From: hees@itp.uni-frankfurt.de   
      
   On 11/12/2023 13:26, Luigi Fortunati wrote:   
   > Tom Roberts il 10/12/2023 11:52:28 ha scritto:   
   >> On 10/23/23 6:31 AM, Luigi Fortunati wrote:   
   >>> [...]   
   >>   
   >>       [The context of this question is clearly Newtonian mechanics.   
   >>        But my answer holds for relativistic mechanics as well.]   
   >>   
   >> To definitively answer the question "is inertia a vector", one must find   
   >> "inertia" in some equation(s). Unfortunately, "inertia" does not appear   
   >> in any equation of mechanics. So the question is meaningless, or at   
   >> least unanswerable.   
   >>   
   >>       [This includes Newton's original "vis insita".]   
   >>   
   >> Note: do not be confused by "moment of inertia" -- look at its   
   >> definition and you'll see it is misnamed, and is really the second   
   >> moment of mass.   
   >>   
   >> In modern physics,the closest quantity to "inertia" is mass, which is   
   >> clearly a scalar (i.e. not a vector).   
   >>   
   >> Tom Roberts   
   >   
   > What is mass for you?   
   >   
   > If for you mass is just a quantity of matter, you are right: it is a   
   > scalar, because it has no direction.   
   >   
   > Instead, if the mass is an inertial body or a body that reacts, it has   
   > direction.   
   >   
   > In fact, the inertial body moves with uniform rectilinear motion (and   
   > the motion is a vector) and the body that reacts exerts an opposing   
   > force (and the force is a vector).   
   >   
   > This is why inertia is a vector: because it moves in only one direction   
   > or reacts in only one direction.   
   >   
   > Luigi Fortunati   
      
   This discussion is of course entirely semantic. There is no quantity in   
   usual physics communication called "inertia". You also have to   
   distinguish, whether you argue within Newtonian or relativistic physics.   
      
   In Newtonian physics, indeed mass is the measure of inertia, and   
   concerning the transformation properties under the Galilei group, which   
   is the symmetry group of Newtonian spacetime, it is a scalar.   
      
   This becomes most clear in the analysis of non-relativistic quantum   
   theory, where the mass occurs in the representation theory of the   
   Galilei group as a central charge of the corresponding Lie algebra.   
   There's even a superselection rule forbidding superpositions of state   
   vectors belonging to different (total) mass of point-particle systems.   
      
   In special relativity the Galilei group is substituted by the Poincare   
   group, whose Lie algebra has no non-trivial central charges, and mass is   
   a Casimir operator. The representations leading to a physically   
   meaningful dynamics, satisfying the relativistic notion of causality are   
   massive and massless representations. The mass is thus also a scalar in   
   relativistic physics. The resulting dynamics tells you that it's rather   
   energy than mass that quantifies "inertia".   
      
   --   
   Hendrik van Hees   
   Goethe University (Institute for Theoretical Physics)   
   D-60438 Frankfurt am Main   
   http://itp.uni-frankfurt.de/~hees/   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)