What is quantum mechanics?

Abstract

Consistent schemes for non-adiabatic dynamics derived from partial linearized density matrix propagation J. Chem. Phys. 137, 22A535 (2012) The spectral shift function and Levinson's theorem for quantum star graphs J. Math. Phys. 53, 082110 (2012) Explicit formulas for noncommutative deformations of PN and HN J. Math. Phys. 53, 073502 (2012) Coherent averaging in the frequency domain AbstractWe discuss the arguments for suspecting that there exists a classical, i.e. deterministic theory underlying quantum mechanics. A difficulty is that an explanation must be found of the fact that the Hamiltonian, which is denned to be the operator that generates evolution in time, is bounded from below. The mechanism that can produce exactly such a constraint is identified in this paper. It is the fact that not all classical data are registered in the quantum description. Large sets of values of these data are assumed to be indistinguishable, forming equivalence classes. It is argued that this should be attributed to information loss, such as what one might suspect to happen during the formation and annihilation of virtual black holes.The nature of the equivalence classes is further elucidated, as it follows from the positivity of the Hamiltonian. Our world is assumed to consist of a very large number of subsystems that may be regarded as approximately independent, or weakly interacting with one another. As long as two (or more) sectors of our world are treated as being independent, they all must be demanded to be restricted to positive energy states only. What follows from these considerations is a unique definition of energy in the quantum system in terms of the periodicity of the limit cycles of the deterministic model.An example of a deterministic dissipative model producing exact quantum mechanics is provided for the case of a finite-dimensional vector space. These lecture notes have been produced partly from material published earlier, and as such contain more material than what could be presented in the talk.

Vacuum energy and the cosmological constant

“…83,84 Emergence ideas are further discussed in Refs. 76,77,85,86,87. Patterns in fermion masses have been interpreted 88,89 to suggest that perhaps there is a deeper structure to matter and that perhaps the fermions and W ± and Z 0 bosons might be composite.…”

A master equation for gravitational decoherence: probing the textures of spacetime

“…Here, the search is mainly motivated by an uneasiness in the awkward union between general relativity and quantum mechanics, and the context can be in the settings of quantum gravity or at today's low energy with a classical spacetime structure and quantum matter fields. Adler [18] views quantum mechanics as emergent from a more fundamental theory while 't Hooft views quantum mechanics as a clever way of bookkeeping classical events [19]. For a recent discussion of the differences between intrinsic and environment-induced decoherence, see Ref.…”

Quantizing Geometry or Geometrizing the Quantum?

“…Dissipative emergence of both, quantum and gravity: Dissipative deterministic systems can give rise to quantum operators and symmetries that are not present in the original theory at the microscopic scale [30,31]. Further conjecturing that those symmetries are the ones of diffeomorphism invariance (general relativity) might give an identikit picture of a future theory of quantum gravity.…”