Do we need stochasticity in a discrete spacetime?

In summary, the conversation discusses the possibility of spacetime being discrete and its implications on the probability distributions and transitions of particles. It is noted that current theories are based on a continuum and concepts like probability distribution and trajectory may not apply in a discrete model.
  • #1
Ali Lavasani
54
1
Suppose that the spacetime is discrete, with only certain positions being possible for any particle. In this case, the probability distributions of particles have nonzero values at the points on which the wavefunction is defined. Do we need randomness in the transitions of particles in such a spacetime?

My reasoning is, in a discrete space-time there is no continuous function that would allow to transport the distribution of P into the distribution P'. Basically if any point of the space has a deterministic trajectory and is mapped to another certain point, the distribution cannot change. We don't have this problem in a continuum, but what about a discrete space?
 
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  • #2
Ali Lavasani said:
Suppose that the spacetime is discrete, with only certain positions being possible for any particle. In this case, the probability distributions of particles have nonzero values at the points on which the wavefunction is defined. Do we need randomness in the transitions of particles in such a spacetime?

This question can't be answered because nobody has an actual theory in which spacetime is discrete. All of our theories are based on spacetime as a continuum.

What we do know is that, in a discrete model, concepts like "probability distribution" are not well-defined; a distribution needs a continuous space. In fact even the concept of a "trajectory" doesn't make sense, since it implies a continuous curve. So even your framing of the question makes implicit assumptions that don't apply to the scenario you are proposing.
 
  • #3
Ali Lavasani said:
in a discrete space-time there is no continuous function

Of course not. (Note that the phrase quoted is true without any other qualifications; you could have just left out the rest of the sentence.) A continuous function requires a continuous domain and range. But this doesn't make your reasoning correct; it makes it inapplicable.
 

1. What is stochasticity in a discrete spacetime?

Stochasticity refers to the random or probabilistic nature of a system. In the context of discrete spacetime, it means that the location and behavior of particles or objects are not predetermined and can change based on random events or probabilities.

2. Why is stochasticity important in a discrete spacetime?

Stochasticity is important in a discrete spacetime because it allows for the possibility of unpredictable events and outcomes. This is crucial in understanding the behavior of complex systems and can provide insights into the nature of the universe.

3. How does stochasticity affect our understanding of the laws of physics?

Stochasticity challenges our traditional understanding of the laws of physics, which are based on deterministic principles. It suggests that there may be inherent randomness in the universe and that our understanding of physical laws may need to be revised to account for this.

4. Can we have a discrete spacetime without stochasticity?

It is possible to have a discrete spacetime without stochasticity, but it would require a highly ordered and predictable system. This is not consistent with our current understanding of the universe, which is characterized by randomness and uncertainty at the quantum level.

5. How do scientists study stochasticity in a discrete spacetime?

Scientists study stochasticity in a discrete spacetime through mathematical models and simulations. They also use experimental data and observations to test these models and gain a better understanding of how stochasticity operates in the universe.

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