In a series of papers and books, the late Mendel Sachs introduced Einstein group in order to construct his Unified Field Theory. He wrote that his quaternionic UFT is equivalent with spinor formalism of General Relativity. See one of his paper on Symmetry in Electrodynamics (attached file).
For an introduction to spinor formalism of General Relativity, see for instance Jorge Cardoso at http://arxiv.org/abs/1004.5150.
My question is: Is Einstein group really necessary to construct a Unified Field Theory? If yes then there can be new predictions out of Sachs's new electromagnetic theory. Your comments are welcome.
Hello, I am sorry, I do not know (all) works you mention. I would nevertheless like to note that the Maxwellian electromagnetism (Maxwell equations enriched with two deBroglie's relations and some relations of general relativity) are sufficient to include also the description of gravity (as the secondary electric force). And the same solution of the equations can describe the atom (as a crystal-type structure). But I must warn you that this concept is so simple that nobody considers it to be serious... [more on: arXiv:1012.5763]
Dear L. Neslusan, thank you for the reference, i will check it. Best wishes
Absolutely not! Einstein started with field equations without first defining the forces in terms of Newtonian expressions. I successfully unified the forces after discovering a fundamental charge notation error, and some missed equations in physics regarding two distinct types of charges.
Article Calculations of the Unified Force Theory as Explained in the...
DearVictor! You can find a good review of similar questions in the introductory part of Anatoly Logunov's works where he tried to develop an alternative theory (to Einstein's general relativity theory) with respect to gravity. As concerns the 'unified field theory", please: check, whether such theories indeed reproduce (at least) the electroweak theory by Weinberg and Salam? The latter is well confirmed by the experiment. With the gravitation, we still have some unresolved problems. As an example: are there gravitation waves? Who had detected them unambigiously? So, either formulate well focused and defined (unambigiously) experimental questions, or indicate, what was not answered in experiments, which had been performed, or be careful in your speculations! Itmay be well, that the time for full understanding of "what is the gravity" is in a far future... What is undoubtful: new observable facts must appear: what could be extracted from the known ones had been extracted already.
@David: thanks for your answer
@Dr. E.A. Strokovsky: thanks for your answer, ok i will check Logunov's work. It is a good idea to always keep in mind electroweak theory/experiments, but previously i thought that it is the scope of GUT, while UFT is restricted for unfiying gravitation and electromagnetic theory. What do you think? Best wishes
Page 6. The Dr. Sachs uses unusual, perhaps even childish manipulation of the line integrals. In usual treatment: \int f_i dx_i =\int [f_i dx_i/dL] dL. Thus the result of such integral is function of a single parameter L: \int f_i dx_i = h(L). This parameter corresponds to fixed spacetime line: x=x(L), y=y(L), z=z(L), t=t(L). Thus a derivative of the line integral is dh(L)/dx = [dh/dL] [dL/dx] = [f_i dx_i/dL] [dL/dx]. Note, that [dx_i/dL] [dL/dx] is not the vector [0,1,0,0]. But the Dr. Sachs has considered it as such vector, hasn't he? Moreover, if it would be such vector, then dh(L)/dx = f_x (L) and a second derivative [d/dy] [dh(L)/dx] = [d(f_x)/dL] [dL/dy] is again not giving us the Dr. Sachs desired behavior [d/dy] [dh(L)/dx] = [d(f_x)/dy].
Page 4: "then there is an implication in the experimental result of Wu et al that the electromagnetic and the nuclear forces also violate space-reflection symmetry, as well as time reversal symmetry." Me: how the Dr(?) Wu accopished the time reversal? The time-machine is not constructed yet. Dr(?) Wu must have the time machine, because he found the time reversal breakdown EXPERIMENTALLY. If do believe the Dr. Sachs.
No, I am pretty sure. There seems to be something right about gauge theory, and in gauge theory a unification of the fields rests on a unification of the groups, This most likely requires small changes in those groups that are unstable (in the sense of I Segal), like the diffeomorphism group.
Furthermore diff implies a space-time continuum, and further unification might well require analyzing space-time into quantum elements.
@Prof. David Finkelstein: thank you so much for your answer. I really appreciate that. Best wishes
Dear Victor Christianto, see the general field as a variant of Unified Field Theory,
at http://en.wikiversity.org/wiki/General_field .
@Sergey: thanks for the link. Elsewhere i also read that there is a theory called Generalized Field Theory (A. H. Klotz). Does it have similarity with your General field theory? Best wishes
Dear Victor, thanks for ref. to GFT by Klotz. As I see at http://www.actaphys.uj.edu.pl/_old/vol19/pdf/v19p0533.pdf
in GFT the difference is used between metric tensor of general relativity and Riemannian metric tensor, and connection is from Schrodinger's equation. All of this is geometrical approach, when field properties connects to space-time.
In the concept pf general field all particular fields are independent on space-time and connect to different properties of matter interaction.
@Sergey: thanks for your answer. What are main observables related to your General field theory? Best wishes
As the general field has particular fields as its components. then the observables of these fields are observables of the general field.
Einstein's idea of Unified Field Theory, which seems to be very profound and attractive,is, in fact, misleading. This idea was natural at Einstein's times but now one can find serious arguments to put it in question. It hardly possible to explain them in a few words. However, a general remark is that in UFT people are trying to combine some incompatible from mathematical point of view quantities. This is a rather delicate point, which requires a special sensibility to some aspects of the modern mathematics that were not at the hands of Einstein. Second, one can see, for instance, from Hamiltonian mecanics that the concept of a force is not at all basic. Say, classical rational mecanics can be easily and directly deduced from the classical observability principle and the concept of energy. So, any theory, for instance, the standard model, based on the idea of some "fundamental forces" is destinated to be incomplete.
Dear Dr. A.M. Vinogradov: thanks for your answer. With regards to your remark: "So, any theory, for instance, the standard model, based on the idea of some "fundamental forces" is destinated to be incomplete." Do you mean that all theory is incomplete, just as Godel's Incompleteness theorem? Best wishes
Not : Goedel's theorem concerns axiomatic theories, while the field theory is expressed in terms of differential calculus and hence is not an axiomatic one. With my remark I would like to stress that the structure of Hamiltonian mechanics shows that forces are not basic building blocks of the theory. Historically, the idea of a force was guiding in the long process of adequate mathematical formalization of mechanics. By mental inertia people continue to use it in a rather different context, say, field theory. Of course, it may sometimes happen that it leads to some reasonable results. But such situations are mostly exceptions.
@Dr. A.M. Vinogradov: thanks for your answer. With regards to dichotomy between particle and field theory, i recall a book by Einstein and Infeld, with title: Evolution of Physics. As far as i can remember, in that book the authors want to tell us that the history of ideas in physics can be categorized as follows:
A. Everything is formed by particles (since Demokritus)
B. Everything is formed by Field
And may be one can come up with a third alternative:
C. Everything is formed by waves
I think we can discuss many theories in physics based on the above three categories, what do yo think? Thanks
In my opinion, everything is formed by matter particles similar to nucleons and electrons. According to Infinite Hierarchical Nesting of Matter, https://en.wikiversity.org/wiki/Infinite_Hierarchical_Nesting_of_Matter
the analogues of the proton at the star level are magnetars, at lower level of matter - praons. We have also field particles such as neutrinos and photons which are components of graviton field and genereted by praons, nucleons, neutron stars and so on. The role of field particles is creation the matter particles with the help of gravitation in Lesage model of gravitation. See http://vixra.org/abs/1209.0076 .
The neutrinos and photons are the waves of graviton field. See the photon model at http://vixra.org/abs/1205.0044 and neutrinos model in the book: 'The physical theories and infinite hierarchical nesting of matter', Volume 1, LAP LAMBERT Academic Publishing, pages: 580, ISBN-13: 978-3-659-57301-9', at https://www.lap-publishing.com/catalog/details//store/gb/book/978-3-659-57301-9/the-physical-theories-and-infinite-hierarchical-nesting-of-matter-volume-1.
The different forces reflect different properties of particles interaction. For every such force we can construct the 4-potential and find field equations. See http://vixra.org/abs/1406.0135 . And it was found that field equations for all fields are similar to Maxwell's equations. See http://vixra.org/abs/1406.0173.
@Sergey: thanks for your links, i will read them. Btw for the Einstein and Infeld's book, see this link: https://archive.org/details/evolutionofphysi033254mbp
Dear Victor, concerning your remark "I think we can discuss many theories in physics based on the above three categories, what do yo think?" I think that
1. By manipulating with these categories one may combine something reasonable only accidentally. At the present we have no principles to distinguish fantasies written in terms of these categories from real physics. I am affraid that the great part of contemporary theoretical physics should be called "terminological physics" !
2. I find that affirmations like "everything is formed by matter particles similar to nucleons and electrons" reflect just personal mental prefernces as in the choice of a religion to follow.
3. An adequate and exact formulation of a physical theory is possible in a suitable mathematical language only. If the necessary mathematics does not exist at the moment, then all tempations to build the physical theory take the form of a fantasy. Think, for instance, about the situation in mechanics before invention of differential calculus and Descartes' "unified theory".
4. The existing QFT is a book of recipies properly because the necessary mathematics is not yet at disposal of physisists. More detaliled discussion of this topics you can find in my article "From symmetries of partial differential equations towards secondary (”quantized”) calculus", J. Geom. and Phys., 1994, vol. 14, pp.
146-194. Also in the book by J.Nestruev, Smooth manifolds and observables, (Springer, series: Graduate Texts in Mathematics, vol. 220, 2002), you will find a rigorous formulation of the observability principle in classicalm physics and a direct deduction from it of both differential calculus and Hamiltonian mechanics.
When will scientists realize that Einstein's theory of relativity is wrong? And abandon it?
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