Exploring Non-Local Dynamics in Quantum Mechanics and Spacetime Manifold

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In summary, the conversation discusses the mathematical formulation of non-local dynamics in quantum and the spacetime manifold. It mentions non-local terms in the hamiltonian and the need for a connecting function between operators. The concept of quantum non-locality is also brought up, specifically in the context of Bohm Implicate Order where the entire universe is contained in every small part. The conversation ends with a question about other theories that can handle quantum non-local dynamics.
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riezer
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Hi,

What could possibly be the mathematical formulation of non-local dynamics in quantum and the spacetime manifold?
 
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For example, non-relativistic quantum electrodynamics--the kind usually taken as the starting point for theoretical developments in condensed matter physics... this contains non-local terms in the hamiltonian wherein creation and annihilation operators at different points in space multiply each other.

In any local action you have operators all evaluated at the same spacetime point (and integrated over that spacetime location), but if the operators were not evaluate at the same point the theory would not be non-local... normally one would need some kind of function connecting the operators (all spacetime points being integrate over), e.g., the coulomb potential in condensed matter physics
 
  • #3
olgranpappy said:
For example, non-relativistic quantum electrodynamics--the kind usually taken as the starting point for theoretical developments in condensed matter physics... this contains non-local terms in the hamiltonian wherein creation and annihilation operators at different points in space multiply each other.

In any local action you have operators all evaluated at the same spacetime point (and integrated over that spacetime location), but if the operators were not evaluate at the same point the theory would not be non-local... normally one would need some kind of function connecting the operators (all spacetime points being integrate over), e.g., the coulomb potential in condensed matter physics

I'm talking about quantum non-locality and how its dynamics can possibly occur. In Bohm Implicate order. Non-locality is the fundamental aspect where every thing is part of everything just like a holographic image containing the entire object even in tiny nanometer size of it. Similarly in Bohm Implicate Order the entire universe (or at least section) of is contained in every small part of the Implicate Order. It is only when it is exfolded as Explicate Order that the spacetime manifold is created and physical distance is artificially constructed.

Besides Bohm Implicate Order. What other theories can handle quantum non-local dynamics?
 

1. What is non-local dynamics in quantum mechanics and spacetime manifold?

Non-local dynamics in quantum mechanics and spacetime manifold refers to the study of the behavior and interactions of quantum particles at a distance, without any direct physical connection or exchange of information between them. It also involves the examination of the structure and properties of the underlying spacetime manifold that allows for these non-local interactions to occur.

2. How is non-locality different from classical mechanics?

In classical mechanics, all physical interactions are local, meaning that they occur at a specific point in space and time. However, in quantum mechanics and spacetime manifold, particles can exhibit non-local interactions, meaning that they can influence each other's behavior without being in direct contact or exchanging information.

3. What are the implications of non-local dynamics in quantum mechanics?

The existence of non-local dynamics in quantum mechanics challenges our understanding of causality and the concept of locality in the universe. It also has implications for the development of quantum technologies, such as quantum communication and computing, as well as our understanding of the fundamental laws of physics.

4. How do scientists study and explore non-local dynamics in quantum mechanics and spacetime manifold?

Scientists use a combination of theoretical and experimental methods to study and explore non-local dynamics in quantum mechanics and spacetime manifold. This includes mathematical models, computer simulations, and experiments using advanced technologies, such as quantum entanglement and superposition.

5. What are some real-world applications of non-local dynamics in quantum mechanics?

Non-local dynamics in quantum mechanics has potential applications in quantum communication and cryptography, where the non-local behavior of particles can be harnessed for secure communication. It also has implications for the development of quantum computers, which could perform certain calculations much faster than classical computers by utilizing non-local interactions between particles.

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