DR. ANDREW S. FRIEDMAN
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(a) Animation 5a corresponds to Fig. 2a of Friedman+2013 for the case in which the event redshifts are fixed to zA=5 and zB=3.65, while the angular separation α as seen from Earth is allowed to vary from 0 to 360 degrees (or, without loss of generality, 0 < α < 180 degrees by symmetry about the x-axis). As in Animation 4, the green circles show the projection of the past lightcones on the hypersurface τ=τAB when the lightcones first intersect; these are also shown as black circles projected onto the τ=0 plane. For these redshifts, events A and B have a shared causal past for angles below some critical value (α <= α) but do not for angles greater than that value (α > α), where α is found from Eq.~31 of Friedman+2013. The movie represents a point in the zA - zB plane which lies in the white box in the upper right region of Fig 3b of Friedman+2013, where event pairs do not have a shared causal past with each other as long as the angular separation α exceeds some critical angle α. Since zA > 3.65 for any angle α, event A also does not have a shared causal past with our worldline along the τ-axis from the origin. Since zB=3.65, event B just barely has a shared past with our worldline for all angles α.

(b) Animation 5b for the same case as in Animation 5a, as viewed in the τ=0plane at the big bang.

Massachusetts Institute of Technology Harvard University Astronomy Smithsonian Astrophysical Observatory UC Berkeley Astronomy NSF Graduate Research Fellowship NASA Graduate Student Research Program Peters Automated Infrared Imaging Telescope (PAIRITEL) NASA Swift Satellite
Last Updated: Andrew Samuel Friedman, 5/2014

This material is based upon work supported by the National Science Foundation under Grant # 1056580 through an NSF Science, Technology, and Society Postdoctoral Fellowship at MIT.

Original animations are shared under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 US License