Why is this Pilot-wave model on a discrete spacetime stochastic?

In summary, the paper discusses a pilot-wave model on a discrete spacetime lattice, which introduces a Markovian process to describe the motion of quantum particles. It also mentions the necessity of stochasticity in a Bohmian model when the space and time are discrete, and the potential for multiple ways to define a deterministic Bohmian theory on a discrete spacetime. The reason for invoking stochasticity is to fulfill the requirement of transitions from every state into a single subsequent state when transforming a discrete distribution. It is not necessary for a Bohmian model to be stochastic in a discrete spacetime, but there may be more than one way to define a deterministic theory in this scenario.
  • #1
Ali Lavasani
54
1
Look at the paper in the link below:
https://link.springer.com/content/pdf/10.1007/s10701-016-0026-7.pdf
It introduces a pilot-wave model on a discrete spacetime lattice. However, the pilot-wave model is not deterministic; the motion of quantum particles is described by a |Ψ|^2-distributed Markov chain. It mentions that "Introducing Markovian process is crucial, if time is discretized" and "The discreteness is by itself responsible for the randomness of the motion on the basic level".

My question is, WHY must a Bohmian model be stochastic if the space and time are discrete, in other words, what happens if one tries to simply generalize the commonplace deterministic Bohmian mechanics to the case in which the spacetime is a discrete lattice?
 
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  • #2
Bohmian mechanics certainly does not necessarily need to be stochastic when space and time are discrete. But if you want it to be deterministic, then there is more than one way to do it, so the theory is not unique.
 
  • #3
This is another thing they have mentioned:

The transformation of a discrete distribution|t0|^2, e.g. at the slits, into the discrete distribution|t|^2, e.g. far from the slits, cannot be made in a non-stochastic manner, as it would require transitions from every (initial or intermediate) state into a single subsequent state."

Of course there might be several ways to define a deterministic Bohmian theory on a discrete spacetime, but what are these ways? My question was, why we would fail if we just repeat what we did in the continuous spacetime in the discrete one, without any change? What's the reason they have invoked stochasticity, what requirement has it fulfilled?
 

FAQ: Why is this Pilot-wave model on a discrete spacetime stochastic?

1. Why is the pilot-wave model necessary on a discrete spacetime?

The pilot-wave model is necessary on a discrete spacetime because it provides a way to explain the behavior of particles at the quantum level. In this model, particles are guided by a wave that determines their motion, rather than being subject to random and unpredictable behavior as in traditional quantum mechanics.

2. What is the significance of having a stochastic aspect in the pilot-wave model?

The stochastic aspect of the pilot-wave model allows for randomness in the motion of particles, which is a fundamental aspect of quantum mechanics. This stochasticity is essential for explaining certain phenomena, such as the double-slit experiment, where particles exhibit both wave-like and particle-like behavior.

3. How does the pilot-wave model on a discrete spacetime differ from other interpretations of quantum mechanics?

The pilot-wave model on a discrete spacetime differs from other interpretations of quantum mechanics in that it combines elements of both classical and quantum mechanics. It maintains a deterministic framework, similar to classical mechanics, while also incorporating the probabilistic nature of quantum mechanics.

4. What evidence supports the use of a discrete spacetime in the pilot-wave model?

There is currently no direct evidence for a discrete spacetime, but it is a common assumption in many theories that seek to reconcile quantum mechanics with general relativity. Additionally, the pilot-wave model has been successful in predicting and explaining various quantum phenomena, providing support for its use on a discrete spacetime.

5. Are there any limitations or criticisms of the pilot-wave model on a discrete spacetime?

One limitation of the pilot-wave model on a discrete spacetime is that it is not yet a complete theory and cannot fully explain all quantum phenomena. Additionally, some criticisms of the model include its complexity and the lack of experimental evidence for a discrete spacetime. However, ongoing research and developments in the field may address these limitations in the future.

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