# Continuity/Locality and Discreteness/Nonlocality

• cryptist
In summary, the conversation discusses the relationship between continuity and locality, as well as discreteness and nonlocality in space time. The idea that continuous space time allows for the principle of locality and discrete space time leads to nonlocality is explored. The possibility of a relationship between these concepts is also mentioned, with reference to nonrelativistic quantum mechanics and physical models based on cellular automata.
cryptist
Is there a relationship between Continuity and Locality? or between Discreteness and Nonlocality?

For example can we say that, if space time is continuous then, principle of locality must hold? Similarly, can one say discreteness of spacetime leads to nonlocality?

I don't know why, but I feel like there is a relationship between these. Can anyone inform me about these issues?

## 1. What is the difference between continuity and discreteness?

Continuity refers to the smooth and uninterrupted nature of a system, where all points in the system are connected without any breaks. Discreteness, on the other hand, refers to the existence of distinct, separate elements or values within a system. In other words, continuity is about the flow of a system, while discreteness is about the individual components within that system.

## 2. How does locality relate to continuity and discreteness?

Locality refers to the idea that events or interactions within a system are influenced only by nearby events or interactions. In other words, there is a limit to the range of influence within a system. Locality is closely related to continuity, as the smooth and uninterrupted nature of a system is necessary for locality to exist. Discreteness, on the other hand, can exist in both local and non-local systems.

## 3. What is nonlocality and how does it differ from discreteness?

Nonlocality refers to the idea that events or interactions within a system can be influenced by events or interactions that are not nearby, or even outside of the system. This is in contrast to locality, where there is a limit to the range of influence. While discreteness is about the existence of distinct elements within a system, nonlocality is about the relationship between those elements.

## 4. How do continuity and discreteness impact our understanding of the natural world?

The concepts of continuity and discreteness are fundamental to our understanding of the natural world. Many physical phenomena can be described using continuous or discrete models, and understanding the appropriate model is crucial for making accurate predictions and interpretations. Additionally, the presence or absence of locality and nonlocality can greatly impact our understanding of how systems behave and interact.

## 5. Can a system be both continuous and discrete?

Yes, a system can exhibit both continuity and discreteness. This is often the case in the natural world, where there may be a continuous flow of energy or matter, but it is made up of discrete particles or events. For example, water flowing in a river can be described as a continuous system, but it is made up of individual molecules that are discrete. Additionally, quantum mechanics has shown that particles can exhibit both wave-like and particle-like behavior, blurring the lines between continuity and discreteness.

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