Very interesting question. To me, best answer is given by Roger Penrose using the paradigm "The three worlds of reality": the Physical World, the Mental World, and the Platonic World (Mathematics lives here).

The claim is that Platonic World "maps" onto Physical World and hence all possible physical universes are constructs of information consistent with Mathematics.

Obviously Physical World "maps" onto Mental World (because we live in the physical world); and Mental World "maps" onto Platonic World. But the three worlds are different.

For a much better explanation you can see Penrose's book "The Emperor's New Mind"

This is interesting. Plato was not an experimentalist. The typical Greek philosophy considered the truth could best be resolved through thoughtful reasoning. There were others that did experiment but this did was not adhered to for a millennium. Galileo experimented. Others measured natural systems. Einstein used thought experiments and reasoning to develop the mathematics for the theory of relativity. Measurements of natural systems were performed to test the theory, to help prove it. These included the displacement of star light around the Sun and the changes in the orbit of Mercury. But the equations describing the relationships were derived from first principles of physics. There were no values that came from experiments. Then he included the cosmological constant to address subsequent findings of the expansion of the universe. Later he felt this was not appropriate. Subsequently, others derived this 'fug factor' from first principals.

Since I am stating this, this is my opinion. There are different viewpoints of our perceptions of reality. There are different formulations for describing gravity. That is, we can form mathematical models of systems that produce results that match what we observe. The we may have a variety of concepts of how we develop the different models. Just because the model produces results matching our measurements does not mean our concepts of the internals are what actual happen. The question is in what we value. We can build a neural network to match the measurements from a given system. We can use this to predict what the system will do in the future. But that does not mean we know how the machine works on the inside. So the question is, what do you want the model to do?

Very interesting question. To me, best answer is given by Roger Penrose using the paradigm "The three worlds of reality": the Physical World, the Mental World, and the Platonic World (Mathematics lives here).

The claim is that Platonic World "maps" onto Physical World and hence all possible physical universes are constructs of information consistent with Mathematics.

Obviously Physical World "maps" onto Mental World (because we live in the physical world); and Mental World "maps" onto Platonic World. But the three worlds are different.

For a much better explanation you can see Penrose's book "The Emperor's New Mind"

MAIEUTICS: is the geometry a priori structure ( in a neokantian position)? This old book of Tullio Livio-Civita give a new strong support to a neokantian interpretation of reality because the original paper of absolute differential calculus was published together with M. M. G. Ricci in 1905, 10 years before Einstein published general relavity.

Dear Carlos Cesar Aranda

The building block of universe is a Quantum Mechanics phenomenon. This reality is telling us, everything must have QM foundation, on the other word, nothing is working mechanically to write mathematic theorem for it. Two more reality, our knowledge on universe is a sand it the ocean, and second reality is, we never give universe any credit for its entity. The Universe with billions of galaxies, where each galaxy is running billions of solar system like ours, can not have any mechanical gravity as Sir. Isaac Newton, or Mr. Einstein stating. Gravity is Internal not external

Article Gravity is an Internal Force

regards

I think your question is not well posed!

Firstlty, we must note that differential calculus represents now only a very little part of mathematics. Also, we must note that mathematics offers now a multitude of possible structures(spaces, manifolds with a lot of possible properties), which can be models for many different types of reality.

Secondly, we have only pure mathematics or applied mathematics! What do you mean by " pure experimental mathematics"? The philosofical aspects do not offer nothing regarding the study of the universe by rigorous methods, to find and research the true reality, the functionallity of everything! "Everything" may be the multiverse or simply something else...not necessarily The Universe in the acceptance of most current theories.

The gravitation is a physical phenomenon, which holds locally, on the one hand, but holds also globally, on the other hand. The astrophysicists can not confirm now, by experiment, how gravity works globally, although some theoretical studies offer ideas about; theoretical studies using pure mathematics, applied to some conditions obtained by observations given by Hubble, Voyager1 and 2 and others.

Very nice! "pure experimental mathematics" is a nonempty intersection between the geometry world and the reality in Plato's cosmology. We can confirm how gravity works globally with the gravitational waves!, they are really to very big scales and very big energy scales, I observated several times the even dimensionality of the large scale of the universe, just analize the wave with the lacunary theory of Petrovsky and you see experimentally and mathematically that the large scale of the universe is even in coincidence with general relativity. Also you can see very primitive super massive black holes, than means really belong to a early period of the universe. and they work with general relativity.

https://www.researchgate.net/publication/343097694_Can_We_Quantify_Time_Through_Light

Dear Sergey P. Klykov

I read the article, still one part was missing to me, TIME. how do we define Time through light? as far as unit?

To me Time is relative.

https://www.academia.edu/38071066/Time_is_Relative

regards.

Dear Javad Fardaei .

Sorry for the delay.Good question. I think this is a matter for the future.

Greetings,

Sergey Klykov

Sure ???

Mathematical physics is a branch of physics characterized by a mathematical tendency unparalleled in any other sciences. Physics tries to find mathematical solutions to explain natural phenomena and formulate them into comprehensive theories. A sound theory is that theory that is not limited to explaining a certain phenomenon only, but its application extends to predicting the results of other phenomena related to the phenomenon that has been explained mathematically.

An example of this is Einstein's theory of relativity, where his calculations indicated the diffraction of light when it passes through the gravitational field of a large celestial body, as according to general relativity, gravity causes space to bend around the celestial body, which works on the diffraction of light (that is, that the ray of light bends from its straight path) passing through this field And it changes direction.

Dear Stefan

I am rejecting mechanical Gravity. Gravity is Internal not External, GR gravity can not be reality.

you are the best candidate to find an error in this article of Gravity.

https://www.academia.edu/41587434/Gravity_is_an_Internal_Force

regards.

Emile Borel stated in INTRODUCTION GEOMETRIQUE A QUELQUES THEORIES PHYSIQUES, Gauthier-Villars 1914, that to separate mathematics and reality is a very bad pedagogical mistake. According to Mr E. Borel the origen of the mathematics is almost all originated in observation and experience.

Theopile de Donder lectured Mathematical Theory of Relativity in 1913!

This book includes ten lectures on the Mathematical Theory

of Relativity, as I have developed it during the last twelve

years. These lectures were delivered at the Massachusetts

Institute of Technology during the Spring Term of the academic

year 1925-1926.

I desire to express to this Institute my deepest gratitude

for the invitation which has been extended to me to give these

lectures. It was very pleasant to think that I would be able

to collaborate in the scientific research of this important and

celebrated institution, and to renew the ties of friendship with

the intellectual elite of the American people. I have not been

disappointed in my hopes. The cordial reception extended to

me by my colleagues in the Departments of Physics and Mathematics, the interesting conversations and exchanges of ideas

I have had with them, have played no small part in creating

this feeling. In the domain of thought we are all citizens of

the same country. Barriers appear only where science ceases

to cast its light; and these frontiers recede ever toward more

remote regions. Thanks to science, the world becomes vaster

and richer. The only revolutionists are scholars and artists,

for they create new conditions and they change the aspect of

the universe. To be sure, this evolution sometimes carries

along with it sudden and terrible changes. Think of the

Great War ! The present adaptation towards the universality

due to science is still painfully felt in many countries. In my

fatherland, scientific reconstruction was greatly helped by the

C. R. B. This Committee for Relief in Belgium was organized,

during the war, for avoiding famine and, in collaboration with

other American organizations, has helped Belgium very much

in its new organization of teaching and scientific research.

Indeed, Belgium will always remember with thankfulness and

admiration that noble initiative of the United States of America.

Before closing this brief preface, I wish to express my sincere

thanks to my colleague, Professor M. S. Vallarta, who has

aided me, with his deep knowledge of the subject, in the final

writing of these lectures.

TH. DE BONDER.

Massachusetts Institute of Technology

May, 1926

However, the precision of pure math defines our existence...

No idea! but my new mathematical theory predicts black holes explosion:

According to NASA and others, the Ophiuchus Supercluster explosion was the biggest explosion seen in the observable universe since the MS 0735+74 explosion.[1][2]

Ophichus Supercluster ExplosionEvent typeExplosionInstrumentChandra X-ray Observatory, XMM-Newton, Murchison Widefield Array, Giant Metrewave Radio TelescopeConstellationOphiuchusDistance390 million light-years[edit on Wikidata]📷Ophichus Constellation

This extremely powerful eruption occurred in the Ophiuchus Supercluster, which is located about 390 million light-years from Earth. A paper describing these results appeared online on 27 February 2020 in The Astrophysical Journal, and a preprint is available on arXiv.[3] This explosion was caused by a supermassive black hole spraying out jets of extremely active particles.[4]. Its total huge energy is estimated to 5 X 1061 erg, or 5 X 1054 J.[3] Furthermore, the cavity produced by the outburst is so big that would be possible to put 15 galaxies of Milky Way's dimensions in a row.[5]

The authors of this paper are Simona Giancintucci (Naval Research Laboratory, Washington, DC), Maxim Markevitch (Goddard Space Flight Center, Greenbelt, Maryland), Melanie Johnston-Hollitt (International Centre for Radio Astronomy, Australia), Daniel Wik (University of Utah), Qian Wang (University of Utah), and Tracy Clarke (Naval Research Laboratory). The 2016 paper by Norbert Werner et al. was published in the Monthly Notices of the Royal Astronomical Society.

This observation is a result of collaboration among various space-based and Earth-based observatories including the Hubble Space Telescope, the Chandra X-ray Observatory, ESA’s XMM Newton X-ray space observatory and radio data from the Murchison Widefield Array (MWA) in Australia and the Giant Metrewave Radio Telescope (GMRT) in India.[6][7]

Dear Sydney Ernest Grimm Disagree with the whole things.

Math is just set of a rules that it is working mechanically, and always must have friction. But nature doe not act mechanics and does not have friction.

Math was/is powerful tool for all the innovation that human accomplish, and it the best tool for communication among of human, but it would be exhausted to calculate the nature. i.e. it can not distinguish millions of colors, taste, odor. or Even can not calculate simple outcome of shape of popcorn or snowflake.

Einstein wrote a formula for creation or shape of universe, and explain how the universe is should work, while universe is working on its nature and does not looking at Einstein's formula, but it is sad that we think math does all the trick, but it does not.

Article How the Quantum Universe Works

Quotation from " THE FOUNDATION OF MATHEMATICS A STUDY IN THE PHILOSOPHY OF SCIENCE' by E. W. Beth, published by Harper & Row 1966.

Aristotle's Theory or Science

The essentials of Aristotle's theory of science1) may be compressed

into the following definition of the term "deductive" or, as Aristotle says "apodeictic" -"science": A deductive science is a system S of sentences, which satisfies the following postulates:

(I) Any sentence belonging to S must refer to a specific domain

of real entities;

(II) Any sentence belonging to S must be true;

(III) If certain sentences belong to S, any logical consequence of

these sentences must belong to S;

(IV) There are in S a (finite) number of terms, such that

(a) the meaning of these terms is so obvious as to require no

further explanation;

(b) any other term occurring in S is definable by means of

these terms;

(V) There are in S a (finite) number of sentences, such that

(a) the truth of these sentences is so obvious as to require no

further proof;

(b) the truth of any other sentence belonging to S may be

established by logical inference starting from these sentences.

The postulates (I), (II), and (III) will be called, respectively, the

reality, the truth, and the deductivity postulate. The postulates (IV)

and (V) together constitute the so-called evidence postulate; 3) the

fundamental terms and sentences, referred to in postulates (IV) and

(V), are called the principles of the science under consideration.

It is known that Aristotle's doctrines met with a fierce and systematic

opposition from the School of Megara, the founder of which, Euclides

of Megara, though himself a disciple of Socrates, had already been

engaged in dispute with Plato (c/. Section 3 on Diodorus Cronus,

Section 9 on Eubulides of Miletus, and Section 22 on Stilpo).

Nevertheless, these objections, though taken quite seriously in Antiquity —

later authors, such as Prantl and Zeller, dismiss them abusively as

trivial fallacies —

could not prevent the triumph of Attic philosophy.

Informative

So it is possible to imply that the mathematical theory of gravitation is an a Aristotle's science? Is the string theory also science? what kind of science? .

"The luminary of Leuven's physics department in those years was George Lamaitre who is now recognized as the father of both the big bang theory and the theory of expanding universe, (the later is often mistakenly attributed to Edwin Hubble). Lamaitre as a catholic priest and for a time the head of the Pontificial Academy pf Science. A superb mathematician, ha had developed his two cosmological theories in 1925 as solutions to Einstein's field equations for general relativity, which had appeared only nine years earlier. At first. even Einstein didn't believe in the physical reality of Lemaitre's solutions telling him famously ' your calculations are correct, but your physics is abominable'. But Einstein and the rest of the scientific community came around when Hubble provided the first observations evidence to support Lamaitre's theories about two years afters he proposed them." QUOTATION in The Telescope in the Ice, by M. Bowen published by ST Martin's Press, N.Y. 2017

Dear Sydney Ernest Grimm Your research is a valuable always.

We all have potential to improve ourselves, by contradicting each other. I will be more appreciate to hear from you as well.

My research is very simple, which each research should be easy for layman to understand, not by jargon and esoteric mathematic that no one would understand it, even researcher.

I wish you all success.

Kant and Quantum Gravity Ozge Ekin Gun Institute of Philosophy, Freie University Berlin January 2, 2017 In quantum gravity space and time lose their status as fundamental parts of the physical reality. However, according to Kant, space and time are the a priori conditions of our experience. Does Kantian characterization of these notions give constraints to quantum gravity, or does quantum gravity make Kantian characterization of space and time an invalid approach? This paper provides answers to these questions with a philosophical approach to quantum gravity.

In late 18th century Immanuel Kant was articulating the approach that shapes have to conform to the axioms and rules of Euclidean space. According to Kant, space and time are pure intuitions, meaning that they are the results of the formation of human mind and is acquired independently from experience.(cf.[15], A26/ B42). Mathematical constructions, which are a priori intuitions, are possible due to pure intuitions space and time. Space and time are forms of sensibility and a priori conditions of one’s experience, and this space is Euclidean. For this reason, all figures that are exhibited in this space should conform to the Euclidean rules.

"In contrast to explanations of three-dimensionality based on anthropic arguments, we support the search for a theory that provides a justification for the dimensionality of space based on a combination of deductive and inductive reasoning applied to science. In doing so, we argue that Kant correctly approached the question in “Thoughts on the true estimation of living forces” (1747) by connecting space dimensionality and the inverse square law. In expounding the strategy of Kant’s argument, we describe the main features of a general Kantian explanation of the dimensionality of space and discuss them with respect to current accounts of explanation in the philosophy of science, such as inference to the best explanation and the deductive-nomological model." QUOTATION authors S. De Bianchi and J. D. Wells.

In this context gravitation, mathematics and universals: The problem of universals is an ancient question from metaphysics which has inspired a range of philosophical topics and disputes. Should the properties an object has in common with other objects, such as color and shape, be considered to exist beyond those objects? And if a property exists separately from objects, what is the nature of that existence? Roger Penrose contends that the foundations of mathematics can't be understood absent the Platonic view that "mathematical truth is absolute, external and eternal, and not based on man-made criteria mathematical objects have a timeless existence of their own..." The school of realism makes the claim that universals are real and that they exist distinctly from the particulars that instantiate them.

Dear Sydney Ernest Grimm

Our physics needs improvement, and the only way to improve it is on us, not last century scientists that they are not longer with us. I give you example. GRAVITY subject is slashed by teachers, because mechanical gravity of Sir Isaac Newton needs improvement. If someone ask you with g=9.81 gravity force of earth, WHY THE MASS OF WATER IS GOING UP? You can not answer this question, or no one can answer this simple question through g force.

All the teacher would say that mass of water would be lighter than atmosphere and it goes up. Here we never use g-force, but when something is drooping to the ground we use this force.

It is sad that we are trying to correct last century scientists.

Here is the problem.. we do not give our universe any credit as a complete well organized entity.

This simple recognition, place us that our universe is not following our mathematic jargon that we dictate to universe. Or nothing is coming out of nothing as all the scientists from last century said. Our universe is not working like a car mechanically,

Our universe is the most accurate entity that all its elements working in detail, that is including ATOMS to any planets, moons, and suns by nature.

We can not describe the universe's nature by our math, period.

The character of nature means, nothing in the universe is the same, not even HYDROGEN that it is the smallest, most complete unit of our universe, but they are carrying 99.99% the same thing, like us. .

EVIDENCE? Non of the snowflake is the same, non of five ocean's color the same, non of corn grain pop the same way. just I would like to invite you to read new things, and update your thought.

Article Hydrogen's Journey in the Universe

regards.

Sydney Ernest Grimm If there was no matter around but only photons then the other "fundamental forces" would be missing as well ie no strong or electroweak forces. In such a system only quantum electrodynamics would matter. But there is a problem here as well .. if photons have high enough energy then there is the possibility that it transforms itself to a matter antimatter pair that may of may not annihilate themselves to recreate a photon. Its an extremely tricky question since at the quantum level the force of gravity would be man many orders of magnitude smaller than the other forces we know today.

Sydney Ernest Grimm Thanks for the paper link .. I will take a look.

Hi many thanks for every one! I have my experimental verification! on my proposed quantum gravity..

Solving The Mystery Of The Disappearing Quasar Using the Poincare's Balayage Mechanism in Quantum Field Theory

Using Ponicare Balayage we stablish the quantum field mechanism of creation and anhilation of gravitons, giving and Occam's razor explanation to the mystery.

I think physical and mathematical nature.