Quantizing Geometry or Geometrizing the Quantum?

In summary: I think the idea has a lot of potential, but it's still in its early days. There's a lot of discussion to be had, and I'm looking forward to seeing where it goes.In summary, Koch discusses a possible approach to quantum gravity that starts with the proposition that geometry is fundamental, and quantum mechanics is emergent. There is a lot of discussion to be had on this idea, but it has a lot of potential.
  • #1
inflector
344
2
From the "Intuitive content of Loop Gravity--Rovelli's program" thread:
MTd2 said:
http://arxiv.org/abs/1004.2879

Quantizing Geometry or Geometrizing the Quantum?

Bejamin Koch
(Submitted on 16 Apr 2010)
The unsatisfactory status of the search for a consistent and predictive quantization of gravity is taken as motivation to study the question whether geometrical laws could be more fundamental than quantization procedures. In such an approach the quantum mechanical laws should emerge from the geometrical theory. A toy model that incorporates the idea is presented and its necessary formulation in configuration space is emphasized.

From the paper:
Given the problems in applying the laws of quantum mechanics to the geometry of space-time we want to ask the following question:
“Could it be that (classical) geometry is more fundamental than the rules of quantization?”

I haven't seen any discussion of this paper here or the approach: starting with the proposition that geometry is fundamental with quantum mechanics being emergent.

Koch does show how others have proposed emergent quantum mechanics:
The idea that quantum mechanics might not be fundamental but rather emerge from an underlying classical system has been proposed in various ways.

He then goes on to list papers by many other physicists who have proposed an emergent quantum mechanics.

How seriously is this idea being taken within the quantum gravity community? Does anyone know of any other papers that are approaching quantum gravity in this way?
 
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  • #2
Has anyone (besides MTd2 obviously) read the paper? What did you think of it?
 
  • #3
Well, t'Hooft made a proposal of QM based on a classical dissipative system. But there are problems in coming up with a QFT version, but I am not sure.
 
  • #4
No one else finds the paper interesting?
 
  • #5
inflector said:
No one else finds the paper interesting?
I do. :smile:
 
  • #6
Kevin Knuth 27 Sept.2010:
In the last decade, our fundamental understanding of probability theory has led to a Bayesian revolution. In addition, we have come to recognize that the foundations go far deeper and that Cox's approach of generalizing a Boolean algebra to a probability calculus is the first specific example of the more fundamental idea of assigning valuations to partially-ordered sets. By considering this as a natural way to introduce quantification to the more fundamental notion of ordering, one obtains an entirely new way of deriving physical laws. I will introduce this new way of thinking by demonstrating how one can quantify partially-ordered sets and, in the process, derive physical laws. The implication is that physical law does not reflect the order in the universe, instead it is derived from the order imposed by our description of the universe. Information physics, which is based on understanding the ways in which we both quantify and process information about the world around us, is a fundamentally new approach to science.
http://arxiv.org/abs/1009.5161

Koch's geometry may be derived from the notion of ordering of the quantum events. This ordering creates the space-time.
Do you think is it possible ?
 
  • #9
inflector said:
How seriously is this idea being taken within the quantum gravity community? Does anyone know of any other papers that are approaching quantum gravity in this way?

check out this thread, it debates Torsten's paper with himself being involved


https://www.physicsforums.com/showthread.php?t=412582


http://arxiv.org/abs/1006.2230
On the geometrization of matter by exotic smoothness
Torsten Asselmeyer-Maluga, Helge Rose
 
  • #11
Thanks qsa, those were interesting threads.
 

1. What is the concept of quantizing geometry?

Quantizing geometry is the process of applying the principles of quantum mechanics to the study of geometry. It involves representing geometric objects and their properties using mathematical operators and equations, similar to how particles and their interactions are described in quantum mechanics. This approach allows for a deeper understanding of the fundamental nature of space and how it behaves at a microscopic level.

2. How does quantizing geometry relate to the quantum world?

Quantizing geometry is a way to bridge the gap between classical geometry and quantum mechanics. By quantizing geometry, we can better understand the underlying structure of space and how it interacts with particles and energy on a quantum level. It also helps us to develop a more unified theory of physics that can explain both the macroscopic and microscopic worlds.

3. What are some applications of quantizing geometry?

Quantizing geometry has various applications in theoretical physics, including string theory, loop quantum gravity, and quantum field theory. It also has potential applications in quantum computing, as it provides a framework for understanding how space can be manipulated and used to store information.

4. How does geometrizing the quantum help in understanding the universe?

Geometrizing the quantum helps us to better understand the fundamental nature of the universe by providing a mathematical framework that can describe both the macroscopic and microscopic worlds. It allows us to study the behavior of space at a microscopic level and how it interacts with matter and energy, providing insights into the origins and structure of the universe.

5. What are some challenges in quantizing geometry?

One of the main challenges in quantizing geometry is reconciling the principles of quantum mechanics with those of classical geometry. This requires developing new mathematical tools and techniques that can accurately describe the behavior of space at a quantum level. Additionally, there is still much to be explored and understood in this field, and further research and experimentation are needed to fully apply and utilize the concept of quantizing geometry.

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