Coming back to the subject, I think that providing mathematical definitions for physical entities is the real problem. All physical quantities should be physically defined. Then the definitions will be simple and understandable. And the end result, I think, will be a 'real physical world' explained fully in unambiguous terms.

However, the most fundamental terms 'energy' and 'force' have no physical definitions. These are defined on the basis of Newton's laws of motion, which are mathematical. Newton, I think, considered his laws to be primarily mathematical. That may be the reason why he named the book as 'principia mathematica'.

The laws of motion, though mathematical, can be used for physical systems. But the physical system should be 'physically' defined before we use the laws. But, newton's laws are erroneously (in my opinion) used as physical laws, and the definitions turned out to be mathematical. So I think the correction should start from there.

Last edited by finiter; 08/31/11 11:19 AM.