Spin Foam models in Loop Quantum Gravity

In summary, Spin Foam models are a way of describing the dynamics of spacetime in Loop Quantum Gravity. They use a discrete approach, breaking spacetime into discrete "atoms" and using mathematical structures called spin networks to represent their interactions. This allows for a more detailed understanding of the quantum nature of spacetime and has potential implications for the unification of quantum mechanics and general relativity. However, there are still challenges and open questions in this field of research.
  • #1
asimov42
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Hi all,

I fairly basic question about spin foam models in loop quantum gravity. I just want to verify that spin foams represent effectively represent all of spacetime (in a quantum form), and that the idea is that general relativity can be obtained in the classical limit? Not sure if that's correct?
 
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  • #2
Also, what does is mean, roughly, for time to be absent in LQG theories - isn't time required to recover relativity? (I believe this is known as the "problem of time')
 
  • #3
Spin foams are like Feynman diagrams, which represent steps used to calculate a quantity called the "transition amplitude" that is used in normal quantum mechanics (ie. not quantum gravity) to calculate the probability of transitioning in time from state A to state B.

Regarding "time" in spin foams, Jonathan Engle says in his review "It is clear, therefore, that in quantum gravity one cannot interpret the Feynman path integral in terms of time evolution, as was done in (4). In fact, the interpretation is dierent. Instead, in the interpretation of the path integral, the time evolution map is replaced by a projector P onto [solutions of the Hamilton constraint]." https://arxiv.org/abs/1303.4636 (p9)

I think the hope is that general relativity can be obtained in the classical limit, but I don't think that has yet been shown. Nor whether the theory is a consistent quantum theory.
 
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Indeed the Hamiltonian constraint generates time gauge transformations and solving it is solving a gauge transformation equation.

Physical meaning to transition amplitudes and time evolution however can be obtained, when it comes to background independent scattering amplitudes for example.

There the idea is to study the boundary amplitude, namely a path integral over a finite space-time region, seen as a function of the boundary value of the field, peaked on a semi-classical state which, of course, includes the gravitational field itself. The usual meaning to spatital-temporal separation can be obtained from the state of the gravitational field on the boundary of the spacetime region considered.
 
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Can we say that the path integral over all spin foams that connect an input spin network I to an output spin network O is the probability amplitude PA(I,O) for I to be followed by O in a time sequence that emerges from the theory?
Can we say that the O with the highest P (PA squared in the usual sense) is the probable successor of I in a time sequence that emerges from the theory?
Can we say that this defines a time sequence in the classical limit?
If so, what is a good reference? I have been looking but everyone seems to keep as ambiguous as possible.
 
  • #6
julian said:
There the idea is to study the boundary amplitude, namely a path integral over a finite space-time region, seen as a function of the boundary value of the field, peaked on a semi-classical state which, of course, includes the gravitational field itself. The usual meaning to spatital-temporal separation can be obtained from the state of the gravitational field on the boundary of the spacetime region considered.
Is there a good reference on this?
 

1. What is a spin foam model in loop quantum gravity?

A spin foam model is a mathematical framework used to describe the dynamics of space and time at the quantum level. It is based on the principles of loop quantum gravity, which combines elements of general relativity and quantum mechanics. In this framework, space and time are viewed as discrete and granular, rather than continuous. Spin foams are used to represent the quantum states of space and time, and their interactions.

2. How are spin foam models different from other quantum gravity theories?

Spin foam models are different from other quantum gravity theories in that they are based on a discrete and granular view of space and time, rather than a continuous one. They also incorporate the principles of general relativity, which describe how gravity works on a large scale, and quantum mechanics, which describes the behavior of matter and energy on a small scale. This combination allows spin foam models to potentially reconcile the discrepancies between these two theories.

3. What are the main challenges in developing spin foam models?

One of the main challenges in developing spin foam models is the difficulty in reconciling the principles of general relativity and quantum mechanics. These two theories have been incredibly successful in their respective domains, but they are fundamentally different and have not yet been unified. Additionally, there is still much research to be done in understanding the dynamics of space and time at the quantum level, which is necessary for the development of spin foam models.

4. How are spin foam models tested and validated?

Spin foam models are primarily tested and validated through mathematical calculations and simulations. Scientists use these models to make predictions about the behavior of space and time at the quantum level, and then compare those predictions to experimental or observational data. If the predictions match the data, it provides evidence for the validity of the spin foam model. However, since these models are still in the development stage, there is currently limited experimental evidence to support them.

5. What are the potential implications of spin foam models in loop quantum gravity?

The potential implications of spin foam models in loop quantum gravity are vast. If confirmed, these models could provide a better understanding of the fundamental nature of space and time and potentially lead to a unified theory of physics. They could also have implications for our understanding of black holes, the origin of the universe, and the behavior of matter and energy at the smallest scales. However, further research and testing are needed to fully realize the potential implications of spin foam models in loop quantum gravity.

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