We show that the resonance shifts in the fluorescence of a cold gas of rubidium atoms substantially differ from those of thermal atomic ensembles that obey the standard continuous medium electrodynamics. The analysis is based on large-scale microscopic numerical simulations and experimental measurements of the resonance shifts in a steady-state response in light propagation.PACS numbers: 42.50. Nn,32.70.Jz,42.25.Bs An ensemble of resonant emitters can respond strongly to electromagnetic fields. With sufficiently closely-spaced emitters, the radiative response of a single, isolated emitter is no longer a simple guide to the behavior of many. The response of the sample becomes collective due to strong resonant dipole-dipole (DD) interactions [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. Owing to improving experimental control, the collective radiative interactions have recently experienced a resurge in interest, both in fundamental studies and in the developments of technological applications. Among the systems investigated are cold atoms [17,[21][22][23][24][25][26][27], thin thermal cells [28], photonic crystals [29], metamaterial arrays of nanofabricated resonators [30][31][32], arrays of ions [33], and nanoemitters [34][35][36]. Atoms provide an especially promising system for the studies of collective radiative phenomena, since they make a well-characterized medium with precisely determined radiative resonance frequencies and linewidths, without any true absorption where radiation is lost. Furthermore, cold atomic ensembles form homogeneously broadened systems where the effect of the thermal motion of the atoms on radiative resonance frequencies may be ignored.Recent numerical simulations [16] have highlighted how the optical response of cold, dense atomic ensembles can be dramatically different from that of thermal atoms. In cold atomic gases the incident light can induce position-dependent correlations between the atoms due to the light-mediated resonant DD interactions. The thermal motion of hot atoms, in contrast, introduces Doppler shifts in the resonance frequencies of the atoms, which modifies the optical response by suppressing these correlations. With increasing inhomogeneous broadening the atoms are simply farther away from resonance with the light sent by the other atoms, which reduces the lightmediated interactions, as demonstrated in Ref. [16].The standard textbook theory of macroscopic electromagnetism [37,38] in a polarizable medium represents an effective-medium mean-field theory (MFT) that assumes each atom interacting with the average behavior of the surrounding atoms. In such models the spatial information about the precise locations of the pointlike atomsand the corresponding details of the position-dependent DD interactions -is washed out, resulting in the absence of the light-induced correlations and in approximations in the calculations of the optical response. In thermal atomic ensembles, at sufficiently high temperatures, the suppression of the DD interac...