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**‘Deterministic systems’- minimum length – QMLS**

An understanding of minimum length is not limited to what I have been doing, Quantum mechanic uses ‘Deterministic systems’ which is equal to QMLS.

http://arxiv.org/PS_cache/quant-ph/pdf/0604/0604008v2.pdf

The mathematical basis for deterministic quantum mechanics

Gerard ’t Hooft

26 June 2006

This was brought up in

https://www.physicsforums.com/showthread.php?t=116791&page=2

't Hooft 5 (daveb, davey, hawk, hossi, scott)

Do the above people have any comment on minimum length?

Follow up work is in progress in the following papers.

Those who voted for Gerard 't Hooft can take pleasure in the fact that his paper has probably caused a flurry of papers on trying to find the minimum length.The mathematical basis for deterministic quantum mechanics

Gerard 't Hooft quant-ph/0604008 (April 2006)

Citations

The citations are based on preprints held within the arXiv database and articles published by IoP Publishing.

Quantum fields, cosmological constant and symmetry doubling

Hans-Thomas Elze hep-th/0510267 (2005) [Preprint]

The Cosmological Constant Problem, an Inspiration for New Physics

Stefan Nobbenhuis gr-qc/0609011 (2006) [Preprint]

The Gauge Symmetry of the Third Kind and Quantum Mechanics as an Infrared Limit

Hans-Thomas Elze hep-th/0605154 (2006) [Preprint]

Gauge Symmetry of the Third Kind and Quantum Mechanics as an Infrared Phenomenon

Hans-Thomas Elze quant-ph/0604142 (2006) [Preprint]

Is there a relativistic nonlinear generalization of quantum mechanics?

Hans-Thomas Elze quant-ph/0704.2559 (2007) [Preprint]

http://arxiv.org/PS_cache/arxiv/pdf/0704/0704.2559v1.pdf

Is there a relativistic nonlinear generalization of quantum mechanics?

Hans-Thomas Elze

19 April 2007

http://www.jinr.dubna.su/publish/Proceedings/Burdik-2005/pdf/elze.pdf [Broken]Abstract. Yes, there is. – A new kind of gauge theory is introduced, where the minimal coupling and corresponding covariant derivatives are defined in the space of functions pertaining to the functional Schr¨odinger picture of a given field theory. While, for simplicity, we study the

example of a U(1) symmetry, this kind of gauge theory can accommodate other symmetries as well. We consider the resulting relativistic nonlinear extension of quantum mechanics and show that it incorporates gravity in the (0+1)-dimensional limit, where it leads to the Schr¨odinger-Newton equations. Gravity is encoded here into a universal nonlinear extension of quantum theory. The probabilistic interpretation, i.e. Born’s rule, holds provided the underlying model has only dimensionless parameters.

A quantum field theory as emergent description of constrained supersymmetric classical dynamics

Hans-Thomas Elze

Also, presented at Brazilian Journal of Physics, vol. 35. no. 2A, June, 2005Deterministic dynamical models are discussed which can be described in quantum mechanical terms.

http://www.sbfisica.org.br/bjp/files/v35_343.pdf

Determinism and a Supersymmetric Classical Model of Quantum Fields

Hans-Thomas Elze

http://arxiv.org/PS_cache/hep-th/pdf/0605/0605154v1.pdfThus, ’t Hooft’s proposal to reconstruct quantum theory as emergent from an underlying deterministic system, is realized here for a field theory.

THE GAUGE SYMMETRY OF THE THIRD KIND AND QUANTUM MECHANICS AS AN INFRARED LIMIT

HANS-THOMAS ELZE

16 May 2006/ Received April 19, 2007

Reading the following paper was enlighteningWe introduce functional degrees of freedom by a new gauge principle related to the phase of the wave functional. Thus, quantum mechanical systems are dissipatively embedded into a nonlinear classical dynamical structure. There is a necessary fundamental length, besides an entropy/area parameter, and standard couplings. For states that are sufficiently spread over configuration space, quantum field theory is recovered.

1. How little I know

2. How much I still have to learn

3. My approach to minimum length and structure is still valid

http://arxiv.org/PS_cache/gr-qc/pdf/0609/0609011v1.pdf [/URL]

The Cosmological Constant Problem, an Inspiration for New Physics

Stefan Nobbenhuis

04 Sept 2006

[quote]…p. 131 On a more positive note, the idea that gravity shuts off completely below 10−3 eV is a very interesting idea. The cosmological constant problem could be solved if one were to find a mechanism showing that flat spacetime is a preferred frame at distances l < 0.1 mm. The model of Sundrum is an approach in this direction, and one of very few models in which gravity becomes weaker at shorter distances. Moreover, another obvious advantage is that it can at least be falsified by submillimeter experiments of the gravitational 1/r2 law.[/quote]

It appears that there are many ways of getting finding the minimum length: ‘Deterministic systems’, ‘Limiting Curvature Construction’, ‘Quantum Geometry’, and ‘QMLS’.

Who will be the “math kid” that can combine all of the approaches? ( If I was a betting man, I would put my money on Gerard 't Hooft and group because they are already analyzing “structures”.)

The final model should be able to produce the required dynamics that would give us a better understanding of the universe.

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