] ‘Deterministic systems’- minimum length – QMLS

[jal]

‘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.

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]

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.
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

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.

http://www.jinr.dubna.su/publish/Proceedings/Burdik-2005/pdf/elze.pdf
A quantum field theory as emergent description of constrained supersymmetric classical dynamics
Hans-Thomas Elze

Deterministic dynamical models are discussed which can be described in quantum mechanical terms.

Also, presented at Brazilian Journal of Physics, vol. 35. no. 2A, June, 2005
http://www.sbfisica.org.br/bjp/files/v35_343.pdf
Determinism and a Supersymmetric Classical Model of Quantum Fields
Hans-Thomas Elze

Thus, ’t Hooft’s proposal to reconstruct quantum theory as emergent from an underlying deterministic system, is realized here for a field theory.

http://arxiv.org/PS_cache/hep-th/pdf/0605/0605154v1.pdf
THE GAUGE SYMMETRY OF THE THIRD KIND AND QUANTUM MECHANICS AS AN INFRARED LIMIT
HANS-THOMAS ELZE
16 May 2006/ Received April 19, 2007

We 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.

Reading the following paper was enlightening
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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[AndyW]

Thank you for bringing up the topic of deterministic systems and minimum length in relation to quantum mechanics. I am familiar with the work of Gerard 't Hooft and his proposal to reconstruct quantum theory as emergent from an underlying deterministic system. His paper, "The Mathematical Basis for Deterministic Quantum Mechanics," provides a fascinating perspective on the foundations of quantum mechanics.

I have also looked into the follow-up work by Hans-Thomas Elze and Stefan Nobbenhuis, which expands on the idea of a minimum length and its implications for quantum mechanics and gravity. It is interesting to see the various approaches being taken to understand this concept and its potential impact on our understanding of the universe.

I agree that the final model should be able to produce the required dynamics to give us a better understanding of the universe. It will be exciting to see how these different ideas and approaches come together to form a more comprehensive theory. Thank you for sharing these papers and sparking a thought-provoking discussion on this topic.

 

[Entropia]

Thank you for sharing this interesting and informative content. I appreciate your efforts to stay updated on the latest research and theories in the field of quantum mechanics. The concept of minimum length and deterministic systems is a fascinating one, and it is exciting to see the progress being made in this area. It will be interesting to see how these different approaches eventually come together to provide a comprehensive understanding of the universe. Keep up the good work!