Question

What is meant by self consistency ? can you give any real life example or example from physics to explain self consistency ?

Answer 1

If a theory is self-consistent, It implies that the theories must not produce contradictions or anomalies.

Firstly if we treat a physical theory to be self-consistent simply because otherwise, it stops making sense. Here is an example of a set of rules that is not self-consistent:

1. The sky is red.

2. The sky is blue.

Well, that does not make sense. Self-consistency just means that there are no such rules that contradict each other.

What physics tries to do

Physics tries to find such rules that describe what we see in nature. It tries to see that if these rules are self-consistent and consistent with the experiment.

Because a theory is an explanation of observations. A theory which is inconsistent with past observations is invalid. If it produces inconsistent predictions of observations, it does not serve a purpose.

For example, quantum mechanics is initially found to be inconsistent because intermediate states involve superpositions of inconsistent states. However, with the development of quantum physics, this was found to be false because what quantum physics does is to provide probability distributions and not specific events. So long as the probability distributions are internally consistent everything is fine.

Reference https://www.physicsforums.com/threads/does-a-physical-theory-need-to-be-self-consistent.118502/