From: nospam@de-ster.demon.nl   
      
    wrote:   
      
   > It is not so much the question of what *additional* axioms are   
   > needed, but which ones need to be removed. Physical quantities are   
   > not numbers, so that not all the infrastructure of a field (or more   
   > generally: of the number system) has physical meaning with them;   
   > both rather only a substructure thereof.   
   >   
   > The dimensions associated with the quantities are connected with   
   > constraints on which ways they may be combined; namely that for   
   > quantities of different physical dimensions, addition and subtraction   
   > are not meaningful operations.   
      
   It is really the other way round.   
   What can be added and multiplied is determined by the laws of physics.   
   (as formalised in some unit system)   
   We are not trying to add or multiply physical quantities at random.   
   The calculus of dimensions merely formalises what we know already   
   from the laws of physics.   
      
   > On Saturday, July 15, 2017 at 3:54:00 PM UTC-5, J. J. Lodder wrote:   
   > > Before going on it is necessary to understand   
   > > that dimensions have no physical reality.   
   >   
   > Quite the contrary: they are deeply connected with the operational   
   > meaning of the various quantities involved.   
      
   That doesn't give them physical reality.   
   Dimensional analysis is meta analysis.   
   It doesn't deal with nature,   
   it deals with systems of equations that describe nature.   
      
   > The most notable example   
   > being E and B whose "variability" of dimensions "in different   
   > systems" is grounded in a confusion of concepts; namely the confusion   
   > of E and B with D and H.   
      
   That is complete nonsense. (sorry to be that blunt)   
   The dimensions of E and B cannot be determined from physics.   
   They have to be decided upon by convention.   
   (as happened in real life at an expert conference   
   on the dimensions of the electrical quantities in the 1920-s)   
      
   As for E and B, they -are- the same thing, (at a fundamental level)   
   as is obvious from the fact that they Lorentz-transform into each other.   
   You can hide this fundamental equality by choosing an inconvenient   
   system of units, but you can only confuse yourself that way.   
      
   [snip]   
      
   > All systems for (E,B,D,H) have these dimensions. Appearances otherwise   
   > are rectified by bringing back out the various quantities that the   
   > respective system has Sapir-Worfed away (and making explicit again   
   > the *relevant* Physics it omitted by doing so!)   
      
   This is obviously wrong.   
   In MKSA the unit of electric field is the Volt/meter,   
   which is the kg m sec^-2 Amp^-1, with corresponding MKSA dimension.   
   In Gaussian units the electric field   
   is the square root of an energy density, (directly from the Lagrangian)   
   with corresponding Gaussian MLT dimension.   
   In natural units (on basis of energy) an energy density   
   is Energy L^-3, which is Energy^4, so the electric field E   
   has dimmension Energy^2. (or idem directly from E = e/r^2)   
   Three unit systems, three different dimensions,   
   for the same physical quantity.   
      
   It should have been obvious already in the 1920-s that giving   
   charge or current a non-I dimension is just a mistake. [1]   
   Max Planck had already shown twenty years before that   
   in his fundamental work on unit systems   
   that charge is naturally dimnsionless.   
   THe electron charge is just the square root   
   of the fine-structure constant,   
      
   Jan   
      
   [1] It was error upon error, made nearly inevitable   
   by the fact that c had not been given its due   
   in Maxwell's equations, fifty years earlier.   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)