Logic is indeed not empirical in the sense that it is not derived from or dependent on empirical observations. Logic is a formal system of reasoning and inference that is based on principles of valid reasoning, such as the rules of deduction and inference. It provides a framework for constructing valid arguments and drawing conclusions based on premises.
Quantum theory, on the other hand, is a mathematical framework that describes the behavior of quantum systems and their interactions. It provides a set of mathematical equations and rules that govern the probabilities of different outcomes in quantum experiments.
The consequences of logic not being empirical for quantum theory are primarily related to the nature of the relationship between logic and empirical observations in the context of quantum phenomena. While logic itself is not empirical, it is often used to reason about and interpret empirical observations. In the case of quantum theory, logic is used to construct arguments and interpretations based on the mathematical formalism of quantum mechanics.
One consequence is that the interpretation of quantum theory relies on logical reasoning rather than direct empirical evidence. There are various interpretations of quantum mechanics, such as the Copenhagen interpretation, the many-worlds interpretation, and others, which attempt to make sense of the mathematical formalism and provide explanations for the observed phenomena. These interpretations often involve philosophical and conceptual considerations, using logical reasoning to interpret the empirical results.
Another consequence is that logical consistency and coherence are important criteria for evaluating and refining theories in the context of quantum physics. The mathematical formalism of quantum mechanics is subject to logical analysis and consistency checks. For example, contradictions or logical inconsistencies within a proposed interpretation would raise concerns about its validity.
It's worth noting that while logic is not empirical, the predictions and outcomes of quantum theory can be empirically tested and verified through experiments. The empirical verification of these predictions is crucial for confirming the validity of the theory and its mathematical formalism. Empirical observations provide the necessary input for reasoning and drawing logical conclusions within the framework of quantum theory.
In summary, while logic is not empirical, it plays a crucial role in interpreting and reasoning about the empirical observations within the framework of quantum theory. Logical consistency is important for evaluating interpretations, and empirical verification is necessary to test the predictions of the theory.