  We study the effect of thermal blurring caused by the use of (momentum-space)
rapidity as a proxy of coordinate-space rapidity in experimental measurements
of conserved charge fluctuations in relativistic heavy ion collisions. In
theoretical studies assuming statistical mechanics, calculated fluctuations are
those in a spatial volume. Experiments, on the other hand, can measure
fluctuations only in a momentum-space in the final state. In a standard
argument to compare experimental results for a momentum space with theoretical
studies for a coordinate space, rapidities of particles are implicitly regarded
as equivalent to their coordinate-space rapidity. We show that the relation of
two fluctuations is significantly altered by the existence of the thermal
motion, i.e. thermal blurring. We discuss that the thermal blurring can be
regarded as a part of the diffusion process, and the effect can be understood
by studying the rapidity window dependences of fluctuations. Centrality
dependence of the thermal blurring effect is also discussed.
