- #1
member 11137
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
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
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