Hi! I have been developing similar picture past few months as well. My results vary from yours though. I will be submitting soon.

Very well. Thus, the quantum mech is not natural. Thus, the QM has someone supernatural. Agree?

The contrary would have been annoying as the subject of Feynman's phd thesis ("A new approach to quantum physics", 1942) was just that : using the principle of least action in quantum mechanics.   

Hi All,

To my opinion, quantum mechanics is mathematically sound but not physically. Whether quantum mechanics is natural or not very much depends on your perception of the subject. From what I've shown in my work, even the most foundational principle of physics, which is the principle of least action, is needed to be re-examined at the quantum level. It seems it is not possible to formulate an ultimate theory because there is always a question that arrives naturally from it. But we always have hopes, so keep moving on. Hi Vikash, this work is actually from my PhD thesis published in 1996. Please let me know when you submit your work.

Dear Dr Guibert Crevecoeur,

I am not very sure what you mean by “using the principle of least action in quantum mechanics” because as far as I know there is no principle of least action in Feynman's formulation of quantum mechanics. To be clear, let me quote from my favourite little book  Variational Principles in Dynamics and Quantum Theory by W. Yourgrau and S. Mandelstam, “in fact, Feynman’s expression for the transition amplitude between eigenstates does not represent a variational principle at all. However, within the limits in which classical mechanics prevails, these new formulations reduce to the principle of least action.”  And this should be expected for all formulations of quantum mechanics.

Kind regards,

Vu B Ho.

Dear Vu,

You are probably right that the reference to the principle of least action is not explicit in books like "Quantum Electrodynamics" A Lecture Note and Reprint Volume, by R. P. Feynman (ed. W.A. Benjamin,Inc., New York, 1961). For instance, in the preface of this book, he writes : "...Nevertheless, this course is complete in itself, in much the way that a course dealing with Newton's laws can be a complete discussion of mechanics in a physical sense although topics such as least action or Hamilton's equations are omitted." (I underline)

In my reaction,I just wanted to draw your attention that your findings could probaby also be seen as a confirmation of the coherence and continuity in Feynman's thinking (using the principle of least action) as his work stemmed from his 1942 phd thesis which is explicitly devoted to approaching quantum mechanics having the principle of least action in mind.

Unfortunately, my version of this thesis is a translation into French and I fear that there are very few original versions still available in English (a quick search on Internet did not give anything !).

In order to allow you to better understand what I mean, please find hereafter a translation of the content of Feynman's thesis. It is a free "reverse" translation by me from French to English, so please apologize for the poor English !

CONTENT

"The principle of least action in quantum mechanics (by Richard P. Feynman)

I - Introduction

II - The principle of least action in classical mechanics

III – The principle of least action in quantum mechanics

Feynman then afterwards published an article with the path integral formulation in : Rev. Mod. Phys., 20, pp. 367-387 (1948). And the remainder followed.

Dear Guibert,

Thank you for your kind considerations. When I did research for my PhD at Monash University in Australia in1993 I only had Feynman’s article entitled “Space-Time Approach to Non-Relativistic Quantum Mechanics” with very little mention of the principle of least action, even in classical limits. Following your guidance, I found Feynman’s original PhD thesis entitled “Principles of least action in quantum mechanics”. I am not going to comment on this one, but to be honest, I totally agree with what W. Yourgrau and S. Mandelstam said.

Schrodinger's equation can be derived by minimizing an action integral. See for example:

Dear Vu,

thanks for your question and quoted paper by J.H. Field on http://arxiv.org/abs/1204.0653.

Results contained in this paper can be considered as examples of my more general results contained in the book published in 1996.

https://books.google.it/books?hl=it&lr=&id=O5IbRdY7gqQC&oi=fnd&pg=PA307&dq=Geometry+of+PDE's+and+Mechanics+by+Prastaro+A.&ots=J5NLZFOWjH&sig=cBqqa4P-Td9UMqJQRebPlKCFFbY#v=onepage&q=Geometry%20of%20PDE's%20and%20Mechanics%20by%20Prastaro%20A.&f=false

(See pags. 594-619.)

Unfortunately J.H.Field does not quote my book. Of course this means that Field's results even if correct, do not open new horizons ...

My best regards,

Agostino

Hi All,

Thanks for your participation. Yes, it is true that Schrodinger's wave equation can be derived by applying the variational principle, because Schrodinger himself did just that. I am sorry I should have been more specific. In quantum mechanics, Feynman's path integral formulation uses all paths, on the other hand, the principle of least action in classical mechanics is used to determine a unique trajectory. The question is whether there is any ground for Feynman's method or it is just a postulate, like Bohr's postulates in his theory of a hydrogen-like atom. By the way, as shown in my work, by trying to find a ground for Feynman's postulate I also found a ground for Bohr's postulate of the quantisation of angular momentum in terms of topology.  

Dear Biswajoy,

I've had a look at J.H.Field paper but I could not see anything new from it. We all know that Schrodinger used a trick to derive his wave equation by letting S=kln(ψ), therefore the action integral can be regarded as a phase of any wave function. Feynman developed further by formulating a sum over random paths. However, as I mentioned in a quote before, his formulation does not represent the principle of least action at all.  

Kind regards,

Vu.

Dear Vu,

whether you look to my book, quoted in my previous post, you can find what you asked, namely

'... The question is whether there is any ground for Feynman's method or it is just a postulate....'

In fact I proved that one can quantize a classical PDE by using what I called quantum cobordism. In a scattering problem this can be identified with the Feynman structure. In particular when the PDE is of variational type then such a quantization is related to its variational constraint. In other words in my quantization of PDEs, the Feynman's method becomes a theorem and can be related to variational constraints. (See in particular Theorem 5.42 at page 604.)

My best regards,

Agostino

I can give you another reference. Quantum Gravitation: The Feynman Path Integral Approach, By Herbert W. Hamber (UC Irvine), pages 55-57. This book has a chapter on Feynman path integral. The author states that  

A stationary phase approximation of path integral, valid in the limit hbar ->0, leads to principle of least action of classical mechanics.

I suppose this is a known result. You may find it in other books also.

Dear Biswajoy,

the book that you quote has been published in 2009  and considers the Einstein's PDEs  only ... (my book has been published 13 years before... and is a more general theory concerning any differential equation and well algebraic topologic founded...) Let me also add that despite the title used in the book that you quote, the quantization of a classical dynamical equation cannot fully interpret quantum world and neither quantum gravity. In fact such quantizations concern only quantum fluctuations of classical systems ...

Quantum gravity is a more complex theory ! In the same my 1996 book this more complete quantum gravity has been formulated for the first time, even if I published only in 2009 a more complete work on this subject.

Dear Biswajoy,

We don't deny and it is true that the classical limit of Feynman's path integral formulation reduces to the principle of least action. And it doesn't matter which book you refer to you will find they would state the same as what you have quoted. On the other hand, what I want to discuss about is the non-classical-limit of Feynman's expression of the transition amplitude. The formulation uses all classical paths in order to describe the quantum dynamics of a particle, and as shown in my work, by using de Broglie's relation and geometry the principle of least action "endorses" such an assumption. 

Dear Agostino,

Your book is very high standard and I hope we could describe all physical processes precisely as that. I don't believe in the current format of quantum physics and I think the unpredictability of quantum mechanics takes its origin from geometry and topology. I also think what we should do first is to identify all quantum observables in terms of geometrical and topological objects and to try to uncover what behind all "principles" in physics. To my opinion, to propose a principle is very much the same as to sweep the unknown under the carpet. It is acceptable to use it to progress, however, we should not use it as an ultimate knowledge of all. (I hope you will not say: who cares what you think!)

Dear Vu,

thanks  for your reply. However, I do not understand your remarks about ...' "principles" in physics.'

Please be more explicit, ... I will be glad to answer to you.

Regards,

Agostino

Dear Agostino,

There are many so-called principles in physics that formulations of physics rely on. In classical physics, we have the principle of least action, the equivalence principle, ... In quantum physics, we have the uncertainty principle, the principle of exclusion, the complementary principle, and so on. What I want to talk about is: why do we need to propose a principle? Of course the answer is to formulate a theory (based on what we don't really know). So what's the theory for? Of course the answer is to interpret something else (for application). In physics, a principle is very much like a rule,  but nowadays it has become more like an axiom in mathematics. In mathematics you need to accept a system of axioms in order to construct a mathematical model without further questions. But do we need to do the same in physics by accepting principles without questioning why? I am more on the physical side, so my view may be different from yours. Have you ever questioned yourselves why mathematics exists?

Dear Vu,

I see that your problem is about justification of the mathematical structure encoding a model for physical world. With this respect you try to compare mathematical axioms of a mathematical theory with physical principles for some mathematical physical model.

No ! I do not agree on this parallelism ...

Really mathematical axioms are starting definitions in a mathematical theory. Instead physical principles are some 'Inbegrifff' of experimental observations that instead must be justified as theorems in a mathematical physical model.

For example the Kepler's laws for planets play the role of some principles in the sun system. They can be obtained as theorems in the Newton's gravitational theory or in the Lagrange analytical mechanics. Another example is the Heisenberg uncertainty principle in quantum mechanics. This becomes a theorem in my quantization theory of classical dynamical equations in classical mechanics and in classical field theory, but also in my quantum gravity theory.

Your last question:

'Have you ever questioned yourselves why mathematics exists? '

admits only one answer:

Mathematics is a language, the more precise that humans have codified. Therefore it exists since humans exist !

Nowadays does not exist mystery in Epistemology ... all is already well encoded in the Galileo's method ...

My best regards,

Agostino

Dear Agostino,

I think you misunderstood my statements. What I wanted to talk about were exactly like what you have said. Physical principles should be explained in terms of mathematics. On the other hand, I don't agree with you on one important point, mathematics is not a human language, it is a nature's language and that's why all physical laws should be expressed in terms of it. All languages sound differently but they mean the same thing. 

Dear Vu,

you have written:

'... I don't agree with you on one important point, mathematics is not a human language, it is a nature's language and that's why all physical laws should be expressed in terms of it.'

Sorry I cannot share your opinion ... Mathematics is a production of humans. The belief that it is the language of Nature is completely unfounded.

In fact, whether this should be true, any mathematical model should encode Nature, but this is not true.

Unfortunately many mistakes in Science history can be recognized, when humans placed themselves in 'the center of universe' ...

Physical laws do not exist for themselves. They exist like interpretations of our mathematical models that try to encode Nature. In fact they evolve in the time and become, step by step more general and inclusive.

Does this knowledge-process can stabilize like in a Noetherian topological space ? It is impossible to answer to this question, since we cannot say what is Nature.

But at this point I prefer to stop myself since the discussion necessarily enters in a philosophical domain ... and any people can believe what he wants therein.

Dear Agostino,

Thank you very much for your time and your valued opinions. I agree that we have entered a bit too far into the philosophical domain. Actually when I asked you that question I did not expect to discuss about it at all, because I know we may have different views about it. I am sorry about that. I want to tell you one last thing, your book is very helpful.

Best regards,

Vu

Thanks Vu.

Hi All,

I have developed my works and have re-written them to form a more complete and coherent theory. It has been posted on RG entitled: A TEMPORAL DYNAMICS: A GENERALISED NEWTONIAN AND WAVE MECHANICS. In this work it is shown that a temporal dynamics can be derived directly from the theory of special relativity using the general principle of relativity. You will also find that the spin of a particle in quantum mechanics can also be expressed naturally in a 3-dimensional space which is associated with a 3-dimensional temporal manifold.  We all have different views on most of formulations of physics, therefore to have them discussed thouroughly, even though to make our views more different, is always helpful. Thank you for your participation.

Kind regards,

Vu.

Dear All,

In Feynman's formulation of quantum physics, in order to determine the dynamics of a quantum object we only use concepts such as path, surface and hypersurface. Therefore I am not very sure if classical concepts such as particle, string and branes are still relevant in Feynman's methods. Furthermore, for example, we don't need a string in order to form a surface, so, why a physical theory should be started with a string? Unless it is only considered as a mathematical method.

Kind regards,

Vu.

Dear Vu,

you focused an important aspect in the usual string theory (ST). In fact even if ST considers reactions between quantum particles encoded by 2-dimensional surfaces, when it calculates scattering amplitudes it reconsiders quantum particles as point-like objects. Therefore it appears that the representation of quantum particles as extended objects are unnatural mathematical methods only ... However it is worth to underline that also the Feynman's path method is a mathematical artefact built to obtain quantization of classical theories.  On the other hand quantum gravity is another thing with a more deep meaning ! Therein it is possible to understand that quantum particles truly are extended objects ...  See my already posts ...

My best regards,

Agostino

Dear Agostino,

I am a very down-to-earth physicist whose view on the physical world is very physical. I have read your book and some of your articles, but they appear to be too mathematical to me. All that I need is a clear mathematical model that can be used to describe physics at all levels in the manner of classical physics. String theory is not a candidate. It is a dreamworld for mathematicians. As I said many times before, I admire mathematicians but I would not hire any of them to do a physics job. I believe that the universe is a biological system and all particles and interactions between them are produced, probably through evolution, so that they can function according to what required of them. Therefore, there is no point of trying to unify the known forces. All forces are different but united. They play their roles like players of a football team. And also according to my works (and beliefs) there are more forces in Nature than those that have been discovered. These are short-lived and time-dependent forces. And don't forget the Fractional Laplacian!

Kind regards,

Vu.

Dear Vu,

you have written:

'... there is no point of trying to unify the known forces.'

The unification of different aspects (forces) is the main road in Physics. Einstein's Relativity has allowed the unification of electric and magnetic force in only one, namely the electromagnetic force. The study of quantum electrodynamics has allowed to unify electromagnetic force with the weak force in the quantum world (Glashow-Salam-Weinberg). The quantum gravity allows the unification of the other forces at the quantum level. To confute this process it is equivalent to reject Science.

Furthermore you have written:

' I admire mathematicians but I would not hire any of them to do a physics job. '

This assumption conflicts with Science History ! It is impossible to do physics without mathematics ! Mathematics is the language of Physics.

Moreover you have written:

' I have read your book and some of your articles, but they appear to be too mathematical to me. All that I need is a clear mathematical model that can be used to describe physics at all levels in the manner of classical physics.'

But this is just my quantum gravity theory ! Of course it is necessary to play mathematics in order to understand it. The situation is similar to what happens in music. Whether you look to a Bach's score you cannot understand the beauty of his music without to be able to read music and to play organ.

Do not forget that in order to follow a job it is necessary to learn handling its tools.

My best regards,

Agostino

Dear Agostino,

I totally agree with some of what you have said. Bach' scores are beautiful music, but unfortunately not all musical scores will make music, let alone a beautiful one. And importantly, you only need to listen to music to appreciate its beauty, without being able to read and play them. The same for food, you don't have to be a professional cook in order to know the food you are eating is terrible. I only need and handle tools for my job, also unfortunately not any tool will do. Newton discovered his physics first and then invented his calculus to describe his laws. Nowadays, people want to invent mathematics and then try to fit physics into them. It may be good for mathematicians, but I cannot find a way to pick out the physical world that I want to know from 10500 possibilities using the string theories. I also said this before, I can arrange the English alphabet to form a spectacular pattern that follow some particular rules, but none of them would make any sense. That's why I did not write them down here because I know that you would not understand them. There are two things that I don't like about quantum gravity. Firstly, I think quantisation is not a true and proper method to be used to "unify" general relativity and quantum physics. Secondly, I myself regard general relativity is no more than a potential theory, like that of Poisson's and Laplace's. It can be used to describe the structure of a particular space-time formation, but not how such a formation is formed.  And finally, the main road in physics is not about trying to unify things as you said. It is about finding out what's going on in Nature and trying to describe them in the way that we can understand it. Mathematics is the language of physics, therefore it can be that of the English language as I've just talked about. Wait until you can tell me the nature of mass, charge and quantum of energy then you can tell me how to unify them. Warning: Big Bang is only good for TV show.

Kind regards,

Vu.

Dear Vu,

in your last post your conclusive words are the following:

'Wait until you can tell me the nature of mass, charge and quantum of energy then you can tell me how to unify them.'

Well ! You touched just the right points that justify my quantum gravity theory. In fact in my formulation, mass, charge and quantum of energy are all encoded by the quantum Hamiltonian.

But in order to seriously understand it is necessary to read my work.

My best regards,

Agostino

Dear Agostino,

To be honest, I am not very interested in sophisticated mathematical methods, especially those new mathematical methods that are used to express old physical ideas. I am a physicist therefore I think in order to progress in physics we need to find new physical laws, not new mathematical methods to express old physical laws. You are an extremely talented mathematician therefore naturally you would think the other way (In order to progress in mathematics). I have searched your site but not sure which papers would contain the information that you have referred to. It would be very grateful if you could send me only those works of yours that relate to them. Anyway, how can you tell me your quantum Hamiltonian is the origin of the whole thing? In physics, Hamiltonian is no more than a principle. You cannot use a principle to explain the nature of physical entities. If you accept the quantum ideas as your starting points for your formulations then I think you'd better say: This is my axioms for my mathematical formulations of quantum physics. And I cannot work out how you can explain a quantum of energy by using it as one of your axioms. And this is true for any mathematical theory that is needed to be quantised in order to be recognised as a physical theory.

Kind regards,

Vu.

Dear Vu,

my quantum gravity theory is formulated in the following paper:

[1] http://www.sciencedirect.com/science/article/pii/S1468121812000491.

A similar version can be found on arxiv: http://arxiv.org/abs/0906.1363. (You can look Section 3 only therein.)

For more extensive applications in high energy physics, you can see the following works:

[3-4] http://arxiv.org/abs/1205.2894.

[5] http://arxiv.org/abs/1206.4856.

I prefer to skip on your philosophical considerations about physical theories since I would be more concrete. In fact, one cannot reject my quantum gravity theory since it gives a full justification of our knowledge, but also opens a window on a new physics.

My best regards,

Agostino

Dear Agostino,

Thank you. Your works are impressive. It may take me some time to study them. I tried to download the work No 5 from your list but the website said the work is not recognised. Anyway, I think I had more than enough. I hope your works will shed some truth about the working of Nature.

Kind regards,

Vu.

Dear Vu,

sorry for the previous incomplete coordinates of paper [5]. Look the following.

[5] http://arxiv.org/abs/1206.4856.

My best regards,

Agostino

Dear Agostino,

Your papers look great. I wish I could live in the world of mathematicians. We can twist around and then turn into nowhere, because that's where everything was originated. I still have a few questions that I need to consult with you though. I will ask you when I finish my works. 

Kind regards,

Vu.

Dear Agostino,

I have painstakingly gone through your works. I have to say that mathematicians have turned physics into something that gradually becomes increasingly incomprehensible (physically). In fact, it is possible to understand why the observable universe is expanding with an accelerating rate within classical framework of general relativity with normal matter defined in classical physics. Maybe more mass, but no exotic matter required. I need to remind you that according to my views, general relativity is no more than a potential theory, therefore my views on the subject may be different from yours. If you don't believe in what I have said, please see my article ON REPULSIVE GRAVITY posted on RG for details and calculations.

Kind regards,

Vu.

Dear Vu,

I looked to your interesting paper ! With this respect let me remark the following:

1) You refer to Einstein's PDEs (2) with the cosmological constant Λ . It is well known that such a constant allows expansive solutions. (This was an Einstein's result.) Your potential is therefore a variation of the Einstein's result.

2) When in an equation encoding physical phenomena, appears some empirical constant, it means that theory is founded on hidden unjustified phenomena. This holds also for the Einstein's PDEs (2). (This was well understood by Einstein....)

3) Repulsive gravitational founded on antimatter (e.g., Villata's approach) is a big mistake, as I have already written in some RG thread, caused by a misleading interpretation of antimatter..

4) Expansion of universe is caused by its Planck epoch, that produces an exotic nonlinear quantum propagator in the sense I proved in my paper.

The reason that you find this paper '... increasingly incomprehensible (physically)', is to ascribe to the fact that you did not understand the space-time boundary contribution of the solution encoding the universe propagation.

5) Let me also add that in my quantum gravity theory there are not  phenomenological constants ....

My best regards,

Agostino

Dear Agostino,

Your papers are written in highly mathematical standards, most of which can only be understood mathematically but not physically. For example, a closed 4-dimensional space-time can be perceived in terms of mathematics using categories of cobordisms but not in terms of physics. I myself had tried to use geometry and topology to deduce physical laws by showing that physical interactions are just bordism relations, but due to illness I had to abandon most of my research for more than 20 years. I re-started my research work only recently and now I am more on the physical side than mathematical. Even Einstein himself admitted that the cosmological constant is not natural. It was added in in an ad hoc manner. It could be true, as you observed, that my potential is a variation of Einstein's result, in the sense that I had to introduce an energy-momentum tensor with Yukawa potential into the field equations of general relativity, but at least Yukawa potential has been used in physics. No one, except mathematicians, can understand the space-time boundary contribution of the solution encoding the universe propagation because physically there is no universe propagation as a compete physical entity by itself. With your vast mathematical knowledge, I hope you can formulate a quantum theory of gravity without using the quantisation procedure.

Kind regards,

Vu.

Dear Vu,

you have written:

1) '... For example, a closed 4-dimensional space-time can be perceived in terms of mathematics using categories of cobordisms but not in terms of physics.'

'... No one, except mathematicians, can understand the space-time boundary contribution of the solution encoding the universe propagation because physically there is no universe propagation as a compete physical entity by itself.'

I do not use a closed space-time ... but bordism of compact 3-dimensional manifolds ... Any physical theory can be developed by using such an approach ! Also Einstein's GR is built in this way. In fact any 4-dimensional space-time in GR is a solution of the Einstein's PDEs solving some boundary value problems. Furthermore, any observed natural phenomena is of dynamical type, hence any physical theory must be encoded by a dynamic equation. Universe cannot escape from this natural law.

2)  '... but at least Yukawa potential has been used in physics.'

 Yukawa potential has been used in nuclear physics ... but that were old theories of potential scatterings, by now abandoned ... or that can be used only for heuristic reasons.

 3) '... I hope you can formulate a quantum theory of gravity without using the quantisation procedure.'

 I do not use some quantization procedure in my quantum gravity theory ! This is just the great novelty ! Instead I formulated a new dynamical geometric theory in a new category of noncommutative manifolds (quantum (super)manifolds). In fact the logic of quantum world is noncommutative.

By conclusion, your problems with my quantum gravity theory are caused by some your misleading interpretations.

All the best,

Agostino

Dear Agostino,

Perhaps, one of the reasons that make me dislike quantum theory is the role played by Planck’s constant. The Planck’s constant does not have the character of mass and charge in classical physics, because even though mass and charge do not tell you what they are, at least they can tell you what they are doing in terms of interactions. And certainly Planck’s constant is not simply a dimensional constant either. So, if we do not satisfy with the current formulation of quantum theory then we need to find a way to solve the Planck’s constant’s problem first. Recently, I have been able to show that a quantum of energy is a maximum amount of energy transferred to an elementary particle by a quantum system, and the process is entirely classical (Please see attached). However, the mystery of Planck’s constant is still remained. From these analyses, I can conclude that Planck’s constant must be a composite constant, which is a product of other physical constants at the quantum level that we have not been able to probe experimentally (Can’t believe a tiny weasel can shut the whole giant LHC down LOL). These other physical constants are responsible for interactions at the quantum level. Yukawa potential is not exclusive to strong interaction. In classical physics, the two most fundamental but distinctive laws are Newton’s law of gravitation and Coulomb’s law of electrostatics and both have identical forms. Finally, you should remember that any form of non-classical commutator is a quantum commutator, therefore a quatisation procedure.

Kind regards,

Vu.

Working Paper A TEMPORAL DYNAMICS: A GENERALISED NEWTONIAN AND WAVE MECHANICS

No Vu,

the Planck constant does not hide some mystery ...

As I have already said, a physical mathematical model of quantum world must not contain empirical constants. 

Dear Agostino,

I think we must agree to disagree here about the Planck's constant. But, how can you interpret the physical world without any kind of empirical constants? Isn't charge, for example, an empirical constant? If you want to build a physical mathematical model, as you said, you would need to identify mathematical objects with physical entities, otherwise your mathematical model would be just a mathematical model. And by measurements, some physical entities just happen to be constant and some are not, and some are discrete and some are continuous. If with just symbols how can you distinguish, for example, Newton's law of gravitation V=GM/r and Coulomb's law of electrostatics V=kq/r?

Kind regards,

Vu.

Dear Vu,

a satisfactory mathematical model for quantum phenomena must be a pure geometric formulation. The mass of a quantum particle is determined by the spectrum of quantum Hamiltonian, say H, and similar considerations hold for its charge. Really H has some structure that allows to identify these properties. Therefore, do not exist empiric parameters like mass, charge and so on. These are dynamic properties ... Otherwise you should assume that there exists a substructure that justifies these 'empirical constants' ... In such a case a theory should not be a fundamental theory.

My best regards,

Agostino

Dear Agostino,

I like the idea of a pure geometric formulation and a pure quantum Hamiltonian. All of these would be purely mathematical. And therefore a purely mathematical model of Nature. The only problem is we are living in a physical world that requires some kind of measurements to determine which is which and how things work. If without empirical evidence, how many laws of the form, for example, V=GM/r, would be needed for your purely mathematical quantum Hamiltonian and importantly how would we know your purely mathematical theory is correct? You would not feel a thing when you are near Einstein's field equations of general relativity, but certainly you would be in big trouble if you are near a physical black hole.  

Kind regards,

Vu.

Dear Vu,

the relation between quantum model and observed quantum phenomena, is obtained by means of the process of quantum measurements. My quantum gravity allows to study also quantum black holes and to prove they evaporate ... This is the unique serious road to prove the Hawking's radiation. (See some my works about ...)

My best regards,

Agostino 

Dear Agostino,

So finally you have to admit that you have to link your purely mathematical model to some kind of physical measurements to make it work. Quantum or not quantum, a physical measurement is a physical measurement and all measurements produce empirical results and in those empirical results you will find some empirical constants because we are living in a local environment that seems to be stable, otherwise there would not be you and me here to talk about them. I don't know why you are trying to prove something that have not been proved to exist. Only mathematicians can imagine a radiating black hole. That would not be a black hole in the first place, wouldn't it?  Mathematics is very deceptible. At the moment mathematicians can use the uncertainty in physics to imagine things but that will not be lasting long. Mathematicians have been forcing their way of thoughts to physicists to such a point that many physicists do not dare to propose their views because they are not expressed in a highly mathematical standard. That's why I told you that I would not hire a mathematician to do a physics job because they don't seem to be able to distinguish between mathematics and physics. I once submitted my work for publication and then quickly received a comment from a reviewer telling me that all that I would need to do is to solve Einstein's field equations. What a dumb reviewer! Einstein was very lucky to have most of his works published without peer-review. A very funny story is that of Heaviside. He had had some of his works published without a peer-review, but then when the editor decided to send his works for reviewing they all got rejected. I appreciate your patience and kindness.

Kind regards,

Vu.

No Vu !

In your last post you touche many different subjects and give your personal misleading interpretations ...

In the following my remarks.

1) 'So finally you have to admit that you have to link your purely mathematical model to some kind of physical measurements to make it work. Quantum or not quantum, a physical measurement is a physical measurement and all measurements produce empirical results.'

No ! My quantum measurements have a pure geometric meaning. Therefore they are not empirical objects ! Instead my quantum measurements allow to compare theory with experimental results. Probably you talk about thinks that you do not know since you did not read my quantum gravity theory yet !

2) 'I don't know why you are trying to prove something that have not been proved to exist. Only mathematicians can imagine a radiating black hole. That would not be a black hole in the first place, wouldn't it?'

No ! The situation about experimental proofs of the Hawking's radiation was resumed in

https://en.wikipedia.org/wiki/Hawking_radiation.

But recently there are confirms in this direction by Jeff Steinhauer, Technion - Haifa, Israel

http://arxiv.org/abs/1510.00621.

3)  'I would not hire a mathematician to do a physics job because they don't seem to be able to distinguish between mathematics and physics. I once submitted my work for publication and then quickly received a comment from a reviewer telling me that all that I would need to do is to solve Einstein's field equations. What a dumb reviewer!'

No ! Sorry I cannot follow you on this artificial opposition between Mathematics and Physics ... Mathematics and Physics have been created by the same scientists ...

But you talk also about another important subject ...

4) 'Einstein was very lucky to have most of his works published without peer-review. A very funny story is that of Heaviside. He had had some of his works published without a peer-review, but then when the editor decided to send his works for reviewing they all got rejected.'

Really you refer to the 'peer review method' ... As I have occasion to say in other RG threads, this method should be the best one to adopt in order to accept a paper for publication. Unfortunately journals are not always able to produce a serious peer review, and lobby competition considerations can distort the noble meaning of the 'peer review'...

On the other hand from the Science History we can learn many considerations ... Galileo Galilei probably is the most known one ... but it is also the proof that Mathematics is the Physics language, and that good mathematical models for physical systems are the ones that well fit experimental results. But Galileo's case teaches also that a good research holds independently where is published ... and independently from the leader 'peer review' ...

My best regards,

Agostino

Dear Agostino,

I think I need to go through with you point by point again.

1. I did go through your works. Your quantum measurements are no more than theoretical predictions. It just shows how out of touch mathematicians have become with regards to formulating a physical theory. How can a purely geometric object be a physical measurement? You can make a purely geometric object on papers with your purely mathematical symbols, but in order to make a measurement you need an experimental apparatus to measure what you want to measure that are resulted from a physical process.

2. Hawking's radiation is just a theoretical speculation but not a proved experimental result. What I want to talk about is like: you see a black hole then you don't see a black hole. You define a black hole then in order to progress you need to modify it, and all of these can be hidden under quantum uncertainty. All the works that you referred to are about analogue black holes, not the true black holes as defined in terms of solutions of general relativity. I myself don't think there exists any true black hole. They are just mathematical mishaps. Close but not quite. Physical theories have been formulated by trial and error and approximation methods, therefore modification of physical theory is a normal process. Do you know Hollywood is very much in favour of the fantasy aspects of science?

3. I don't want to argue much about this point either because I know you are a very talented mathematician. However, I am not sure if you've ever heard of what Einstein said. He said, ever since mathematicians invaded relativity he has not been able to understand his own theory anymore. And I think Newton would say the same because he invented most of physics and mathematics himself.

4. I prefer peer-review process myself. Just funny things can happen anywhere anytime. A collision of contradicted viewpoints certainly occurs on the ground of uncertainty. And it is happening now.

Kind regards,

Vu.

Dear Agostino,

I forgot to ask you a question about topology. We know that the observable universe is expanding with astronomical objects moving away from each other. Is there any topological structure that can be used to describe the phenomenon as a flow within itself so we can avoid the concept of expansion altogether?

By the way, I have added a discussion on the possibility that the field equations of general relativity can be seen consistent with Feynman's hypothesis of path integral. We know that the field equations of general relativity can be derived from Hilbert's action through the principle of least action. In the case of n=2, the field equations can be satisfied by any metric tensor if the energy-momentum tensor is directly related to it, similar to the relationship between the momentum of a particle and the curvature of its path in Bohr's model. Please see attached for more details.

Kind regards,

Vu.

Working Paper ON REPULSIVE GRAVITY

Dear Vu,

I answer again to your remarks since you show did not understand my previous clarifications.

1) You confused experimental measurements and theoretical predictions. Sorry but my theory must give theoretical predictions ... Therefore your remarks are nonsense.

2) Hawking's radiation can be justified at quantum level. Let me emphasize that any nuclide can be considered a quantum black hole. Quantum reactions obtained in laboratories just verified evaporation phenomena ... Therefore it is natural consider experiments simulating gravitational black holes as recently made ...

Black holes exist at the quantum level since they can be identified with nuclides (concentration of quantum gravity ...) and exist also at the macroscopic level, since can be observed at the center of galaxies (concentration of gravity ...) What is misleading is their name ... but this has been mediated by the 'black body' ...

3) Einstein is a good example as an experimental physicist convinced himself to become a mathematician, when he understood that in order to encode the subject of his mental experiments it was necessary to use a lot of new mathematics formulated by Italian mathematicians (Ricci-Curbastro and Levi-Civita ...). I do not add other considerations about ...

Of course Newton can be considered over the top ...

4)  On the 'peer review method' we have already discussed, and I skip on ...

5) Here I answer to your further post asking:

' ... Is there any topological structure that can be used to describe the phenomenon as a flow within itself so we can avoid the concept of expansion altogether?'

It is well known that a non-compact space-time admits Alexandroff compactification  to an infinite null hypersurface N. The light geodesics will rise N in an infinite time.   This could be 'an exapansion without expansion' ... but I have the proof that our universe expands from its Planck epoch, since it evolves like all natural phenomena ... The space-time can have big bangs, or big crashes respectively,  ... but when they occur the space-time starts from the quantum vacuum, or ends in the quantum vacuum.

6) Your attached paper about a possible interpretation of repulsive gravity via Yukawa-type potential is surely interesting ... even if it appears not well physically justified.

All the best,

Agostino

Dear Agostino,

I've just realised that we have been a bit over the line, therefore from now on I will accept your works without further questioning. I have to admit that there are more in your works than I could chew. Although your works are represented in highly mathematical standards, they seem to be too vast to be fundamental. In classical physics, Galileo's simple experiment from the leaning tower of Pisa can be seen as fundamental to the theory of gravitation and modern quantum physics is based on the two simple relations of Planck's and de Broglie's. I believe that in the end physics will be formulated entirely in terms of differential geometry and topology and I hope that you are on the right track.

Kind regards,

Vu.

Dear Agostino,

In cosmology, the expansion of the universe can be visualised only in 2-D on the surface of a sphere. The perception that cosmological objects are observed to move away from each other has been explained as due to the expansion of the surface. However, if we consider the surface to remain constant, then the expansion can be seen as a real expansion due to a flow as viewed from each point on the surface. In this case each point on the surface must be a source. This situation can be extended to 3-D, but I am not sure if it can be described mathematically.

Best regards,

Vu.

Dear Vu,

I do not understand the meaning of your last post ... The two points of view that you consider therein are completely equivalent ! ...

Dear Agostino,

As I suggested the Planck's constant should be considered as a composite constant which is a product of other physical constants at the quantum level, but you did not listen. I have proved my view by formulating a temporal general relativity in which Planck's constant plays the role of GM in Newtonian gravity. And there is a temporal black hole as well. I am trying to work out what interaction that might be.

Kind regards,

Vu.

Working Paper A THEORY OF TEMPORAL RELATIVITY

Dear Vu,

I looked to your quoted paper ... but I cannot recognize therein nothing that could justify a connection with the quantum world.

For example you write:

'This amount of energy that is transferred to an elementary particle from a quantum system is equal to the energy of the ground level of the harmonic oscillator.'

It is not enough to insert the Planck constant to say that we are talking of quantum world ... Topological quantum effects do not encode quantum world ! This last is encoded by a noncommutative geometry, not by the 'Feynman’s postulate in the path integral formulation of quantum mechanics' ... I understood the motivation to reverse the role between time and space coordinates, but frankly this your exotic necessity is caused from the fact that the path method is a semiclassical approach to encode quantum world. This approach cannot work for a simple reason: it is founded on the old wrong concept of wave of probability !

My best regards,

Agostino

Dear Agostino,

What I mean is not the one you quoted. It is from the potential V(t)=h/t. The appearance of Planck's constant in this form should be interpreted in terms of other physical constants. I agree with you that the concept of probabilistic wave will be washed away. I have studied your works more carefully recently, but what is the true physical meaning of a non-commutative geometry? Doesn't it simply mean an uncertainty? In other words, it is simply a quantisation method, and you can not get rid of the wave ideas as you would like to. Other thing I'd like to mention here is that if your works can be applied to Einstein's general relativity then they should also be applied to my temporal general relativity. 

Kind regards,

Vu.

Dear Vu,

please consider the following.

1) In Einstein's GR there is not time and space ! These concepts are related to an observer. The situation with your approach is so completely different. In other words your exotic observer is not a 1-parameter diffeomorphism group, say fR, but a 3-parameter diffeomerphism group, say fE, here E is a 3-dimensional vector space. This means that whether your space-time M continues to be 4-dimensional, then  M/E=N is a 1-dimensional space. Thus your space is not more 3-dimensional ... All can be down, but let me be surprised for your choice at least !

2) Let me also add that in my approach of quantum gravity the old dualism particle-wave is completely solved !  In fact nonlinear quantum propagators identify dynamics of quantum particles encoded by extended objects. Therefore, these nonlinear quantum propagators are the unique real nonlinear waves

3) You have written:

' I have studied your works more carefully recently, but what is the true physical meaning of a non-commutative geometry? Doesn't it simply mean an uncertainty? In other words, it is simply a quantisation method, and you can not get rid of the wave ideas as you would like to.'

No ! Waves in my quantum gravity theory do not come from the uncertainty relation, but are just precise geometric objects encoding the quantum dynamics in quantum PDEs. (See point 2).).  Uncertainty relations are obtained in next situations, when one effects quantum measurements on quantum systems .

4) There is not quantization in my approach. Quantum system is encoded by quantum PDE.

My best regards,

Agostino

Dear Agostino,

According to my view, Einstein's general relativity is a description of a gravitational field using 3 dimensions for space and 1 dimension for time, and this 1-dimensional time is the radial time of a 3-dimensional temporal continuum. There must be a space and a time for a natural physical description. For a complete description we should use a 6-dimensional space-time manifold. It is possible to formulate a gravitational field for this type of space-time manifold. In my works, for simplicity and being able to apply those mathematical methods that  are available, I only describe the dynamics of an elementary particle for a radial spatial motion with a 3-dimensional temporal continuum. 

I studied your works along with those of Alain Connes and others. I like your approaches and I think they are proper, especially bordism formulation, but it seems to me you all are trying to connect your works with the so-called standard models. I don't know why they should be regarded as standards at all, because they are very ad hoc and patched up, fitting numbers to match up with experiments. What else after colors will they think of? Or that's the end of physics for them? Completely ridiculous!

Kind regards,

Vu.

Dear Vu,

of course you can assume a 6-dimensional space-time ! In such a case the proper space of an observer, identified with a 3-parameter diffeomorphism group, should be 3-dimensional. But it remains the problem how to justify this choice ...

About the relation between my quantum gravity theory and the Standard Model in particle physics, let me underline the following.

My theory does not assume the Standard Model (SM) as starting point, but it can recover results of the SM. On the other hand any theory that is more general of previous ones must also contain as particular cases already theories ...

My best regards,

Agostino

Dear Agostino,

I think if we want to formulate physics in terms of geometry and topology then physical concepts such as charge and mass must be replaced by rates. With this in mind, and with an attempt to understand the wave-particle duality in quantum physics, I have tried to introduce a time component for the electric field and the magnetic field, whose rates of change with respect to time is the electric charge density and the magnetic charge density, respectively. If you have time please have a look to see if they can be justified.

Kind regards,

Vu

Working Paper ON THE WAVE-PARTICLE DUALITY IN QUANTUM PHYSICS

No Vu,

what you have written in your quoted paper, is a simple 4-dimensional rewriting of the Maxwell equation ... No, in this way you cannot justify electric charge ...

Dear Agostino,

Thank you for your comments. However, I will find a way to prove that the time components of the electric field and the magnetic field exist without relying on the concepts of electric and magnetic charges. For example, the time component of the magnetic field is constant with respect to time therefore it may be responsible for the spin of an elementary particle, and if the time component of the electric field is a Heaviside-like step function then it may be responsible for the quantisation of charge. In order to be fitted into a geometrical and topological formulation of physics, physical constants are needed to be made dynamical, not constants. If you still use them as constants then it doesn't matter how well you "encode" them (your preferred term) they would not tell you what they are and there would be no progress.

Kind regards,

Vu.

Dear Vu,

at quantum level the so-called dynamic constants are not more constant since their spectrum is not reduced to a point ...

This has been well explained in some my works:

[1] http://www.sciencedirect.com/science/article/pii/S0362546X08006986.

[2] http://www.sciencedirect.com/science/article/pii/S0362546X08006068.

All the best,

Agostino

Dear Agostino,

Reading your works makes me feel foreign to my own field.

Sometime ago I told you that I wanted to get an ebook entitled Geometry of PDEs and Mechanics that you edited but you said they are not available. Could you please check the link below to see if it is yours. If it is yours then I will order one. 

http://www.worldscientific.com/worldscibooks/10.1142/2986

Kind regards,

Vu.

Dear Vu,

the quoted book is a book of mine. There exists also a google preview at the following link:

https://books.google.it/books?hl=it&lr=&id=O5IbRdY7gqQC&oi=fnd&pg=PA307&dq=Geometry+of+PDE's+and+Mechanics+by+Prastaro+A.&ots=J5NLZFOWjH&sig=cBqqa4P-Td9UMqJQRebPlKCFFbY#v=onepage&q=Geometry%20of%20PDE's%20and%20Mechanics%20by%20Prastaro%20A.&f=false

About '... humble physicists ... '  I cannot completely share your opinion ... In fact, Galilei, Newton, Maxwell, Poincare', Hilbert, Einstein,... were  physicists too ... of course they were, or become, mathematicians also. Thus History teaches us that a good physicist must be also a good mathematician ...

My best regards,

Agostino

Dear Agostino,

Thanks for your advice and your book. To be honest, that's the first time I heard someone said a good physicist must be a good mathematician. Do you know we can do physics without mathematics whatsoever? That's why there exist the so-called experimental physicists, and many of them are the founders of physics. But what about the other way around? It seems to me that mathematics is suffocating physics. Anything that is too much is no good, even the good ones. I will buy an ebook of yours anyway.

Kind regards,

Vu.

Dear Vu,

the differences between mathematical physics, theoretical physics and experimental physics are academic only. In fact their academic curricula are quite different. Therefore an experimental physicist does not necessitate to be a good theoretical physicist or mathematical physicist ,,, and vice versa. The distinction is more thin  between theoretical physics and mathematical physics. In fact even if from the academic point of view the corresponding curricula are different too, professional tools are the same focused on Mathematics. Furthermore, taking into account that mathematics used for advanced research is not always just ready, but must be built yet, often theoretical physicist and mathematical physicists are called to build their mathematical tools.

This is not my opinion, but is the well-known History's teaching.

Therefore I am surprised for your reaction ... Really I suppose that you are a theoretical physicist or a mathematical physicist ... in such a case never mathematics is too much !!!

Let me add that the best that one could obtain is a mathematician that is also mathematical physicist and experimental physicist. These was possible to Galilei and Newton times ... but also to Fermi times ... However, nowadays the complexity of experimental systems does not allow such a perfect syncretism.

With this respect I would like to recall the Princeps mathematicorum, Carl Friedrich Gauss, who was also Director of the astronomical observatory in Göttingen, perhaps the last mathematician director of an experimental physical laboratory ...

All the best,

Agostino

Dear Agostino,

I appreciate your detailed interpretation. Probably I did not express clearly what I wanted to say. Mathematics itself is never too much, if only for the sake of mathematics, but at the moment mathematical representation of physics is overflowing. I admire those people that you mentioned and even now I still prefer their way of associating physics and mathematics. Balanced and clear. Let consider the bounded system of a hydrogen atom, for example. I want to represent the system in terms of a bordism relation in which the electron and the proton are considered as boundaries and from which the Coulomb's physical law of electrostatics can be derived. How can I purify and obtain those that I need from your works? By the way, do you know even Gauss did not dare to show his radical view on non-Euclidean geometry? So why wasting so much papers on hundred-plus-dimensional universes when you cannot even talk about those that are right in front of your clearly three-dimensional eyes?

Kind regards,

Vu.

Dear Vu,

you ask:

'... Let consider the bounded system of a hydrogen atom, for example. I want to represent the system in terms of a bordism relation in which the electron and the proton are considered as boundaries and from which the Coulomb's physical law of electrostatics can be derived.'

Whether you are interested to encode hydrogen atom, then the classical Maxwell equation is not enough. On the other hand it is well-known that also the classical QM with the Schroedinger equation allows to describe hydrogen atom only in a first approximation. By the way a more realistic description of hydrogen atom can be encoded in my quantum gravity theory, where this problem can be encoded inside the observed quantum super Yang-Mills PDEs, as a boundary value problem. More precisely the solution of this problem is dynamically encoded by an observed nonlinear quantum propagator V, as pictured in the attached figure. In other words V encodes the quantum reaction p+ + e- -> H. Then the observed quantum energy content of H can be expressed in term of p+, e- and the propagator V.

In this way one can get the best evaluation of hydrogen atom energy spectrum. 

Let me add that the Gauss-Janos-Bolay story, about non-euclidean geometry, teaches us that it is wrong do not publish our serious advanced researches for fear of possible controversy ...

All the best,

Agostino

Dear Agostino,

Thanks for your answer to my question. But that's not precisely what I expected. I would like to know if we can derive a dynamics from a bordism relation. I think we should start from a bordism relation and try to find a relation between physical quantities defined in terms of mathematical objects and then derive a dynamics. I have posted a work on a possible relationship between the size and the mass of an elementary particle on RG. This can be seen as an example. If you have time, please have a look.

Kind regards,

Vu.

Research Proposal ON THE RELATIONSHIP BETWEEN THE MASS AND THE SIZE OF AN ELEM...

Dear Vu,

one says that all roads go to Rome ... By the way from the dynamical point of view, bordism properties are related to a fixed dynamical PDE.

Therefore you must first decide what is your dynamics, otherwise you have not dynamics at all ...

About your quoted paper ... it contains fables only ...

Sorry but the spectrum of a quantum object is a subset of C, the set of complex numbers, ... therefore in general the mass-gap can be any non-zero complex number. For observables the spectrum is inside R, the subset of real numbers, and the corresponding mass-gaps are non-zero real numbers.

Your idea that quantum particles with negative mass are so-small to be non-observable is frankly a fable ...

Dear Agostino,

Viva Italia, but Rome the great was no more. That's why I'd like to ask you to build a new road from Rome, not to Rome. How do you decide a dynamics in the first place?

Please tell me one thing why my idea of negative mass is a fable? Non-observability is certainly not a fable, otherwise you would be in big trouble with those inventors of the quark model. Simplicity is certainly not a fable either, otherwise you would also be in big trouble with Newton's dynamics. The whole spectrum of observable and non-observable masses fit perfectly into my model. Except for the fable quarks, all elementary particles such as photon, electron, proton, neutron, ..., you name it, sit on the curve. 

You should know that because of complex numbers, quantum physics is living on borrowed time.

Kind regards,

Vu.

Dear Vu,

my quantum gravity theory encloses as a particular case Standard Model, and justifies also mass-free neutrino ...

The idea that negative mass-gaps cannot be observed is completely wrong. In fact negative mass-gaps usually enter in the quantum energy balances of quantum reactions. See, e.g., appendices in my paper:

 http://arxiv.org/abs/1206.4856.

 Therefore, it does not exist contradiction with what it is already known. Furthermore, to classify non-observable quantum phenomena (solutions) having complex spectrum it does not exclude that they mathematically exist ... even if they cannot enter into a representation of the world by means of real numbers. But this is only a representation problem. In other words, human approach to representation passed from flat-epoch, to four-dimensional one, through the tridimensional perspective representation ... Unfortunately what is against our usual experience it is considered impossible ... an example for all: 'quantum entanglement'.

 When one talks of quantum world one must drastically enlarge our point of view ... one must pass from the usual commutative geometry built on the algebra R. of real numbers, to the noncommutative geometry built on the quantum (super)algebra A of quantum numbers, as I introduced ...

To insist to remain in R it means to insist to remain on the flat-land ...

 Therefore, let me conclude that a good new physical theory is one able to enclose all already ones as particular cases, but also able to open new horizons in such a way to justify what it is not yet understood.

 My quantum gravity theory is just a new road from Rome, ... but also to Rome ...

 My best regards,

 Agostino

Dear Agostino,

After going through your works few times, I have to say that mathematically your works look great, but physically they are not very practical. For example, from my work on the size of an elementary particle I showed that the size of a photon and the size of an electron are almost identical, and from this result at least I can say with confidence why an atom that is composed of electrons can absorbs a photon smoothly, due to some form of resonance. Another example, I've been trying but still haven't found a way to solve a simple equation like Equation (26) that involves a Yukawa potential, please see my attached paper on the hydrogen atom, and other equations that involved Fractional Laplacians. Your works are totally hopless in these cases. Unfortunately, true physicists are born and die on the flat-land, but not on a super-manifold. Warning: wash your salad before you put them into your bag!

Kind regards,

Vu.

Working Paper ON THE STATIONARY ORBITS OF A HYDROGEN-LIKE ATOM

Dear Vu,

you have written:

'Unfortunately, true physicists are born and die on the flat-land, but not on a super-manifold.'

NO ! You are wrong !

No true physicist can think he bears and dies on the flat-land ... Otherwise he could be a  FLAT-EARTH SOCIETY member only ... To such type of physicist I can suggest do not read may work, but to read the following link:

http://www.theflatearthsociety.org/cms/.

All the best,

Agostino

Dear Agostino,

Oops! I did not realise that they still exist. But your flat-land is the real number line, anyway. What do you think about complex numbers? I think that they may exist but we don't have an ability to perceive them. In that case your works may become more significant.

Kind regards,

Vu.

P.S. You still have not answered my questions on my equations. 

Dear Vu,

you have written:

' What do you think about complex numbers? I think that they may exist but we don't have an ability to perceive them. In that case your works may become more significant.'

NO ! You are wrong !

Mathematics used in our models to represent World does not exist ... It is a human creation ... Do not exist the natural numbers N, do not exist the relative numbers Z, do not exist the rational numbers Q, do no exist the complex numbers C and so on ... They are human abstract constructions only ... We have also created some mathematical models where they play important roles to represent World. In particular it is well known that complex numbers are fundamental to represent QM and QFT. Therefore I have not necessitate to prove the utility of complex numbers ... Instead I enlarged the horizon and I introduced quantum numbers too. I proved with my quantum gravity theory that quantum numbers are very important numbers, containing as particular cases also complex numbers and real numbers. Without quantum numbers it is impossible to have a correct representation of Quantum World, and as a consequence of Macroscopic World.

About your equation (26) ... Your approximated considerations appear appropriate. By the way this equation is not so terrible as you claim, since it is an analytic linear equation of the second order of the type

a(r)\psi''+b(r)\psi'+c(r)\psi=0

where a, b and c are known analytic functions of r and \psi =\psi(r).

All the best,

Agostino

Dear Agostino,

I always regard you as a very talented mathematician from Rome therefore I need your help with the following problem. In quantum physics, fermions are particles that can't occupy the same place in space but bosons can. Physically, it is not possible to imagine how two particles can occupy the same place in  space, unless the mathematics that is used to describe such situation is not the normal mathematics that we are using. For example, to describe two bosons occupying the same place in space is the same as using a mathematics in which 1+1=1. Is this some form of Boolean algebra? On the other hand, for fermions we can use a mathematics in which 1+1=0. What is this? It looks like a binary system.

Kind regards,

Vu.

Dear Vu,

the mathematics to which you refer is just driven from the Boolean algebra Z2=\{0,1\}, with 0+0=0, 0+1 =1, 1+1=0. Quantum super algebra, namely the algebra of quantum numbers, has just a Z2-gradiation to interpret boson-statistic and fermion-statics. These encode the Pauli exclusion principle. Thanks to this macroscopic bodies cannot occupy the same position at the same time.

The difference between quantum Bose-Einstein condensates and quantum Fermi-condensates is just that these last necessarily create degenerate material states since fermions cannot overlap on the same energy level.

It is interesting to understand that neutron stars can originate, after bosenization, and taking account my quantum gravity theory, black holes having the structure of quantum Bose-Einstein condensates of quantum gravitons.

All the best,

Agostino

Dear Agostino,

Thanks for your explanations. But I think Pauli exclusion principle is a constraint which has a geometrical and topological characteristic. It is a dynamics therefore it can not be determined by an algebraic structure of a mathematics. Can you build a mathematics based only on your algebra of quantum numbers so we can forget about the rest? It seems to me mathematics is the problem, not physics.

Kind regards,

Vu.

No Vu !

You are wrong ! You confuse quantum dynamics with quantum numbers ...

Let me explain with a more simple example. In classical continumm mechanics you have the necessity to consider the algebra of real numbers R, and the temperature is always considered non-negative. Of course dynamics is encoded by means of differential equations built on a geometric framework (configuration bundle) starting just from R, but in order to consider non-negative temperature it is enough that you consider this constraint on the configuration bundle ... no on the differential equation !!!

Similarly in quantum world ... Quantum algebra must be Z2-graded to take into account fermions and bosons. The Pauli exclusion principle is just an empirical principle ... that can be justified from the theoretical point of view by considering that the total wave function for identical fermions is antisymmetric with respect to exchange of the particles. This means that the wave function changes its sign if the space and spin co-ordinates of any two particles are interchanged. For bosons instead the total wave function is symmetric.

Therefore your question:

'Can you build a mathematics based only on your algebra of quantum numbers so we can forget about the rest?'

does not apply to what I have written ... it is a nonsense.

Dear Agostino,

Is your algebra of quantum numbers logical? If it is not logical, how can it be an algebra? On the other hand, I think we can build a mathematics on any logical algebra, so why my question is a nonsense if your algebra of quantum numbers is logical? You caused me confused. In the last post you said your algebra encoded Pauli exclusion principle and now you say Pauli exclusion principle is just an empirical principle, and in fact this is exactly what I said, it is a dynamical constraint that can be derived from a physical setup, such as a hydrogen atom, which in turns has a particular topological character that we need to investigate.

It's a shame that you lost to Ireland.

Kind regards,

Vu.

NO Vu !

You are writing nonsense.

'Is your algebra of quantum numbers logical?'

What means ?

'It's a shame that you lost to Ireland.'

What means ?

By the way it is time to stop our conversation in this thread ...

All the best,

Agostino

Dear Agostino,

Thanks for your patience and advice. When I say an algebra must be logical I mean it has no self-contradiction, and only in that case a mathematics can be built on it. For a bit of fun, I thought you, as most Italians, are soccer-mad. It's hard to believe the Italian soccer team had lost to Ireland. Bye now, but if I have a serious question about your quantum gravity then I will ask you again. 

Kind regards,

Vu.

Dear Vu,

 your paper focused on a Coulomb-Yukawa potential in the study of the hydrogen atom with classical methods is surely interesting and worthy to be considered.

However, let me also add that you use two old tools to force your model to be concerned with quantum world:

1) quantization of the angular momentum; 2) Schroedinger equation.

In such a way you recover well-known results ... Your idea that in such a way one can explain why electron does not radiates more is not well justified from the Coulomb-Yukawa potential. In fact this is related to points 1) and 2) as in the usual old approaches.

With this respect, it is clear that one cannot obtain satisfying enough advancements by simply playing with generalized Yukawa potentials ... The potential scattering gold times in quantum physics are passed by now.

My best regards,

Agostino

P.S.: I was not able to post my comments on your quoted paper since this option does not more work on my computer ...

Dear Agostino,

Thanks for your remarks. But I think all quantum roads lead to Schroedinger equation, like all roads used to lead to Rome.

I have another problem that I need to consult you. I think I might have proved that black holes cannot exist. In quantum physics, bosons are elementary particles that can occupy the same place in space, but to not accumulate like classical particles, as having been shown in recent experiments on photons where tens of thousands of particles behave as a single quantum particle. Please see the attached link.

http://physicsworld.com/cws/article/news/2010/nov/24/bosons-bossed-into-bose-einstein-condensate

This result can be interpreted mathematically if we use a mathematics in which 1+1=1. And from this we obtain 1+1+1+1...=1, in other words ∞ =1. This kind of mathematics has the form of a Boolean algebra. We can't use it but bosons can.

If the above considerations are also applied to Higgs bosons and because Higgs bosons are assumed to give mass to other particles, then matter with infinite density cannot be achieved, in other words, a black hole cannot be formed.

For fermions, we should use a mathematics in which 1+1=0.

Kind regards,

Vu.

 No Vu !

 You have written:

 'But I think all quantum roads lead to Schroedinger equation,....'

 NO ! You are playing with words ... Whether you use Schroedinger equation then it means that you decided to quantize classical mechanics of point-like particles ... Therefore you cannot more say that you justify the lack of electron radiation foreseen in classical mechanics, by using the Yukawa potential  ... This your statement is completely wrong !

Furthermore, you have also written:

'I think I might have proved that black holes cannot exist.'

No ! You are wrong ! In fact the motivation is founded on a wrong interpretation ... By the way this simply means that you did not read my post at page 8 of this thread about black holes.  In fact therein I justified black holes quantum structure with my quantum gravity theory.

All the best,

Agostino

Dear Agostino,

I am not playing with words. It is the truth. What else if not Schroedinger equation? I did read your post, but all you did was to assume there exist a black hole. What I am talking about is how a black hole is formed, or in fact not formed?

After this post, please give me one week so I can study your works more carefully. Your works are huge and they look great, mathematically.

Kind regards,

Vu.

Dear Agostino,

After going through your works, I think I stand by what I have said. Contributions that mathematicians have made in physics are no more than sophisticated mathematical representations of what that are normally represented clearly by true physicists. Why can't you just jump on the wagon and develop in more detailed a Boolean mathematics that is justified by experiments and that shows that a black hole can't exist.

Kind regards,

Vu.

No Vu,

you arrived to wrong conclusions ...

Black holes can be generated by neutron stars according to the following process driven by quantum gravity:

NEUTRON STAR -> (quarks + gluons+ gravitons) ->(bosonization) ->  MASSIVE-GRAVITONS

Therefore we get the following steps:

1) Neutron stars are degenerate systems of fermions. The degeneration state is according to the Pauli exclusion principle forced by quantum gravity.

2) Thanks to quantum gravity neutron stars can rise very high temperatures such to break neutrons in its constituents, namely quarks+gluons+gravitons. Here, according to my quantum gravity, gravitons are considered bound states of gluons. Furthermore, gluons and gravitons inside neutron must be quantum particles with mass-gap.

3) Thanks to quantum gravity, quarks can be forced to collapse into quantum bosons with mass-gap. Of course this is allowed by the Boolean algebra since 1+1=0. Thus at this step we get that the neutron star becomes a quantum boson system with mass-gap. The corresponding spins of bosons entering in such a system can be 0, 1, 2.

4) Thanks to quantum gravity, quantum bosons at the step 3) can generate bound states of entangled massive-gravitons. These are quantum condensate of bosons that can interpret black holes.

Therefore black holes can exist as in fact they do.

Agostino

Dear Agostino,

Your theory of quantum gravity has a high level of significance, even though I am not in favor of the quark model in the present formulation. I think elementary particles have internal topological structures that make them behave as observed by experiments. For example, protons and neutrons can be visualised as spheres with pointed handles that make them appear as containing point-like objects called quarks.

I do know those astrophysical theories about the formation of stellar objects with great density and I have no problems with finite-sized objects which have a gravitational force which is so strong even light can’t escape. These are perfect classical black holes. All of these can be formulated in terms of classical physics and no sophisticated mathematical representation is required. What I want to talk about is similar to the following quote

Gravitational collapse requires great density. In the current epoch of the universe these high densities are only found in stars, but in the early universe shortly after the big bang densities were much greater, possibly allowing for the creation of black holes. The high density alone is not enough to allow the formation of black holes since a uniform mass distribution will not allow the mass to bunch up. In order for primordial black holes to form in such a dense medium, there must be initial density perturbations that can then grow under their own gravity. Different models for the early universe vary widely in their predictions of the size of these perturbations. Various models predict the creation of black holes, ranging from a Planck mass to hundreds of thousands of solar masses. Primordial black holes could thus account for the creation of any type of black hole.

What was the density of matter before the time of the early universe shortly after the big bang?

In fact, I don’t even have any problems with these problems either. What really concerns me is why these models should be taught as standard models that surely will make generations of pure and impure physics students to believe in. I am sorry to say this, but you seem to be an example. A mathematician has to adopt some form of physics to start with anyway.

https://en.wikipedia.org/wiki/Black_hole#Primordial_black_holes_in_the_Big_Bang

Kind regards,

Vu.

NO VU !

You continue do not understand ! ...

You confuse the quantum Planck epoch with the actual situation. In fact at the Big Bang there is zero quantum energy, since the nonlinear quantum propagator encoding universe at that epoch, has there (Big Bang) a  neck-pinching singularity, Therefore at the Big Bang there is not a black hole !!! Big Bang is a point in the quantum vacuum. (See the following link at page 3

https://www.researchgate.net/post/Is_the_universe_eternal/3.)

You have written:

'These are perfect classical black holes. All of these can be formulated in terms of classical physics and no sophisticated mathematical representation is required.' 

NO ! YOU ARE WRONG !

The structure of black hole cannot be justified without my quantum gravity ! Look to my previous post in this thread, and you will understand that all the steps driving a neutron stars in a black holes can be justified only with my quantum gravity theory. Production of a set of (quarks,gluons,gravitons), Bosonization and quantum entangled graviton condensate. All this process cannot be found in a classical theory !!!

You have written:

'What was the density of matter before the time of the early universe shortly after the big bang?'

At the Big Bang the density is zero !

You have written:

'In fact, I don’t even have any problems with these problems either. What really concerns me is why these models should be taught as standard models that surely will make generations of pure and impure physics students to believe in. I am sorry to say this, but you seem to be an example.'

NO ! YOU ARE WRONG !

After all I explained to you continue to misunderstand what I posted. Moreover whether you have carefully read my paper

http://arxiv.org/abs/1206.4856

you should have a more clear understanding of my quantum gravity and therefore last above your words are completely unacceptable ...

Finally you have written:

'A mathematician has to adopt some form of physics to start with anyway.'

NO ! YOU ARE WRONG !

A mathematician that aims to formulate physical models, has to see whether his mathematical models well interpret physical phenomena to which he aims to be applied.

Dear Agostino,

Despite according to your view I've been wrong most of the time, but I think the following point must be right because if you say I am wrong then you will also be wrong as well. According to your theory, at the Big Bang episode, the matter density is zero. This is no other than to assume that only space exists at the beginning. But this is exactly what my theory said. It said space was created first then matter in terms of elementary particles with appropriate physical properties were produced after that. They form a spectrum that nicely fits into an undeniable prediction of a physical theory. Actually my theory has a slight advantage because it is a physical process, on the other hand, yours is just an assumption. I think that's the main difference between a true physicist and a mathematical physicist. Please prove me wrong!

Kind regards,

Vu.

NO VU !

You are completely wrong !

Space and time exist only with respect to an observer ! ... To say that the space has been created first is a non sense !

Dear Agostino,

Did you mean there would be no space-time if there was no one to observe it? This is an out-of-date philosophy. 

Kind regards,

Vu.

NO VU !

Unfortunately you confuse space-time with space and time !!!

At the macroscopic level, in the Einstein's GR, space-times are solutions of the Einstein's PDEs. Whether you introduce an observer you can split space-time in the proper-space of the observer and in its proper-time ... Therefore at the macroscopic level space-time can exist without an observer, but space and time NO !

At the quantum level you can yet represent phenomena with respect to an observer, hence with respect the proper-space and the proper-time of the observer, or the spec-time of the observer.

Therefore to say that first has been created the space is a non sense !

Dear Agostino,

I think I get more confused from what you have described than between space-time and space and time. Space-time is simply a unified description of space and time. In simple terms, would we need a butcher to split space-time into space and time? Where did the butcher come from? My guess is he emerged from a single Higgs boson that follows your physical theory of quantum gravity and my mathematical theory of Boolean algebra.  

Kind regards,

Vu.

OK VU !

You like to random talk ... Any scientist should know what is an observer (no butcher ...) and how he can split macroscopic space-time in proper-space and proper-time. Now you jump on the Higgs field ... or on the Boolean algebra ... why ?

Sorry, I think that it is time to stop our conversation in this thread. In fact by now I have given my answer to your question. Furthermore, I am afraid that your attitude to jump to some other subjects does not produce more clearness in RG users ...

By the way I hope that any RG user can understand that your sentence

'... first has been created the space ...'

is a non sense ...

All the best,

Agostino

Dear Agostino,

Because I am a down-to-earth physicist therefore my thinking is also down-to-earth. Matter is supposed to be contained in space therefore it is natural to think that space should be created first. And this is no other than Newtonian physics. 

Proper space and proper time of what? Isn't it required the existence of at least an elementary particle? An elementary particle is supposed to be formed from the Higgs field, isn't it? Any Higgs field is composed of bosons. And Higgs bosons are those elementary particles that you adopt to start your theory of quantum gravity. And according to the experiment that I quoted to you, they seem to follow the Boolean algebra of 1+1=1. And that's all about that. 

In fact it was a surprise that you had the patience to follow my questions. Thanks anyway. According to my assessments, your mathematical representations of theoretical physics have a very high mathematical standard but they lack physical insights in order to be of your owns. In particular, also according to my assessments, the so-called Standard Model is not a good adoption to start with. It is the dead end to any theoretical development of physics. 

If I have a serious question about your quantum gravity I will ask you again. But why quantum gravity instead of Prastaro's quantum theory, for example? By for now.

Kind regards,

Vu.

Dear Vu,

Newton was born three century before me !!! ...

This long period did not pass in vain for Science ... Perhaps for you is so ... In fact you appears to ignore Einstein's GR and QFT with its Standard Model. Even if you consider yourself down-to-earth physicist, you cannot remain to the Newton's times ... In particular to spit on the Standard Model is non sense, even if it cannot be considered the last milestone in the long road of the Science ...

By the way my quantum gravity theory is not founded on Einstein's GR and QFT-SM, even if it justifies these theories as particular cases. This means to seriously do Science !

Therefore for a down-to-earth physicist your opinions appear completely unrelated to the reality ...

All the best,

Agostino

P.S.: Higgs field is a boson field, hence it is an even field and in the Boolean algebra it satisfies to 0+0=0 (In the Boolean algebra 1+1=0 ...)

Dear Agostino,

I am not looking down at the Standard Model, as I said many times before, there is no reason why students should be forced to follow that path.

Even though I am a great admirer of GR, but by no means it is a standard model. Very much the same for QFT. Unless you simply accept them, of course.

If you look at my theory of temporal dynamics, you can see that the concept of time is much more complex than even that of GR. And furthermore, a dynamic time can be used to describe reality more than the best formulation of quantum physics can do. I arrived at equations with Fractional Laplacians that no mathematician can solve. What a pity! So, down-to-earth can be more realistic than you might think.

An even field is what you define according to your mathematical formulation. The photons from the experiment  that I showed you seemed to follow the rule 1+1=1. And this is a form of Boolean algebra. Because photons are bosons, therefore I just suggested that fermions should follow a different algebra of the form 1+1=0.  

Few posts ago, when I asked you how you determine your dynamics, you said you determine it by adopting the Standard Model. I have to admit that that is the best adoption that a mathematical physicist can do at the moment, but as Hawking once said that would be the end of physics (He has admitted that what he had said was wrong anyway).

What physical foundation that your quantum gravity is based on?

Kind regards,

Vu.