From: PointedEars@web.de   
      
   Stefan Ram wrote:   
   > Anthk NM  wrote or quoted:   
   >> Hidden dimensions could explain where mass comes from   
   >   
   >   So now you might ask yourself: what exactly is "mass"?   
   >   
   >        These days, that kind of question usually comes up in the   
   >   context of quantum field theory.   
   >   
   >        There we use something called a Lagrangian density, which is kind   
   >   of a pain to write in plain ASCII, but it basically looks like this   
   >   for a free field (no interactions):   
   >   
   > Lagrange = Psi-bar( i gamma^mu diff_mu - m )Psi.   
   >   
   >   In Unicode form, it would be more like:   
   >   
   > 𝓛 = 𝛹̅( i 𝛾^𝜇 ∂_𝜇 - m )𝛹.   
   >   
   >   Here, the first term (the one before the minus sign) is the "kinetic   
   >   term", and the second one is the "mass term".   
   >   
   >        For fields we already know, this lines up with what we normally   
   >   mean by mass.   
   >   
   >        So if you come across some new kind of field theory that ends   
   >   up giving you a Lagrangian of this general form, then whatever shows   
   >   up in place of that "m" is what we call the "mass".   
      
   Not quite.  The m there is a mass *in natural units* (hbar = c = 1),   
   therefore it is more precisely called "mass *parameter".  The actual   
   (expectation value of the) mass of a particle in SI units would be m hbar/c   
   (Unicode: m ℏ/c) if there are no interactions; otherwise one must use the   
   *renormalized mass* m_r and multiply that by ℏ/c to obtain the mass in SI   
   units.   
      
   --   
   PointedEars   
      
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