Stochastic spacetime

[Philip Thrift]

Dimensional flow and fuzziness in quantum gravity: emergence of stochastic spacetime

https://arxiv.org/abs/1706.02159

Stochastic space interval as a link between quantum randomness and macroscopic randomness?

https://www.sciencedirect.com/science/article/pii/S0378437117310725

A Universe Made of Tiny, Random Chunks

(The space-time that makes up our universe is inherently uncertain.)

http://nautil.us/issue/2/uncertainty/a-universe-made-of-tiny-random-chunks

@philipthrift

[Lawrence Crowell]

These ideas run into an empirical problem. As I have indicated before, data on the arrival times of photons of different wavelengths from burstars indicates spacetime is incredibly smooth. It is smoother than the Planck scale by 1:50. There is no foam, graininess or discontinuous properties at all. Nottale scale relativity implies there is a fractal structure to spacetime that defines different properties at different scales. What is found empirically is nothing of the sort; spacetime has no preferred structure on any scale. It is smooth. 

What may be happening has possible connections to many body theory. Many body theory has these domains of regular dynamical solutions, which can be fairly robust against perturbations, within a larger "sea" of chaos. Quantum physics can exhibit a form of fractal dynamics in scarring of wave function, or where the destructive and constructive interference of a wave can become deformed into filigree. Quantum mechanics though abhors nonlinearity in actual wave functions. General relativity on the other hand is C^∞, so far as I can tell, and so completely smooth. Though there may not be actual fractal structure to spacetime, it is plausible that spacetime can exhibit topology changes that have correspondences with turbulent hydrodynamics. So if quantum mechanics is linear with a form of fractal structure this should exist in different Fourier modes for different spatial configurations. Yet this may only correspond to separable states off the entanglement or entropy surface of a coherent or condensate of states that have classical correspondence.

LC

[Philip Thrift]

On Tuesday, November 26, 2019 at 8:03:05 PM UTC-6, Lawrence Crowell wrote:

These ideas run into an empirical problem. As I have indicated before, data on the arrival times of photons of different wavelengths from burstars indicates spacetime is incredibly smooth. It is smoother than the Planck scale by 1:50. There is no foam, graininess or discontinuous properties at all. Nottale scale relativity implies there is a fractal structure to spacetime that defines different properties at different scales. What is found empirically is nothing of the sort; spacetime has no preferred structure on any scale. It is smooth. 

What may be happening has possible connections to many body theory. Many body theory has these domains of regular dynamical solutions, which can be fairly robust against perturbations, within a larger "sea" of chaos. Quantum physics can exhibit a form of fractal dynamics in scarring of wave function, or where the destructive and constructive interference of a wave can become deformed into filigree. Quantum mechanics though abhors nonlinearity in actual wave functions. General relativity on the other hand is C^∞, so far as I can tell, and so completely smooth. Though there may not be actual fractal structure to spacetime, it is plausible that spacetime can exhibit topology changes that have correspondences with turbulent hydrodynamics. So if quantum mechanics is linear with a form of fractal structure this should exist in different Fourier modes for different spatial configurations. Yet this may only correspond to separable states off the entanglement or entropy surface of a coherent or condensate of states that have classical correspondence.

LC

Regarding stochastic spacetime defined in terms of stochastic metric spaces, there is no fundamental fractalness or foaminess involved that I can see.

Stochastic metric space and quantum mechanics

https://iopscience.iop.org/article/10.1088/2399-6528/aaa851/meta

From the stochastic metrical point of view, the distance between two points (the proton and electron positions) is given as a stochastic variable. When distances are given stochastically, their distribution must be Gaussian following the central limit theorem, variance of the distance possibly be proportional to distance.  

@philipthrift

[John Clark]

On Tue, Nov 26, 2019 at 9:03 PM Lawrence Crowell <goldenfield...@gmail.com> wrote:

> data on the arrival times of photons of different wavelengths from burstars indicates spacetime is incredibly smooth. It is smoother than the Planck scale by 1:50. There is no foam, graininess or discontinuous properties at all. Nottale scale relativity implies there is a fractal structure to spacetime that defines different properties at different scales. What is found empirically is nothing of the sort; spacetime has no preferred structure on any scale. It is smooth. 

If the Planck Length and the Planck Time have no physical significance then perhaps the reason a Quantum Theory of Gravity has been so hard to find is that such a theory does not exist. Perhaps we should try messing with Quantum Mechanics to make it fit in with General Relativity rather than the other way around.

John K Clark

[Philip Thrift]

That's in the direction of (I think)

Stochastic Metric Space and Quantum Mechanics

Yoshimasa Kurihara

(Submitted on 13 Dec 2016 (v1), last revised 22 Dec 2017 (this version, v5))

A new idea for the quantization of dynamic systems, as well as space time itself, using a stochastic metric is proposed. The quantum mechanics of a mass point is constructed on a space time manifold using a stochastic metric. A stochastic metric space is, in brief, a metric space whose metric tensor is given stochastically according to some appropriate distribution function. A mathematically consistent model of a space time manifold equipping a stochastic metric is proposed in this report. The quantum theory in the local Minkowski space can be recognized as a classical theory on the stochastic Lorentz-metric-space. A stochastic calculus on the space time manifold is performed using white noise functional analysis. A path-integral quantization is introduced as a stochastic integration of a function of the action integral, and it is shown that path-integrals on the stochastic metric space are mathematically well-defined for large variety of potential functions. The Newton--Nelson equation of motion can also be obtained from the Newtonian equation of motion on the stochastic metric space. It is also shown that the commutation relation required under the canonical quantization is consistent with the stochastic quantization introduced in this report.
The quantum effects of general relativity are also analyzed through natural use of the stochastic metrics. Some example of quantum effects on the universe is discussed.

Comments:	39 pages, 0 figures
Subjects:	General Relativity and Quantum Cosmology (gr-qc); Quantum Physics (quant-ph)
Journal reference:	J. Phys. Commun. 2 (2018) 035025
DOI:	10.1088/2399-6528/aaa851
Cite as:	arXiv:1612.04228 [gr-qc]
	(or arXiv:1612.04228v5 [gr-qc] for this version)

@philipthrift 

[Brent Meeker]

Or push the entropic theory of gravity, which might go well with the entanglement theory of spacetime.

Brent

[Bruno Marchal]

That seems more plausible than messing with quantum mechanics. The problem with the attempts to change the quantum theory is that it makes everything worst if we want to keep it as a good approximation. Sternberg (and plaza in this list) have shown rather convincingly that a slight “delinearisation” of QM makes the many universes even more real, as they not only can interfere, but also can interact (making both GR false, but also violating the laws of thelmrmodynamic. I doubt that we can change the quantum base of physics, and indeed, it becomes a necessity when we assume mechanism, meaning that we would need a non-mechanist theory of mind, also.

Bruno

Brent

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[Philip Thrift]

On Wednesday, December 4, 2019 at 5:04:20 AM UTC-6, Bruno Marchal wrote:

On 30 Nov 2019, at 00:40, 'Brent Meeker' via Everything List <everyth...@googlegroups.com> wrote:

On 11/29/2019 2:38 PM, John Clark wrote:

On Tue, Nov 26, 2019 at 9:03 PM Lawrence Crowell <goldenfield...@gmail.com> wrote:

> data on the arrival times of photons of different wavelengths from burstars indicates spacetime is incredibly smooth. It is smoother than the Planck scale by 1:50. There is no foam, graininess or discontinuous properties at all. Nottale scale relativity implies there is a fractal structure to spacetime that defines different properties at different scales. What is found empirically is nothing of the sort; spacetime has no preferred structure on any scale. It is smooth. 

If the Planck Length and the Planck Time have no physical significance then perhaps the reason a Quantum Theory of Gravity has been so hard to find is that such a theory does not exist. Perhaps we should try messing with Quantum Mechanics to make it fit in with General Relativity rather than the other way around.

Or push the entropic theory of gravity, which might go well with the entanglement theory of spacetime.

That seems more plausible than messing with quantum mechanics. The problem with the attempts to change the quantum theory is that it makes everything worst if we want to keep it as a good approximation. Sternberg (and plaza in this list) have shown rather convincingly that a slight “delinearisation” of QM makes the many universes even more real, as they not only can interfere, but also can interact (making both GR false, but also violating the laws of thelmrmodynamic. I doubt that we can change the quantum base of physics, and indeed, it becomes a necessity when we assume mechanism, meaning that we would need a non-mechanist theory of mind, also.

Bruno

An example of "entanglement theory of spacetime" is path integrals on stochastic metric spaces:

https://iopscience.iop.org/article/10.1088/2399-6528/aaa851

@philipthrift

[Bruno Marchal]

How is the stochastic distribution chosen, or just motivated? What is an entanglement in that theory? It seems nice to related an entanglement theory of space-time with path integral on some stochastic spaces, but it seems only to be a relation of consistency where I would hope for a relation of necessity.

Bruno

Bruno

@philipthrift

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[Philip Thrift]

On Thursday, December 5, 2019 at 7:12:35 AM UTC-6, Bruno Marchal wrote:

How is the stochastic distribution chosen, or just motivated? What is an entanglement in that theory? It seems nice to related an entanglement theory of space-time with path integral on some stochastic spaces, but it seems only to be a relation of consistency where I would hope for a relation of necessity.

Bruno

re: https://iopscience.iop.org/article/10.1088/2399-6528/aaa851/pdf

To utilize the SM-space for relativistic field theories, the stochastic metric should be introduced on a Minkowski manifold. The Minkowski manifold equipping the stochastic metric is referred to as the stochastic Lorentz metric space (SLM-space) hereafter. 

It is shown that the QM of a mass point are equivalent to its classical mechanics on the SLM-space. The path integration, quantum equation of motion, uncertainty relation and commutation relations were re-formulated on the SLM-space and shown to be consistent with standard definitions. In the formalism proposed in this study, QM is formulated based on the extremal entropy principle a priori before classical mechanics. If the path integration described in this work is more fundamental than the standard definition, the path integral is mathematically well-defined on the Gaussian white-noise measure space.

@philipthrift