Talk:PlanetPhysics/QED
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\section{Quantum electrodynamics (\em Q.E.D)}
Q.E.D-- is the advanced, standard mathematical and quantum physics treatment of electromagnetic interactions through several approaches, the more advanced including the path-integral approach by Feynman, Dirac's \htmladdnormallink{operator}{http://planetphysics.us/encyclopedia/QuantumOperatorAlgebra4.html} and QED Equations, thus including either Special or \htmladdnormallink{general relativity}{http://planetphysics.us/encyclopedia/SR.html} formulations of electromagnetic phenomena. More recent approaches have involved \htmladdnormallink{spinor}{http://planetphysics.us/encyclopedia/ECartan.html} (Cartan and Weyl) and twistor (Penrose) \htmladdnormallink{representations}{http://planetphysics.us/encyclopedia/CategoricalGroupRepresentation.html} of Quantum \htmladdnormallink{Hilbert spaces}{http://planetphysics.us/encyclopedia/NormInducedByInnerProduct.html} of quantum states and \htmladdnormallink{observable}{http://planetphysics.us/encyclopedia/QuantumSpinNetworkFunctor2.html} quantum oprators. QED results are currently at precision levels beyond 10−29 , and thus it is one of the most precise, if not the most precise, physical theories that however does not encompass gravity.
\subsection{Measurements and Quantum Field Theories}
{The question of measurement in \htmladdnormallink{quantum mechanics}{http://planetphysics.us/encyclopedia/QuantumParadox.html} (\htmladdnormallink{QM}{http://planetphysics.us/encyclopedia/FTNIR.html}) and
quantum field theory (QFT) has flourished for about 75 years. The
intellectual stakes have been dramatically high, and the problem
rattled the development of 20th (and 21st) century physics at the
foundations. Up to 1955, Bohr's Copenhagen school dominated the
terms and practice of quantum mechanics having reached (partially)
eye--to--eye with Heisenberg on empirical grounds, although not the
case with \htmladdnormallink{Einstein}{http://planetphysics.us/encyclopedia/AlbertEinstein.html} who was firmly opposed on grounds on
incompleteness with respect to physical reality. Even to the
present day, the hard philosophy of this school is respected
throughout most of \htmladdnormallink{theoretical physics}{http://planetphysics.us/encyclopedia/PhysicalMathematics2.html}. On the other hand, post
1955, the measurement problem adopted a new lease of life when von
Neumann's beautifully formulated QM in the mathematically rigorous
context of Hilbert spaces. Measurement it was argued involved the
influence of the Schr\"odinger equation for time evolution of the
\htmladdnormallink{wave}{http://planetphysics.us/encyclopedia/CosmologicalConstant.html} \htmladdnormallink{function}{http://planetphysics.us/encyclopedia/Bijective.html} $\psi$, so leading to the notion of entanglement of
states and the indeterministic reduction of the wave packet. Once
$\psi$ is determined it is possible to compute the probability of
measurable outcomes, at the same time modifying $\psi$ relative to
the probabilities of outcomes and observations eventually causes
its collapse. The well--known paradox of Schr\"odinger's cat and
the Einstein--Podolsky--Rosen (\htmladdnormallink{EPR}{http://planetphysics.us/encyclopedia/FluorescenceCrossCorrelationSpectroscopy.html}) experiment are questions
mooted once dependence on reduction of the wave packet is
jettisoned, but then other interesting paradoxes have shown their
faces. Consequently, QM opened the door to other interpretations
such as `the hidden variables' and the Everett--Wheeler assigned
measurement within different worlds, theories not without their
respective shortcomings.
Arm--in--arm with the measurement problem goes a problem of `the right logic', for quantum mechanical/complex biological \htmladdnormallink{systems}{http://planetphysics.us/encyclopedia/GenericityInOpenSystems.html} and \htmladdnormallink{quantum gravity}{http://planetphysics.us/encyclopedia/LQG2.html}. It is well--known that classical Boolean truth--valued logics are patently inadequate for \htmladdnormallink{quantum theory}{http://planetphysics.us/encyclopedia/SpaceTimeQuantizationInQuantumGravityTheories.html}. Logical theories founded on projections and self--adjoint operators on Hilbert space $H$ do run in to certain problems . One `no--go' \htmladdnormallink{theorem}{http://planetphysics.us/encyclopedia/Formula.html} is that of Kochen--Specker (KS) which for $\dim H \geq 3$, does not permit an evaluation (global) on a Boolean system of `truth values'. In Butterfield and Isham (1999)--(2004) self--adjoint operators on $H$ with purely discrete \htmladdnormallink{spectrum}{http://planetphysics.us/encyclopedia/CohomologyTheoryOnCWComplexes.html} are considered. The KS theorem is then interpreted as saying that a particular \htmladdnormallink{presheaf}{http://planetphysics.us/encyclopedia/CommutativeRingWithUnit.html} does not admit a global \htmladdnormallink{section}{http://planetphysics.us/encyclopedia/IsomorphicObjectsUnderAnIsomorphism.html}. Partial valuations corresponding to local sections of this presheaf are introduced, and then generalized evaluations are defined. The latter enjoy the structure of a Heyting algebra and so comprise an intuitionistic logic. Truth values are describable in terms of sieve--valued maps, and the generalized evaluations are identified as subobjects in a \htmladdnormallink{topos}{http://planetphysics.us/encyclopedia/GrothendieckTopos.html}. The further relationship with interval valuations motivates associating to the presheaf a \htmladdnormallink{von Neumann algebra}{http://planetphysics.us/encyclopedia/QuantumOperatorAlgebra4.html} where the supports of states on the algebra determines this relationship.
We turn now to another facet of \htmladdnormallink{quantum measurement}{http://planetphysics.us/encyclopedia/CosmologicalConstant.html}. Note first that \htmladdnormallink{QFT}{http://planetphysics.us/encyclopedia/CategoricalQuantumLMAlgebraicLogic2.html} \htmladdnormallink{pure states}{http://planetphysics.us/encyclopedia/PureState.html} resist description in terms of \htmladdnormallink{field}{http://planetphysics.us/encyclopedia/CosmologicalConstant.html} configurations since the former are not always physically interpretable. \htmladdnormallink{Algebraic Quantum Field Theory}{http://planetphysics.us/encyclopedia/CosmologicalConstant.html} (\htmladdnormallink{AQFT}{http://planetphysics.us/encyclopedia/PureState.html}) as expounded by Roberts (2004) points to various questions raised by considering theories of (unbounded) operator --valued distributions and nets of von Neumann algebras. Using in part a gauge theoretic approach, the idea is to regard two field theories as equivalent when their associated nets of observables are isomorphic. More specifically, AQFT considers taking (additive) nets of field algebras over subsets of Minkowski space, which among other properties, enjoy either Bose--Einstein (for \htmladdnormallink{particles}{http://planetphysics.us/encyclopedia/Particle.html} of integer or xero \htmladdnormallink{spin}{http://planetphysics.us/encyclopedia/QuarkAntiquarkPair.html}) or Fermi (for particles of spin-1/2) commutation \htmladdnormallink{relations}{http://planetphysics.us/encyclopedia/Bijective.html}. Although at first glance there may be analogs with \htmladdnormallink{sheaf theory}{http://planetphysics.us/encyclopedia/PAdicMeasure.html}, theses analogs are severely limited. The typical net does not give rise to a presheaf because the relevant \htmladdnormallink{morphisms}{http://planetphysics.us/encyclopedia/TrivialGroupoid.html} are in reverse. Closer then is to regard a net as a precosheaf, but then the additivity does not allow proceeding to a cosheaf structure. This may reflect upon some incompatibility of AQFT with those aspects of quantum gravity (\htmladdnormallink{QG}{http://planetphysics.us/encyclopedia/LQG2.html}) where for example sheaf--theoretic/topos approaches are advocated (as in e.g. Butterfield and Isham (1999)--(2004)).}
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