By Stephen L. Adler
Even though it is our such a lot winning actual thought, quantum mechanics increases conceptual matters that experience at a loss for words physicists and philosophers of technology for many years. This e-book develops a brand new procedure in response to the idea that quantum concept isn't a whole, ultimate concept, yet, in reality, an emergent phenomenon coming up from a extra profound point of dynamics.
Read or Download Quantum Theory as an Emergent Phenomenon: The Statistical Mechanics of Matrix Models as the Precursor of Quantum Field Theory PDF
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Extra resources for Quantum Theory as an Emergent Phenomenon: The Statistical Mechanics of Matrix Models as the Precursor of Quantum Field Theory
23d) which substituting Eq. 23e) s in agreement with Eq. 23a). 24a) and the corresponding trace dynamics equation of motion of Eq. 15b). Thus, for Weyl-ordered Hamiltonians formed with c-number coefficients, we conclude that the trace dynamics equations of motion generated by H agree with the Heisenberg picture equations of motion generated by H , on an initial time slice on which the phase space variables are canonical. It is also evident that on this time slice [H, i] = 0. 24b) But since Eq. 24b) guarantees that the Heisenberg picture equations of motion preserve the canonical algebra on the next time slice, integrating forward in time step by step then implies that trace dynamics agrees with Heisenberg picture dynamics at all subsequent times, and therefore can be extended to a unitary dynamics in this case.
The example of Eq. 20c) required the use of two pairs of canonical variables q1,2 , p1,2 ; using our Weyl-ordering result, we shall now show that any trace dynamics for a single 36 Trace dynamics pair of bosonic variables q, p, when extended to the canonical algebra [q, p] = i, always can be represented as a unitary Heisenberg evolution. We shall proceed by induction, and assume that the result has been proved for any trace dynamics generated by a trace Hamiltonian H = TrH of degree n or less in p and q.
We conclude that as of this writing the localization model is favored, both because the assumptions needed to derive it within our framework are more robust, and because there are unresolved problems with the mechanisms that have been proposed to explain reduction in the energy-driven model. Finally, in Chapter 7 we indicate how our proposal for an emergent quantum theory addresses the motivational questions raised above in Section 3, and discuss some of the issues that will be relevant for future developments.