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- Thread starter mmzaj
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The special theory of relativity was inspired by classical electromagnetism, but does not follow from it. It is more general, whereas electromagnetism applies only to light. So once you have a more complete theory, namely SR, it turns out that you can do quantum mechanics, or quantum field theory ontop of that. Now QFT indeed corrects electromagnetism, but those corrections are still in keeping with special relativity, and so that doesn't need modification.

All hell breaks loose when you try to treat gravity and quantum mechanics on the same level. But you can do QFT "on top" of gravity, in the same way you can do QFT on top of special relativity.

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It might be useful to know that quantum field theory may be thought of as quantum mechanics with the Poincare group (symmetries of special relativity) as it's symmetry group.

Maxwell equations aren't that fundamental, really. There are many more systems out there than just electromagnetism. In any case, it is possible that we might find corrections to our theories but those corrections are likely to be improvements. Just as special relativity is an improvement of Newtonian mechanics and doesn't invalidate it at low velocities, another theory might be an improvement of QFT and won't invalidate it at low energies.

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first of all excuse my technical terms , physics was my major before switching to electrical engineering .

you know , this is exactly what i had in mind : poincare group !! i know that maxwell equations aren't that fundamental , but still any lorentzian transformation should leave them invariant , if not , then we expect a modification !! just like schrodinger's equation was modified to G.K and later to Dirac equations . the same applies for yang-mills generalization , but in this case things went the other way : poincare group was taken into consideration when the Y-M equations where put . until now i reason things perfectly , but - and it's a big fat but - the modifications that QFT implied on electromagnetism were consistent with S.R 'cause the latter was a "given" in the formulation of QFT , right ?? so what if we adapt another technique : generalize maxwell equations - lets say Y-M picture - without poincare group being the symmetry group , but rather an "unknown" symmetry which is to be revealed , now S.R derived from this new theory is certainly different from einstein's S.R !!! . a QFT ontop of this new S.R would modify -say - Y-M equations in a different way , and we end up with a new "degree of freedom" : the symmetry group we chose .. i know i'm being obsered and all , but it just hit me right now .

you know , this is exactly what i had in mind : poincare group !! i know that maxwell equations aren't that fundamental , but still any lorentzian transformation should leave them invariant , if not , then we expect a modification !! just like schrodinger's equation was modified to G.K and later to Dirac equations . the same applies for yang-mills generalization , but in this case things went the other way : poincare group was taken into consideration when the Y-M equations where put . until now i reason things perfectly , but - and it's a big fat but - the modifications that QFT implied on electromagnetism were consistent with S.R 'cause the latter was a "given" in the formulation of QFT , right ?? so what if we adapt another technique : generalize maxwell equations - lets say Y-M picture - without poincare group being the symmetry group , but rather an "unknown" symmetry which is to be revealed , now S.R derived from this new theory is certainly different from einstein's S.R !!! . a QFT ontop of this new S.R would modify -say - Y-M equations in a different way , and we end up with a new "degree of freedom" : the symmetry group we chose .. i know i'm being obsered and all , but it just hit me right now .

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