4 For isotropic illumination, H$_{F}$ = H 0 F and which, for large times, vanishes for all proper fragments. This is plotted in Fig. 2(b), which shows that the mutual information barely rises from zero before fading away, never yielding a single redundant copy. This behavior is due to the fact that the component of the environment in which information about the object is stored—the photon directional states—is initially fully mixed and so cannot hold any new information. However, this situation is very unnatural since the di- rectional photon states must be perfectly mixed. In phys- ical situations (e.g., objects lit by light bulbs, the Sun, or ambient light), we expect illumination to be nonuniform and the initial mixedness of the photon environment to decrease the redundancy by only a factor of order unity, in accordance with detailed calculations made of spin- 1 2 systems [6]. Future research could explore the precise de- pendence of the redundancy on the degree of directional mixedness as well as investigate the spatial distribution of the redundant information. We have shown in this Letter that collisional decoher- ence, a ubiquitous phenomenon in everyday life, leads to the proliferation of information about objects into the environment at a rate linear in time and (for most sys- tems) on an extremely short time scale. Indeed, after being illuminated by the Sun for just 1 µ s, a grain of dust 1 µ m across will have its location imprinted about 100 × 10 6 times in the scattered photons. Such extensive proliferation allows multiple observers to independently determine an object’s position by monitoring the envi- ronment, such that the object has an objective, classical location. The redundancy seen in the photon scatter- ing system is much larger than the abstract examples of quantum Darwinism previously studied because (a) the photon environment, like most real decohering environ- ments, is essentially infinite and (b) the photons that have scattered from the system keep records of its loca- tion forever. We thank Michael Zwolak and Haitao Quan for help- ful discussion. One of us (WHZ) is especially grate- ful to Charles Bennett, whose penetrating discussion of information propagation and records in (photon and other) environments [18] provides a useful setting for the study of quantum Darwinism. This research is sup- ported by the U.S. Department of Energy through the LANL/LDRD program. with ˜ C$_{Γ}$ = 57600 ζ (7) /π 3 ≈ 1873, in agreement with [11]. In the intermediate region, Δ x ∼ λ , τ$_{D}$ has a complicated dependence on both Δ x and θ . The results of the present work are valid for all Δ x so long as the correct τ$_{D}$ is used. 1 ˜ τ$_{D}$ = ˜ C$_{Γ}$ I ˜ a $^{6}$k3 $_{B}$T 3 c $^{4}$ℏ4 I$_{S}$$_{:}$$_{F}$$_{f}$ = H$_{S}$$_{d}$$_{E}$ − H$_{S}$$_{d}$$_{E}$$_{/}$$_{F}$ (16) = ∞ ∑ n =1 Γ (1 − f ) n − Γ n 2 n (2 n − 1) , (17) [1] M. Schlosshauer, Decoherence and the Quantum-to- Classical Transition (Springer-Verlag, Berlin, 2008); E. Joos, H. D. Zeh, C. Kiefer, D. Giulini, J. Kupsch, and I.-O. Stamatescu, Decoherence and the Appearance of the Classical World in Quantum Theory (Springer- Verlag, Berlin, 2003); W. H. Zurek, Rev. Mod. Phys. 75 , 715 (May 2003). [2] W. H. Zurek, Nature Physics 5 , 181 (2009). [3] W. H. Zurek, Ann. Phys. (Leipzig) 9 , 855 (Sept 2000); H. Ollivier, D. Poulin, and W. H. Zurek, Phys. Rev. Lett. 93 , 220401 (Nov 2004). [4] R. Blume-Kohout and W. H. Zurek, Found. Phys. 35 , 1857 (2005). [5] M. Zwolak, H. T. Quan, and W. H. Zurek, Phys. Rev. Lett. 103 , 110402 (2009). [6] M. Zwolak, H. Quan, and W. H. Zurek, Phys. Rev. A 81 , 062110 (2010). [7] R. Blume-Kohout and W. H. Zurek, Phys. Rev. Lett. 101 , 240405 (2008). [8] J. P. Paz and A. J. Roncaglia, Physical Review A 80 , 042111 (2009). [9] E. Joos and H. D. Zeh, Zeitschrift f¨ ur Physik B Con- densed Matter 59 , 223 (1985). [10] L. Diosi, Europhys. Lett. 30 , 63 (1995). [11] M. R. Gallis and G. N. Fleming, Phys. Rev. A 42 , 38 (Jul 1990). [12] K. Hornberger and J. E. Sipe, Phys. Rev. A 68 , 012105 (Jul 2003); K. Hornberger, Phys. Rev. Lett. 97 , 060601 (2006). [13] D. A. Kokorowski, A. D. Cronin, T. D. Roberts, and D. E. Pritchard, Phys. Rev. Lett. 86 , 2191 (Mar 2001). [14] H. Uys, J. D. Perreault, and A. D. Cronin, Phys. Rev. Lett. 95 , 150403 (Oct 2005). [15] J. D. Jackson, “Classical electrodynamics,” (John Wiley, New York, 1999) p. 459, 3rd ed. [16] The decoherence rate does not increase for arbitrarily large Δ x . Rather, this expression is only valid in the Δ x ≪ λ limit we are considering here. For Δ x ≫ λ , the decoherence rate saturates [17] R. Blume-Kohout and W. H. Zurek, Phys. Rev. A 73 , 062310 (Jun 2006). [18] C. H. Bennett, in Quantum Computing: Back Action 2006 , edited by D. Goswami (AIP, New York, 2006) pp. 11–17.