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

[member 11137]

Contribution to another great discussion

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.

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

 

[member 11137]

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/[/URL]

Best regards

 

[member 11137]

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/[/URL]

Best regards[/QUOTE]

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.

 

[member 11137]

News

Recent developments of my approach.

 

[member 11137]

Time, thesis, derivation, angular momentum

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)

 

[member 11137]

Commentaries

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.

 

[member 11137]

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.

 

[member 11137]

Coming back to the reductions of the EM tensor

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

 

[member 11137]

Extended products and loops

Natural introduction of the notion of extended product

 

[member 11137]

important commentaries

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 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;

 

[member 11137]

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

 

[member 11137]

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

 

[member 11137]

A new procedure to find masses?

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/[/URL]), 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 explanation. 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 explanation 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 explanation 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]

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, let's 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

 

[member 11137]

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, let's 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.

 

[member 11137]

Trying to explain better

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.

 

[member 11137]

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.

Sorry; erratum: there is naturally a big mistake at the end of this etgb983.doc document. But I am sure you did understand the idea and make the correction yourself. I should have written:
0 = c. grad f + c. (...). u. {[F]. u} - ... S + ...
It does not change the spirit of this small section.

Best regards

 

[member 11137]

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

Gradient (W). u + u. [F]. u + S + (1/c). ([symbol]d[/symbol]W/[symbol]d[/symbol]t) = 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.

 

[member 11137]

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.

 

[member 11137]

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.

 

[member 11137]

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​

 

[member 11137]

basics for a gauge theory?

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.

 

[member 11137]

(E) Theory, local metric tensor and gauge field.

It's extremely 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 components g_a_b of the local metric tensor the property to be a gauge field.

Next coming soon...

 

[member 11137]

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

 

[member 11137]

The hope to be again in the reality

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

 

[member 11137]

Relative intensity of gravitational and EM field

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 components of the Riemann Christoffel tensor. The purpose is the construction of a Lie group. The idea is: the components of the tensor, even if very small, are never totally vanishing...

 

[member 11137]

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 components 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

 

[member 11137]

Extended products and Lorentz transformations

This is an illustration of my work with and around the extended products, a kind of continuation of some recent thoughts about the E8 group. I beg your pardon if it is a stupid construction. Otherwise, I hope you enjoy and profit of this intervention to begin some conversations. Best regards

 

[member 11137]

This is an illustration of my work with and around the extended products, a kind of continuation of some recent thoughts about the E8 group. I beg your pardon if it is a stupid construction. Otherwise, I hope you enjoy and profit of this intervention to begin some conversations. Best regards

Oops: may be the proposed plausible reprsentation, relation (15), is not correct and should be reduced to a row (with label zero). It does not avoid the realiztion of the important idea: the neutral element exists and can be connected to the Lorentz transformations. The difference is that we have now to consider [n] and its transposed via the exponential to get the transformations.

I come back in a few days with a better version. Thanks