Why It Is so Difficult to Discuss with Physicists

My experience as a mathematician is that discussing some aspect of physics with a physicist many times leads into an abyss of confusion. A root cause is that the distinction between definition and physical fact can be unclear to a physicist with inspiration from Einstein who was a master of double-speak using this confusion to win any argument. 

For a both a mathematician and man in the street the nature of a definition is clear as a specification of how to use language. A definition has no truth value as concerns some factual circumstance. To define a meter to be equal to 100 centimeters is just a clarification of a short hand notation. To make an experiment to test the physical validity of this definition would not make any sense. 

But to a physicist there are two fundamental laws, which act as definitions but are viewed to be physical facts: (i) constancy of the speed of light and (ii) $E=mc^2$ , both directly connected to Einstein as master of double-speak. The units of length, time, energy and mass are today defined so that (i) and (ii) are upheld no matter what the Creator of World could have to say. To question (i) or (ii) would be met by a physicist only as a sign of ignorance about physical facts: The speed of light is constant, and energy is equal to mass.  

But does it matter if (i) and (ii) are definitions or physical facts or maybe both at the same time? Yes, such an ambiguity would not make a mathematician feel well at ease, and probably not a man in the street either. Only a physicist inspired by Einstein would welcome the confusion as a way to stay on top of the discussion.

What can then be the pitfall to confuse definition and physical fact? Well this would invite to view (i) and (ii) as physical fact which cannot be wrong. It gives the physicist rock solid knowledge about the physics of the world which cannot be contradicted by any observation of the physics of the world. It gives the physicist a very strong position when asking for more taxpayer funding of fundamental physics. In particular massive funding has gone into experimental investigation of (i) and (ii) always coming out as full confirmation and always asking for an even more precise confirmation. But it could also lead astray in navigation and misdirect research on energy production. 

In any case, the mathematician and man in the street would clearly understand that the meter is defined in terms of a preset value of the speed of light and of unit of time in terms of a certain atomic clock, and mass is defined as  $\frac{hf}{c^2}$ in terms of electromagnetic energy $hf$ with preset value of Planck's constant $h$ and frequency $f$ as periods per unit of time, that is would understand that (i) and (ii) are definitions only and not physical facts. A physicist inspired by Einstein would not agree, and so discussion is very difficult as an experimental fact. 

But what then about the mass defect in nuclear reactions claimed to be the difference in mass before and after nuclear reaction? Is it not real? Or is it just the result of attributing energy release in nuclear fusion to decrease of mass, then measured in terms of mass? Here a physicist would insist that the decrease in mass is real and not just a matter of book keeping performed by clerk physicists. If mass is measured in terms of energy then energy production requires loss of mass. But what is mass in fact? Isn't it rather connected to gravitation as gravitational mass = inertial mass as in classical physics?

This connects to the recents posts on RealNucleus as a model of an atomic nucleus with total energy carried as Coulomb potential energy in the same way as chemical energy, thus without connection to mass. If this model describes physics, then there is no need of a strong force and a window towards  a Grand Unified Theory including both Newtonian mechanics with gravitation and atomic physics, appears to be open.