What is derivation? How does derivation differe from an experiment or theory?

derivation-- proving something that has already been proved

experiment---- not a full proof derivation ( may need many trials)

theory --- has been proved and takem as a given


Derivation is a process in which you obtain a result or conclusion by reasoning or logical deduction. It involves starting with a set of known facts, principles, or assumptions and using logical steps to logically infer or deduce new information or conclusions from them. It is commonly used in mathematics, physics, and other scientific disciplines as a way to obtain new knowledge or derive formulas and equations from existing principles or laws.

Derivation is different from an experiment or a theory in several ways:

1. Experiment: An experiment is a procedure carried out with the goal of testing a hypothesis or verifying a specific prediction. It involves interacting with the real world by making observations, collecting data, and conducting experiments under controlled conditions. In contrast, derivation is a purely deductive process that uses existing knowledge and logical reasoning to derive new information or conclusions without the need for empirical observations or experiments.

2. Theory: A theory is a well-substantiated explanation of some aspect of the natural world, backed by a large body of evidence and used to make predictions about future observations or experiments. Theories are typically built upon a combination of experimental evidence, observational data, and logical reasoning. While derivation may rely on established theories or laws as starting points, it focuses more on the logical deduction of new information or conclusions from those established principles, rather than aiming to develop a comprehensive explanation of a phenomenon.

3. Empirical vs. deductive: Both experiments and theories are based on empirical evidence obtained through observation and experimentation. They deal with the real world, making predictions that can be tested and verified. In contrast, derivation is a deductive process that relies on logical reasoning and existing knowledge to derive new conclusions. It is more focused on logical consistency and mathematical rigor rather than direct empirical verification.

In summary, derivation involves the logical deduction of new information or conclusions from existing knowledge, while experiments and theories are more concerned with empirical testing and comprehensive explanations, respectively.