Definitions are important!
If you cannot define a word you use, then you do not know what you are talking about (that is a true statement by definition!)
force5 said:
What is understood to be the fundamental "states" of energy? Not referring to the various "forms" of energy.
Thanks for any input.
The conventional definition of "energy" is that it is the ability to do work. The basic problem with that definition is that it requires one to know the definition of "work". The conventional definition of "work" is that it is "force" applied over a "distance". Now we have to define "force" and "distance". (Does this seem to be a growing problem?)
"Force" is conventionally defined through Newton's "F=ma" and "distance" is measure of difference between two positions in our "coordinate system". Now we have to know what "mass" and "acceleration" are and exactly how that coordinate system is set up; which must include a definition of "difference". (At this point it should be quite clear that this is a "growing" problem!)
All we can really say about "mass" is that it is a measure of something associated with things and how they move under a "force". (Whoa, is this reasoning starting to sound a little circular?) Acceleration is defined to be the second derivative of position with respect to time. Now at least we are getting down to the characteristics of that coordinate system. So we need to get a solid hold on how that coordinate system is defined!
Well, now I am in big trouble. In order to make sense, I need to define that coordinate system without referring to any of the concepts above as they are all defined in terms of that coordinate system (all except mass perhaps; but even mass appears to be a phenomenological entity defined by the rest of the concepts).
The problem I find myself with is that the geometry held as valid by modern physicists is defined by the need to make all those other definitions roughly consistent with what we observe (I say "roughly" because conventional physics only requires the definitions make sense when brought back to the Newtonian picture where the concepts are somewhat well defined). Now that seems to me to be circular in its very essence. The attack, as it is presented by the scientific community, is irrational on the face of it.
Why not just cut to the chase and
define[/color] our expectations to be given by some algorithm \vec{\Psi}^\dagger\cdot\vec{\Psi} (an absolutely general expression for producing a number capable of being seen as a measure of expectation: i.e., an number in the range zero to one).
Define[/color] time to be an argument of \vec{\Psi} and finish the problem by
defining[/color] "energy" to be the expectation value of the derivative with respect to time where the "expectation" of a mathematical operator is given by \vec{\Psi}^\dagger\cdot(that operator)\vec{\Psi}.
Now every thing is clear and well defined. We at least know what we are talking about. If you can, think about that for a while! Hurkyl, you are the mathematician, tell me if what I have said is rational or irrational.
Have fun -- Dick
