Steve Agnew,
"There is no equation for mass...nor is there an equation for action."
There is an equation for mass...and there is an equation for action. I have put them both in print here at FQXi.org. Mass is defined and action is explained. I have previously put forward the explanation that the units of action are newtons, meters, and seconds. Those units are informing us that action is energy times momentum. Both energy and momentum are conserved. That is why the least action principle works. Action is not about energy being the conjugate of time or momentum being the conjugate of length. An understanding of action follows from my definition of mass.
"Both mass and action simply exist as axioms that we learn to believe in by the age of two or so. Someone who does not believe in mass and action cannot make any sense out of reality and those people only survive with the help of others."
Physics is not about beliefs; it is about definitions. I make sense out of reality because I define properties. Theoretical physics does not make sense out of reality. Theoretical physics reaches outside reality for mathematically workable substitutes to serve in place of definitions. It reaches outside reality to invent substitutes for that which physicists have failed to learn from empirical evidence. It is not the empirical evidence that is lacking in meaning. Empirical evidence informs us of everything we will ever know about the mechanical operation of the Universe.
"Belief is a fundamental proposition for physics and to deny that is very problematic. What are your axioms? All the definitions you give are circular identities and reveal no fundamental truths."
I gave no circular definitions. There is no physics definition for space and I gave none. There is no physics definition for time and I gave none. There is no physics definition for length and I gave none. There is no physics definition for duration and I gave none. I gave a definition for mass and it immediately reveals fundamental truth. The 'F'in F=ma is not only defined, it is explained. The explanation for force reveals fundamental truth about the Universal Gravitation Constant. It reveals what temperature is. It removes the current circular definition for electric charge.
"Temperature is really just energy, ... "
What is the equation that shows that "temperature is really just energy"? What is the equation that shows that degrees Kelvin are really just joules?
" ... and energy is equivalent to mass... "
What is the equation that shows that energy is equivalent to mass? What is the equation that shows that joules are equivalent to kilograms?
"... and so you see we are back to arguing about mass."
We aren't arguing about mass. We are arguing about whether or not physicists must define their properties one of which is mass. You have no definition for mass. Are you arguing that you don't need to define mass?
"Mass flows from one source to another depending on many different properties ... "
A controlled specimen of isolated mass has been observed to move from one container to another container?
" ... and what we call temperature is certainly one of those properties."
What we call temperature is an undefined, unexplained property. What does a thermometer measure?
" ...So mass and action define temperature just fine, ..."
What is temperature? What is a thermometer measuring? What is the equation that defines temperature?
" ...but you must still simply believe in mass and action."
Theoretical physicists must go back to the beginning of interpreting empirical evidence and define all properties that empirical evidence infers exist. Three of those properties that theoretical physics failed to define are: Mass, temperature, and, electric charge.
"There is an equation for time: the differential of action with mass, i.e. the atomic clock."
That is an equation for duration.
"There is an equation for space: the product of c with time."
That is an equation for length.
"Mass and action, though, are axioms that you simply believe in, even when you say that you have no such beliefs."
What I say is that physics requires definitions. I ask for definitions. After all that has been said these official facts remain: Mass in undefined; Temperature is undefined. Unofficially both have been defined by me and their definitions have been presented here at FQXi.org. They have been put to use and many of the results have been presented here are FQXi.org. I let empirical deliver its message. Its message is that fundamental unity exists. The presence of fundamental unity in the equations of physics leaves no need for indirect or circular explanations.
James Putnam