Connection between General Relativity & Chaos Theory?

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Discussion Overview

The discussion explores the potential connections between General Relativity and Chaos Theory, particularly focusing on the implications of causality and the influence of events across distances in the context of relativistic effects. Participants engage with concepts of causation, the role of light speed in these interactions, and the nature of chaos within a relativistic framework.

Discussion Character

  • Exploratory
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant questions whether event A can have a potential effect on event B if light cannot travel between them in the time frame of their occurrence, seeking guidance on the topic.
  • Another participant asserts that if "have a potential on" means "causally affect," then event A can only affect event B if light can travel between them, referencing the principles of relativity.
  • Some participants clarify that if light cannot reach event B from event A in time, then A cannot affect B, but events occurring earlier at A could potentially influence B.
  • A participant expresses confusion about the concept of "relativistic chaos" and seeks a clearer understanding of how chaos theory might relate to relativistic principles.
  • One participant proposes that relativity modifies chaos theory by altering the set of events that can influence the future of an object, emphasizing the importance of the past light cone in this context.

Areas of Agreement / Disagreement

Participants generally agree on the principle that causal effects cannot travel faster than light, but there is uncertainty regarding the specific relationship between General Relativity and Chaos Theory, with some participants expressing confusion and seeking clarification.

Contextual Notes

Participants note the complexity of defining causality and the implications of relativistic effects on chaos theory, indicating that the discussion may depend on specific definitions and assumptions about causation and event influence.

MyoPhilosopher
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TL;DR
Would chaos theory (of two events) only be in the realm of possibility if light could travel from locations of both events in the given delta time.
I am very new to such ideas but was wondering if there is any connection to what I am asking.
Taking two events, let's say at opposite ends of the globe. Would even A, only have a potential on event B, if light could travel between these event in the given time frame of these event occurring. Would other ideas play a role?
If I am totally wrong, I would appreciate any guidance on learning more on the topics. This was just an idea that kind of lingered in my head as I have started reading on relativity.
Looking forward to improving my understanding.
 
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MyoPhilosopher said:
Would even A, only have a potential on event B, if light could travel between these event in the given time frame of these event occurring

If "have a potential on" means "causally affect", then yes; relativity says that causal effects can't travel faster than light.

I'm not sure why you refer to chaos theory specifically; what I said above about relativity applies to any causal effect.
 
I'm not entirely clear on what you are asking. If light would not have time (even on the shortest possible route) to travel from A to B then whatever happened at A cannot affect B. Events further back in time at the same place (however that's defined) as A could affect B.
 
Ibix said:
I'm not entirely clear on what you are asking. If light would not have time (even on the shortest possible route) to travel from A to B then whatever happened at A cannot affect B. Events further back in time at the same place (however that's defined) as A could affect B.
PeterDonis said:
If "have a potential on" means "causally affect", then yes; relativity says that causal effects can't travel faster than light.

I'm not sure why you refer to chaos theory specifically; what I said above about relativity applies to any causal effect.
To clarify my confusion: my initial thought was that there must be relativistic chaos. However I was struggling to conceptualize it past my above example. Would there be a better way of thinking about relativistic chaos for someone very new to the ideas?
 
The only change relativity makes to chaos theory (or, more precisely, its application to the real world) is that it changes which set of events you need to know about to predict the future of an object. In non-relativistic physics, everything happening simultaneously with an event can, in principle, affect it. In relativity, everything inside its past light cone can affect it. You still can't know all of that with arbitrary precision.
 
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