Quantum Geometry and Schwarzschild Singularity?

In summary, the authors discuss the possibility that a quantum Einstein's equation can describe a process of space-time "leaping" between two regions of space. This process is possible using quantum evolution and would lead to the cessation of the classical boundary of space-time. There are implications for zero boundary constraints and the possible existence of multiple universes.
  • #1
Spin_Network
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In a recent paper Ashtekar and Bojowald:http://www.arxiv.org/abs/gr-qc/0509075
gave details (page's 25-26) of the backwards quantum evolution of a specific process of Space-time "leaping".

Quote from page 25: " For our quantum Einstein’s equation (55), this coefficient is given by p|τ − 2δ| +p|τ |. By inspection, it never vanishes. Therefore, the backward quantum evolution remains well defined and determines the wave function not only for τ > 0 but also in the new region
with τ ≤ 0.
In this precise sense, the classical black hole singularity can be traversed using quantum evolution and thus ceases to be a boundary of space-time."

Here is a few words from their end of paper discussion:" Results of the last two sections support a general scenario that has emerged from the analysis of singularities in quantum cosmology. It suggests that the classical singularity does not represent a final frontier; the physical space-time does not end there. In the Planck regime, quantum fluctuations do indeed become so strong that the classical description breaks down. The space-time continuum of classical general relativity is replaced by discrete quantum geometry which remains regular during the transition through what was a classical singularity. Certain similarities between the Kantowski-Sachs model analyzed here and a cosmological model which has been studied in detail [10] suggest that there would be a quantum bounce to another large classical region. If this is borne out by detailed numerical calculations, one would conclude that quantum geometry in the Planck regime serves as a bridge between two large classical regions. Space-time may be much larger than general relativity has had us believe."

So what are the consequences for zero boundary constraints?..do quantum waves transverse/emerge from below the Planck limit, and carry information of a much larger "inner-inverse", Quantum-Quantum/Planck Domain?

Are there muti-universe's contined within every single volume's of atoms?
 
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  • #2
There is a lot of activity on the Brane, String/M-Theory and Loop Quantum Wave arena's.

This beautiful thinker:http://physics.harvard.edu/randall.htm

has been tackling "observation" limits and Observer dependence for instance:
http://arxiv.org/abs/hep-th/0506053

for a number of years. A recent article by Her here:http://www.edge.org/3rd_culture/randall05/randall05_index.html

does not really give the details of the problem of Quantum"selective" Spacetime.

What appears to be detailed within Ashtekar and Bojowald's recent expose, is that the more you discrete Relativity, or specifically a first choice "spacetime", there is a threshold at or near the Planck limit, and as you cross this limit you enter a domain on a par with Randall's, your feet so to speak, are in two-dimensional space, but your observational frame remains 'fixed' into a three-dimensional spacetime.

So compacting along the Einstein Equational route, one starts to be reduced to a finite limit, one can allude that this is also an "observational" limit, whereby what I state here in posting #35 and 37:https://www.physicsforums.com/showthread.php?p=747712#post747712

is actually a quantisized fact of "observational-limit". The QM, or the specific Copenhagan Intepretation, needs to factor the above scientific papers into their intepretations. In Ashtekar's paper the quantum volume of a finite space, can be emerging from within a 'Quark Volume', its value is that of a Quantum Vacuum State, or specifically an Electro-Magnetic "flux".

What is really interesting is that the Vacuum Flux within Quantum Space/volume's, is identical to that of the Cosmological Vacuum!

The above papers are, without actually stating the obvious, saying that String Theories and Quantum Geometry, have Macro as well as Micro origins, when one emerges from below the Quantum "hidden" scale, and derive out into the extended spacetime of Cosmos Volume, you arrive at the same Vacuum Flux Singularity, and conversely if you Travel from a Macro domain, into the Quantum Field, you do not arrive at a boundary limit Singularity.

At a certain scale, you "hop" from 3-D spacetime to 2-D space-time without noticing any "observational" effects whatsoever?

There are implications of this that will go a long way to explain emerging Entropic order from a "perfect" Quantum Vacuum. The Classical boundery of spacetime the Universe, has an "observational" horizon, a boundary you cannot physically "see", as it extends along 3-D spacetime, a Singularity inside this boundary, can be breached and transversed.

If you choose to approach a Blackhole Singularity, you are Cosmologically Compacting and Transversing in a "MACRO" to "MICRO" format, 3-D to 2-D converging at the Event Horizon at a finite discrete limit, you would emerge, into another "Universe", and whatsmore you would pop into existence, from a Quark-Soup, that may or may not be in a bowl, standing/cooling on the back of a Leatherback Turtle, who works 9 till 5 in a local chippie ?:rolleyes:

I think not :bugeye:
 
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  • #3
It may be that the rush of recent papers are in direct competition with the upcoming Loop Conference, trying to 'invoke' a "next" move stimilation?..or just getting their own back on the recent string conference, that coincedently had a large number of LQG papers just prior to the conference opening date!
 

1. What is quantum geometry?

Quantum geometry is a mathematical framework that combines principles from quantum mechanics and general relativity to describe the behavior of space and time at very small scales. It is a proposed theory that seeks to unify the laws of the microscopic world (quantum mechanics) and the laws of the macroscopic world (general relativity).

2. How does quantum geometry relate to the Schwarzschild singularity?

The Schwarzschild singularity is a theoretical point of infinite density and zero volume at the center of a black hole, predicted by general relativity. Quantum geometry attempts to resolve this singularity by describing space and time as discrete, rather than continuous, entities. This means that at very small scales, the fabric of space-time is made up of individual building blocks, which can prevent the formation of singularities.

3. Can quantum geometry explain the behavior of black holes?

Quantum geometry is still a developing theory and its application to black holes is an area of active research. While it offers some potential explanations for the behavior of black holes, such as the avoidance of singularities, it is not yet a complete or widely accepted theory.

4. Are there any observable effects of quantum geometry on our everyday lives?

At this point, there is no evidence of observable effects of quantum geometry on our everyday lives. The principles of quantum geometry are only applicable at extremely small scales, such as those found in the quantum realm. In our macroscopic world, the effects of quantum geometry are likely to be negligible.

5. What are some potential applications of quantum geometry?

If proven to be a valid theory, quantum geometry could have significant implications for our understanding of the universe and the laws of physics. It could potentially provide a unified theory of all the forces of nature, including gravity. It could also have practical applications in fields such as quantum computing and materials science.

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