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S4b. Why are observable densities state-dependent?
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In the preceding, the mass and charge density of a n-particle system
(or of a single particle) depends on its quantum state. This is
sometimes regarded as a reason for denying the 'reality' of the
mass and charge density. However, such a reasoning is misguided.
Indeed, the phenomenon is already present in classical mechanics.

That mass and charge density depends on the state is no more 
surprising than that the trajectory of a classical particle depends 
on its classical state (its position and momentum), or that the 
density of a cloud in the sky depends on its classical state 
(the position and momentum of all its particles, or, in the customary 
fluid mechanics approximation, its mass density field and its velocity 
field).
  
Of course it has to, to match a particular real life situation.

What seems strange at first sight is that the above applies already to
a single, indivisible particle. But this is really strange only if one
assumes that the particle is pointlike - which we know is the case only 
for unphysical, bare particles, but not for the physical, renormalized 
ones. (See the entry ''Are electrons pointlike/structureless?'' 
elsewhere in this FAQ.) Once one realizes that physical particles are 
extended (although they are indivisible), there is enough room to 
accommodate the internal structure described by densities.

Thus the only quantum paradox that remains is that particles with 
nontrivial internal structure (and shape) can nevertheless be 
indivisible, a fact coming from the representation theory of the 
fundamental symmetry group of our universe: Indivisibility of an 
object just means that this object is described by an irreducible 
representation which cannot be decomposed further without violating 
a fundamental symmetry.