The (E) theory: A new attempt to unify EM and gravity [Archive]

Blackforest

Nov12-05, 02:37 PM

This paper (broken into three peaces; see attachments below) introduces a re-discussion of the Lagrange density. The tool to get this result is a new mathematical operation whose existence can be guessed from some considerations concerning the calculation of the variations along the time of the Poynting’s vector in any part of space-time without charge or current source. We show how it can be rooted in the tensor calculus. We demonstrate that it allows a re-writing of the very usual Maxwell’s EM field tensor and after that of the momentum-energy tensor carried out by the EM field. A part of it is calculated (the Lagrange density) and can be addressed to a spin-spin self-interaction. We suggest a connection with the variations of the 3-D volumes and with the QM representation. Keywords: polarizations; tensor calculus; reformulation of the Maxwell’s EM field tensor, reformulation of the Lagrange density, spin-spin interaction.

1. The opening post must contain an abstract stating the results obtained and how the new theory is at variance with currently accepted theories.

The introduction of what I have called "the (E) question" during the calculation of the partial derivates of the Poynting's vector with the help of the Maxwell's Laws for EM fields in vacuum yields an unexpected dynamical law... This was for me the starting point for series of explorations. After a systematic investigation of the question in any 3D space and a verification, I could rewrite my first intuitions under a better formalism and prove that the (E) question is connected to the introduction of a new mathematical operation that is an extension of the tensor calculus (actually only in French language).
Also starting from the systematic exploration in any 3D mathematical space, I could win the irrational sensation that the Maxwell's EM field tensor should be in any manner connected to this extended vector product. This was the beginning for the development of the so-called Russian Dolls Method which, in turn, is now leading to a quite more general approach and formalism for this tensor.

I have abandoned the obligatory and limiting reference to the esthetic of the tensor to concentrate myself on the idea that this tensor must have an alternative formalism connected with the existence of a special family of extended vector products. Doing so, I am slowly but surely suggesting the necessity to substitute the traditional EM potential vector by the cube* locally defining the extended vector product under consideration.
This point is (I think) the detail where the present theory (still under construction) is at variance with currently accepted theories.

2. The opening post must contain a section that either cites experiments that have been done that decide between the new and old theories, or it must propose experiments that could be done to decide between the two. If the submission contains a theory that is empirically equivalent to an existing theory, then this section may be substituted with a section that demonstrates the empirical equivalence and that compares and contrasts the insights gained from the submitted and existing theories.

This is done with the document etgb43.pdf (not enougth place to upload, sorry; but was submitted in my first essay) which is practically devoted to demonstrate the ability of the present theory to absorb (incorporate) the question of the anomalous Hall effect. This section does not pretend to give an exact correspondence with the experiments made by the team cited in the reference. It is only opening a road.

3. All references to relevant prior work must be documented in the opening post.
4. Quantitative predictions must be derived, wherever appropriate, and mathematical expressions and equations must be presented legibly, using LaTeX whenever necessary. This should be done in the opening post. 9. External links will be permitted only for lengthy derivations and for diagrams. Any other expository text pertaining to the submitted theory must be posted at Physics Forums. Please note that this is a temporary Guideline that will remain in place only while we work on enlarging the maximum allowable attachment size in the IR Forum. Once that happens, we will require that all material pertaining to the theory be either posted at Physics Forums or attached to the thread.

As recommended by the administrator of this website, I have broken my documents.

5. New theories must not be already strongly inconsistent with the results of prior experiments.
6. If a new theory is strongly inconsistent with prior experiments, but the theorist is insisting that the experiments were either misconducted or misinterpreted by the scientific community, then the thread will be rejected. Instead the theorist should rebut the contradicting scientists in an appropriate journal.
7. Theories containing obvious mathematical or logical errors will not be accepted.
8. Threads which contain obvious misrepresentations or gross misunderstanding of basic accepted science, especially when used in attempt to compare one's personal theory to currently accepted science, will not be accepted.

Since this it is an allowed re-submission, I suppose that my theory is not containing too much errors (at least I hope it). Otherwise, I am spending an enormous quantity of time to built a coherent theory respecting all current admitted miles stones of physics. In this sense it must not be so original and interesting. But I am arguing that a re-lecture of a well-known reality with my new binoculars can perhaps open doors that was until now closed.

This theory is indeed yielding a new formalism for the Maxwell's EM tensor. This formalism takes the local metric tensor into account without introducing any necessary choice for it; this is in accordance with the way of doing developed by the general relativity (GR).

This new formalism also allows a reasonable connection with (and demonstration of ) the Lorentz-Einstein Law, provided a certain number of hypothesis which are in particularly reducing the number of independent coefficients in the local cube*. It can be shown that such reduction can transform the local cube* into a set of (4-4) matrices defined up to the term in position (0-0); that is a set of matrices with at most 15 independent terms. Such kind of reduction is transforming the definition of the extended vector product in a 4D space in such manner that it can be understood as very similar with the definition made intuitively in our systematic exploration for 3D spaces.
The substitution (EM potential vector -> cube) is mathematically compatible with the use of the total differential of any quantity with two labels.

It also allows the definition of the EM fields in terms depending on the coefficients of the cube and, as said above, to take in consideration the anomalous Hall effect. Some fundamental laws of electromagnetism are yet under examination; a first step shows the compatibility with the Kähler's metrics.

Despite of its actual incompleteness, the theory provides a great number of investigations and the first interesting results in mathematics and in physics. Next steps will focus on the discovery of a group structure for the polarized matrices and on the construction of a perturbation theory based on the exploration of the Holonomy of the group. An original connection between conoides and spinors is under study.

Best regards / Black forest

Blackforest

Dec14-05, 09:24 AM

Blackforest

Dec17-05, 09:39 AM

First of all, want to say thank you for this posssibility to get an official discussion about my work; hope it will not be extremly short because of a stupid error from me. Thank you in advance for your critics...
If someone wants to know more, he must please visit my homepage. Waiting for your opinions, jugements, critics or suggestions I can adress the first auto-critic to myself: the (E) theory only is a "theory" and because of this, it can be seen as a difficult speculation without connection with the reality; a kind of mathematical alternative presentation of the EM theory. For my defense and to justify a such complicated formulation (in comparison with the usual one), I am arguing that it naturally owns a formal possibility to incorporate the description of the Hall effects. Even if my concrete knowledges about this subject are too limited (I try to learn more), actual litterature introspecting f.e. photonic crystals can be regarded as a natural field of application for my research. So, I think it is in this sense a strategic item for the modern research (quantic computers, ...).

Blackforest

Dec17-05, 09:46 AM

Concerning this Hall effect I have proposed a formal investigation in etgb43.pdf

Tom Mattson

Dec17-05, 12:24 PM

I am digging into the first paper, and I will post questions once I formulate them.

Blackforest

Jan21-06, 03:11 AM

I am digging into the first paper, and I will post questions once I formulate them.

One month later, the time is come for the first commentaries. In between I did appreciate the developments of the GEM Theory on the other sub forum and, specially, the help of Lawrence B. Crowell whose interventions can be helpful for both: the GEM and the (E) approach. Doug’s work as he likes to say it himself lies more on the real ground and mine is sometimes flying in the kingdom of the speculations.

But I did have a great pleasure to read last commentaries concerning the point “bi-photons”. And I reproduce here this point for the comfort of coming discussions:
“At this stage I would say with the GEM proposal that one of two things need to be done. Either the graviton and photon sectors, the abuse with the term graviton with standing, need to be clearly indicated in some way. This might be done with some tetrad formalism or with the embedding of GR and EM into some larger group. Another approach is to somehow show that the spin-2 field of gravity, say in particular in the pp-wave solutions, can be built up from some coupling of photons. A gravity wave is a bi-vector, and in quantum optics there are phenomena of photon bunching or "bi-photons" which are similar to gravity waves. I say similar, for they still interact with electric charges and so forth. In such a theory two photons with aligned spins would interact to form a graviton. Currently such an interaction for counter spin aligned photons generate the particle of weak interactions. In this way at very high energy, probably approaching the Planck energy, two photons would generate a graviton. How this would fit into Doug's theory is a bit unclear. Maybe if Randall et al. are right with so called "soft black holes" that occur at the TeV range in energy the other fields that the photon interacts with have some mass matrix so that there are oscillations between gravitons and photons. By this two photons correlated in a Hanbury Brown-Twiss manner will have some probability of being a graviton. Yet this is pretty speculative. The dust bin of physics is littered with a lot of quantum field theory speculations.”

At this stage I must explain some choices I have done in the construction of my theory. For example and it is a difference with the Mortimer’s approach (other sub forum here) or with the Klein Kalusa approach, I decided intentionally to work so far as it is possible in a 4D frame. The reasons for this are connected with irrational ideas: something like: if the world we are living in really owns N dimensions, then our mathematics to describe it must also have a N-D underground; since the most part of the population can accept the fact that N = 4, … I agree it is not a scientific demonstration and the representation of the world that our brain is able to built is century dependent; take as example the slow introduction of the notion of time in physics. That’s true: the human brain only built a coherent image of the real world and it acts a little bit like a lens : real world ® image of the world on which the brain can work.

The other point on which I want to insist after the commentaries of Lawrence B. Crowell is the capacity of my approach to built the Lorentz Einstein Law starting from a matrix representation of the EM field tensor [see etgb31c3.pdf in webpage; visit the panorama page; letter “O”]. This seems to be an encouragement to purchase the research concerning the “bi-photons”. The (E) approach is suggesting a strong mathematical connection between graviton and bi-photon (or something like that) within the frame of validity of the demonstration. It is the first time for me that I discover that my speculations have a correspondence in the reality and that’s why it is a great day for me.

Best regards

sweetser

Jan23-06, 09:21 PM

Blackforest

Jan24-06, 01:41 PM

Hello Blackforest:
I've noticed a behavoir in physicist: when they come to an issue they don't understand, they stop. I've seen this in my own work, where I try to explain something, they don't get this one point, and they do not get around that issue.
I have been very fortunate. This has happened to me at least a half dozen times. It would often take me two or three months, but then I would see why they stopped. When I saw that, I could see that in fact, I was wrong. The fortunate part was that I found ways around the problem that initially was hard for me to see.
In your paper, I get stopped write at the definition of the (E) question. I don't get simple things like why one would use ()'s. I don't get hard questions like how one could work in 3D when the deep lesson of the elegant theory of special relativity is 4D. I have taken classes in SR 3 times! It is very much against my outlook to embrace a 3D explanation of something that works brilliantly in Minkowski spacetime. I did not get passed 1.1.2.
doug
Thank you for the hints. One point is certain: English is not the language of my mother and I understand that it induces for me and you a hard challenge for a good communication. It is a pertinent critic, I accept it and one could say: I should present my work in France in French... In my next life, perhaps.
But I am a stupid dreamer and I believe in the universality of the human being. Otherwise, I had until now no occasion to do what I should have done.
The definition of the (E) question that I introduce in (1.1.2.) is a special and very reduced formulation of a general one that acts not only in a 3D space. If you own a kind of product on a vector space E of dimension N on K, call it "o" (that means a function o: E x E --> E) and if you take two vectors u and w on E, can you allways find a square matrix (N-N) with components in K call it [M] and a rest vector z of E so that u o w = [M]. w + z? That is the (E) question. If you make the particular choice of N = 3, o = cross product and if you do the calculation, you will find a trivial answer given by (1.1.2.1.). I hope you can understand me.

Why do I make this simple choice? For the pedagogy of what is coming after this definition: the demonstration of the existence of an equation motion in Maxwell's vacuum.

Sure, mathematically speaking, it is a reduced and simple formulation. But I think that it contains important informations for physics. Considering a classical point of view: why should we find any neutral stream in Maxwell's vacuum?

sweetser

Jan24-06, 08:57 PM

Blackforest

Jan25-06, 08:35 AM

Hello Blackforest:
I was not, and will not, complain about your English. That would be unfair. Communication may be inefficient, but I can adjust to that. I think even in German that using a pair of () around a single letter is odd, in an almost English way.
Math does translate pretty darn well across cultures. But then you must learn the proper math language. Take this line:
>If you own a kind of product on a vector space E of dimension N on K, call it "o" (that means a function o: E x E --> E)
This looks like basic group theory in some ways, the function o acting on elements of a vector space E stays within E. If this really is group theory, then you are obligated to use the language of group theory.
>you allways find a square matrix (N-N) with components in K call it [M] and a rest vector z of E so that u o w = [M]. w + z
This makes no sense to me. I have no idea what a "rest vector z of E" means. The function "o" is so general that the equality looks meaningless. I don't know if that "." is the end of a sentence or not. At this point I stop. If I were to continue, which I initially didn't, you claim now that the function o is the cross product. So the cross product can be written as a matrix, not news. I still see no logical connection to w and z. I see no question at all. That is my unvarnished reaction.
doug
Hello sweeter
Nobody can force you to have an eye and a ear for my work. If you understand what I mean in reading my exposé despite a bad esthetical presentation, then you understand the message, the information, the most important part of the work. Outfit is another side of the whole thing; and for me, it comes only at the end, only if the main ideas own some value. If you stop the analyze just because of this point, I am sure you are missing a lot of beautiful and meaningful sides of the life. (Black forest; personal and general philosophy)

Concerning a matrix formulation for the cross product, indeed, no news. The small difference is perhaps that we get a lot of possible solutions ([M], z) to this mathematical problem. Definition of a rest vector is given in the work (if you take the time to read it).

It is not because a mathematical problem (question) is a priori embedding a great number of special cases that it is uninteresting. I think exactly the opposite.

Take this other eventuality: The “o” product is supposed to be defined on E, N = 4 , [M] is a Lorentz matrix and z is a translation; then you remark that this special formulation of (E) question in a 4D space is inducing another one: “Can we find a subset of E, call it U = {u so that u o w is the transformed of w in SR}?” It is another way to scrutinize a well known problem in physics (look at the Poincaré transformations).

But you are obliged neither to read nor to see. Thank you for the effort to make me better...
Best regards.

Blackforest

Jan25-06, 12:28 PM

Hello sweeter
Just for fun and to demonstrate that I can work with the usual laws of physics in a 4D space
Best regards.

sweetser

Jan25-06, 09:31 PM

Hello Blackforest:

I think you are missing the point. In my thread, Careful thought what I had written was math nonsense. It is right on the first post: (\nabla_{\mu}A^{\nu}+\nabla_{\nu}A^{\mu}). It took me a while, but I eventually agreed with Careful: it is math nonsense. It was fairly easy to correct, just make all the indices be on the same level.

I have no doubts you can work in 4D, and that you have put a big investment of time into your efforts. We have small side comments by two other people that indicate they may have printed out your pdf's, but so far have not posted here. They may be having a similar reaction: the (E) question is not a well-formed mathematical expression. Oh, it has parts of a well-formed expression, but that is like having parts of a well-formed sentence that ends in something that no one else can understand. With the LaTeX tools available here, you should be able to clarify what is the (E) question. At this point, I completely do not get it.

doug

Blackforest

Jan26-06, 03:04 AM

I am mising something but I get the biggest difficulties to understand what. General presentation of the mathematical problematic is written pages 5-7 in the first document. I think the difficulty comes from the fact that one have in fact two questions in one: 1) the extended vector product that is an inner operation on E; 2) the problem of the decomposition of any extended vector product in a mixed matrix-language, i.e. the ([M], z) pairs. The frontier between these two sides of the problematic are perhaps a little bit unclear in my exposé. I have tried to give the essence of my thougths and probably I did not spent enough time in the important details of a more extensive presentation. Perhaps is it what you mean? Or do I miss again?

sweetser

Jan28-06, 04:17 PM

Blackforest

Jan29-06, 05:06 AM

I still have no idea what the (E) question is. This may or may not be relevant, but I will say what I know about group theory and fields.

The real numbers are a field. That means there is a group operation, lets call it plus, on any two members of the reals such that there is an identity (zero, because 5 + 0 = 5) and an inverse (5 - 5 = 0). There is another group operation on the real numbers without the additive identity, and that is multiplication. There is an identity (one, because 5 * 1 = 5) and there is always an inverse (5 * .2 = 1). Many folks do not realize that the foundations of calculus depend on the properties of mathematical fields.

The complex numbers are also a field. The additive identity is (0, 0) on the R^2 manifold, and there is an inverse for any given complex number. If one excludes zero, then the multiplication operator has both an identity (1, 0) and an inverse (z*/||z||).

What comes next? I hope you know the answer already, because if you are concerned about the completeness of number theory, this is a fundamental thing to know. The next field is known as the quaternions. For folks who have never heard of them, you can visit my web site devoted to the subject, quaternions.com. The words scalar, vector, curl, cross product, divergence, gradient, and curl were all coined by Hamilton for his description of quaternion operations. Gauss was the first one to find them, and Rodriguez put them to use independently for 3D rotations. The Pauli matrices are a bad copy of quaternions, where an extra factor of i is tossed in, making the Pauli matrices extremely convenient. Frobenius was able to prove that if you wanted to work with a division algebra over the real numbers, there were only three choices: real numbers, complex numbers, and quaternions. If you drop the requirement that multiplication is associative, then one can add octonions or the Cayley algebra to the list.

Remember, I don't understand your question at all, so I am going to guess at what it proposes. It looks like you wonder if the cross product is enough in R^3 along with addition to make a mathematical field. If the question is something like that, the answer is known: that much algebra is too little. One needs to work in four dimensions. The product is more than just the cross product, because one would be leaving out the vector dot product and two scalar-vector products.doug

Hallo sweeter
Concerning the first part of your intervention, basics knowledges about group theory, ring theory, “body” (corps; e.g. real numbers or complex numbers) are present in my small and personal package. Quaternion as well and I know an article demonstrating the possibility to write some fundamental equation of the general relativity (GR) with. You can actually read my efforts to develop the “extended vector product” like a group operation on my webpage in etgb54.pdf (news). It is not trivial at all but very interesting.

The (E) question is not something like that you say in your remark; at least not in my head. I shall try to explain more precisely. The reason why I did start this mathematical exploration was the demonstration of the equation of motion in Maxwell’s vacuum. In the past (thirty years ago), when I have developed it, following the work of some physicist, I only was a student and did not own the necessary package to write these things in a 4D language. Despite of this lacuna, the demonstration exists, makes use of the (E) problematic with the cross product and tells the question of the existence of some streams in Maxwell’s vacuum. Today, this point is perhaps not surprising because of the development of the modern physics.

There stay actually two interesting items for me; can we consider vacuum like a dielectric body and make one of the two hypothesis that was yielding the final result of my demonstration? Can we make use of this (E) question in the context of a vacuum; and if yes, can we develop it more generally; in a 4D language for example?
You ask more or less directly if it is relevant. Because we now know the existence of neutral energetic streams in vacuum and because the quantum theory furnishes quite better tools to explain and explore this side of the nature, this quasi classical approach can give the sensation to be an old timer tool. Or can give the hope to connect two different approaches of the same thing.

Concerning the 3D formulation, I think that one can argue that what happens to us takes always place in a local time slice of our own chronology. Thus, a apparently limited formulation in 3D must contain enough interesting informations about the whole thing occurring in a 4D world. It is our duty to guess, reveal and formulate the truth that is implicitly contained in a restricted formulation. The hidden side of the Maxwell’s equations certainly is the geometric context where they act. Despite the fact that we never take care of it because we usually don’t have to do it (due to the Euclidian nature of our direct environment), a more general theory must include the unconscious perception that our geometry is only one of the possible one. The (E) question is this crazy attempt to connect the way how a cross (or more generally an extended vector) product of two vectors can split [the ([M],z) pairs] in accordance with the local geometric nature at the place where this product is calculated. Thus, my theory says: if our world wouldn’t be Euclidian, then we would do all our mathematical operations in a different way; but there exists a tool to connect these different ways: this is the (E) theory. Do you follow me?

And that’s why I think the (E) question is complicated, relevant and a kind of philosophical extension to the theory of the relativity. I really hope that I can convince you and some other people. Blackforest

Blackforest

Feb2-06, 03:39 AM

This is extremely difficult and disappointing to speak in the desert; it looks like if nobody here would be interested in my essay.

As supplementary advantage concerning the development of the (E) theory, one can also remark that division of vectors does not directly exist inside the mathematics. We only own the concept of modulo-spaces ...

Following some remarks made on an other sub forum here, one can remark that:
1) in the LE2 basis of the (E) theory, i.e. basis where the Lorentz Einstein Law can be understood as a vector differential operator of second order (a method that I have proposed to develop an approach "à la Froebienus"), the set of all Christoffel's symbols (what I call a cube in my poetic language) is a Z2-grading set...
2) Otherwise, basis of which the deformations are satisfying a description via the moving frame method by approximation up to the third order are naturally yielding a set of Graßmann variables...
3) The extended vector product acts like a projection for positions vectors only in a LE2 basis

Mortimer

Feb2-06, 07:05 AM

This is extremely difficult and disappointing to speak in the desert; it looks like if nobody here would be interested in my essay.
Hello Blackforest,
Interest must be cultivated. The mathematical context of your discussions with Sweetser is beyond me but putting that aside I think the problem with your essay is that it does not appeal right from the beginning, due to its layout.

The first few sentences of your essay:
1. Introduction:
1.1. Context of the initial discussion:
A great number of equations is not necessary the best medium to explain a way of thinking even if calculations must be done and must be exact to support and supply a theory. This is why I shall try to explain the main ideas developed here with the usual language.
1.1.1. Definition: Maxwell’s vacuum.
The Maxwell’s vacuum is a set of events....
The most important text in any article is the abstract. Reading your first lines, it seems that the abstract is supposed to be in the Introduction. So the essence of your story is expected there. The essence of your introduction is the statement that "A great number of equations is not necessary the best medium to explain a way of thinking", so for the unwary reader this obviously is what you are trying to tell him in your article. Next there is a great number of mathematical definitions where at no point it is clear what all these definitions are going to lead to, apart from the fact that it immediately contradicts your statement in the introduction. I think most readers drop out halfway your definitions.
You don't have an abstract that gives a concise overview of the main ideas and points you want to make. Next, your introduction should at least give an overview of the chapters and their purpose, as well as perhaps some background that any reader should have. [EDIT: I must correct this slightly: there is an abstract in your opening post but that is not reflected in the article itself]
In short: your article would not be accepted by any journal, purely because of its layout.
I can fully understand Sweetser's remarks about not knowing what the (E) question is. I don't know either.
Please take this as positive criticism.
Regards,
Rob

Blackforest

Feb2-06, 01:40 PM

Hello Blackforest,
... Please take this as positive criticism ...
Regards,
Rob
No problem; that's exactly what I wanted to ear: the truth! OK, fine; and thanks.

So, considering that I shall never be able to master your language and the language in general (even in my own one), I shall consequently leave the discussion here because the challenge is too high and will bring me no ligth.

Mentors of this forum can erase this sub-discussion.

TP alias BF

Blackforest

Feb3-06, 09:27 AM

Does someone knows something about this new model suggesting:
..."that shocking a crystal will produce synchronized light".
Materials Update alert 03 February 2006 (Nature review)

Blackforest

Feb4-06, 07:04 AM

Hello Mortimer, some more commentaries without importance for the theory:
Interest must be cultivated. The mathematical context of your discussions with Sweetser is beyond me but putting that aside I think the problem with your essay is that it does not appeal right from the beginning, due to its layout ...
... In short: your article would not be accepted by any journal, purely because of its layout.

Black and Mortimer are two well known heroes in the world of the cartoons; I recommand you to read it to relax from your work. Your childrens will also certainly appreciate. Once more time the critic here lies on the layout, not on the ground of my work.

I can fully understand Sweetser's remarks about not knowing what the (E) question is. I don't know either.
I cannot believe that well educated people like you on these forums don't understand the simple (E) question. That's why I am now convinced that nobody does really want to discuss it and that you only want to see how far an amateur like me can go. And byside, if I sometimes have a good idea, you can always borrow it; isn't it? That's the reason why I shall no more take part to the pseudo discussions unless there is some one here to explain me a good reason to do it.

Please take this also as positive criticism.
Tchao bye

Blackforest

Feb14-06, 03:45 PM

<See "etgb531.pdf"> Extended Vector Product; (E) question; A.D.M. approach [12 - 14 February 2006; 3 pages; .pdf]
Some readers seem to be lost in the (E) Theory because they don't understand its purpose or what one can do with it. As we could show in the "elementary properties of any extended vector product (EVP)"<see etgb54.pdf">, a given EVP is entirely defined by real physical circumstances. The EVP itself is a general mathematical concept. The cross product in a 3D space, the commutator of two basis vectors in any N-D space, ... are particular examples of a quite more general tool.
I purchase here the development of the hypothesis that an actually unknown kind of EVP is defined in the universe that must allow the description of any EM field in accordance with the Maxwell's Laws. It has the important consequence that the Faraday Maxwell tensor should split under the: [F] = p.[G].[P] - q.[P]<sup>t</sup>.[G]
formalism where (p, q) is a pair of scalars, where [G] is the local matrix representation of the metric tensor and where [P] is the local matrix representation of the split of the unknown EVP we are looking for.
I consider here the A.D.M. slice between space and time and apply it to the research of the [P] (4-4) matrix for the case (p,0). I show that relatively simple solutions exist.

sweetser

Feb15-06, 06:27 AM

Hello Blackforest:

I will give a few more hints about my complete lack of understanding of any of your work. I do not think it is fair to an audience in an http based forum to reference pages in a pdf. I for one do not have the time to print out and reference it. The basic idea should be easy enough to explain with words and a few equations. So you tried a number of posts ago...

The (E) question is this crazy attempt to connect the way how a cross (or more generally an extended vector) product of two vectors can split [the ([M],z) pairs] in accordance with the local geometric nature at the place where this product is calculated. Thus, my theory says: if our world wouldn’t be Euclidian [sic], then we would do all our mathematical operations in a different way; but there exists a tool to connect these different ways: this is the (E) theory. Do you follow me?

OK, "how a cross (or more generally an extended vector) product of two vectors" sounds like what is called an exterior product or Grassmann algebra. I do NOT understand the topic myself. If you are doing a variation on Grassmann algebras, you must stick to the language that those folks use. I have no idea what M is or z or why they should come as a pair. This phrase sounds undefined: " the local geometric nature at the place". Geometric nature? Is that topology? Is it the structure of the manifold?

At this point, I do not know what the pair of things are, nor how they are to be evaluated in terms of geometry. So no, I do not follow you.

Then I am confused by this statement: "if our world wouldn’t be Euclidian [sic]". Minkowski spacetime is not Euclidean, nor are the dynamic metrics of general relativity or my own work Euclidean (and by that I mean multiplying to vectors generates the sum of the squares of all the component parts).

I consider it a warning sign when independent researchers use new abbreviations, such as EVP. I go to great effort to avoid them myself.

For me, the E question remains poorly formed and not comprehensible.

doug

Blackforest

Feb15-06, 09:39 AM

Hello Doug, at the end I find our dialog a bit funny and your behavior not only full of sympathy and patience for me but courageous.

still don't get it

Hello Black forest: I will give a few more hints about my complete lack of understanding of any of your work. I do not think it is fair to an audience in an http based forum to reference pages in a pdf. I for one do not have the time to print out and reference it. The basic idea should be easy enough to explain with words and a few equations. So you tried a number of posts ago ...
OK. But how do you want to discuss seriously about physics and mathematics only with words? I can agree with your principle that the author should be able to explain his theory with the usual vocabulary; conversely, you will probably also agree that an obligatory trip into the darkness of sometimes long and complicated calculations (despite my stupid introduction as noticed by Mortimer) cannot be avoid. This means: the documents that you can visit on my webpage are the illustrations of the thoughts I try in vain to explain here. Furthermore, I hope that my mathematics can equilibrate the defaults of my language. Or said with other words: reading my mathematics will perhaps give you the sentences that I am unable to formulate with the pencil or the tongue. I have at least hoped it. I thought that mathematics was a kind of international language for which you don’t need a translation in the literature or that the reader can translate itself in his own language. Apparently, I am thinking wrong or you don’t totally agree with my viewpoint.

Originally Posted by black forestThe (E) question is this crazy attempt to connect the way how a cross (or more generally an extended vector) product of two vectors can split [the ([M],z) pairs] in accordance with the local geometric nature at the place where this product is calculated. Thus, my theory says: if our world wouldn’t be Euclidian [sic], then we would do all our mathematical operations in a different way; but there exists a tool to connect these different ways: this is the (E) theory. Do you follow me?

OK, "how a cross (or more generally an extended vector) product of two vectors" sounds like what is called an exterior product or Graßmann algebra. I do NOT understand the topic myself. If you are doing a variation on Graßmann algebras, you must stick to the language that those folks use.
If you speak of Graßmann algebra, this means either that you visited my webpage (Thank you) or that my problematic implicitly contains this topic (I am glad of this). I must give it: this topic is also new for me. I don’t know how you proceed to built your own GEM, but since I am not a genius and since I only follow my intuitive representations of the universe, I progress by step. At each step I need mathematical tools of which I did not necessary knew the existence before. A typical sickness for an amateur, I suppose.
I am now sure that the difficult things here is not my bad English but that I am following several roads at the same time. The question with the Graßmann algebra arises not from the article that I have proposed here on this forum for independent research, but from a parallel investigation concerning a construction of the general relativity (You remark: I didn’t write GR) based on a small personal treatment of the “moving frame method”. In this special investigation, the (E) question does not immediately plays a role.
I have no idea what M is or z or why they should come as a pair. This phrase sounds undefined: " the local geometric nature at the place". Geometric nature? Is that topology? Is it the structure of the manifold? At this point, I do not know what the pair of things are, nor how they are to be evaluated in terms of geometry. So no, I do not follow you.
Then I am confused by this statement: "if our world wouldn’t be Euclidian [sic]". Minkowskian space time is not Euclidean, nor are the dynamic metrics of general relativity or my own work Euclidean (and by that I mean multiplying to vectors generates the sum of the squares of all the component parts).
Of course “Minkowskian space time is not Euclidean” [sic], but the spatial part of it is … and your remark makes me totally clear that you do not understand the idea, the mathematical idea. If I could: I would cry! How can I explain it? Try to give a little bit liberty to your mind. Not for definitively abandon the rationalistic way of thinking; just to understand the idea.
For example, try to remember all your basic lessons in mathematics and make a list of all mathematical operations you know on N, Z, R, C, and so and… After that look if you can find somewhere in the list “the division of two vectors”. As state in “Essential Mathematical Methods for Physicists” (Weber and Arfken; international edition; Elsevier; 2004), you will not; of course, there is not! The very initial idea on which lies the (E) problematic is based on this remark.
We can multiply two vectors: it is the cross product (in N = 3 space) or the wedge product if you prefer the generalized version. And now take a vector, any one; take another one and try to find what the result of a division of the first by the second could be; try to find it in thinking that the wedge product between the hypothetic result we are looking for and the second vector you have chosen should yield the first vector. You intuitively guess that this result must (or should) be a combination of a rotation [the hypothetic M matrix] and of any translation (the z-vector; other said: the rest vector). If you don’t understand this step, I am afraid, I shall be obliged to give up my explanations. My neighbor who has a PhD level does understand my preoccupations and the main idea even if he says, like you, that the things are not optimal formulated. But try to do it yourself in German or in French language (joke!).
If you accept this first intuitive introduction for the (E) problematic, then, yes, you can understand that I have tried to extend it in considering an extension of the wedge product that I have called the extended vector product; secondly you will rapidly understand that the split into ([M], z) is clearly depending on the topology of the space where it occurs.
I consider it a warning sign when independent researchers use new abbreviations, such as EVP. I go to great effort to avoid them myself. For me, the E question remains poorly formed and not comprehensible.
When an independent researcher use new abbreviations, such as EVP, it is only because he is describing his own concept in a more convenient manner… just because it realizes an economy of ink! But despite your courageous try to understand my way of thinking, I feel through your words that you are tired of it. Nicht desto trotz: Thank you for your efforts.

Blackforest

Mar5-06, 04:28 AM

[QUOTE=Blackforest]Hello every body, some more precisions to get light into this difficult theory that I am trying to present. Perhaps Doug gets a better vision on it, I hope.

Blackforest

Mar5-06, 05:35 AM

You certainly understand that with this definition, any connection can be used to define a precise extended vector product and that if the extended vector product is define somewhere by the components of the connection, then the evp of two given vectors, say u and w, is the difference between the covariant derivative of w with respect to u and the usual derivative of w with respect to the vector u.

Blackforest

Mar5-06, 05:43 AM

If the components of the extended vector product are those of the local connection and if w is parallely transported with respect to u, then the extended vector product of u by w is zero and the so-called trivial matrices of the possible split are in fact N-N matrices of the usual derivates of the components of w with respect to the components of u.

Blackforest

Mar5-06, 05:55 AM

If you reduce the general discussion to N = 4 (this seems to be a normal ambition for physicists) then you rapidly remark that the simple fact to write an extended vector product simultaneously with one of its split is automatically yielding a set of equations that can be red either as a system depending on the componenets of u or like a system depending on the components of w.
In the first configuration (depending on u) you realize that components of u are not free but connected each others. Thus there obligatory exists a condition of existence for the (E) problemetic.
Recent thougths are leading me to the idea that these conditions could be themselves connected to the respect of some geometrical necessity (for example: the preservation of the metric; see more on my website on the French part: Trajectoires.pdf / This idea explain why and how this theory can propose an alternative for the description of the trajectories of any duality:wave-particle).
As a matter of fact everybody can see that the Lorentz Einstein Law is a kind of natural (E) problematic.
So, with these few short explainations, I hope to get more comprehension from profis and amateurs. Have a nide day.

Blackforest

Mar10-06, 05:35 PM

Now to give more thickness to my work, I propose the following papers:
1) the first one is known: it is the first part of my proposition here;
2) the second one is a way to situate the discussion in a more usual context.

Terry Giblin

Mar14-06, 02:50 PM

The apperent duality of the electron is caused by the observe not the electron.

We observe only what we can see - An electron does not exist, until it is observed.

The effects of a single "cloud"(droplet) of rain cannot be compared with a flowing river, the effects are bond to be diiferent. Have you ever heard of a stamped of one.

Especially when you are in Dirac Sea with no holes only quantum wells and probabilities of 1 or imaginary 1's (-1), zero acts as a quantum well or wall, 1 or -1 or both, but never in the same plane or place.

Any good GUT must include a solution and explaination to the DSE and Quantum Tunnelling, two pilars of Quantum Mechanics and Electro-Magnetism............

The Dirac Equation can explain them without a problem, but it has taken 85 years to interpretate the real and imaginary results.

Simply turn the equation on its side. Consider the electron as zero and it has two choices, backward in time or forwards in time, imaginary or real - electron entering a wire is the equivalent of a positron leaving the coil, flow is in both directions the imaginary past and the imaginary future.......whilst time ticks on by in its own direction in the real world we live in.

Not much maths or physics, but its an easy picture to visualize.

Regards

Terry Giblin

If you reduce the general discussion to N = 4 (this seems to be a normal ambition for physicists) then you rapidly remark that the simple fact to write an extended vector product simultaneously with one of its split is automatically yielding a set of equations that can be red either as a system depending on the componenets of u or like a system depending on the components of w.
In the first configuration (depending on u) you realize that components of u are not free but connected each others. Thus there obligatory exists a condition of existence for the (E) problemetic.
Recent thougths are leading me to the idea that these conditions could be themselves connected to the respect of some geometrical necessity (for example: the preservation of the metric; see more on my website on the French part: Trajectoires.pdf / This idea explain why and how this theory can propose an alternative for the description of the trajectories of any duality:wave-particle).
As a matter of fact everybody can see that the Lorentz Einstein Law is a kind of natural (E) problematic.
So, with these few short explainations, I hope to get more comprehension from profis and amateurs. Have a nide day.

Blackforest

Mar14-06, 04:01 PM

Perhaps you are trying to explain me in a poetic and soft way that many of what I am doing has still be done since a long time and in a quite better manner. That is certainly true. Perhaps you suggest that the challenge of a good GUT is not inside the possibilities of a simple amateur like me. That is certainly true. The term wave-particle described as duality in my text was not of importance. It is not my subject and and don't want to discuss about this because I have no doubt about this point. It was just to make certain for my readers that I do not ignore this question. Thank you for the hints concerning the necessity to incorporate the Dirac see and the tunnelling effect. My efforts are actually concentred on the development of a description of the trajectories (series of dx) via the ([P], z) pairs in a rationalistic way. For this purpose it is important to discover or to make the choice of a convenient condition on the dx. The circumstances of the description must be precised: flat or curved space? In a curved space, we know at least one condition that could be ok: the post point short action ... calculations are running ... per hand.

Thanks again.

The apperent duality of the electron is caused by the observe not the electron.

We observe only what we can see - An electron does not exist, until it is observed.

The effects of a single "cloud"(droplet) of rain cannot be compared with a flowing river, the effects are bond to be diiferent. Have you ever heard of a stamped of one.

Especially when you are in Dirac Sea with no holes only quantum wells and probabilities of 1 or imaginary 1's (-1), zero acts as a quantum well or wall, 1 or -1 or both, but never in the same plane or place.

Any good GUT must include a solution and explaination to the DSE and Quantum Tunnelling, two pilars of Quantum Mechanics and Electro-Magnetism............

The Dirac Equation can explain them without a problem, but it has taken 85 years to interpretate the real and imaginary results.

Simply turn the equation on its side. Consider the electron as zero and it has two choices, backward in time or forwards in time, imaginary or real - electron entering a wire is the equivalent of a positron leaving the coil, flow is in both directions the imaginary past and the imaginary future.......whilst time ticks on by in its own direction in the real world we live in.

Not much maths or physics, but its an easy picture to visualize.

Regards

Terry Giblin

Blackforest

Mar15-06, 11:42 AM

To avoid a quiproquo: the former remark of me doesnot mean that the duality is not an important item, in a general discussion. But I try to focuse the discussion in another direction. Here the part 2 of the work that I have proposed and a complementary discussion

Blackforest

Mar26-06, 09:05 AM

Just to go further in my approach, even if this step will not bring a wonder. I try to confront my extended vector product and the notion of split of it with the concept of fiber bundles... I hope you can find some interesting thougths in this... Conversely, if you think that it is totally stupid, don't have any hesitation: tell me. Regards

Blackforest

Mar29-06, 12:27 PM

And to finish. Best regards

eljose

Apr11-06, 03:04 PM

Blackforest

Apr12-06, 04:38 AM

Hello...i think that to give some unification of EM and Gravity we should have a Lagrangian density in the form:

L=L_{G}+L_{EM}+ interaction terms

where the "interaction" terms should be invariant scalars for example of the form:

g_{ab}\Psi^{+}\Psi or some kind of angular momentum interacting the metric and the vector potential A.. the sub-indices G and EM account for Gravity and Electro-magnetism.

Classically speaking, you are absolutely right … but I have a stupid dream and another manner to understand the word “unifying”. Certainly a question of semantic but it is important here. To unified things or ideas or opinions or what you want (e.g. EM and gravitation) you get the usual following way to do it. You generally try to find a greater set than the set to which belongs each object under consideration. Example: one given apple belongs to the set of all apples and one given orange to the set of all oranges but apples and oranges are fruits; so you can unify them via the set of all fruits. The problem that is arising in this way of doing is the following: did we put everything inside the same basket just for the purpose to satisfy our need of unification? If yes there is a risk to have created an artificial theory or set; it can certainly be a beautiful illustration of the human intelligence… but it owns no real existence except on the paper. It is like if you would force people who are detesting each other to live together. In general this union does not survive a long time. Thus the question of a successfully unification is (for me) merely synonymous of the discovery of a greatest set where the different objects included in are in fact different visages of the same more abstract object. At the limit, my dream is so to find an expression of the stress energy tensor containing this more abstract object (the cube A and its components -which is not necessarily a tensor) and able to describe the whole set of usual situations: EM field alone, gravitation field alone, a mixture of both… If I did reach …or not… my purpose with my attempt is another point. At least I have tried to explain you my way of thinking and of working.

My idea is that a fundamental extended vector product (relative position by relative position or relative speed by relative speed or position by speed, I don’t actually have a definite point of view on this important point*) is related to each physical phenomenon in universe. Each phenomenon is known to have a relative position, a relative speed (eventually a spin) which are known with a relative precision. Thus each phenomenon is supposed to own a trajectory (even if reduced to an infinitesimal oscillation around a point in some extreme situation –static object with uncertainty on the central position). The trajectory can be cut in series of infinitesimal pieces, each of them being associated with a relative position vector. It interacts either with itself or with the relative speed with which the piece of trajectory has been described*via this fundamental extended vector product and this interaction must satisfy the local constraints to which the phenomenon is submitted. To be in accordance with the fact that …“The particle responds according to the Lorentz force law (LLE) to a field (“Gravitation” Misner Thorne and Wheeler, American edition, New York, 1970-1973, chapter 20: equations of motion derived from field equation (A. Einstein) pages 472-475)”… this fundamental extended vector product should be an image of the local form of the LLE. And finally from this interaction can sometimes result an acceleration (the rest of the LLE understood as being a split of this extended vector product).

This is a short explanation of the logic way I am following by now. Perhaps is there a fundamental logical mistake or a pure mathematical inconsistency inside this way of thinking: I am open to critics.

Blackforest

Apr13-06, 08:12 AM

13 April 2006
Let us consider the stress energy tensor for an EM field (Lichnerowicz; Masson and Co; 1955; Théories relativistes de la gravitation et de l’électromagnétisme):
T_{ab} =¼. g_{ab}.F_{cd}.F^{cd} – F_{ar}.F_{b}^{r}

Let us consider the quadratic form
F = ½. F_{ab}.dx^{a} x dx^{b}

1°) Let us then remark that:
½. F_{cd}.F^{cd} = <F. F>
is the scalar product of F with itself [and can be sometimes interpreted as |E|² - |B|² where E is the electric field and B the magnetic field].

2°) Also note that my own hypothesis, the existence of a decomposition of the Maxwell EM field tensor so that (see etfgb03.doc above; equation 10.21):
F^{ab} = scalar. [g_{bc}.A_{ea}^{c} – A_{eb}^{c}.g_{ca}].v^{e}

has the necessary consequence that the term:
T_{ab} = … – F_{ar}.F_{b}^{r}

can be written:
T_{ab} = … – D_{ef}.v^{e} v^{f}

At the end, note that the stress energy tensor for any EM field inside my theory can be written:
T_{ab} = ½. g_{ab}.<F. F> – D_{ef}.v^{e}.v^{f}

and make a comparison with the stress energy tensor proposed for a perfect fluid… within the generalized theory of relativity, … one could propose to identify:
1°) – ½. <F. F> and p the pressure of this fluid;
2°) the eigenvalues of D_{ef} should give us the possible values for (density + pressure).

Thus, to make short, if logical with itself, my theory is investigating the possibility to interpret any EM field with a fluid and sometimes with a perfect fluid. This would change a little bit the usual analysis made in Lichnerowicz where (although the author notes himself – page 18 of the same reference- the provisory character of the form proposed for) the stress energy tensor is the sum of the general form of a stress energy tensor in harmony with the requirements of the generalized theory plus the stress energy tensor for any EM field arising from the considerations made within the restricted (special) theory of relativity.

In my approach, these two components are the same. EM fields can be understood as being fluids with eigen-fluctuations. Rationalistic (= in relation with some experiments) or totally crazy (= only a mathematical toy theory)?

Blackforest

Apr13-06, 12:15 PM

2°) Also note that my own hypothesis, the existence of a decomposition of the Maxwell EM field tensor so that (see etfgb03.doc above; equation 10.21):
F^{ab} = scalar. [g_{bc}.A_{ea}^{c} – A_{eb}^{c}.g_{ca}].v^{e}

has the necessary consequence that the term:
T_{ab} = … – F_{ar}.F_{b}^{r}

can be written:
T_{ab} = … – D_{ef}.v^{e} v^{f}

At the end, ...

First autocritic: D_{ef}.v^{e} v^{f} is unfortunately not D_{ab}.v^{a} v^{b}. Thus an identification appears to be possible for a limited number of circumstances. But not impossible, a priori.

Blackforest

May12-06, 11:52 AM

Perhaps you did not realize that my new homepage adress is now:
http://www.vacuum-world-net.eu
The discussion is going further here; thanks for your attention.

Blackforest

May13-06, 10:51 PM

Blackforest

May19-06, 11:10 AM

The above discussion concernin the relationship between extended vector product and parallel transport makes sense and allows a conform re-formulation of the FAraday Maxwell tensor if one applies it to the parallel transport of the EM potential 4-vector A. This is supposing a parallel transport of this (in fact) gauge vector by respect for the trajectory of what (a wave, a particle, or whatsoever) is moving. Does it makes sense: that's another question. Independently of the answer to this fundamental question, the new mathematical formalism allways is (local decomposition of the tensor in any 4D space):
F = (metric tensor x trivial matrix) - (transposed of the trivial matrix x metric tensor) + complementary term related to the (first order) variations of the metric.
The correct proposition:
You didn’t hear of me since a long time. Theoretical research is a challenge for professionals and only a “Neben-produkt” for amateurs. The progression is depending on how many free time one gets to do it …
In between, you certainly realized that I have made a lot of errors concerning the description of the (covariant) components of the Faraday-Maxwell tensor (henceforth called “the tensor”). I should have written for the trivial proposition, or better said, for the proposition involving a trivial matrix in the split of the extended vector product (I note it here with the symbol “x” because I don’t have a better possibility to translate my own symbol with Tex) ^{(4)}u “x” ^{(4)}w supposed to be associated with this representation of the tensor, in extenso: F = scalar one. (metric tensor time trivial matrix) + scalar two. (transposed of the trivial matrix time metric tensor), the following relation:
F_{ab} = (s_{1}. g_{ac}. A_{eb}^{c} + s_{2}. A_{ea}^{c}. g_{cb}). u^{e} (1)

The test:
If we consider that EM physical phenomenon are occurring when following conditions are realized:
a) The local cube defining the extended vector product supposed to be involved in the discussion (the E Theory hypothesis) contains 64 scalars corresponding to a local connection;
b) The fundamental extended vector product under consideration is in fact the extended vector product of the "EM-potential 4-vector" by the local position 4-vector;
c) The "EM-potential 4-vector" is parallel transported with respect to the local position 4-vector.

Then:
1) starting from the historical definition of the tensor (involving neither the total derivates D nor complementary terms, e.g. Yang Mills, but only the partial derivation that I shall exceptionally note here d –problem with tex):
F_{ab} = d_{a} A_{b} – d_{b} A_{a} (2)
2) and supposing that usual universal rules of the differential calculus are locally valid, it is straightforward to demonstrate that hypothesis a), b) and c) above lead to:
F_{ab} = [g_{ac}. A_{eb}^{c} - A_{ea}^{c}. g_{cb}]. A^{e} + [d_{a} g_{eb} – d_{b} g_{ea}]. A^{e} (3)
where it is easy to recognize the equation (1) for s_{1} = - s_{2} = 1 in the first part of (3).

Conclusion:
Assuming the hypothesis a) b) and c) above allow to write:
F = (G. T – T^{t}. G) + [… (d_{a} g_{eb} – d_{b} g_{ea}). u^{e} … ] (4)
where the u^{e} … = A^{e} … are now the contra-variant components of the EM potential four vector A, G is the matrix representation of the local metric tensor whilst T is those of the trivial matrix and T^{t} of its transposed.

For negligible variations of the local metric, the second term in (4) vanishes and we stay with:
F = (G. T – T^{t}. G)
which is the expression corresponding to our intuitive representation of the tensor. Next steps will analyze the possibility to generalize the proposition (1) to others circumstances than those described by a) b) and c).

Blackforest

May19-06, 12:09 PM

A) The above demonstration starting from (2) did not verify if the proposed formalism satisfies some any basic properties of the tensor. In fact it is not necessary since it lies on an accepted definition of the tensor and since it only needs a minimum of very simple and acceptable circumstances to be valid. These verifications must only be done if we conversely start from (1). For example, the proposition (1) must satisfy elementary constraints:
F_{aa} = 0 (5)
This is equivalent to:
F_{aa} = (s_{1}. g_{ac}. A_{ea}^{c} + s_{2}. A_{ea}^{c}. g_{ca}). u^{e} (6)
Since a GR compatible metric should be symmetric, this is yielding:
F_{aa} = (s_{1}. g_{ac}. A_{ea}^{c} + s_{2}. A_{ea}^{c}. g_{ac}). u^{e} (7)
At this moment, we theoretically get two possibilities:
a) the body K on which the theory is built is commutative and we get:
0 = ( s_{1} + s_{2}). g_{ac}. A_{ea}^{c}. u^{e} (8)
1) For this proposition to be valid independently of the contra-variant components u^{e} … we must write:
0 = s_{1} + s_{2} (9)
This is corresponding to the special case encountered in the demonstration made above and starting from (2).
2) For this proposition to be valid independently of the two scalars we must write:
0 = g_{ac}. A_{ea}^{c}. u^{e} (10)

b) the body K on which the theory is built is not commutative and we get complications that we leave for later.

B) The demonstration is apparently valid for any local metric. The formalism:
F = (G. T – T^{t}. G) (11)
as still explained in former interventions on this forum allows a discussion within an A.D.M. time-slicing procedure.

Blackforest

May19-06, 03:49 PM

Now there is something else that we did not examine in the demonstration above [starting from (2)]: the nature of the connection represented by the cube A. And we also didn’t precise if it is a connection compatible with the g_{ab} metric. For the coherence of our approach we shall now suppose that yes. Yes the cube A is coinciding with a Levi-Civita connection metric compatible and we can write the well-known formula for it:
A_{ea}^{c} = ½. g^{cp}. (d_{e}g_{ap} + d_{b}g_{ep} - d_{p}g_{ae}) (12)

Then (although it is a little bit tedious) we can demonstrate that:
(d_{a}g_{eb} – d_{b}g_{ea}). A^{e} = - 2. [g_{ac}. A_{eb}^{c} - A_{ea}^{c}. g_{cb}]. A^{e} (13)

Thus, starting from (4), this is yielding:
F = - (G. T – T^{t}. G) (14)
So we see that it gives the great advantage of a very simple non zero formulation for the tensor and this formulation, up to a minus sign, is in coincidence with our first intuition. But the most interesting here lies in the fact that the second term of (4) in someway vanishes, as if it was absorbed by the special property of the connection to be metric compatible. And we finally stay with the desiderated formalism independently of the eventual local variations of the local metric.

If we adopt the Yang Mills formulation for the tensor, this means that the tensor is:
F = (T^{t}. G - G. T) + […[A_{a}, A_{b}] …] (15)

Blackforest

May19-06, 04:17 PM

Non trivial solutions of the splits
It must be clear now that we deal with ^{(4)}A “x” ^{(4)}X extended vector products where ^{(4)}X is the local four vector giving the position. These products can split into P. ^{(4)}X + ^{(4)}Z where P is a (4-4) matrix built with elements of K and where ^{(4)}Z is called the rest of the split.

Since it can be shown that non trivial solutions P exist that own the following formalism:
G. (P – T) = - Q (16)
Where Q is a Hessian matrix depending on a h( ^{(4)}X) function it is straightforward to show that:
G. P = G. T - Q
P^{t}. G = T^{t}. G - Q^{t}
(T^{t}. G - G. T) = (P^{t}. G - G. P) + (Q^{t} - Q)
and:
F = (P^{t}. G - G. P) + (Q^{t} - Q) + […[A_{a}, A_{b}] …] (17)

Thus, the tensor can own the intuitive formalism:
F = (P^{t}. G - G. P) (18)
If:
^{(4)}A “x” ^{(4)}X = P. ^{(4)}X + ^{(4)}Z (19)
and if there exists a h( ^{(4)}X) function so that:
[0] = (Q^{t} - Q) + […[A_{a}, A_{b}] …] (20)
The special property of the Q matrix is so that if h( ^{(4)}X) has no discontinuity, then:
[0] = (Q^{t} - Q) (21)
and consequently :
[0] = […[A_{a}, A_{b}] …] (22)
The non Abelian term vanishes.

This suggests that the formalism (18) can also hold when a discontinuity of h( ^{(4)}X) exists. In this case one must have (20). The difficulty is to find the solutions of this equation.

Blackforest

May20-06, 03:01 AM

Good question isn't it? The demonstration above lies on (16) for which I have a general demonstration which is too long to be exposed here. The result of my approach is that we can connect the non abelian term of the Yang Mils formulation of the tensor with a discontinuity of a vector(ial) fonction h(X). As we know through other chapters of the physics that propagation of waves can be related with the propagation of discontinuities (Hadamard), we are pushed to believe that the h(X) function has something to do with the propagation of the EM phenomenon under consideration in this theory... A door for a solution concerning the (mass) gap in the Yang Mils Theory? I hope it. I would, at this step enjoy critics and discussions because it is hard to work alone. Thanks. Blackforest.

Blackforest

May21-06, 05:28 AM

Then (although it is a little bit tedious) with (12) we can demonstrate that:
0 = [g_{ac}. A_{eb}^{c} - A_{ea}^{c}. g_{cb}]. A^{e} (13)

So, I must apologize for this stupid error; ... sorry. I slowly think that either I should do something else or look into the direction of non abelian mathematical structure. Otherwise: what does it mean: "a parallel transported EM potential 4-vector"? Since this potential is understood as a gauge field, it owns an arbitrary signification more for the use of the mathematician than for the use of the physics; even if it can help to explain phenomenon (Aharonov-Bohm shift). The point of view of the demonstration starting from (2) pre-supposes the existence of such a gauge field every where and at each moment that would be effectively encountered by the EM phenomenon under consideration... It says nothing on the procedure involved in the eventual motion from a point to the other.

At the end, concerning our approach in the case of a metric compatible connection, the tensor is reduced to the second term on the right hand of (4) post 40. Plus the non abelian terms eventually in a quite more general approach.

Blackforest

May21-06, 01:36 PM

By the wonder of the calculus, this embarrassing situation (13) post 45 is equivalent to:
T^{t}. G - G. T = [0] (23)
and to the residual result :
F_{ab} = (d_{a}g_{eb} – d_{b}g_{ea}). A^{e} (24)
But if the connection (cube) A is metric compatible, this is also leading to:
F_{ab} = (2. A_{cba} – d_{c}g_{ab}. A^{c} (25)
and to:
F_{ab} = (2. g_{be}. A_{ca}^{e} – d_{c}g_{ab}. A^{c} (26)
We recognize:
F = 2. T^{t}. G – […d_{c}g_{ab}. A^{c}…] (27)
Thus, because of (23), we could write:
F = ( G. T + T^{t}. G ) – […d_{c}g_{ab}. A^{c}…] (28)
… This is the correct expression for the tensor in a metric compatible connection; instead of (14) post (42).

Why all these things (bis). Not only for the challenge but for the pleasure to learn and to research. Essentially to connect with the problematic of the polarizations; here in a 4-D space. The important variables of this theory are the metric tensor G and the matrix T (or more generally P) resulting from the split of the fundamental extended vector product under consideration. This approach allows also a theoretical connection with the problematic of the Berry's phases (shift) because it is intimely connecting the expression of the Faraday Maxwell tensor with the local metric. A lot of work must now be done to develop these foundations, I agree.

Blackforest

May24-06, 09:44 AM

The former steps could convince ourself that the intuitive formalism proposed for the tensor in a 4D space was not totally stupid. Let us now demonstrate that the esthetic of the things is not a sufficient argument to valid this approach. At least one more important condition is needed.

Since we try to connect our own approach with the historical one which is related to the existence of a gauge field ^{4}A which is a 4-vector of E_{4}, a vector space built on what we call a “body” K, and since a gauge field offers some freedom, even if this freedom will have later a price (i.e. we shall have to verify if the choice made for the gauge yields at the end a coherent theory), we decide to fix the gauge with the following relation:
{For any subscripts a and b = 0, 1, 2 or 3: d_{c}g_{ab}. A^{c} = 0} (29)
This choice leaves us with:
F = ( G. T + T^{t}. G ) (30)
We know that the T_{ab} are the 16 components of T and that the component in position (a, b) of T^{t} writes T_{ba}. So that (30), in a coordinates language is:
F_{ab} = g_{ae}. T_{eb} + T_{ea}. g_{eb} (31)

For this proposition to really describe an EM field one must have:
F_{ab} + F_{ba} = 0 (C.1)
F_{aa} = 0 (C.2)
Let us study the implications of these condition, and recall that GR compatible metrics are symmetric (H.1).

For the first condition (C.1) above, let us make an inversion of the subscripts a and b in (31):
F_{ba} = g_{be}. T_{ea} + T_{eb}. g_{ea} (32)
Let us make use of the symmetry of the metric:
F_{ba} = g_{eb}. T_{ea} + T_{eb}. g_{ae} (33)
Let us make the important hypothesis that K owns an anti commutative multiplication:
{For any element a and b of K: a. b + b. a = 0} (H.2)
Let us make use of this hypothesis (H.2) in (33):
F_{ba} = - (T_{ea}. g_{eb} + g_{ae}. T_{eb}) (34)
If the addition of two scalars of K is “usual”, then:
F_{ba} = - (g_{ae}. T_{eb} + T_{ea}. g_{eb}) (35)
and finally, we get (C.1):
F_{ba} = - F_{ab}

For the second condition (C.2) above, let us write, starting from (31):
F_{aa} = g_{ae}. T_{ea} + T_{ea}. g_{ea} (36)
Let us make use of (H.1):
F_{aa} = g_{ae}. T_{ea} + T_{ea}. g_{ae} (37)
It is obvious that (C.2) holds if K is an anti commutative body.

Conclusion at this moment:
Our proposition of a locally parallel transported gauge field (by respect for a local position 4-vector) in a metric compatible connection fixed by the relation (29) above is acceptable ( = satisfies two elementary conditions C.1 and C.2) if the theory extends on a vector space E_{4} built on an anti commutative “body” K.

Next step:
We shall have to verify an important condition written:
e^{abcd}. d_{b}F_{cd} = 0 (C.3)

Blackforest

May24-06, 12:44 PM

We reach now the next important step for this theory. We shall have to verify:
e^{abcd}. d_{b}F_{cd} = 0 (C.3)

Let us recall that e^{abcd} is a so-called « pseudo-tensor » of which the only non zero components are those for which all indices are different. Let us consider a given value for a (e.g. a = 0). It remains only 3 possible values for the b, c and d. Accordingly to the fact that there are 2 x 3 = 6 permutations for three indices without repetition, each sum described by (C.3) contains 6 terms. In extenso and for example, we have the following possibilities for the component 0: {0123} {0231} {0312} {0321} {0213} {0132}.

Let us write the generic term d_{b}F_{cd} in taking care of (31):
d_{b}F_{cd} = d_{b}g_{ce}. T_{ed} + d_{b}T_{ec}. g_{ed} + g_{ce}. d_{b}T_{ed} + T_{ec}. d_{b}g_{ed} (38)

And let us write the sum related to a = 0 in extenso. Terms for which the permutation is clockwise have a +1 signature; the others have a signature – 1. This gives:
d_{1}F_{23} = d_{1}g_{2e}. T_{e3} + d_{1}T_{e2}. g_{e3} + g_{2e}. d_{1}T_{e3} + T_{e2}. d_{1}g_{e3} (38.1)

d_{3}F_{12} = d_{3}g_{1e}. T_{e2} + d_{3}T_{e1}. g_{e2} + g_{1e}. d_{3}T_{e2} + T_{e1}. d_{3}g_{e2} (38.2)

d_{2}F_{31} = d_{2}g_{3e}. T_{e1} + d_{2}T_{e3}. g_{e1} + g_{3e}. d_{2}T_{e1} + T_{e3}. d_{2}g_{e1} (38.3)

d_{3}F_{21} = d_{3}g_{2e}. T_{e1} + d_{3}T_{e2}. g_{e1} + g_{2e}. d_{3}T_{e1} + T_{e2}. d_{3}g_{e1} (38.4)

d_{2}F_{13} = d_{2}g_{c1}. T_{e3} + d_{2}T_{e1}. g_{e3} + g_{1e}. d_{2}T_{e3} + T_{e1}. d_{2}g_{e3} (38.5)

d_{1}F_{32} = d_{1}g_{3e}. T_{e2} + d_{1}T_{e3}. g_{e2} + g_{3e}. d_{1}T_{e2} + T_{e3}. d_{1}g_{e2} (38.6)

Let us organize all these 24 terms better. We first consider all terms with a component of the metric and regroup them in taking care of the (H.2) hypothesis (K is anti commutative). Let us begin with terms of this kind in (38.1, 2 and 3):
d_{1}T_{e2}. g_{e3} + g_{2e}. d_{1}T_{e3} + d_{3}T_{e1}. g_{e2} + g_{1e}. d_{3}T_{e2} + d_{2}T_{e3}. g_{e1} + g_{3e}. d_{2}T_{e1} =

- g_{e3}. d_{1}T_{e2} + g_{2e}. d_{1}T_{e3} - g_{e2}. d_{3}T_{e1} + g_{1e}. d_{3}T_{e2} - g_{e1}. d_{2}T_{e3} + g_{3e}. d_{2}T_{e1} =
Let us make the (H.1) hypothesis (symmetric metric):
g_{1e}. (d_{3}T_{e2} - d_{2}T_{e3}) + g_{2e}. (d_{1}T_{e3} - d_{3}T_{e1}) + g_{3e}. (d_{2}T_{e1} - d_{1}T_{e2} ) (g+)

Let us continue with terms of this kind in (38.4, 5 and 6):
d_{3}T_{e2}. g_{e1} + g_{1e}. d_{2}T_{e3} + d_{1}T_{e3}. g_{e2} + g_{2e}. d_{3}T_{e1} + g_{3e}. d_{1}T_{e2} + d_{2}T_{e1}. g_{e3} =

- g_{e1}. d_{3}T_{e2} + g_{1e}. d_{2}T_{e3} - g_{e2}. d_{1}T_{e3} + g_{2e}. d_{3}T_{e1} + g_{3e}. d_{1}T_{e2} - g_{e3}. d_{2}T_{e1} =

Let us make the (H.1) hypothesis (symmetric metric):
g_{1e}. (d_{2}T_{e3} - d_{3}T_{e2}) + g_{2e}. (d_{3}T_{e1} - d_{1}T_{e3}) + g_{3e}. (d_{1}T_{e2} - d_{2}T_{e1}) (g-)

Let us compare (g+) and (g-) and not forget that (g+) has the signature + 1 whilst (g-) has the signature -1. It is thus obvious that (H.1 and 2) are not sufficient hypothesis to prove that in fact: (g+) - (g-) = 0. We must add a new important hypothesis (H.3), namely that the trivial matrix must be a symplectic one:
T + T^{t} = [0] (H.3)

Since T is a trivial matrix for the extended vector product under consideration and since the gauge field is parallel transported, this is yielding:
T_{eb} = - d_{e}A^{b} (39)
Such that if T is a symplectic matrix, then:
T_{eb} = - T_{be} = - d_{b}A^{e} (40)
This is a crucial statement because each expression of the following formalism then vanishes:
(d_{a}T_{eb} - d_{b}T_{ea})
= (d_{a}d_{b}A^{e} - d_{b}d_{a}A^{e} )
= 0 (41)
This is thus now clearly eliminating each term of (g+) and of (g-) separately; at the end we have eliminated 12 terms of the component 0 with the three hypothesis (H.1, 2 and 3). Remark that we did loose a part of the generality and that because of (H.3) the tensor must now be written in a reduced form:
F = G. T – T. G (42)

At this moment we only did have made the half of the way that we have to do to get (C.3)

Blackforest

May25-06, 05:25 AM

We actually are studying 6 terms with a + 1 signature:
d_{1}g_{2e}. T_{e3} + T_{e2}. d_{1}g_{e3} (38.1)
d_{3}g_{1e}. T_{e2} + T_{e1}. d_{3}g_{e2} (38.2)
d_{2}g_{3e}. T_{e1} + T_{e3}. d_{2}g_{e1} (38.3)
and 6 other terms with a (– 1) signature:
d_{3}g_{2e}. T_{e1} + T_{e2}. d_{3}g_{e1} (38.4)
d_{2}g_{c1}. T_{e3} + T_{e1}. d_{2}g_{e3} (38.5)
d_{1}g_{3e}. T_{e2} + T_{e3}. d_{1}g_{e2} (38.6)
If they would not be the question with the signature, it would be evidently zero for a theory working with an anti commutative body K.

Since we have to take care of the signature, the result of this calculation is not obvious. It looks like if we could regroup the terms so that:
T_{e1}. (d_{3}g_{e2} - d_{2}g_{e3}) +
(d_{2}g_{3e} – d_{3}g_{2e} ). T_{e1} =
Since K satisfies (C.2):
T_{e1}. (d_{3}g_{e2} - d_{2}g_{e3}) -
T_{e1}. (d_{2}g_{3e} – d_{3}g_{2e}) =
and since the metric satisfies (C.1):
2. T_{e1}. (d_{3}g_{e2} - d_{2}g_{e3}) =
Since the connection is metric compatible:
2. T_{e1}. (2. g_{3p}. A_{2e}^{p} – d_{e}g_{32}) = (42)
In the generalized theory of the relativity, we have the following relation (Lichnerowicz; page 266; 79-8):
d_{e}g_{ab} = g_{pb}. A_{ae}^{p} + g_{ap}. A_{eb}^{p}
This yields here for a = 3 and b = 2:
d_{e}g_{32} = g_{p2}. A_{3e}^{p} + g_{3p}. A_{e2}^{p}
Making use of this relation in (42):
2. T_{e1}. [2. g_{3p}. A_{2e}^{p} – (g_{p2}. A_{3e}^{p} + g_{3p}. A_{e2}^{p})] = (42)
2. T_{e1}. (g_{3p}. A_{2e}^{p} – (g_{p2}. A_{3e}^{p}) = (42)
We can expect to get similar terms by permutation:
2. T_{e2}. (g_{1p}. A_{3e}^{p} – (g_{p3}. A_{1e}^{p})
2. T_{e3}. (g_{2p}. A_{1e}^{p} – (g_{p1}. A_{2e}^{p})
We can now regroup terms with the same metric component and obtain the generic factor:
T_{e2}. A_{3e}^{p} - T_{e3}. A_{2e}^{p}
Since T is a trivial matrix, this yields:
A_{q2}^{e}. A^{q}. A_{3e}^{p} - A_{q3}^{e}. A^{q} . A_{2e}^{p}
and finally, we get:
(A_{q2}^{e}. A_{3e}^{p} - A_{q3}^{e}. A_{2e}^{p}). A^{q}
If the connection defines an “associative” extended vector product (see other sections of this theory), then this term is zero in any gauge field ^{4}A and the second part of the demonstration valids the homogeneous Maxwell’s law.

Conclusion of this part:
Except an error (who does not make some?) concerning the delicate procedure of a term ordering (that would have been done for example here above at the step where the relation connecting the Christoffel’s symbols of second kind and the components of the metric has been introduced), our approach seems to allow a coherent new definition of the Faraday Maxwell tensor within a theory extending in a space vector E_{4} built on an anti commutative body K, with a metric compatible connection A defining an associative extended vector product corresponding to the picture of a parallel transported gauge field respecting the fixation rule (29): For any subscripts a and b = 0, 1, 2 or 3: d_{c}g_{ab}. A^{c} = 0. At the end we have the simple symmetric relation: F = G. T – T. G. It will be the starting point of a further development.

I hope you did enjoy this presentation. And I hope I could give some interesting proposition for professional searchers in physics; specially people working about non commutative geometry. Best regards.

Blackforest

May25-06, 03:07 PM

I shall now verify my calculus; it is a tedious thing as you could see. Independently of the result of this verification I think that the presentation above contains important ideas and informations about the nature of some EM fields. The formulation that has been obtained, i.e. F = G.T - T. G allows a very special interpretation of F if G, the metric tensor, can be interpreted as a spinor. Fundamentaly speaking, spinors always own a tensorial character. We actually know some litterature proving that this interpretation is possible in a Minkowskian space. The representation of F, above, allows to understand the EM field as a "parallel transport" inside a theory based on arguments due to Cartan. Bye. I shall come later again. Be patient.

Blackforest

May28-06, 05:48 AM

As still mentioned somewhere else on these forums about some other discussion (important or not), I should ask myself if the approach under study owns any significant importance before doing so much calculations and, perhaps, loose so many time. If you did loose your time because of my research, I apologize. I had the pleasure to learn more about a fascinating domain: physics. Since gluons fields are described via gauge fields satisfying the usual equations within a Yang Mills formulation (Quantum Chromo Dyn.) of the EM fields, it looks like if my theory could describe gluons interacting with a gravitational field; any one: the own gravitational field or an exterior one. The next question is: where do we encounter gluons interacting with a gravitational field in the nature? If gluons can gravitationaly interact with themself, the answer is: everywhere where gluons exist. This is giving a new consistence to this essay... It seems to be very actual and in someway the boarder of the science. This is why I am not sure to be able to go further. It's over my head (intellectual level) and it's a country-land for professionals only, I suppose. Have a nice day. Blackforest

Blackforest

Jun1-06, 02:52 AM

No revolutionary informations. I did verify my calculation above. Everything seems to be ok with the mathematics except that the trivial matrix does not need to be a symplectic one to valid the homogeneous Maxwell's law. (It makes this approach one step more general). Concerning the physics, I am now learning about interactions between elementary particles (difficult I must say) to try to discover if my scenario makes sense. You can now read all these things in clear text in english on my home page. Thanks for attention.
p.s. Don't forget to write me directly if you think that it was a relevant "essay" or if you have critics. I do appreciate some human communication and feel sometimes like "a lonesome cow-boy far from home... (lucky lucky, a wellknown French cartoon)". Bye

Blackforest

Jul16-06, 05:29 AM

Hey people, I think I have get it !!! Shake the vacuum in a certain manner and you get the ligth ... More seriously: it can be proved that some geometric deformations (= some gravitational fields) generate EM fields and conversely. Relatively to the gravitational fields, EM fields are perhaps what the water is relatively to the molecules of water ... (just a pictorial illustration).

eljose

Jul16-06, 06:08 AM

Blackforest

Jul16-06, 03:07 PM

-But..isn,t supposed that the Kaluza-Klein model unified EM and Gravity?...by adding a fifth dimension?...and getting a similar Einstein Lagrangian?..i don,t know what,s the purpose of this post...:?:?

If the Klein-Kaluza model would be the more useful one, this would be known. Since we don't have the certitude to live in a world with 5 dimensions, I think that any attempt to unify gravitation and EM in our usual 4-D world certainly represents a progress. If the problem is not interesting, then I ask why so many clicks on this thread or on the other one. I ask why so many theoretical efforts to unify these two separate fields of our knowledge, why - for example - people are working so hard to understand the quantified Hall effect or any other effect where not only the EM side of the reality is involved in (but also the topology), a.s.a...

In fact I don't understand that you don't understand : why this post.

Blackforest

Jul23-06, 01:54 PM

-But..isn,t supposed that the Kaluza-Klein model unified EM and Gravity?...by adding a fifth dimension?...and getting a similar Einstein Lagrangian?..i don,t know what,s the purpose of this post...:?:?
Sorry for having been a little bit direct with you in my answer to you.

But I insist. Look at post 35 of this ("discussion") quasi-monologue. And consider my argumentation attentively. All others attempts (e.g. Mortimer here on this subforum; Klein - Kaluza at the begining of the 20th century) follow the historic example of the construction of the relativity. I.e.: the progress at the end of the 19th century was to be able to go from the 3D+1 world to a full 4-D space. Every researcher is now thinking that "increasing the number of dimensions of the theoretical discussion" is a good way to follow because it did work once. This way is equivalent to my example with the basket full of apples and of oranges. Of course, they are both fruits but, for example, it doesn't explain to me if they have any common points in their genetic code that would allow me to classify them in the same familly via this deeper argument.

The claim of the (E) approach is to find realistic calculations and physical situations for which a reasonable relationship between gravitation fields (represented by the connections; Christoffel's symbols) and EM fields are possible in a 4D background. This is why I think it is an original approach and, I hope it, a progress. Some lectures that I could recently do encourage me in this direction.

Best regards

Blackforest

Aug20-06, 09:19 AM

Thank you for the patience. This is absolutely not easy to put the chaotic development of my thoughts into a well organized work. If I try to take some distance with my own research, I slowly get the sensation that all my efforts are concentrated into one direction: to demonstrate the existence of some physical circumstances inside a usual 4-D world where gravitational and EM phenomenon are strongly connected together. Since EM phenomenon are quantized, a success story in this try would immediately imply a quantized version for the gravitation; which is the “holy Graal” of all modern research.
The reduction of any tensor within any group theory giving a representation of it (my example: the Faraday Maxwell tensor) does not represent a theoretical scoop; I agree. The particularity of my representation lies in two facts, I believe: i) it takes place in M(4 x 4, K) where K is any “corps” on which the space vector E is built; eventually an anti-commutative one; and ii) the reductions that I propose could allow a comparison with some other usual one involving spinors. For this proposition to be acceptable is requiring that spinors also own a representation in any ad hoc sub set of M(4 x 4, K). If this proposition – interpretation holds, then we propose to interpret some of the possible reductions as prototype representations of the Lorentz-Einstein Law.
This motivates my answers concerning the Lagrangian and the necessary limited informations that I can actually propose concerning it. I think that it is still too soon to give a definitive answer and a correct interpretation of the Lagrangian naturally implied by the reductions of the tensor. It should be more convenient to first get a serious link with a measure theory before doing any prediction concerning the energy contained into the EM field.

Blackforest

Sep1-06, 10:19 AM

If you did follow the last developments of my theory, you certainly understand that I did find an interesting course on non commutative geometry and that it gives me the link to a measure theory. My actual efforst are made to prove that some ad hoc trilinear form (see etf71.pdf) is a cyclic cocycle of dimension 2; things are turning out so that they suggest that the relativistic invariant 0 = (ds)^2 = g_{\alpha \beta} dx^\alpha d x^\beta could also be seen as an invariant logicaly arising from the co-homology theory... if some criterium are fullfilled (This is the matter of the present research but I am stopped by some stupid difficulties). If this proposition is true it will have enormous consequences for the physics.
The reduction of the Faraday Maxwell tensor that I propose in my (E) theory can be also interpreted inside this co-homologie theory*. In extenso F = [G, P] could be understood as F = dP and for me this is the door for a natural quantization inside *.
Best regards.

Blackforest

Sep2-06, 03:50 AM

At the begining of this thread, I said that I wanted to propose an other formulation for the Lagrangian of the EM field.

This section of the (E) Theory develops the consequences of the proposed reductions of the Faraday Maxwell tensor F for the Lagrangian of the EM field. As a matter of facts we could demonstrate the perfect coherence with the Maxwell’s laws of the F = G. P + P*. G (1) reduction if the cube A defines an associative extended product on (E4, K) when
i) K is anti-commutative
ii) G is the local representation of the metric tensor (symmetric) and
iii) P is a trivial matrix (and P* is its transposed here; sorry for the notation but it is a little bit long with tex) relatively to this product.

See pleasae etgb100.pdf on my homepage or the discussion on this subforum. Note that reductions in (E4, K) with K abelian also exist; of course.

Since, in language matrix F = G. F'. G, (where F' is exceptionally here the dual of F) we get F' = G^-1. F. G^-1.
For the simplicity let us exceptionally work on basis where G² = I.
This yields a simplification in the calculations:
F' = G. F. G
and consequently:
F. F'
= (G. P + P*. G). [G. (G. P + P* G). G]
= (G. P + P*. G). [G. (G. P. G + P*)]
= (G. P + P*. G). [P. G + G. P*]
= G. P². G + (G. P). (G. P*) + (P*. G). (P. G) + (P*. G). (G. P*)
= G. P². G + (G. P). (G. P*) + (P*. G). (P. G) + (P*)²
This Lagrangian contains 4 terms and one of them has no direct relation with the metric tensor. The same kind of conclusion would hold for:
F'. F
= [G. (G. P + P* G). G]. (G. P + P*. G)
= (P. G + G. P*). (G. P + P*. G)
= (P. G). (G. P) + (P. G). (P*. G) + (G. P*). (G. P) + (G. P*). (P*. G)
= P² + (P. G). (P*. G) + (G. P*). (G. P) + G. (P*)². G
In one case or in the other we do have a priori four different components and the “pure” term not directly depending on the metric is related to this extended product that we decided to introduce.

If we refer to some classical lecture concerning the Lagrangian of the EM field, we should incorporate a complementary expression and so we have theoretically in fact 4 supplementary terms but we can suspect that they own the same structure than the four that we still got. Perhaps something like:
G. F. F' = P². G + P. (G. P*) + G. (P*. G). (P. G) + G. (P*)²
This means that if we propose:
T = G. F. F' + F. F'
then we get:
T = P². G + P. (G. P*) + G. (P*. G). (P. G) + G. (P*)² + P² + (P. G). (P*. G) + (G. P*). (G. P) + G. (P*)². G
If the multiplication would also be anti-commutative for the matrices, then we would have:
(P. G). (P*. G) + (G. P*). (G. P)
= (P. G). (P*. G) + (-P*. G). (-P. G)
= (P. G). (P*. G) + (P*. G). (P. G)
= [0]
and the reduced form:
T » P². [I + G] + G. (P*)² + P. (G. P*) + G. (P*)². G + G. (P*. G). (P. G)
In the Minkowskian limit of the metric (Here we note it h; Note that this metric satisfies h² = I) :
T » P². [I + h] + h. (P*)² + F. (h. P*) + h. (P*)². h + h. (P*. h). (P.h)
Where we must remark that the first term yields T(0,0) = [P²](0,0) and T(k,beta) = 0 because [I + h] is a matrix with only one component which is non zero : the one in position (0,0).

That is: the first term introduces no impulsion and no deformation but only the mass (or the energetic density) and, in my approach, it seems to directly depend on the square of the trivial matrix P.

Continuing...

Blackforest

Sep3-06, 04:28 AM

Hye, dear members of this forum; here we are: it is the 60th intervention and accordingly to old rules here the last one. It was the possibility for me to catch your attention and try to convince you of the interest of my approach.

So let us dream a while and think that instead of one unique representation F related to a given and momentary value of an EM field under consideration, we could consider a set of such matrices; i.e. the F_i matrices for i = 1, 2, ..., N and now F = sum of F_i.
The Lagrangian obtained before (and with it a kind of correspondance between the energetic density and the trivial matrices) is suggesting that, if each event in the world is a mixture of EM fields, we could propose a kind of probabilistic interpretation for the components of the P² matrices (and for the P² matrices themselves) involved in a representation F of a given mixture.
I am not sure that I am really clear with my bad English language but I hope that you understand my idea.
So, at the end, we get a way to connect a relativistic approach and a statistic one, that is a possible link between relativity and a probabilistic approach.
If, to this vision one adds the fact that a symplectic collection of trivial matrices would give us the possibility to write any reduction of the F_i under the bracket representation F_i = [G, P_i] that we could interpret within the context of a "co-homological" theory introducing the quantized calculus with this bracket notation (which is supposing that G² = I and that G is a self-adjoint operator in an Hilbert space), I think we get an interesting link between the relativistic approach (involving the metric tensor and its variations) and the quantum approach...

The strange thing of my approach is that it is suggesting that, accordingly to the equivalence principle, EM fields around an atom could be so strong that they are locally curving space-time as if they would define geodesics where we would have such or such probability to find the electrons ...

So, it was just a dream... a vision to connect two sides of our theories. There is certainly still a lot of work to do to precise and confirm this vision, I agree. No idea if I did really success and bring some progress. Hope you enjoyed my proposition and wish you all a very good and long life. If it was good enough and if you need my help, please tell me.
Blackforest

Blackforest

Oct5-06, 02:04 AM

Dear members, "never say never more"
commentaries in my mouth are perhaps not so relevant as commentaries coming from a professional staff. But, if you give me the permission, I shall try to give point of view as “amateur”.

Steven Carlip in his book: “Quantum Gravity in 2 +1 dimensions” mentions a lot of arguments (page 2) sketching the essential differences between the Quantum mechanical approach and the relativistic one. They agree with the analyze made by Lee Smolin at the beginning of the article arXiv: quant-ph/0609109v1 14 September 2006; example: the question of non-locality. (see other sub-forum: beyond the standard model)

For me, the essential question-answer asked by L. Smolin is (page 2): “Is it possible to solve the measurement problem with a realistic ontology that is not doubled, as Boehm’s is? The idea that quantum mechanic is an approximation to a non-local, cosmological theory offers new possibility for doing this because the missing information, which makes quantum theory statistical, would be found, not in a more detailed description of the sub-system, as it is in the Bohmian mechanics, but in hidden variables which describe relationship between the subsystem and the rest of the universe.”

I would like to say thank you to Mr. Smolin because he is just saying with words what I was saying with my calculations in my investigations devoted to the following question: “Is there any possibility to analyze the Lorentz-Einstein Law as a PDE of second order?”

Even if it does not appear clearly at the beginning of the investigation, the later owns a deep relationship with the way of thinking proposed by L. Smolin. Why? The answer to my modest question is: yes, it is quasi-unique and it is compatible with a space time that would be for a short while without curvature. What do we learn with this? In fact that we can begin a Sturm Liouville analysis of the Lorentz-Einstein Law that is a Law describing locally a long distance effect of some masses and (or and) electrical charges repartitions in the universe. And this analysis can be done in a temporary flat space time which is exactly the frame where the quantum mechanics seems to take place.

For me, the sub-system where things are quantized is the slice of time where we live in; at each instant of our life. And naturally, we get informations inside of our sub-system from the rest of the universe around us via the natural time evolution which is only a temporary and local translation of the laws describing how the nature of the things are changing every where at any time. In other words, the quantum mechanic is a tool developed in accordance with our extremely strong locality. It reports on the apparent flatness of every slice of universe as soon as the slice is tiny enough. And our life is a very tiny thing.

Best regards, I hope I could help to increase the understanding of the position developed by a) Smolin and b) by my self.

Blackforest

Oct21-06, 11:38 AM

Blackforest

Dec27-06, 10:22 AM

Dear members, this is really my last intervention since nobody wants to speak directly with me about the subject that I want to develop. But as "thank you" for the time you gave me here on this "podium" and to demonstrate to Mortimer or to Sweet that I did care of their critics, I propose this small work in the attachment. Every new developmemt is on my home page: http:www.vacuum-world-net.eu/4579/

Best regards

I wish you all an happy Christmas. Some commentaries on the etgb76.pdf document are available on my homepage and here if you want. My research is progressing slowly but I did not give up.

Blackforest

Jan27-07, 01:47 PM

Recent developments of my approach.

Blackforest

Mar16-07, 12:44 PM

Life is hard; are we free to discuss about these things? I don't know. Nevermind I continue my intellectual progression and I hope you can enjoy it.

Here is a small work to tell you about the recent progresses and I think that it is a good example to illustrate my approach : the "extended angular momentum" (introduction)

Blackforest

Mar17-07, 01:04 PM

This demonstrates how the introduction of the notion of extended product modifies our way to calculate the variations (derivations) of a vector. This also illustrates the fact that we have to separate the role of the geometric connection (the Christoffel’s cube) from those of the cube defining the extended product locally; even if both cubes can be sometimes in coincidence.

Since the Christoffel’s cube vanishes in any inertial frame: we state that the “derive” of L(M, t), [the first term of the LHT in (6)], disappears in any inertial frame. The derive of the angular momentum, as we call it, is the variation of the angular momentum which is induced by a variation of the cube defining the initial very classical cross product. As expected, there is no derive of this definition in any inertial frame. Otherwise, we would be informed of that!

This is exactly the point of view that we want to develop with our principle of elasticity:
“… There must be (or there should be) a relationship between a) the "manner how" we intuitively and historically decided to define the different mathematical operations we are customized to calculate with (e.g. scalar and cross product of two vectors, and so forth) and b) our Euclidian geometry. With other words: the geometry acts on our brain in a way of which we do not necessarily have the consciousness but determinates our strategy to calculate. If our world would have been curved (like it certainly is for the sub-atomic particles), we would certainly make use of the same operations (scalar and cross products,... ), but in another way, with modified definitions... "

The relation (6) is the necessary condition to annihilate the effects of an eventual variation of the definition of the cross product induced by a variation of the geometry. As long as this relation holds, we cannot be informed of these variations, … if they exist really. We can also imagine a validity of this relation (6) … in average only. The result would be exactly the same four our instruments: an incapacity to detect the “underground” variations.

The second LHT of (6) is examined in the updated version of etgb94.pdf (see my homepage). At the end my theory predicts a natural “derive” of the definition of the cross product. Since the angular momentum is quantized, this derive must be quantized too.

Blackforest

Mar28-07, 04:19 AM

Well I can now define involutive algebras with the extended product and I begin the construction of Fredholm modules... We will see if it gives us something interesting or not.

Blackforest

Apr13-07, 12:03 PM

Here is a discussion concerning the reductions of the EM tensor proposed in the post 40-59.

Blackforest

Apr13-07, 04:07 PM

Natural introduction of the notion of extended product

Blackforest

Apr18-07, 03:45 AM

As claimed a lot of months before, an ocean of complicated calculations owning no serious motivation do not bring any light into a discussion. Thus, I have to motivate my construction; at least to try to do it.

In the following text, formula are not correctly written (I am not a specialist of text); see attachment for this.

The formula we are referring, i.e. ∫daa = ∫Gabg. ag. dxb (1) [01; page 88] is directly parented with the notion of parallel transport of the vector a = aq. eq along a path xb = xb(s) in a curved space (Here a 4D space). To convince us self of this, let us compare (1) with the formula in [02; Appendix C; page 243]: dar + Gbnr. dxb. an = 0 (2). There is no real difficulty to state the similitude (perhaps up to a minus sign) between (1) and (2); one only needs to consider the covariant formulation of a and makes the hypothesis of the absence of torsion for the connection defined by the so-called Christoffel’s cube. Thus, either with (1) or with (2), we should arrive to the same conclusion than in etgb96.pdf if the hypothesis concerning the infinitesimal elements of surface holds true (These elements can be referred to two main directions). By side, what was not said in reference [01], but is very clearly exposed in [02], is that formula (1) or (2) are the starting point for the calculation of the parallel transport matrix [U] and of the holonomy of the curve along which a is parallel transported. If the Stockes’ theorem is valid [02; Appendix C; (C.10) page 245]: Urn = drn - òå Rrnbd . dfbd (3) where å is the surface delimited by the path. So, we get for small enough elements of surface with main directions (db, dc): ∫daa = -2. a. ⌂(▼R), a (db, dc). This is situating the discussion on the notion of extended products directly into the domain of application of the loops.

In an approach based on the loops, like LQG, the vector a has to be an element of a Lie algebra. And it can be proved that the space vector (E4, R)can be equipped with a structure of Lie algebra via the extended products.

Now, referring to this citation (THIS FORUM; INTRODUCTION TO LQG): “… Well, let’s steal some ideas from particle physics... In QFT we have fermionic matter-fields and bosonic force-fields. The quanta of these force-fields or the so called force-carrier-particles that mediate forces between matter-particles. Sometimes force-carriers can also interact with each other, like strong-force-mediating gluons for example. These force carriers also have wavelike properties and in this view they are looked as excitations of the bosonic-force fields. For example some line in a field can start to vibrate (think of a guitar-string) and in QFT one then says that this vibration is a particle. This may sound strange but what is really meant is that the vibration has the properties of some particle with energy, speed, and so on, corresponding to that of the vibration. These lines are also known as Faraday’s lines of force. Photons are "generated" this way in QFT, where they are excitations of the EM-field. Normally these lines go from one matter-particle to another and in the absence of particles or charges they form closed lines, loops. Loop Quantum Gravity is the mathematical description of quantum gravity in terms of loops on a manifold. We have already shown how we can work with loops on a manifold and still be assured of background-independence and gauge-invariance for QFT. So we want to quantize the gravitational field by expressing it in terms of loops. These loops are quantum excitations of the Faraday-lines that live in the field and who represent the gravitational force. Gravitons or closed loops that arise as low-energy-excitations of the gravitational field and these particles mediate the gravitational force between objects.
It is important to realize that these loops do not live on some space-time-continuum, they are space-time !!! The loops arise as excitations of the gravitational field, which on itself constitutes “space”. Now the problem is how to incorporate the concept of space or to put it more accurately : “how do we define all these different geometries in order to be able to work with a wave function … ?”,

I introduce the notion of split. It is for me the way to connect a set of second order differential operator to the set of the different expressions of the Lorentz Einstein Law (LEL). Indeed, supposing that $ ([P]a, ka) Î M4(Â) x (E4, Â, ⌂(▼R), a) | ⌂(▼R), a. Extpr(db, dc) = [P]. dc + k yields ∫daa = -2. a. {[P]a. dc + ka}. For the special cases where a = dc, this is nothing but ∫da = -2. a. {[P]. a + k} and obviously a quadratic equations depending on a. With a few complementary hypothesis (see etgb96.pdf), this is exactly this kind of relation that can connect any second order differential operator with a precise expression of the LEL provided I interpret a as being the position vector in the Riemannian space and ∫daa as being the ath coordinate of the “projection” in a flat space of aa , and indirectly, because of that, of a. Let us note it: xa(a). The advantage of this procedure is that the second order differential operator is acting on x and that a Sturm-Liouville treatment can give him the Schrödinger equation formalism. Inside this procedure, we didn’t make any precise hypothesis concerning the nature of x. This is suggesting the possibility to consider it as a spinor.

This procedure must be analyzed: is it coherent? Does it make sense? If it holds true, than I can say that I have developed a new tool to connect QM and GTR. This was the foundations of this (E) attempt.

Bibliography:
[01] ART ;Torsten Fließbach ; 4. Auflage; Spektrum der Wissenschaft; 2003
[02] Quantum Gravity in 2 + 1 Dimensions; Steven Carlip; Cambridge Monographs on Mathematical Physics; 2003;

Blackforest

Apr22-07, 09:56 AM

The (E) attempt is the theory that tries to find a meaningful mathematical correspondence between the set of all particular expressions of the Lorentz Einstein Law, say S(LEL), and the set of all particular expressions of the Schrödinger equation, say S(SE). Such a search is motivated by a now more than eighty years old problem which is the need to find an equivalence between two fundamental and sometimes but not always equivalent descriptions of the nature. Both theories, the GTR and the QM, do have excellent experimental confirmations but none of the high performing schools, universities or communities was able, until now, to furnish a tool to connect them correctly despite the evident fact that they are describing the same universe: ours. These theories are in someway like two persons speaking a different language and looking for the lexicon that will give them the possibility to translate their respective thoughts. They implicitly know that they are thinking about the same topics but none of them can understand what the other is really saying. Thus we were looking for a dictionary. The (E) attempt is the first proposition for this book. It tries to define the set of the correspondences between concepts developed in each theory. In this sense it firstly appears to be a mathematical theory more than a physical one; but the topic is concerning physics so deeply that one can never escape from it. In fact, and it is a situation in opposition with some initial hopes of the construction, this attempt does not put GTR and QM into the same pot. It only draws the links between the two sisters. Mathematically, these links are quadratic forms (the conoides in our language) between the positions space of the GTR related to any connection (flat or not) and the spinors space of the QM related to the flat connection of the Minkowskian space. Physically, these same links are interpreted as being the expressions of some “loops” or “derives” along some (actually not clearly defined) paths of which the property is to project the Riemannian space of the GTR onto the flat space of the QM. These derives or loops are shifting one set to the other one. Since S(LEL) and S(SE) are describing the same particles, these derives should be the equivalent representation, in the language of the transformations, of the particles.

This is the hope of the (E) attempt.

Now, I think I did try to explain my theory in the best way I could hope to do it. The discussion can begin (but I think there will be no one). Best regards. Have a good sunday evening

Blackforest

May16-07, 12:27 PM

Amazingly I am not the only one making this analyze concerning the connections between the GTR and QM. It is the item of the future discussion between Smolin and Darmour in June in Paris... (see other thread in beyond the standard model)

Otherwise and despite the fact that nobody seems to be ready to have any discussion with me (it's sad), I propose you this new contribution: etgb98.pdf.

Lorentz Einstein Law / Extended products / equivalent scalar / energy and ... Ricci flow?

You can always read the homepage http://www.vacuum-world-net.eu for more explorations

Blackforest

Jun25-07, 05:14 AM

Dear members,
your absence of reaction was motivating my own silence. This does not mean that I was not looking attentively the evolution of the debates; for example: the “war” between LQG and ST. After having been hearing via Internet the debate between L. Smolin and Th. Damour in Paris (6 Juny 2007; n. b.: you have a link on the forum “Beyond the standard model” at www.cite-sciences.fr/), even if a fair confrontation can only re-enforce the foundations of each theory, the actual situation appears to my amateur's eyes a little bit strange. Each “school” has(d) good reasons to develop its strategy like it did during the 30 past years (short said: efficiency, rapidity, results for the american way; extensive and general explorations for the european way). Applying a principle of tolerance and freedom lead us to respect the respective choices. But the layman (and the citizen) has also the right to ask: “What did they do with my money? Where are the results? What did we really learn from this research? Where are the new products that could be develop thanks the progresses of this fundamental research?” That was all these things that I was thinking about today morning, doing the beens to help my wife and dreaming about my own research. That's exactly that: I was thinking that we are a special kind of people: “Dreamers; dreaming the future; trying to reveal the exact structure of the nature.”

All news are not bad. The Gravity probe B experiment could give us a very recent confirmation of Einstein's work; for ex. Coming back to the former post. You never react to my propositions; so, I cannot know if it is correct or no; the number of “click” on my thread is the only possibility for me to get an image of my work... (But Mortimer who did make no more intervention since a year also get some “clicks”!) I don't know what you are thinking about me or my approach. And it makes things complicated. Amateurs like me get the feeling that they are doing a stupid quest or that they are totally at the wrong place here. But I am neither a spy nor a dealer or a bad boy; I am only a dentist and I like physics.

The last work calls for an explaination. The procedure might sounds a little bit crazy or at least strange. In a first and too rapid critic, one would reject it because it is supposing that the Lorenz Einstein Law (LEL) could be not exactly true or that the equation of motion of a particle could be under the influence of something else modifying the LEL describing a first and given particle.

But this first reaction would forget at least two things:
1)I can imagine the existence in vacuum (the cosmological one; not the quantic approach of this notion) of a see of waves (with a average volumetric density of energy equivalent to 10 – 29 kg/cubic meter) and correlatively: of a function describing the local distribution of the energy. (In a similar way that has been used to describe semi-conductor with the Boltzman equality).
2)The quantum approach admits the spontaneous birth of particles. It is not forbidden to believe that the behavior of each of these particles is also represented by a LEL. Their existence is a natural explaination for a perturbation of the LEL describing the first particle under consideration.
I thus have two good reasons to accept the eventuality for S (the scalar associated to a representation of the LEL) not to vanish. And so, two physical motivations to introduce S.

The other non explained hypothesis that I did make is the following. I decided to correlate the non vanishing S to the non vanishing of a Hessian. (At the beginning of my quest, I must give it, I thought it was possible to connect S with the Laplacian of the potential of gravitation. It would have been a great result of my approach if it would have work in that way; but it didn't!).

This investigation finaly results in 3 relations. The first one tells us a comfortable story: the more the duration (dt) is long, the more (Toutes choses étant égales par ailleurs) S vanish. That is: the more the LEL of the first particle under consideration becomes true again after having been perturbated by any phenomenon. Great, isn't?

I leave the second relation for the end because it receives a clear explaination via the third one. (See the document in attachment). For me it has the advantage to explain what the h function is (wave function of the particle for example). Correlatively, what the Hessian of this function could be.

The second relation, if interpreted as a special formulation of the relation: mass by speed is invariant, tells us the circumstances for which this approach makes sense and yields the masses for these circumstances...

Is this a new road in physics to describe and to discover the spectrum of real masses (energy)? I believe it. Please help me to understand if it is true or not. I get f... up to work alone. Is there any professor here to help me? Sorry for the complaint. Oh I must come back to the kitchen and help my wife for the preparation of the lunch.

Thanks for your attention. Bye.

sweetser

Jun25-07, 09:54 AM

Hello:

I was the second person to respond to your thread, so you should know my reaction. I don't think you are either 1. right, or 2. wrong. There is a third, much wider possibility: 3. you are not understandable. I vote for 3.

As a simple example, lets discuss the LEL. I have MANY books on special relativity and general relativity. Not a one of them uses those three letters, LEL, to describe any of Einstein's work. I know English is not your first language, but you need to use the vocabulary of physics to communicate with physicists. The Lorentz transformation law has to do with special relativity, and gravity probe B has to do with general relativity. The equations for these two topics are very different. At all costs, avoid making up new jargon.

It is clear you have a bunch of technical words in your head, and you have constructed a web of connections. Since your words are used in different ways from practicing physicists, it is not possible to follow the way you interconnect them.

When I started working in physics, I babbled like a baby babbles: put together words I don't actually understand in ways that don't make sense. I was aware of this, and mostly kept to myself (my own mother did get to hear some of this early stuff). I went and read stuff, lots of books and papers. I also spent much time participating in the newsgroup sci.physics.research. At the time, it was an active place of discussion.

Over a period of two decades, I have gotten better at speaking coherent physics. Yet I do still mess up. Professors today are professors due to their intellectual precision with words and ideas. I have accepted that I will never get to that level, my mind is too loose a cannon. I try and see new things, and put them in reasonable technical packages.

It is my opinion - and only an opinion - that you do not speak the language of physics close enough to the way it needs to be spoken to be understood. This would explain the observation that no one is entering a dialog with you. I want to make clear that I am not offering to teach you how to become clear. I hope you had a good lunch.

doug

Blackforest

Jun25-07, 03:11 PM

Hello:

I was the second person to respond to your thread, so you should know my reaction. I don't think you are either 1. right, or 2. wrong. There is a third, much wider possibility: 3. you are not understandable. I vote for 3.

Well... It could be that you are right. It is difficult to introduce a new way of thinking, new roads to explore...

As a simple example, lets discuss the LEL. I have MANY books on special relativity and general relativity. Not a one of them uses those three letters, LEL, to describe any of Einstein's work. I know English is not your first language, but you need to use the vocabulary of physics to communicate with physicists. The Lorentz transformation law has to do with special relativity, and gravity probe B has to do with general relativity. The equations for these two topics are very different. At all costs, avoid making up new jargon.

The LEL is the equation resulting from an easy confrontation and can be seen in a lot of books (I read a german one called : Allgemeine.Relativitäts.Theorie. from Torsten; 2003<means Generalized Theory of Relativity for you>). On the left side (for example) you write the total derivate of the speed vector (4D); on the other side you write the Faraday-Maxwell tensor and you multiply it by the 4D speed vector. It is also explained in the documents that I did upload on this forum...

It is clear you have a bunch of technical words in your head, and you have constructed a web of connections. Since your words are used in different ways from practicing physicists, it is not possible to follow the way you interconnect them.

My point of view lies on the idea that if you are not able to confront different parts of the physics, then you are not able to built a general theory. You are specializing on a given topic. I am not saying that it is wrong or bad but this is not my purpose.

When I started working in physics, I babbled like a baby babbles: put together words I don't actually understand in ways that don't make sense. I was aware of this, and mostly kept to myself (my own mother did get to hear some of this early stuff). I went and read stuff, lots of books and papers. I also spent much time participating in the newsgroup sci.physics.research. At the time, it was an active place of discussion.

Over a period of two decades, I have gotten better at speaking coherent physics. Yet I do still mess up. Professors today are professors due to their intellectual precision with words and ideas. I have accepted that I will never get to that level, my mind is too loose a cannon. I try and see new things, and put them in reasonable technical packages.

It is my opinion - and only an opinion - that you do not speak the language of physics close enough to the way it needs to be spoken to be understood. This would explain the observation that no one is entering a dialog with you. I want to make clear that I am not offering to teach you how to become clear. I hope you had a good lunch.

doug

Thanks; the lunch was excellent. Have a nice day. Blackforest.

Blackforest

Jun26-07, 04:30 AM

First of all, I want to apologize; the reference for the LEL is written by the Pr. Torsten. Fliessbach (His name).

Let us come back to the first argument proposed to introduce the scalar S: …“I can imagine the existence in vacuum (the cosmological one; not the quantum approach of this notion) of a see of waves (with a average volumetric density of energy equivalent to 10 – 29 kg/cubic meter) and correlatively: of a function describing the local distribution of the energy. (In a similar way that has been used to describe semi-conductor with the Boltzman equality)”...

My reference here is a German book with the title: “Physik; Moleküle und Festkörper; Horst Hänsel, Werner Neumann; Spektrum Akademischer Verlag, Heidelberg, Berlin, Oxford; 1996. Pages 522-525”. In this reference, one is speaking about electrons and it has been made the hypothesis that df = 0.

Since I have no time to work with tex, I prefer to send an attached document. Best regards.

Blackforest

Jun26-07, 04:26 PM

Blackforest

Jun27-07, 04:53 AM

So, you did make the correction and find something like that:

Gradient (W). u + u. [F]. u + S + (1/c). (dW/dt) = 0

Obviously, S owns the units of a power. If the idea to correlate this scalar S with a Hessian makes sense (as developed and explained in etgb98.pdf), then we get the first relation of coherence:

T = dx. Hess(h). dx = S. dt.

The scalar T that can be now understood as a kind of projection of the Hessian of h has consequently the units of an energy. We thus discover a posteriori that the scenario proposed in etgb98.pdf is connecting a certain modification of the Euclidian curvature (given by the Hessian) with the apparition of a certain amount of energy.

With other words, I am making the “toy” hypothesis that temporary modifications of the energetic state (for example in vacuum), respecting the Heisenberg’s principle of uncertainty, can be due to the birth of particles and correspond to a perturbation in the evolution of the local curvature. Do you understand me? Do you understand this idea? Do you agree with?

The domain of validity of my toy model is given by the second relation of coherence in etgb98.pdf. The metric must be Einstein and the masses associated with this toy scenario are the eigenvalues of the matrix of the masses which is proportional to the representation of the metric tensor. Example given: at the Minkowskian limit, we get only two values (+ 1, - 1) corresponding a priori to a particle and its anti-particle (+ m, - m).

If we accept the Big-Bang scenario (what I am doing), we accept the idea of a permanent expansion of the universe. But it takes place in a 4D structure, not only in a 3D one. This means it takes also place in the time dimension, here. So we should not be obliged to look very far to observe effects of this permanent expansion…

Do we really know the mechanism of expansion of our universe, do we know the boarder between something (where the universe still exists) and nothing (where it was not yet present)?

Best regards.

Blackforest

Jul2-07, 02:47 PM

Just want to say thank you (for the place on this forum, for your patience), sorry and good bye (because the professional research is not for me). I continue my crazzy project on a personal blog, just for fun, just to learn and perhaps to bring something positive to the community of physicists (who knows?). Best regards and all the best for all.

Blackforest

Jul10-07, 02:21 AM

If someone here is still interested by my personal research, there is the possibility to look at:

http://thperiat.neufblog.com

This is the new adress of my homepage. It is mainly written in the French language (of course) but I also develop a small corner for English speaking readers (see the link on the right side of the page). The old home page is still runing until the 16 July 2007 and will disappear after this date.

Best regards.

Blackforest

Jul10-07, 09:38 AM

Résumé (less than 2000 words)

Based on an extension of the tensor calculus we define an extended product on a four dimensional Banach space and, generalizing a basic scholar principle, we explore the set of all possible splits of these products. A technique, essentially built on a comparison with the projection of an Hessian, is developed and it allows the discovery of a special family of splits minimizing the scalars that can be associated with. This technique is then applied to the customary expression of the Lorentz Einstein law and yields three relations of coherence. Since the scalar associated with this law is a power (force multiplied by speed) and since the procedure is finally connecting this scalar linearly with the Hessian of the wave function of the particles under study in a way directly involving the local geometric connection, we predict that our approach is a good theoretical tool to scrutinize situations with a “Einstein” metric. It could yield the masses for the particles concerned by these situations.

See etf31v4.pdf (in French language)
See the beginning of the work in English language: etgb98.pdf

Blackforest

Nov3-07, 10:56 AM

The recent development of my approach are the documents NC.pdf (Enghlish) and mce.pdf (French). I try to built a gauge theory in N = 4 dimensions, starting from the Lorenz Einstein law and the introduction of "my" extended products. For this I try to find and define all the ingredients. I think it is a great challenge for a man like me, but so fascinating. Hope you can find some interrest in this approach. Probably nothing very new for the professionals, but at least a way for students. Perhaps a collection of the mistakes that should no more be repeated after me. Have fun.

Blackforest

Nov10-07, 12:34 AM

It's extremly difficult to make a "resumé" of my work (NC.pdf or quite more naive etgb28.pdf in english; mce.pdf in my language) but I shall try to do it. Believing that geometry is influencing our way to think and calculate, naively applying this intuition to the behavior of particles I define the extended product position by speed for any particle. Any such product is supposed to split in a set of pairs belonging to M4(R) x (E4, R). The way how it splits is depending on the "underground" geometry. The discovery of the pais is one of the many challenges of this theory.

Starting "à priori" with this idea, I admit, like everybody here, that the initial characteristics of the motion of the particle can be eventually changed by the action of a force and I "pré" suppose that the action of this force perturbates the split. The work gives a scenario to discover the generic formalism of the new split or of the split attached to the action (consifdering that a force is also representing a kind of particle). I then impose the condition for any split to be coherent with the solutions of the GRT equations. It yields a surprising (for me) relation that seems to be one of the two necessary relations giving to the componants g_a_b of the local metric tensor the property to be a gauge field.

Next coming soon...

Blackforest

Nov10-07, 01:10 AM

In the second part of the document I make a kind of "disgression" into the world of mathematics and study the notion of derivate. I discover, among other things, that a vector space (E4,R) equipped with an extended product of which the cube defining it owns the ad hoc properties is a Lie algebra. For us the Christoffel's cube is not interesting. The Riemann-Christoffel's curvature tensor naturally proposes a set of ad hoc cubes (because of some properties of anti-symmetry). The Lie algebra structure can be "exported" to M4(R) via the trivial splits under some conditions. In this sense, the theorem of surjection introduced in the theory is very interesting. At the end, this is giving the hope to establish a kind of isomorphism between the set of extended products under consideration and their representations in M4(R) x (E4,R).

The third part is a specific scenario of me. The existence of an extended product owning at least one split yields an intrinsic relation : b. {a \wedgeb - [P]. b - z} = 0. this relation is analyzed and seen as the sum of a linear and of a bilinear part. One first make a fundamental hypothesis concerning the variations of b (see document; introducing a non necessarily continuous function; said H) and then calculates the partial derivates of second order starting from the partial derivates of the first order (classic). After that, a comparison between the result of the calculation and the original bilinear part yields a relation of coherence. Since the H function is not necessarily continuous it can be interesting to define the conditions for which it is. This is, amazingly, yielding a new relation of which the formalism seems to be those of the deviation of some specific geodesic of this theory.

Hope you could understand my speech. Don't forget to give me your opinion. I am actually reading the discussions on the others sub-forums and what i can read concerning the Yang-Mills theory seems to be able to be connected with my approach. The discontinuity of my H function (in my head and in my spirit) has something to do with the (mass)gap.

Best regards

Blackforest

Nov18-07, 06:21 AM

There are a lot of interesting discussions on these forums I must say. I recently discovered the work of Garrett Lisi (see Beyond the standard model; A extraordinary simple Theory of everything). I want to thank him for the indirect help contained in his paper. For example it sheds more light on the complicated relationships between mathematics and physics. For the first time in my life I could realized that the Lie structures I was trying to built with my “trivial” matrices could also have something to do with some particles. That was naturally a great day for me. Since I am only an amateur and a man studying very tardy what I did always dreamed to study, I present my work very slowly and piece by piece. Learning and training on the job. Informations he is giving page 4 are particularly important for my own construction.

Even if I now realize the necessity to re-built my approach in including the quaternion numbers into it, from the very beginning, - that is to built my theory not with (E_4, R) but with (E_4, H) - the procedure can be repeated exactly on the same way.
1) Discover the conditions for which an extended product between two vectors can be assimilated to a Lie bracket.
2) Study attentively this structure (generators, …)
3) Export this structure as far as possible on M(E_4, H). Note that one possible representation for these matrices certainly will be (M_8, C) where C is now the set of all complex numbers
4) Study the generators, …
And get the pleasant feeling that this construction must not be so far from the E8 approach.

Now, I know, there is still a lot of work to do and much more to learn. But what a peaceful sensation: at the end, after long months of alone working… coming back to the earth, where other people like me are looking for what (our) the reality is.

Thank you

Blackforest

Nov22-07, 03:36 PM

As recalled in the discussion developed in the other threads, one of the mysteries of physics (and unsolved problem) is the scale problem between the intensity of the EM fields and the intensity of the gravitational fields. One road to surround this problematic (and it is the usual one today) is to believe that the “unity” is recovered for the very high energies (where one expects to obtain circumstances very similar to the initial big-bang).
But can we not imagine another road? Let us abandon for a while our dream to build a cosmology and instead of that let us only start from the evidence: gravitational fields are very tiny but omnipresent. What would it be if the disproportion were not only the result of the time (temporal distance in the actual cosmology starting from the big-bang) but would in some way accelerated by the fact that variations of the second order of the geometry are also producing fields isomorphic to an EM field while the variations of the first order are the origin for the gravitational field (GR approach)? Quantitatively, because of the successive interferences and accumulations, one could expect that the intensity of the EM field would be increasing with the time and would always surpass the intensity of the gravitational field. This is in some way the story contained in ThP04F.pdf (Old document -2004- in French language; pages 25-29).

Concerning the recent developments and the introduction of the quaternions in my work, I could demonstrate the existence of extended products on (E4, H) and the existence of a neutral element acting on the left in some very simple conditions. One can built such a product with the real componants of the Riemann Christoffel tensor. The purpose is the construction of a Lie group. The idea is: the componants of the tensor, even if very small, are never totally vanishing...

Blackforest

Dec2-07, 04:28 AM

Progress in fundamental research is the result of a long and difficult work. So it is for the comprehension of the E8 Theory and gfroup, so it is for my own construction.

As said before, I actually explore the possibility to built a group on (E4, H) equipped with and extended product built on a cube of quaternions. For this one needs a neutral element. It was not too difficult to find one acting on the left and finally only depending on the real componants of the quaternions involved in the cube. I have now discovered that the neutral element acting on the left could also act exactly on the same way (i.e. be a neutrel element acting on the right) if the matrix representing it in M4(R) has the same formalism than the matrix [n] with which one can write the Lorentz transformations matrix in form of an exponential: L(v) = exp {rapidity.[n]}. This seems not to be a hazard and to give a phyical signification to this neutral element inside this approach. I.e. the Lorentz transformations are the representations of this neutral element.

The man who reads (or can read and learn) always get an advantage relatively to the man who cannot get the education and the informations (not new but so important). I recently discovered an article that seems to offer an interesting mathematical background to my calculations. Namely the concepts of "gerbes" and twisted non abelian gerbes... Even if it still is over my head for the details and the complete understanding of the different intrications

www.arXiv.org look for hep-th/0409200v1 20 Sep 2004

I am sure it can be of a great interest for all people working on a better and serious comprehension of E8. It also shows that there is no need to permanently bring the different ways of thinking in opposition. Theories are like different parts of a puzzle and we only have to discover the correct relationships; not to fight together. The truth lies somewhere in the middle, in the work and in the originality.

Best regards