On Configuration Space, Born’s Rule and Ontological States

Elze, Hans‐Thomas

doi:10.1007/978-3-030-34234-0_18

Cited by 2 publications

(4 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In this way, the Born rule is built in by definition! -The Born rule can also be understood as a counting It will often be difficult to relate unitary evolution of OS by permutations to a familiar looking Hamiltonian operator, in particular in presence of interactions [1,2,3,4,8,9,10]. Which makes the accessible spin chain model of Section 3 interesting.…”

Section: A Synopsis Of the Cellular Automaton Interpretationmentioning

confidence: 99%

“…There is nothing to which an OS could be reduced and, therefore, no collapse can occur! 6 procedure related to a conserved two-time function of Hamiltonian cellular automata, which generalizes the norm of QS [10]. -It is is not forbidden by any element of quantum theory to abandon the proportionality between absolute values squared of complex amplitudes and probabilities, however, at the price of unnecessarily complicating its mathematical tools [1].…”

Section: A Synopsis Of the Cellular Automaton Interpretationmentioning

confidence: 99%

“…( 39) and (40), we find a rather involved yet terminating BCH formula. 10 Note that the final expression on the righthand side of Eq. ( 40) can be factorized into exponentials, since only commuting powers of Û are involved.…”

Section: The Baker-campbell-hausdorff Formula Behindmentioning

confidence: 99%

See 2 more Smart Citations

Are quantum spins but small perturbations of ontological Ising spins?

Elze

2020

Preprint

Self Cite

View full text Add to dashboard Cite

The dynamics-from-permutations of classical Ising spins is generalized here for an arbitrarily long chain. This serves as an ontological model with discrete dynamics generated by pairwise exchange interactions defining the unitary update operator. The model incorporates a finite signal velocity and resembles in many aspects a discrete free field theory. We deduce the corresponding Hamiltonian operator and show that it generates an exact terminating Baker-Campbell-Hausdorff formula. Motivation for this study is provided by the Cellular Automaton Interpretation of Quantum Mechanics. We find that our ontological model, which is classical and deterministic, appears as if of quantum mechanical kind in an appropriate formal description. However, it is striking that (in principle arbitrarily) small deformations of the model turn it into a genuine quantum theory. This supports the view that quantum mechanics stems from an epistemic approach handling physical phenomena.

show abstract

Section: A Synopsis Of the Cellular Automaton Interpretationmentioning

confidence: 99%

Section: A Synopsis Of the Cellular Automaton Interpretationmentioning

confidence: 99%

See 1 more Smart Citation

Are quantum spins but small perturbations of ontological Ising spins?

Elze

2020

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…We also wish to thank Lev Vaidman and several other colleagues for stimulating discussions. We thank the latter for the exchange of viewpoints sometimes closely related to our approach, as they also become apparent in their respective works: Herman Batelaan [ 34 ], Ana María Cetto and Luis de la Peña [ 35 ], Hans-Thomas Elze [ 36 ], Basil Hiley [ 37 ], Tim Maudlin [ 38 ], Travis Norsen [ 39 ], Garnet Ord [ 40 ], and Louis Vervoort [ 41 ].…”

Section: Acknowledgmentsmentioning

confidence: 99%

Vacuum Landscaping: Cause of Nonlocal Influences without Signaling

Groessing

Fussy

Pascasio

et al. 2018

Entropy

View full text Add to dashboard Cite

In the quest for an understanding of nonlocality with respect to an appropriate ontology, we propose a "cosmological solution". We assume that from the beginning of the universe each point in space has been the location of a scalar field representing a zero-point vacuum energy that nonlocally vibrates at a vast range of different frequencies across the whole universe. A quantum, then, is a nonequilibrium steady state in the form of a "bouncer" coupled resonantly to one of those (particle type dependent) frequencies, in remote analogy to the bouncing oil drops on an oscillating oil bath as in Couder's experiments. A major difference to the latter analogy is given by the nonlocal nature of the vacuum oscillations.We show with the examples of double-and n-slit interference that the assumed nonlocality of the distribution functions alone suffices to derive the de˜Broglie--Bohm guiding equation for N particles with otherwise purely classical means. In our model, no influences from configuration space are required, as everything can be described in 3-space. Importantly, the setting up of an experimental arrangement limits and shapes the forward and osmotic contributions and is described as vacuum landscaping. * Corresponding author: ains@chello.at; http://www.nonlinearstudies.at arXiv:1806.05466v2 [quant-ph]

show abstract

On Configuration Space, Born’s Rule and Ontological States

Abstract: It is shown how configuration space, possibly encompassing ordinary spatial structures, Born's rule, and ontological states aiming to address an underlying reality beyond Quantum Mechanics relate to each other in models of Hamiltonian cellular automata.

Cited by 2 publications

References 16 publications

Are quantum spins but small perturbations of ontological Ising spins?

Are quantum spins but small perturbations of ontological Ising spins?

Vacuum Landscaping: Cause of Nonlocal Influences without Signaling

Contact Info

Product

Resources

About