empirically satisfactory approximations to quantum field theory and general relativity theory. (3) Make new predictions using Wolfram's automation. (4) Empirically verify the new predictions. Can this be done? I don't know.

Dear David Brown,

You wrote: “IS NATURE INFINITE?”

My research has concluded that Nature must have devised the only permanent real structure of the Universe obtainable for the real Universe existed for millions of years before man and his finite complex informational systems ever appeared on earth. The real physical Universe consists only of one single unified VISIBLE infinite surface occurring eternally in one single infinite dimension that am always illuminated mostly by finite non-surface light.

Joe Fisher, ORCID ID 0000-0003-3988-8687. Unaffiliated

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You wrote: “IS NATURE INFINITE?”

My research has concluded that Nature must have devised the only permanent real structure of the Universe obtainable for the real Universe existed for millions of years before man and his finite complex informational systems ever appeared on earth. The real physical Universe consists only of one single unified VISIBLE infinite surface occurring eternally in one single infinite dimension that am always illuminated mostly by finite non-surface light.

Joe Fisher, ORCID ID 0000-0003-3988-8687. Unaffiliated

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It might be plausible to assume that the physical universe is an infinite surface in some mathematical model. At the present time, it seems to me that the vast majority of string theorists believe that our universe is infinite. If nature is infinite, then it is plausible to assume that physics has infinitely many degrees of freedom. If nature is finite, then nature might have only 78 degrees of freedom. Consider 3 copies of a model of 26-dimenional bosonic string theory, yielding 78 dimensions of bosonic waves. There might be a boson/fermion duality theorem derivable from Wolfram's cosmological automation. There could be 6 "barks" or "big quarks" each carrying a barkload of 12-dimensions of information, yielding 72 dimensions controlled by Fredkin's 6-phase clock, thus 78 dimensions of fermionic information. Each 12-dimensional barkload might represent 4 dimensions of spacetime, 3 dimensions of linear-momentum density, 3 dimensions of angular-momentum density, 1 dimension of quantum-spin density for matter, and 1 dimension of quantum-spin density for antimatter. By redundant representation of information, it might be possible to derive an 11-dimensional model of M-theory and a 12-dimensional model of F-theory — the idea is that the interior of the multiverse would be 72-dimensional in terms of "barkload" data, and the measurable universes would all be 71-dimensional and located on the boundary of the multiverse.

I say that my 3 most important ideas are: (1) Milgrom is the Kepler of contemporary cosmology — on the basis of overwhelming empirical evidence. (2) The Koide formula is essential for understanding the foundations of physics. (3) Lestone's theory of virtual cross sections is essential for understanding the foundations of physics. Are the 3 preceding ideas correct? Can the 3 preceding ideas be explained in terms of string theory with the finite nature hypothesis and/or string theory with the infinite nature hypothesis? Consider 2 more ideas: Fredkin's Finitary Fourfold Hypothesis: Infinities, infinitesmals, perfectly continuous variables, and local sources of randomness are figments of the imagination and never occur in nature. Wolfram's Simple Rules Hypothesis: There exist 4 or 5 simple rules that yield empirically valid approximations to quantum field theory and general relativity theory. Are the 2 preceding hypotheses correct? How might the 2 preceding hypotheses be mathematically formulated?

Is the concept of infinity empirically valid? Is there an infinite continuum of real numbers? If there is an infinite continuum of real numbers, then are there questions in physics that depend upon the truth or falsity of the axiom choice in Zermelo-Fraenkel set theory?

According to Wikipedia, "Jerry Lloyd Bona (born February 5, 1945) is an American mathematician, known for his work in fluid mechanics, partial differential equations, and computational mathematics, and active in some other branches of pure and applied mathematics. Bona received his PhD in 1971 from Harvard University under supervision of Garrett Birkhoff and worked from 1970 to 1972 at the Fluid Mechanics Research Institute University of Essex, where along with Brooke Benjamin and J. J. Mahony, he published on Model Equations for Long Waves in Non-linear Dispersive Systems, known as Benjamin–Bona–Mahony equation. He is probably best known for his statement about equivalent statements of the Axiom of Choice: “The Axiom of Choice is obviously true, the Well–ordering theorem is obviously false; and who can tell about Zorn’s Lemma?"

Jerry L. Bona, Wikipedia

According to Wikipedia, "Jerry Lloyd Bona (born February 5, 1945) is an American mathematician, known for his work in fluid mechanics, partial differential equations, and computational mathematics, and active in some other branches of pure and applied mathematics. Bona received his PhD in 1971 from Harvard University under supervision of Garrett Birkhoff and worked from 1970 to 1972 at the Fluid Mechanics Research Institute University of Essex, where along with Brooke Benjamin and J. J. Mahony, he published on Model Equations for Long Waves in Non-linear Dispersive Systems, known as Benjamin–Bona–Mahony equation. He is probably best known for his statement about equivalent statements of the Axiom of Choice: “The Axiom of Choice is obviously true, the Well–ordering theorem is obviously false; and who can tell about Zorn’s Lemma?"

Jerry L. Bona, Wikipedia

What are fundamental particles in physics? Consider the following 5 questions: What are the most important unsolved problems in science and technology? What are the most important unsolved problems in the foundations of physics? Is energy-density bounded away from zero? Is energy-density bounded away from infinity? In empirical reality, is gravitational energy conserved? According to the Gravity Probe B science team, my basic theory is wrong. I suggest that the 4 ultra-precise gyroscopes functioned correctly and confirmed what I call the Fernández-Rañada-Milgrom effect. In terms of string theory with the finite nature hypothesis, what have I have failed to do? I need to introduce cutoffs for energy-density with respect to the strong interactions and the weak interactions. I need to predict a rest mass for inflatons. I need to suggest plausible values for both the lower bound and the upper bound for gravitational energy-density. I need to make a complete prediction for the Space Roar Profile Prediction. WOLFRAM'S SIMPLE RULES HYPOTHESIS: I need to suggest 4 or 5 simple rules that might yield adequate approximations for quantum field theory and general relativity theory. I have, so far, failed to convince string theorists that Milgrom is the Kepler of contemporary cosmology.

“I came to the subject a True Believer in dark matter, but it was MOND that nailed the prediction for the LSB galaxies that I was studying (McGaugh & de Blok, 1998), not any flavor of dark matter. So what am supposed to conclude? … “ — McGaugh

The MOND pages

“I came to the subject a True Believer in dark matter, but it was MOND that nailed the prediction for the LSB galaxies that I was studying (McGaugh & de Blok, 1998), not any flavor of dark matter. So what am supposed to conclude? … “ — McGaugh

The MOND pages

Dear David Brown

Of course, MOND is superior to Dark matter interpretation. But are you sure that MOND ACCELERATION PARAMETER ao = 1.2 * 10 ^ -10.

I got the value of ao = 6.95818 * 10 ^ -10 and this is the acceleration that divides the attraction from the repulsion, not just at the galaxies.

Regards,

Branko

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Of course, MOND is superior to Dark matter interpretation. But are you sure that MOND ACCELERATION PARAMETER ao = 1.2 * 10 ^ -10.

I got the value of ao = 6.95818 * 10 ^ -10 and this is the acceleration that divides the attraction from the repulsion, not just at the galaxies.

Regards,

Branko

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According to all of the pro-MOND astronomers and astrophysics (so far as I am aware) the MOND acceleration constant a0 is (1.2 ± .02) * 10^-10 meters * sec^-2 ... I am confident that the error estimate is not wrong by an order-of-magnitude.

Scarpa, Riccardo. "Modified Newtonian Dynamics, an introductory review." In AIP Conference Proceedings, vol. 822, no. 1, pp. 253-265. AIP, 2006.

arXiv.org preprint for Scarpa's article

Scarpa, Riccardo. "Modified Newtonian Dynamics, an introductory review." In AIP Conference Proceedings, vol. 822, no. 1, pp. 253-265. AIP, 2006.

arXiv.org preprint for Scarpa's article

"... there is one non-trivial way to extend the spacetime symmetries, and that is to incorporate supersymmetry. ... in any string theory, nature always looks supersymmetric at sufficiently high energy scales. If string theory is telling us something about nature, nature is supersymmetric at some energy scale …” — Joseph Conlon

“Introduction to Supersymmetry” by Joseph Conlon,...

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“Introduction to Supersymmetry” by Joseph Conlon,...

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In 2007, John P. Lestone of Los Alamos National Laboratory, U.S.A., suggested a possible approach to calculating the value of the fine structure constant based upon a heuristic string theory. The electron, the muon, and the tau might each consist of a 2-sphere having precisely three vibrating superstrings. In his 2007 publication “Physics based calculation of the fine structure constant “ J....

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Dear Fellow Essayists

This will be my final plea for fair treatment.,

Reliable evidence exists that proves that the surface of the earth was formed millions of years before man and his utterly complex finite informational systems ever appeared on that surface. It logically follows that Nature must have permanently devised the only single physical construct of earth allowable.

All objects, be they solid, liquid, or vaporous have always had a visible surface. This is because the real Universe must consist only of one single unified VISIBLE infinite surface occurring eternally in one single infinite dimension that am always illuminated mostly by finite non-surface light.

Only the truth can set you free.

Joe Fisher, Realist

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This will be my final plea for fair treatment.,

Reliable evidence exists that proves that the surface of the earth was formed millions of years before man and his utterly complex finite informational systems ever appeared on that surface. It logically follows that Nature must have permanently devised the only single physical construct of earth allowable.

All objects, be they solid, liquid, or vaporous have always had a visible surface. This is because the real Universe must consist only of one single unified VISIBLE infinite surface occurring eternally in one single infinite dimension that am always illuminated mostly by finite non-surface light.

Only the truth can set you free.

Joe Fisher, Realist

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Veritas vos liberat, Wikipedia

Are most truths important? What are the most fundamental mathematical truths? What are the implications of Gödel's incompleteness theorems?

Gödel's incompleteness theorems

What is fundamentally true? What are the most fundamental questions? What are the most fundamental insights? What is important? What is unimportant? What should a person know? What should a person do? What might be the implications of Gödel's 1st and 2nd incompleteness theorems for the preceding 7 questions? There might be at least 2 fundamental responses to Gödel's incompleteness theorems: (RESPONSE 1) Peano Arithmetic and Zermelo-Fraenkel set theory need more axioms. (RESPONSE 2) The concept of a complete infinity is empirically dubious, and the concept of an arbitrarily large positive integer is an empirically dubious concept.

Are most truths important? What are the most fundamental mathematical truths? What are the implications of Gödel's incompleteness theorems?

Gödel's incompleteness theorems

What is fundamentally true? What are the most fundamental questions? What are the most fundamental insights? What is important? What is unimportant? What should a person know? What should a person do? What might be the implications of Gödel's 1st and 2nd incompleteness theorems for the preceding 7 questions? There might be at least 2 fundamental responses to Gödel's incompleteness theorems: (RESPONSE 1) Peano Arithmetic and Zermelo-Fraenkel set theory need more axioms. (RESPONSE 2) The concept of a complete infinity is empirically dubious, and the concept of an arbitrarily large positive integer is an empirically dubious concept.

Are human thoughts merely natural constructions like beaver dams and termite mounds? What are the most fundamental questions? Are questions more fundamental than answers? Are experiments more fundamental than theories? What are the most fundamental goals, meanings, and purposes? As positive integers grow larger do they diminish in meaning, purpose, and significance? Are the numbers 1, 2, and 3...

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"But here, I will argue that, while MOND is unconventional and inconstitent with the current cosmological paradigm, it is by no means in the category of crazy ideas. And we should recall that many constructs of modern physics, such as quarks, were at an early stage considered crazy and condemned quite viciously by renown scientists." — Robert H. Sanders

"A historical perspective on Modified Newtonian Dynamics", 2014, (page 19) arXiv.org

Is Milgrom the Kepler of contemporary cosmology? Is the Koide formula essential for understanding the foundations of physics? Does square-root(mass) have some profound meaning in terms of the foundations of physics? Is Lestone's theory of virtual cross sections essential for understanding the foundations of physics? Is the value of the fine-structure constant a happenstance of the string landscape?

Fine-structure constant, Wikipedia

happenstance, Wiktionary

String landscape, Wikipedia

"A historical perspective on Modified Newtonian Dynamics", 2014, (page 19) arXiv.org

Is Milgrom the Kepler of contemporary cosmology? Is the Koide formula essential for understanding the foundations of physics? Does square-root(mass) have some profound meaning in terms of the foundations of physics? Is Lestone's theory of virtual cross sections essential for understanding the foundations of physics? Is the value of the fine-structure constant a happenstance of the string landscape?

Fine-structure constant, Wikipedia

happenstance, Wiktionary

String landscape, Wikipedia

What is the most fundamental insight in quantum theory? Is it Heisenberg's uncertainty principle?

Uncertainty principle, Wikipedia

What is the most fundamental insight in general relativity theory? Is it Einstein's equivalence principle?

Equivalence principle, Wikipedia

Does string theory with the infinite nature hypothesis suggest that the uncertainty principle needs some modification based upon the string landscape? Does string theory with the finite nature hypothesis suggest that the equivalence principle needs some modification based upon Wolfram's cosmological automaton?

My guess is that the equivalence principle has 4 problems: (1) Dark energy as a weird, negative pressure suggests that dark energy has negative inertial mass-energy with respect to the string landscape. Is dark energy the result of the escape of gravitons from the boundary of the multiverse into the interior of the multiverse? Does dark energy obey the equivalence principle? (2) Does dark matter obey the equivalence principle? Does dark matter have positive gravitational mass-energy and zero inertial mass-energy? (3) Does the equivalence principle fail when energy-density becomes large enough? (4) Does the equivalence principle fail when energy-density becomes close enough to zero?

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Uncertainty principle, Wikipedia

What is the most fundamental insight in general relativity theory? Is it Einstein's equivalence principle?

Equivalence principle, Wikipedia

Does string theory with the infinite nature hypothesis suggest that the uncertainty principle needs some modification based upon the string landscape? Does string theory with the finite nature hypothesis suggest that the equivalence principle needs some modification based upon Wolfram's cosmological automaton?

My guess is that the equivalence principle has 4 problems: (1) Dark energy as a weird, negative pressure suggests that dark energy has negative inertial mass-energy with respect to the string landscape. Is dark energy the result of the escape of gravitons from the boundary of the multiverse into the interior of the multiverse? Does dark energy obey the equivalence principle? (2) Does dark matter obey the equivalence principle? Does dark matter have positive gravitational mass-energy and zero inertial mass-energy? (3) Does the equivalence principle fail when energy-density becomes large enough? (4) Does the equivalence principle fail when energy-density becomes close enough to zero?

To your number 3 and 4 questions concerning violations of the equivalence principle failing due to energy densities being close to zero or very large that is a possibility. However, the violations will still be small enough for GTR to remain valid and this hints at its robustness in our observable Universe. In the low-energy GR will work from outside galactic halos (in interstellar space) all the...

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"It is seen that MOND agrees with observations over at least 6 orders of magnitude in acceleration."

— Riccardo Scarpa

"Modified Newtonian dynamics, an Introductory Review." by R. Scarpa, In AIP Conference Proceedings, vol. 822, no. 1, pp. 253-265. AIP, 2006. (Conclusions section referring to a data plot of about 1000 objects)

"Modified Newtonian Dynamics, an Introduction Review", arXiv.org preprint

— Riccardo Scarpa

"Modified Newtonian dynamics, an Introductory Review." by R. Scarpa, In AIP Conference Proceedings, vol. 822, no. 1, pp. 253-265. AIP, 2006. (Conclusions section referring to a data plot of about 1000 objects)

"Modified Newtonian Dynamics, an Introduction Review", arXiv.org preprint

Dear David Brown.

I have read your essay and suggest that you read Dark Matter http://vixra.org/pdf/1303.0207v3.pdf

Quantum Mechanics claims that an electron can be both spin-up and spin-down at the same time. In my conceptual physics Essay on Electron Spin, I have proved that this is not true. Please read: https://fqxi.org/community/forum/topic/3145 or https://fqxi.org/data/essay-contest-files/Rajpal_1306.0141v3

.pdf

Kamal Rajpal

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I have read your essay and suggest that you read Dark Matter http://vixra.org/pdf/1303.0207v3.pdf

Quantum Mechanics claims that an electron can be both spin-up and spin-down at the same time. In my conceptual physics Essay on Electron Spin, I have proved that this is not true. Please read: https://fqxi.org/community/forum/topic/3145 or https://fqxi.org/data/essay-contest-files/Rajpal_1306.0141v3

Kamal Rajpal

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Kamal Rajpal's idea "... photons with the least energy will correspond to photons with a temperature close to zero kelvin ..." (vixra.org) is likely to be correct provided that nature is finite and digital — and might be correct if nature is infinite. Do least-energy photons exist in nature and not just in theory? Can absolute zero be approximated with arbitrary accuracy?

Dear David Brown,

I agree that ‘zero point photons’ is a theoretical concept. Thanks. The CMB photons at 2.7 K do exist.

Kamal Rajpal

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I agree that ‘zero point photons’ is a theoretical concept. Thanks. The CMB photons at 2.7 K do exist.

Kamal Rajpal

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Observe the chicken. Why did the chicken cross the road? Because we fail to live in an alternate universe in which chickens never evolved. What is observation? What is measurement? Why does measurement exist? Consider 2 concepts:

(1) The observer creates the measurement by causing a selection among quantum possibilities.

(2) Measurement is a natural process that separates the boundary of the multiverse from the interior of the multiverse. The observer's thoughts and actions are entirely caused by Fredkin-Wolfram information.

What are other plausible concepts of measurement?

Measurement problem, Wikipedia

(1) The observer creates the measurement by causing a selection among quantum possibilities.

(2) Measurement is a natural process that separates the boundary of the multiverse from the interior of the multiverse. The observer's thoughts and actions are entirely caused by Fredkin-Wolfram information.

What are other plausible concepts of measurement?

Measurement problem, Wikipedia

What are the most fundamental questions concerning science and technology? Is reality more fundamental than language? Is applied mathematics more fundamental than pure mathematics? Are time, space, energy, and quantum information the 4 most fundamental concepts in physics? In order to unify Newton's 3 laws of motion, Newton's law of gravity, and Maxwell's equations, Einstein introduced spacetime in special relativity (1905) and in general relativity (1916). However, in general relativity, there is a concept of the fundamental geometric tensor and a concept of the energy-momentum tensor. Can spacetime and energy be unified into a single concept? Is string theory the way to mathematically unify energy with spacetime, forming a quantum theory of gravity? If there are n virtual particles that move independently, then should there be a mathematical model having n dimensions? Are the real numbers, the complex numbers, the quaternions, and the octonions the 4 most important mathematical structures? Can 9 copies of the octonions be used in explaining the foundations of physics? In any case, I say that Milgrom is the Kepler of contemporary cosmology.

Modified Newtonian dynamics, Wikiquote

Modified Newtonian dynamics, Wikiquote

"Seen in the light of evolution, biology is, perhaps, intellectually the most satisfying and inspiring science. Without that light it becomes a pile of sundry facts — some of them interesting or curious but making no meaningful picture as a whole." — Theodosius Dobzhansky

Theodosius Dobzhansky

Is it true that biology reduces to chemistry reduces to physics? Is there a unified theory of mathematics and theoretical physics? In materials science, any valid material must pass the tests of chemistry. Can one think of science as a tree of knowledge with a trunk consisting of quantum theory, roots in the multiverse, and branches in chemistry? Is string theory a profound unifying principle for both physics and mathematics?

What are the 4 most important mathematical structures? Could the answer be the real numbers, the complex numbers, the quaternions, and the octonions?

"The octonions" by John C. Baez, Bull. Amer. Math. Soc. vol. 39 (2002)

"Division algebras and quantum theory" by John C. Baez, arXiv.org, 2011

3 copies of the Leech lattice = 9 copies of the octonions = 64 dimension of virtual particle paths + 3 dimensions of linear momentum + 3 dimensions of angular momentum + 2 dimensions of quantum spin ???

Theodosius Dobzhansky

Is it true that biology reduces to chemistry reduces to physics? Is there a unified theory of mathematics and theoretical physics? In materials science, any valid material must pass the tests of chemistry. Can one think of science as a tree of knowledge with a trunk consisting of quantum theory, roots in the multiverse, and branches in chemistry? Is string theory a profound unifying principle for both physics and mathematics?

What are the 4 most important mathematical structures? Could the answer be the real numbers, the complex numbers, the quaternions, and the octonions?

"The octonions" by John C. Baez, Bull. Amer. Math. Soc. vol. 39 (2002)

"Division algebras and quantum theory" by John C. Baez, arXiv.org, 2011

3 copies of the Leech lattice = 9 copies of the octonions = 64 dimension of virtual particle paths + 3 dimensions of linear momentum + 3 dimensions of angular momentum + 2 dimensions of quantum spin ???

Consider a statement made by Leonardo da Vinci:

La natura è piena d'infinite stagioni (o cagioni) che non furono mai in esperienza. (Nature is full of infinite seasons (or causes) that have never been experienced.)

Leonardo da Vinci scienziato, it.wikisource.org

Is nature infinitely complicated? Are string vibrations confined to 3 copies of the Leech lattice? Can string vibrations be interpreted in terms of 3 copies of 26-dimensional bosonic string theory with Fredkin's 6-phase clock? Is it useful to think in terms of measuring space and time with 6 particle beams, consisting of 3 electron beams and 3 positron beams? What about 3 beams of muons and 3 beams of anti-muons? What about 3 beams of tauons and 3 beams of anti-tauons?

"What are the implications of the 3-fold way?" — John C. Baez

Division algebras and quantum theory", 2011, arxiv.org

La natura è piena d'infinite stagioni (o cagioni) che non furono mai in esperienza. (Nature is full of infinite seasons (or causes) that have never been experienced.)

Leonardo da Vinci scienziato, it.wikisource.org

Is nature infinitely complicated? Are string vibrations confined to 3 copies of the Leech lattice? Can string vibrations be interpreted in terms of 3 copies of 26-dimensional bosonic string theory with Fredkin's 6-phase clock? Is it useful to think in terms of measuring space and time with 6 particle beams, consisting of 3 electron beams and 3 positron beams? What about 3 beams of muons and 3 beams of anti-muons? What about 3 beams of tauons and 3 beams of anti-tauons?

"What are the implications of the 3-fold way?" — John C. Baez

Division algebras and quantum theory", 2011, arxiv.org

Does there exist a (1/3)-Koide formula that allows some quarks to have charge ± 1/3 ?

From Wolfram Alpha:

(muon mass) /(electron mass) = 206.7683

(tauon mass)/(electron mass) = 3477.48

(59^3 + 33 * 59^2 + 57 * 59 + 9 )^(1/27) - 1.59983643131952544 = 0 approx.

For a = 1.5998364, x = 206.7683, y = 3477.48,

calculate ( a^3 +(a^2) * x + a * y)/(a^3 + ( a^2) * x^.5 + a * y^.5)^2 Answer: .333333

For the polynomial x —> x^3 + 33 * x^2 + 57 * x + 9 my guess is that 33 + 26 = 59 is meaningful because of 26-dimensional bosonic string theory and the fact that the three primes 59, 59 ± 12 divide the order of the monster group. My guess is that the constant term 9 is meaningful because of Lestone’s heuristic string theory.

Note that 8/5 – 1/(32 * 191) = 1.599836874 ...

For a = 1.5998369, x = 206.7683, y = 3477.48,

calculate ( a^3 +(a^2) * x + a * y)/(a^3 + ( a^2) * x^.5 + a * y^.5)^2 Answer: .333332

Note that 191 = 2 * 72 + 47 and 47, 59, 71 are the 3 largest primes that divide the order of the monster group.

Monster group, Wikipedia

From Wolfram Alpha:

(muon mass) /(electron mass) = 206.7683

(tauon mass)/(electron mass) = 3477.48

(59^3 + 33 * 59^2 + 57 * 59 + 9 )^(1/27) - 1.59983643131952544 = 0 approx.

For a = 1.5998364, x = 206.7683, y = 3477.48,

calculate ( a^3 +(a^2) * x + a * y)/(a^3 + ( a^2) * x^.5 + a * y^.5)^2 Answer: .333333

For the polynomial x —> x^3 + 33 * x^2 + 57 * x + 9 my guess is that 33 + 26 = 59 is meaningful because of 26-dimensional bosonic string theory and the fact that the three primes 59, 59 ± 12 divide the order of the monster group. My guess is that the constant term 9 is meaningful because of Lestone’s heuristic string theory.

Note that 8/5 – 1/(32 * 191) = 1.599836874 ...

For a = 1.5998369, x = 206.7683, y = 3477.48,

calculate ( a^3 +(a^2) * x + a * y)/(a^3 + ( a^2) * x^.5 + a * y^.5)^2 Answer: .333332

Note that 191 = 2 * 72 + 47 and 47, 59, 71 are the 3 largest primes that divide the order of the monster group.

Monster group, Wikipedia

Does square-root(mass) = area ?

In string theory with the finite nature hypothesis, is it possible to use quantum cohomology to calculate (muon mass)/(electron mass) and (tauon mass)/(electron mass) ?

Quantum cohomology, Wikipedia

From Wolfram Alpha:

(muon mass)/(electron mass) = 206.7683

(tauon mass)/(electron mass) = 3477.48

206.7683^(1/4) - 3 - 3^2 * 11 / 5^3 - 3^4 * 14/ 5^11 = 6.59750 * 10^9 approx.

3477.48^(1/4) - 7 - 3/5 - (11/2) * 3^2 / 5^3 = 3.21039 * 10^-6 approx.

In string theory with the finite nature hypothesis, is it possible to use quantum cohomology to calculate (muon mass)/(electron mass) and (tauon mass)/(electron mass) ?

Quantum cohomology, Wikipedia

From Wolfram Alpha:

(muon mass)/(electron mass) = 206.7683

(tauon mass)/(electron mass) = 3477.48

206.7683^(1/4) - 3 - 3^2 * 11 / 5^3 - 3^4 * 14/ 5^11 = 6.59750 * 10^9 approx.

3477.48^(1/4) - 7 - 3/5 - (11/2) * 3^2 / 5^3 = 3.21039 * 10^-6 approx.

I have conjectured that the Koide formula is essential for understanding the foundations of physics and that Lestone's theory of virtual cross sections is essential for understanding the foundations of physics. Note that even if the conjecture that quantum information reduces to Fredkin-Wolfram information is wrong, my Koide conjecture and my Lestone conjecture might still be correct. However, the issue of pole versus running mass would somehow have to be incorporated into a generalized Koide formula and a more mathematically sophisticated Lestone theory.

What is precisely the energy scale of a process?, Physics Stack Exchange, 2015

Pole mass vs. Running Mass vs. Other Running Parameters, Physics Stack Exchange, 2015

What is precisely the energy scale of a process?, Physics Stack Exchange, 2015

Pole mass vs. Running Mass vs. Other Running Parameters, Physics Stack Exchange, 2015

According to Alexander and Yunes, string theory seems to predict that the cosmological constant is induced by supersymmetry breaking. If this breakage occurs at the electroweak scale then the cosmological constant should be about 10^48 times larger than it actually is. If this breakage occurs at the Planck scale then the cosmological constant should be about 10^115 times larger than it actually is.

Alexander, Stephon & Nicolas Yunes. "Chern–Simons modified general relativity." Physics Reports 480, no. 1-2 (2009): 1-55. arXiv.org preprint (page 5)

My guess is that string theory with the infinite nature hypothesis predicts MOND-compatible supersymmetry. (Any form of supersymmetry that is MOND-incompatible is guaranteed to be wrong, according to empirical evidence.)

My guess is that string theory with the infinite nature hypothesis predicts Wolfram's cosmological automaton with no supersymmetry. (Supersymmetry should be replaced by Wolframian pseudo-supersymmetry, whatever that might be.)

Alexander, Stephon & Nicolas Yunes. "Chern–Simons modified general relativity." Physics Reports 480, no. 1-2 (2009): 1-55. arXiv.org preprint (page 5)

My guess is that string theory with the infinite nature hypothesis predicts MOND-compatible supersymmetry. (Any form of supersymmetry that is MOND-incompatible is guaranteed to be wrong, according to empirical evidence.)

My guess is that string theory with the infinite nature hypothesis predicts Wolfram's cosmological automaton with no supersymmetry. (Supersymmetry should be replaced by Wolframian pseudo-supersymmetry, whatever that might be.)

What is measurement? Why does measurement exist? According to Motl, "Observation is always a messy event in principle although, in practice, the inaccuracy of the classical approximation may be extremely, expo-exponentially tiny."

What erases and can restore the interference patterns, The Reference Frame blog, 13 March 2018

In the Copenhagen Interpretation, the observer ultimately creates the observation or at least enables a classical approximation to some quantum event. What precisely is a probability distribution? What precisely is a real number? What precisely is a positive integer? Any definition that uses the concept of a complete infinity (or a potential infinity) might involve an infinite amount of ambiguity. Is observation a natural process that separates the boundary of the multiverse from the interior of the multiverse? Are time, space, energy, and quantum information merely approximations generated by Wolfram's cosmological automaton using Fredkin-Wolfram information? My guess is that string theory with the finite nature hypothesis implies no string landscape and no supersymmetry, while string theory with the infinite nature hypothesis implies the string landscape and MOND-compatible supersymmetry. Google "kroupa milgrom".

What erases and can restore the interference patterns, The Reference Frame blog, 13 March 2018

In the Copenhagen Interpretation, the observer ultimately creates the observation or at least enables a classical approximation to some quantum event. What precisely is a probability distribution? What precisely is a real number? What precisely is a positive integer? Any definition that uses the concept of a complete infinity (or a potential infinity) might involve an infinite amount of ambiguity. Is observation a natural process that separates the boundary of the multiverse from the interior of the multiverse? Are time, space, energy, and quantum information merely approximations generated by Wolfram's cosmological automaton using Fredkin-Wolfram information? My guess is that string theory with the finite nature hypothesis implies no string landscape and no supersymmetry, while string theory with the infinite nature hypothesis implies the string landscape and MOND-compatible supersymmetry. Google "kroupa milgrom".

Is supersymmetry an empirically valid concept? Can supersymmetry predict dark matter particles that can be empirically confirmed?

According to Stephen Hawking and Leonard Mlodinow, "The ultimate theory must be consistent and must predict finite results for quantities that we can measure. We've seen that there must be a law like gravity, and we saw in Chapter 5 that for a theory of gravity to predict finite quantities, the theory must have what is called supersymmetry between the forces of nature and the matter on which they act. M-theory is the most general supersymmetric theory of gravity. For these reasons M-theory is the only candidate for a complete theory of the universe. If it is finite—and this has yet to be proved—it will be a model of a universe that creates itself. We must be part of this universe, because there is no other consistent model."

"The Grand Design", 2011, pages 180–181

Have string theorists underestimated Milgrom, McGaugh, and Kroupa? Have string theorists underestimated Fredkin and Wolfram?

According to Stephen Hawking and Leonard Mlodinow, "The ultimate theory must be consistent and must predict finite results for quantities that we can measure. We've seen that there must be a law like gravity, and we saw in Chapter 5 that for a theory of gravity to predict finite quantities, the theory must have what is called supersymmetry between the forces of nature and the matter on which they act. M-theory is the most general supersymmetric theory of gravity. For these reasons M-theory is the only candidate for a complete theory of the universe. If it is finite—and this has yet to be proved—it will be a model of a universe that creates itself. We must be part of this universe, because there is no other consistent model."

"The Grand Design", 2011, pages 180–181

Have string theorists underestimated Milgrom, McGaugh, and Kroupa? Have string theorists underestimated Fredkin and Wolfram?

Has the Pioneer anomaly been satisfactorily explained? Antonio Fernández-Rañada and Alfredo Tiemblo-Ramos presented a model in which the Pioneer anomaly is a cosmological effect due to a discrepancy between astronomical time and atomic time ... They wrote, "... This shows that the predictions of our model on the cartography of the solar system are exactly the same as in standard physics, independently of which time is used. The model is thus fully compatible with the results obtained by the Viking mission ...."

"On the compatibility of a proposed explanation of the Pioneer anomaly with the cartography of the solar system." arXiv preprint arXiv:0909.0912 (2009) (pages 8–9)

If Wolfram's cosmological automation is empirically valid, then there is a smoothing problem (to approximate energy and spacetime) and there is a flattening problem (to approximate string theory with the infinite nature hypothesis). If string vibrations are approximately confined to 3 copies of the Leech lattice in sting theory with the infinite nature hypothesis, then the Koide formula might be interpreted as square-root(mass) = 16 dimensions of bosonic uncertainty. There might be an interpretation of 26-dimensionals bosonic string theory consisting of 10 dimensions of general relativity + 16 dimensions of bosonic uncertainty from a 16-dimensional unified boson.

"On the compatibility of a proposed explanation of the Pioneer anomaly with the cartography of the solar system." arXiv preprint arXiv:0909.0912 (2009) (pages 8–9)

If Wolfram's cosmological automation is empirically valid, then there is a smoothing problem (to approximate energy and spacetime) and there is a flattening problem (to approximate string theory with the infinite nature hypothesis). If string vibrations are approximately confined to 3 copies of the Leech lattice in sting theory with the infinite nature hypothesis, then the Koide formula might be interpreted as square-root(mass) = 16 dimensions of bosonic uncertainty. There might be an interpretation of 26-dimensionals bosonic string theory consisting of 10 dimensions of general relativity + 16 dimensions of bosonic uncertainty from a 16-dimensional unified boson.

error in previous post: Replace "square-root(mass) = 16 dimensions of bosonic uncertainty" by "square-root(mass) = 4 dimensions of bosonic uncertainty". It might be possible to formulate a duality principle in which mass-energy for bosons corresponds to 16 dimensions of alpha-prime & hbar uncertainty for bosons.

Consider 2 hypotheses:

Hypothesis 1: Time, space, energy, and quantum information are approximations generated by Wolfram's cosmological automaton using a finite network of Fredkin-Wolfram information.

Hypothesis 2: As positive integers grow larger, they become less meaningful in terms of science and engineering.

Consider an admonition from Errett Bishop:

"Do not ask whether a statement is true until you know what it means."

Bishop, Errett. Schizophrenia in contemporary mathematics, page 6. American Mathematical Society, 1973, prl.ccs.neu.edu/img/sicm.pdf

Errett Bishop, Wikipedia

Hypothesis 1: Time, space, energy, and quantum information are approximations generated by Wolfram's cosmological automaton using a finite network of Fredkin-Wolfram information.

Hypothesis 2: As positive integers grow larger, they become less meaningful in terms of science and engineering.

Consider an admonition from Errett Bishop:

"Do not ask whether a statement is true until you know what it means."

Bishop, Errett. Schizophrenia in contemporary mathematics, page 6. American Mathematical Society, 1973, prl.ccs.neu.edu/img/sicm.pdf

Errett Bishop, Wikipedia

I have suggested to Professor Milgrom that relativistic MOND is simply the alleged Fernández-Rañada-Milgrom effect, i.e., replace the -1/2 in the standard form of Einstein's field equations by -1/2 + dark-matter-compensation-constant, where this constant is approximately sqrt((60±10)/4) * 10^-5 — however, Professor Milgrom seems to believe the Gravity Probe B science team. I suggest that the Gravity Probe B science team misinterpreted their own experiment. Have pro-MOND and anti-MOND astrophysicists carefully studied this issue?

Everett, CW Francis, D. B. DeBra, B. W. Parkinson, J. P. Turneaure, J. W. Conklin, M. I. Heifetz, G. M. Keiser et al. "Gravity probe B: final results of a space experiment to test general relativity." Physical Review Letters 106, no. 22 (2011): 221101. arXiv.org preprint

I suggest that the "patch potentials" problem is merely an imagined explanation for an actual detection of the alleged Fernández-Rañada-Milgrom effect. I suggest that the 4 ultra-precise gyroscopes functioned correctly and the calibration procedure which corrected for the "patch potentials" problem actually corrected for the alleged Fernández-Rañada-Milgrom effect. I have suggested to the Gravity Probe B science team that they should investigate the "patch potentials" problem in the manufacturing process for the 4 ultra-precise gyroscopes.

Everett, CW Francis, D. B. DeBra, B. W. Parkinson, J. P. Turneaure, J. W. Conklin, M. I. Heifetz, G. M. Keiser et al. "Gravity probe B: final results of a space experiment to test general relativity." Physical Review Letters 106, no. 22 (2011): 221101. arXiv.org preprint

I suggest that the "patch potentials" problem is merely an imagined explanation for an actual detection of the alleged Fernández-Rañada-Milgrom effect. I suggest that the 4 ultra-precise gyroscopes functioned correctly and the calibration procedure which corrected for the "patch potentials" problem actually corrected for the alleged Fernández-Rañada-Milgrom effect. I have suggested to the Gravity Probe B science team that they should investigate the "patch potentials" problem in the manufacturing process for the 4 ultra-precise gyroscopes.

What are the various ideas for modified theories of gravity?

Clifton, Timothy, Pedro G. Ferreira, Antonio Padilla, and Constantinos Skordis. "Modified gravity and cosmology." Physics reports 513, no. 1-3 (2012): 1-189. arXiv.org preprint

Clifton, Timothy, Pedro G. Ferreira, Antonio Padilla, and Constantinos Skordis. "Modified gravity and cosmology." Physics reports 513, no. 1-3 (2012): 1-189. arXiv.org preprint

Can Litvinov *et alia* provide a decisive test of the alleged Fernández-Rañada-Milgrom effect? If dark matter has positive gravitational mass-energy and zero inertial mass-energy, then an empirical test might soon disconfirm (or confirm) the hypothesis that dark-matter-compensation-constant = sqrt((60±10)/4) * 10^–5 .

Litvinov, D. A., V. N. Rudenko, A. V. Alakoz, U. Bach, N. Bartel, A. V. Belonenko, K. G. Belousov et al. "Probing the gravitational redshift with an Earth-orbiting satellite." Physics Letters A (2017), arXiv preprint

Litvinov, D. A., V. N. Rudenko, A. V. Alakoz, U. Bach, N. Bartel, A. V. Belonenko, K. G. Belousov et al. "Probing the gravitational redshift with an Earth-orbiting satellite." Physics Letters A (2017), arXiv preprint

Consider 3 hypotheses:

Hypothesis 1: If Wolfram's cosmological automaton has a timing mechanism that displays itself in some dramatic physical way, then dark-matter-compensation-constant is likely to be nonzero.

Hypothesis 2: If time is finite, then Einstein's field equations need a Koide cutoff.

Hypothesis 3: If energy-density cannot approach +∞, then Einstein's field equations need a Lestone cutoff.

Does string theory with the infinite nature hypothesis imply supersymmetry and no MOND? Does string theory with the finite nature hypothesis imply MOND and no supersymmetry? Is MOND the key to overthrowing the anthropic principle?

Anthropic principle, Wikipedia

"The anthropic principle is an observation, not an explanation."

— Burton Richter

"Theory in particle physics: theological speculation versus practical knowledge." Physics Today 59, no. 10 (2006): 8.

Hypothesis 1: If Wolfram's cosmological automaton has a timing mechanism that displays itself in some dramatic physical way, then dark-matter-compensation-constant is likely to be nonzero.

Hypothesis 2: If time is finite, then Einstein's field equations need a Koide cutoff.

Hypothesis 3: If energy-density cannot approach +∞, then Einstein's field equations need a Lestone cutoff.

Does string theory with the infinite nature hypothesis imply supersymmetry and no MOND? Does string theory with the finite nature hypothesis imply MOND and no supersymmetry? Is MOND the key to overthrowing the anthropic principle?

Anthropic principle, Wikipedia

"The anthropic principle is an observation, not an explanation."

— Burton Richter

"Theory in particle physics: theological speculation versus practical knowledge." Physics Today 59, no. 10 (2006): 8.

Any scientific theory might be falsified. Here are 3 alternate theories for the dark matter problem:

Vagnozzi, Sunny. "Recovering a MOND-like acceleration law in mimetic gravity." arXiv preprint arXiv:1708.00603 (2017).

Chanda, Prolay Krishna, and Subinoy Das. "Static structure of chameleon dark Matter as an explanation of dwarf spheroidal galactic core." arXiv preprint arXiv:1702.01882 (2017).

Burrage, Clare, Edmund J. Copeland, and Peter Millington. "Radial acceleration relation from screening of fifth forces." arXiv preprint arXiv:1610.07529 (2016).

Vagnozzi, Sunny. "Recovering a MOND-like acceleration law in mimetic gravity." arXiv preprint arXiv:1708.00603 (2017).

Chanda, Prolay Krishna, and Subinoy Das. "Static structure of chameleon dark Matter as an explanation of dwarf spheroidal galactic core." arXiv preprint arXiv:1702.01882 (2017).

Burrage, Clare, Edmund J. Copeland, and Peter Millington. "Radial acceleration relation from screening of fifth forces." arXiv preprint arXiv:1610.07529 (2016).

For a derivation of MOND from first principles, including the value of Milgrom a_{0} from cosmology check

http://vixra.org/abs/1112.0075

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http://vixra.org/abs/1112.0075

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González Alvarez, Juan Ramón, "Modified Newtonian Dynamics and Dark Matter from a Generalized Gravitational Theory" (2011)

"MOND may very well entail loss or replacement of some cherished principles; but which?"

— M. Milgrom, page 10 of 2008 arXiv preprint

"The MOND limit from spacetime scale invariance." The Astrophysical Journal 698, no. 2 (2009): 1630. arXiv preprint (2008)

"MOND may very well entail loss or replacement of some cherished principles; but which?"

— M. Milgrom, page 10 of 2008 arXiv preprint

"The MOND limit from spacetime scale invariance." The Astrophysical Journal 698, no. 2 (2009): 1630. arXiv preprint (2008)

Anyone who wants to pursue string theory with the finite nature hypothesis, might want to consider the following two publications:

According to Wolfram (1986), "Continuum equations are derived for the large-scale behavior of a class of cellular automaton models for fluids. The cellular automata are discrete analogues of molecular dynamics, in which particles with discrete velocities populate the links of a fixed array of sites. Kinetic equations for microscopic particle distributions are constructed. Hydrodynamic equations are then derived using the Chapman-Enskog expansion. Slightly modified Navier-Stokes equations are obtained in two and three dimensions with certain lattices."

Journal of Statistical Physics, November 1986, Volume 45, Issue 3–4, pp 471–526 "Cellular automaton fluids 1: Basic theory" by Stephen Wolfram

Bredberg, Keeler, Lysov, and Strominger (2012) presented a construction which "is a mathematically precise realization of suggestions of a holographic duality relating fluids and horizons which began with the membrane paradigm in the 70's and resurfaced recently in studies of the AdS/CFT correspondence."

Irene Bredberg, Cynthia Keeler, Vyacheslav Lysov, and Andrew Strominger. "From Navier-Stokes To Einstein." Journal of High Energy Physics 2012, no. 7 (2012): 146. (arXiv.org preprint)

Why am I fixated on the nonzero dark-matter-compensation idea? First, the idea seems to me to be compatible with the preponderance of the empirical evidence. Second, the idea seems to me to be the only way of betting against Einstein once without betting against Einstein twice. If any one of my three suggested modifications to Einstein's field equations is empirically wrong, then I would bet 100% on Einstein and back the idea of MOND-compatible dark matter particles that have variable effective mass depending upon nearby gravitational acceleration.

According to Wolfram (1986), "Continuum equations are derived for the large-scale behavior of a class of cellular automaton models for fluids. The cellular automata are discrete analogues of molecular dynamics, in which particles with discrete velocities populate the links of a fixed array of sites. Kinetic equations for microscopic particle distributions are constructed. Hydrodynamic equations are then derived using the Chapman-Enskog expansion. Slightly modified Navier-Stokes equations are obtained in two and three dimensions with certain lattices."

Journal of Statistical Physics, November 1986, Volume 45, Issue 3–4, pp 471–526 "Cellular automaton fluids 1: Basic theory" by Stephen Wolfram

Bredberg, Keeler, Lysov, and Strominger (2012) presented a construction which "is a mathematically precise realization of suggestions of a holographic duality relating fluids and horizons which began with the membrane paradigm in the 70's and resurfaced recently in studies of the AdS/CFT correspondence."

Irene Bredberg, Cynthia Keeler, Vyacheslav Lysov, and Andrew Strominger. "From Navier-Stokes To Einstein." Journal of High Energy Physics 2012, no. 7 (2012): 146. (arXiv.org preprint)

Why am I fixated on the nonzero dark-matter-compensation idea? First, the idea seems to me to be compatible with the preponderance of the empirical evidence. Second, the idea seems to me to be the only way of betting against Einstein once without betting against Einstein twice. If any one of my three suggested modifications to Einstein's field equations is empirically wrong, then I would bet 100% on Einstein and back the idea of MOND-compatible dark matter particles that have variable effective mass depending upon nearby gravitational acceleration.

I have suggested that Heisenberg's uncertainty principle is always empirically valid whenever measurement is possible, but Einstein's equivalence principle fails empirically in 4 different ways.

According to Einstein,

"A little reflection will show that the law of the equality of the inertial and gravitational mass is equivalent to the assertion that the acceleration imparted to a body by a gravitational field is independent of the nature of the body. For Newton's equation of motion in a gravitational field, written out in full, it is:

(Inertial mass) cdot (Acceleration) = (Intensity of the gravitational field) cdot (Gravitational mass).

It is only when there is numerical equality between the inertial and gravitational mass that the acceleration is independent of the nature of the body."

Equivalence principle, Wikipedia

Consider 4 hypotheses:

(1) Dark matter has positive gravitational mass-energy but zero inertial mass-energy.

(2) Dark energy has negative gravitational mass-energy but zero inertial mass-energy.

(3) As energy-density approaches a cosmological maximum, the equivalence principle fails due to the Lestone cutoff. (Leptons and quarks have nonzero virtual cross sections.)

(4) As energy-density approaches a cosmological minimum, the equivalence principle fails due to the Koide cutoff. (The transfer of energy from the boundary of the multiverse into the interior of the multiverse nears completion as energy-density approaches a cosmological minimum. There are 3 generations of fermions because Wolfram's cosmological automaton generates 64 dimensions of uncertainty which are equivalent to 16 dimensions of virtual boson paths plus 48 dimensions of virtual fermion paths. )

According to Einstein,

"A little reflection will show that the law of the equality of the inertial and gravitational mass is equivalent to the assertion that the acceleration imparted to a body by a gravitational field is independent of the nature of the body. For Newton's equation of motion in a gravitational field, written out in full, it is:

(Inertial mass) cdot (Acceleration) = (Intensity of the gravitational field) cdot (Gravitational mass).

It is only when there is numerical equality between the inertial and gravitational mass that the acceleration is independent of the nature of the body."

Equivalence principle, Wikipedia

Consider 4 hypotheses:

(1) Dark matter has positive gravitational mass-energy but zero inertial mass-energy.

(2) Dark energy has negative gravitational mass-energy but zero inertial mass-energy.

(3) As energy-density approaches a cosmological maximum, the equivalence principle fails due to the Lestone cutoff. (Leptons and quarks have nonzero virtual cross sections.)

(4) As energy-density approaches a cosmological minimum, the equivalence principle fails due to the Koide cutoff. (The transfer of energy from the boundary of the multiverse into the interior of the multiverse nears completion as energy-density approaches a cosmological minimum. There are 3 generations of fermions because Wolfram's cosmological automaton generates 64 dimensions of uncertainty which are equivalent to 16 dimensions of virtual boson paths plus 48 dimensions of virtual fermion paths. )

Consider 6 hypotheses:

(1) String theory is the only mathematically plausible way of unifying quantum field theory and general relativity theory.

(2) String theory (with the infinite nature hypothesis) predicts supersymmetry.

(3) String theory (with the infinite nature hypothesis) implies that the equivalence principle is valid for ordinary matter and dark matter.

(4) Einstein found the correct mathematical formulation for the equivalence principle.

(5) String theory (with the infinite nature hypothesis) implies that, after quantum averaging, Einstein's field equations are 100% correct.

(6) String theory (with the infinite nature hypothesis) predicts Einstein's field equations.

Are the 6 preceding hypotheses empirically valid? Consider some ideas of J. D. Bekenstein:

"Literally taken the MOND recipe for acceleration violates the conservation of momentum (and of energy and of angular momentum) ..." (page 2)

"... What principles should the relativistic embodiment of the MOND paradigm adhere to? ...

° Action principle ...

° Equivalence principle ...

° Positivity of energy ...

° Relativistic invariance ...

* Causality ...

° Departure from Newtonian gravity ..." (pages 4–5)

"Tensor-vector-scalar modified gravity: from small scale to cosmology" by Jacob D. Bekenstein, submitted in 2004 & revised in 2005, arXiv.org

I suggest that empirically successful MOND does indeed imply that gravitational energy is not conserved and that string theory with the finite nature hypothesis is empirically valid. (If dark-matter-compensation-constant were equal to zero, then Wolfram's cosmological automaton would not have a uniform timing mechanism.)

(1) String theory is the only mathematically plausible way of unifying quantum field theory and general relativity theory.

(2) String theory (with the infinite nature hypothesis) predicts supersymmetry.

(3) String theory (with the infinite nature hypothesis) implies that the equivalence principle is valid for ordinary matter and dark matter.

(4) Einstein found the correct mathematical formulation for the equivalence principle.

(5) String theory (with the infinite nature hypothesis) implies that, after quantum averaging, Einstein's field equations are 100% correct.

(6) String theory (with the infinite nature hypothesis) predicts Einstein's field equations.

Are the 6 preceding hypotheses empirically valid? Consider some ideas of J. D. Bekenstein:

"Literally taken the MOND recipe for acceleration violates the conservation of momentum (and of energy and of angular momentum) ..." (page 2)

"... What principles should the relativistic embodiment of the MOND paradigm adhere to? ...

° Action principle ...

° Equivalence principle ...

° Positivity of energy ...

° Relativistic invariance ...

* Causality ...

° Departure from Newtonian gravity ..." (pages 4–5)

"Tensor-vector-scalar modified gravity: from small scale to cosmology" by Jacob D. Bekenstein, submitted in 2004 & revised in 2005, arXiv.org

I suggest that empirically successful MOND does indeed imply that gravitational energy is not conserved and that string theory with the finite nature hypothesis is empirically valid. (If dark-matter-compensation-constant were equal to zero, then Wolfram's cosmological automaton would not have a uniform timing mechanism.)

According to Edward Witten, “String theory forces general relativity upon us …”

"Unravelling string theory", Nature, December 2005

Many string theorists seem to think that Milgrom, McGaugh, Kroupa, Sanders, and Scarpa are somehow deluded — but are these string theorists correct? I conjecture that string theory with the finite nature hypothesis implies real MOND and no supersymmetry, while string theory with the infinite nature hypothesis implies pseudo-MOND and supersymmetry. What do I mean by "pseudo-MOND"?

Can the string landscape explain the empirical successes of Milgrom's MOND? Consider 4 hypotheses:

(1) After quantum averaging, Einstein's field equations are 100% correct.

(2) All dark matter particles are WIMPs with D-brane charges.

(3) Within the string landscape there is a D-brane shock wave that makes it appear that Einstein's field equations are slightly wrong (due to D-brane charges acting detectably upon some WIMPs but non-detectably upon other WIMPs.)

(4) In the standard form of Einstein's field equations replace the -1/2 by -1/2 + fake-function, where the fake-function seems to be there because the pro-MOND astrophysics are unaware of the D-brane shock wave acting upon some of the WIMPs.

"Unravelling string theory", Nature, December 2005

Many string theorists seem to think that Milgrom, McGaugh, Kroupa, Sanders, and Scarpa are somehow deluded — but are these string theorists correct? I conjecture that string theory with the finite nature hypothesis implies real MOND and no supersymmetry, while string theory with the infinite nature hypothesis implies pseudo-MOND and supersymmetry. What do I mean by "pseudo-MOND"?

Can the string landscape explain the empirical successes of Milgrom's MOND? Consider 4 hypotheses:

(1) After quantum averaging, Einstein's field equations are 100% correct.

(2) All dark matter particles are WIMPs with D-brane charges.

(3) Within the string landscape there is a D-brane shock wave that makes it appear that Einstein's field equations are slightly wrong (due to D-brane charges acting detectably upon some WIMPs but non-detectably upon other WIMPs.)

(4) In the standard form of Einstein's field equations replace the -1/2 by -1/2 + fake-function, where the fake-function seems to be there because the pro-MOND astrophysics are unaware of the D-brane shock wave acting upon some of the WIMPs.

Are the pro-MOND astronomers and astrophysicists suffering from some type of N-ray delusion?

N ray, Wikipedia

Is MOND empirically invalid?

“Lessons from the Local Group (and beyond) on dark matter” by Pavel Kroupa, 2014, arXiv preprint

Are there paradoxical multiverse quantum jumps, D-brane shock waves, or multiverse wormhole strikes that somehow mimic MOND? I say that the empirical evidence favors Milgrom, McGaugh, Kroupa, Sanders, and Scarpa — however MOND does not make sense in terms of string theory. Imagine that the string landscape makes sense in terms of quantum field theory. There might be gradients of D-brane charges within the string landscape — if the gradients are sufficiently lopsided there might be a multiverse quantum jump (MQJ) of gravitational energy from one alternate universe to another. The alternate universes might be classified into 3 main types: the negative CC universe, the zero CC universes, and the positive CC universes. An MQJ might not be small — it might amazingly large. Think of Einstein's field equations with one side derived from the geometrical tensor and the other side consisting of the energy-momentum tensor. Imagine an analogy between a lightning strike and a MQJ. The ground of the lightning strike corresponds to weird MONDian WIMP particles. Because the pro-MOND astronomers fail to realize that the weird MONDian WIMP particles exist, they have altered the wrong side of Einstein's field equations. The MQJ should be incorporated into the energy-momentum energy according to the true nature of the MONDian WIMP particles. By attempting to model a MQJ that roughly matches MOND, string theorists might find new dualities, new types of compactification, or a new paradigm.

N ray, Wikipedia

Is MOND empirically invalid?

“Lessons from the Local Group (and beyond) on dark matter” by Pavel Kroupa, 2014, arXiv preprint

Are there paradoxical multiverse quantum jumps, D-brane shock waves, or multiverse wormhole strikes that somehow mimic MOND? I say that the empirical evidence favors Milgrom, McGaugh, Kroupa, Sanders, and Scarpa — however MOND does not make sense in terms of string theory. Imagine that the string landscape makes sense in terms of quantum field theory. There might be gradients of D-brane charges within the string landscape — if the gradients are sufficiently lopsided there might be a multiverse quantum jump (MQJ) of gravitational energy from one alternate universe to another. The alternate universes might be classified into 3 main types: the negative CC universe, the zero CC universes, and the positive CC universes. An MQJ might not be small — it might amazingly large. Think of Einstein's field equations with one side derived from the geometrical tensor and the other side consisting of the energy-momentum tensor. Imagine an analogy between a lightning strike and a MQJ. The ground of the lightning strike corresponds to weird MONDian WIMP particles. Because the pro-MOND astronomers fail to realize that the weird MONDian WIMP particles exist, they have altered the wrong side of Einstein's field equations. The MQJ should be incorporated into the energy-momentum energy according to the true nature of the MONDian WIMP particles. By attempting to model a MQJ that roughly matches MOND, string theorists might find new dualities, new types of compactification, or a new paradigm.

Consider this hypothesis: The empirical successes of MOND are the first empirical confirmation of string theory. How so? String theory with the finite nature hypothesis implies MOND (i.e. Fernández-Rañada-Milgrom effect), while string theory with the infinite nature hypothesis somehow allows pseudo-MOND to happen. According to Glashow, "The new theory must incorporate the old theory and say something new."

Viewpoints on String Theory, Sheldon Glashow, NOVA, Elegant Universe, 28 October 2003

I suggest that the most important "something new" is either MOND or pseudo-MOND.

Viewpoints on String Theory, Sheldon Glashow, NOVA, Elegant Universe, 28 October 2003

I suggest that the most important "something new" is either MOND or pseudo-MOND.

Let us assume that string theory with the infinite nature hypothesis is correct.

Professor Bekenstein has enumerated the 4 alternatives:

"Mild failures aside, it is clear that there is a broad range of masses, 10^6 — 10^11 M☉, in which systems adhere to MOND in their systematics. This must be telling us something; logically there are the following possibilities. a) MOND is merely an efficient summary of the way DM is distributed in the said systems? b) MOND reveals the dependence of inertia on acceleration for small accelerations? c) MOND betrays hitherto unknown forces particularly effective at astronomical scales? d) MOND encapsulates departures from standard Newtonian-Einsteinian gravity theory at the mentioned scales?"

"Tensor-vector-scalar-modified gravity: from small scale to cosmology", J. D. Bekenstein, arXiv preprint, 2012 (quote from p. 4)

Kroupa has ruled out (a) — explaining MOND requires a new paradigm for the foundations of physics. (b) is the dark fluid approach. Think of MOND chameleon particles having variable effective mass depending upon nearby gravitational acceleration — the dark fluid causes the variable effective mass. (c) is the holographic approach. The weird unknown force derives from the multiverse via the holographic structure of the multiverse. (d) is the Einstein-Hilbert-Bekenstein action approach. Because MOND is empirically valid, at least one of the 3 approaches (b), (c), (d) should work. My guess is that all 3 approaches can be made to work by sufficiently complicated tweaking.

Professor Bekenstein has enumerated the 4 alternatives:

"Mild failures aside, it is clear that there is a broad range of masses, 10^6 — 10^11 M☉, in which systems adhere to MOND in their systematics. This must be telling us something; logically there are the following possibilities. a) MOND is merely an efficient summary of the way DM is distributed in the said systems? b) MOND reveals the dependence of inertia on acceleration for small accelerations? c) MOND betrays hitherto unknown forces particularly effective at astronomical scales? d) MOND encapsulates departures from standard Newtonian-Einsteinian gravity theory at the mentioned scales?"

"Tensor-vector-scalar-modified gravity: from small scale to cosmology", J. D. Bekenstein, arXiv preprint, 2012 (quote from p. 4)

Kroupa has ruled out (a) — explaining MOND requires a new paradigm for the foundations of physics. (b) is the dark fluid approach. Think of MOND chameleon particles having variable effective mass depending upon nearby gravitational acceleration — the dark fluid causes the variable effective mass. (c) is the holographic approach. The weird unknown force derives from the multiverse via the holographic structure of the multiverse. (d) is the Einstein-Hilbert-Bekenstein action approach. Because MOND is empirically valid, at least one of the 3 approaches (b), (c), (d) should work. My guess is that all 3 approaches can be made to work by sufficiently complicated tweaking.

Consider the following 2 publications:

Volovich, I. V. "D-branes, Black Holes and SU(∞) Gauge Theory." arXiv preprint hep-th/9608137 (1996)

Faddeev, L. D. "New variables for the Einstein theory of gravitation." arXiv preprint arXiv:0911.0282 (2009)

Are Faddeev's "24 components in torsion" related to the 24 in the Ramanujan tau function?

Ramanujan tau function

Volovich, I. V. "D-branes, Black Holes and SU(∞) Gauge Theory." arXiv preprint hep-th/9608137 (1996)

Faddeev, L. D. "New variables for the Einstein theory of gravitation." arXiv preprint arXiv:0911.0282 (2009)

Are Faddeev's "24 components in torsion" related to the 24 in the Ramanujan tau function?

Ramanujan tau function

What is fundamental? What were the most fundamental discoveries and inventions of the past? What are the most fundamental questions? Are experiments more important than theories? What are the most important experiments in the history of science? What are the most important questions in the history of science? What are the most fundamental questions? Are questions more important than answers?

Consider 3 opinions:

Opinion 1. In 1900 the 2 most important questions were:

How can chemistry be explained in terms of physics? How does the sun produce so much energy?

Opinion 2. In 1950 the 2 most important questions were: How can electronic computers be improved? How can biology be explained in terms of chemistry?

Opinion 3. In 2000 the 2 most important questions were: How can robots be improved? How can consciousness be explained in terms of molecular biology?

Are the 3 preceding opinions wrong?

Do dark matter particles exist? Is there a unified theory of mathematics and theoretical physics? Consider the following conjecture:

Dark matter particles exist if and only there exists a proof for the Yang-Mills and mass gap problem.

Yang-Mills existence and mass gap, Wikipedia

Consider 3 opinions:

Opinion 1. In 1900 the 2 most important questions were:

How can chemistry be explained in terms of physics? How does the sun produce so much energy?

Opinion 2. In 1950 the 2 most important questions were: How can electronic computers be improved? How can biology be explained in terms of chemistry?

Opinion 3. In 2000 the 2 most important questions were: How can robots be improved? How can consciousness be explained in terms of molecular biology?

Are the 3 preceding opinions wrong?

Do dark matter particles exist? Is there a unified theory of mathematics and theoretical physics? Consider the following conjecture:

Dark matter particles exist if and only there exists a proof for the Yang-Mills and mass gap problem.

Yang-Mills existence and mass gap, Wikipedia

Are the RAR (radial acceleration relation), the BTFR (Baryonic Tully-Fisher Relation), and MOND 3 logically equivalent formulations?

Wheeler, Coral, Philip F. Hopkins, and Olivier Doré. "The radial acceleration relation is a natural consequence of the baryonic Tully-Fisher relation." arXiv preprint arXiv:1803.01849 (2018)

Wheeler, Coral, Philip F. Hopkins, and Olivier Doré. "The radial acceleration relation is a natural consequence of the baryonic Tully-Fisher relation." arXiv preprint arXiv:1803.01849 (2018)

Acedo, Piqueras, and Moraño (page 13) compared their orbital model to the Juno spacecraft data:

"We see that the agreement is very good but the model systematically underestimates the altitude of the spacecraft as if some outwards anomalous radial acceleration were acting upon Juno during its approximation to the perijove."

"A possible flyby anomaly for Juno at Jupiter", L. Acedo, P. Piqueras, J. A. Moraño, arxiv.org, 2017

Is the alleged Fernández-Rañada-Milgrom effect confirmed by the Juno spacecraft data?

"We see that the agreement is very good but the model systematically underestimates the altitude of the spacecraft as if some outwards anomalous radial acceleration were acting upon Juno during its approximation to the perijove."

"A possible flyby anomaly for Juno at Jupiter", L. Acedo, P. Piqueras, J. A. Moraño, arxiv.org, 2017

Is the alleged Fernández-Rañada-Milgrom effect confirmed by the Juno spacecraft data?

How might supersymmetric vacua in string theory be used to make a prediction for the fine structure constant?

Douglas, Michael R., Bernard Shiffman, and Steve Zelditch. "Critical points and supersymmetric vacua I." Communications in mathematical physics 252, no. 1-3 (2004): 325-358.

Lestone’s theory of virtual cross sections might be applied to the string landscape if the following 4 hypothesis are correct:

(1) Leptons and quarks have nonzero virtual cross sections.

(2) Virtual photons, virtual gravitons, and virtual gluons travel in the string landscape interstitium, which has 1 temporal dimension and 9 spatial dimensions.

(3) When gravitational spacetime is nearly flat, virtual photons travel in a 4-dimensional approximation to the string landscape interstitium and there is a semi-classical approximation that yields an approximate value for the fine structure constant, representing an expectation value derived from the string landscape.

(4) Measurement causes probabilistic clouds of virtual photons, virtual gravitons, and virtual gluons to condense into real particles.

Douglas, Michael R., Bernard Shiffman, and Steve Zelditch. "Critical points and supersymmetric vacua I." Communications in mathematical physics 252, no. 1-3 (2004): 325-358.

Lestone’s theory of virtual cross sections might be applied to the string landscape if the following 4 hypothesis are correct:

(1) Leptons and quarks have nonzero virtual cross sections.

(2) Virtual photons, virtual gravitons, and virtual gluons travel in the string landscape interstitium, which has 1 temporal dimension and 9 spatial dimensions.

(3) When gravitational spacetime is nearly flat, virtual photons travel in a 4-dimensional approximation to the string landscape interstitium and there is a semi-classical approximation that yields an approximate value for the fine structure constant, representing an expectation value derived from the string landscape.

(4) Measurement causes probabilistic clouds of virtual photons, virtual gravitons, and virtual gluons to condense into real particles.

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