I like to mythology . Try to co-relate with science . My mathematical findings forced me to believe that
Quantum Mechanics exists without an
universal symmetry . However , I know
that front level authors working in QM
will not accept it . Probably they will
accept it after twenty years . For them it is an undue discussion . I suggest them to think more and more in symmetry .
B.Rath
Actually in General Relativity, the geometry of the Universe (the container where lives everything) is represented as a 4 dimensional manifold endowed with a metric, which is its physical part. And as such it has physical symmetries, defined by its Killing vector fields, which constitute a Lie algebra of dimension at most 10. They define the physical symmetries of the Universe; given by isometries.
@Jean Claude Dutailly
Thank you for shareing your views . Please suggest the symmetries and its validity in quantum mechanics .
In QM we know CPT , unfortunately none of them is universal . My conclusion is from model operators involving mathematical calculations .
Reply
QM has nothing to do with physics. Symmetries in QM have another meaning. Se my paper QM revisited.
Please send arxiv or pdf file.
If QM has nothing to do with symmetry , then why hundreds of papers are in CPT ? Clarify my doubt .
1) Quantum Mechanics proper (Hilbert space, operator...) does not involve either a physical object or a process, or a symmetry.
2) These axioms are mathematical theorems which can be proven. One of these theorems (about a change of vatable) gives interesting results in the case of symmetries. But of course it does not tell why a system has a symmetry.
3) The PT operators are geometric (they act on the geometry of the universe). Dirac's spinors are a matricial representation of the Clifford algebra Cl(C,4). In any Clifford algebra PT is equivalent to the graded involution, and there are interesting result about the real structures on Cl(C,4) and PT. But spinors in QTF are just supports without physical relation to the geometric space, so the geometric meaning is lost. As for the C operator it would be necessary first to define a charge, which is not done in QTF. And the representation of antiparticles is not done by a C operator.
4) Why so many people work on CPT ? I assume that this is because they are paid for that. For what purpose ? I do not know, but it does not seem to be useful to anybody except themselves. Perhaps you could give us a practical outcome of this work ?
@Jean Claude Dutailly
I read your reply . Please note that in QM, C is not the charge but a symmetry operator havingeigenvalues + -1. See the Bender , Brody and Jones paper . Exploring symmetry leads to conservation & creation of particles , unification of forces etc . Symmetry is a vast subject . If SUSY and symmetry can move together new things will be explored . My discussion was in QM there exist no UNIVERSAL symmetry so also in Universe .
I formulated new type of susy called
Twin - Susy and noticed that no symmetry exists.
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