von Claes Johnson
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Questioning Relativity 16: Definition vs Axiom, January 27, 2012
How can we know if a theory is a physical theory about some real physics or a mathematical theory which does not say anything about physical reality?
Easy enough: Look at the fundamental postulates of the theory and check if they connect to real physics or not. If there is no physics there, then there is no physics anywhere in the theory.
A postulate can take one of the following two forms:
1. A definition is empty of content and only prescribes how to use certain words. A definition is true by its construction, as long as it is not contradictory. Example: There are 100 centimeters on a meter.
2. An axiom makes a statement about the components of the theory, which is not empty of content. Example from Euclidean geometry: Through two distinct points there is a unique straight line. If point and straight line are given a physical meaning, e.g. as single dots and collection of dots drawn by a ruler on a blackboard, then this axiom makes a statement about physical reality: Given two distinct dots it is possible to draw a unique line through the points by the ruler.
This is the distinction made in logic between analytic statements (true by definition or tautologies) and synthetic statements about reality which may be true or false depending on reality.
Let us subject Newtonian mechanics and Einstein’s theories of relativity to this test:
Siehe auch vom Autor in diesem Blog:
- 19. Januar 2014