From quantum theory to stochatic equations

In summary, there is a connection between quantum physics and stochastic maths, where the x and p operators are treated as satisfying stochastic equations and the Dx and Dp are considered as "noise". It is possible to treat the uncertainty in quantum physics as chaos. There are books written about this topic and it is believed that combining stochastic maths with cellular automata can explain many phenomena in physics, such as transfer processes and wave propagation. This is known as the "analytic continuation of the Schrödinger equation" and involves changing t to it. This change leads to the stochastic path integral and Einstein's equation, and has also been discovered in the field of stock options. However, the mathematical implications of this change are not trivial.
  • #1
eljose79
1,518
1
cna we consider quantum physics as stochastic maths..being the x and p operator treated as if they satisfied stochastic equations..and treatign the Dx and Dp as "noise"..in fact could be the uncertaninty in quantum physics be treated as if it was chaos?-..
 
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  • #2
Is this real ? (the connection between quantum physics and stochastic maths)
Has someone written any books about it ?
Because I think stochastic maths combined with cellular automata is the future...in physics...they can explain a lot of things...
For example...transfer processes (water in foam...diffusion...) are explained very well using polistochastic processes...and this looks like wave propagation...
THE FUTURE IS THIS...
 
  • #3
the technical naming for it runs under the line of "analytic continuation of the Shroedinger equation". It amounts to change t--> i t. Under this change, Feynman path integral becomes Stocastic path integral, and Schroedinger Equation becomes Einstein equation (heat diffusion, brownian movement and all that). Also it has been discovered independently by economists, in the field of stock options.

But as you can imagine, the change is not trivial from a mathematical point of view.
 

FAQ: From quantum theory to stochatic equations

1. What is quantum theory?

Quantum theory is a branch of physics that explains the behavior of particles at the atomic and subatomic level. It is based on the idea that particles can exist in multiple states or locations at the same time and can only be described through probabilities.

2. How does quantum theory relate to stochastic equations?

Quantum theory and stochastic equations both deal with the concept of randomness and probability. Stochastic equations use mathematical models to describe the behavior of systems that are influenced by random variables, which is similar to how quantum theory describes the behavior of particles.

3. What are some real-world applications of quantum theory and stochastic equations?

Quantum theory has led to advancements in technologies such as computers, lasers, and medical imaging. Stochastic equations are used in fields such as finance, biology, and engineering to model complex systems and make predictions.

4. How do quantum theory and stochastic equations challenge our traditional understanding of physics?

Quantum theory and stochastic equations have introduced concepts that are counterintuitive and go against our classical understanding of deterministic systems. For example, quantum theory suggests that particles can be in multiple states at once, while stochastic equations show that seemingly random events can be described through mathematical models.

5. What are some current areas of research in the field of "From quantum theory to stochatic equations"?

Current research in this field includes exploring the connections between quantum theory and stochastic equations, developing new mathematical models to describe complex systems, and applying these theories to practical problems in fields such as finance, biology, and artificial intelligence.

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