Unifying GR & QM with Noncommutative Geometry

In summary, the conversation revolves around a recently discovered article on noncommutative geometry and its role in the search for quantum gravity and superstring theory. The article proposes a new approach to unifying general relativity and quantum mechanics using noncommutative geometry. The model's generalized Einstein equation takes the form of an eigenvalue equation for the generalized Ricci operator, and all relevant operators in the quantum sector are random operators. The model is shown to accurately reproduce general relativity and quantum mechanics. The conversation also touches upon the role of groupoids in quantization, and the paper's conclusion that the theory is strongly "non-local" and Machian. The authors of the paper have ties to the Vatican and Warsaw, adding to the intrigue
  • #1
s3nn0c
43
0
I've just found that article about noncommutative model unifying GR & QM.

http://arxiv.org/abs/gr-qc/0504014

A few quotes:

Noncommutative geometry plays an increasingly important role in the present search for quantum gravity. It has also recently been recognized that it is a useful tool in superstring theory. In a series of papers, we have proposed our own approach to the unification of general relativity and quantum mechanics based on noncommutative geometry.

We show that the generalized Einstein equation of the model has the form of the eigenvalue equation for the generalized Ricci operator, and all relevant operators in the quantum sector of the model are random operators; we study their dynamics. We also show that the model correctly reproduces general relativity and the usual quantum mechanics.
 
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  • #2
The role of groupoids in quantisation is a important point :-)
 
  • #3
The big conclusion of this paper (futher elaborated here: http://arxiv.org/PS_cache/gr-qc/pdf/9806/9806011.pdf ) is that their theory is strongly "non-local", in other words, it naturally provides a basis for the EPR experiments which demonstrated that quantum entanglement can allow particles at a distance to communicate superluminally. It is also (?as a consequence?) strongly Machian. The investigators suspect a sub-Plank regime at which this operators and a spin foam like ambiguous micro-spacetime geometry of space.

I must admit that having a principle research in the Vatican, and two others in Warsaw (closely associated with the late Pope John Paul II), does raise an eyebrow or two, but it is an interesting theory.
 
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  • #4
ohwilleke said:
the EPR experiments which demonstrated that quantum entanglement can allow particles at a distance to communicate superluminally.

Did not either.
 

Related to Unifying GR & QM with Noncommutative Geometry

1. What is noncommutative geometry?

Noncommutative geometry is a branch of mathematics that studies spaces and their properties by using algebraic structures known as noncommutative algebras. In contrast to traditional geometry, where the commutative properties of multiplication are assumed, noncommutative geometry allows for noncommutative operations between elements.

2. What is the goal of unifying general relativity and quantum mechanics with noncommutative geometry?

The goal of unifying general relativity (GR) and quantum mechanics (QM) with noncommutative geometry is to create a framework that can accurately describe the behavior of the universe at both the macroscopic and microscopic levels. GR and QM are two fundamental theories of physics that have been successful in explaining different phenomena, but they are incompatible with each other. Noncommutative geometry offers a potential solution to this problem by providing a common mathematical language for both theories.

3. How does noncommutative geometry relate to GR and QM?

In noncommutative geometry, space-time is described as a noncommutative algebra of operators, rather than as a smooth manifold as in traditional geometry. This allows for a more flexible and general description of space-time, which is necessary for incorporating the principles of both GR and QM. Additionally, noncommutative geometry provides a way to combine the concepts of curvature and uncertainty, which are central to GR and QM, respectively.

4. What are some potential implications of unifying GR and QM with noncommutative geometry?

If successful, unifying GR and QM with noncommutative geometry could lead to a more complete understanding of the fundamental laws of physics. It could also potentially resolve some of the inconsistencies and limitations of both theories, such as the incompatibility of GR with the principles of quantum mechanics. Additionally, it could open up new avenues for research and technological advancements.

5. What are some challenges in unifying GR and QM with noncommutative geometry?

One of the main challenges is the complexity of the mathematics involved, as noncommutative geometry requires a deep understanding of advanced mathematical concepts. Additionally, there is currently no consensus on a definitive framework for unifying GR and QM with noncommutative geometry, so there is still much research and debate needed in this field. Furthermore, experimental evidence is needed to test and validate any proposed theories, which can be difficult to obtain at the scale required for studying fundamental physics.

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