when a positron/electron pair annihilate via the two-photon pathway, the emitted photons are momentum correlated. this correlation ensures that they move along a straight line path in opposite directions. an experiment performed in 2004 by dr. v.d. irby measured the time interval between detection of the photons. he observed a decay in the number of counts with increasing detection time interval, which he described using a lorentzian, the line width of which at full-width half-maximum is measured to be 120ps. the data collected by irby is interesting because current theory predicts that because the source is so localized (the effective source width used by irby is safely within 5rnrn) the photons should be detected within a time interval of 􀀶t=d/c where d is the thickness of the source. this time interval corresponds to 17ps. this thesis fits the results to an exponential, and shows that this exponentially decaying nature of the coincidence time interval is characteristic of the entanglement of the two photons. we find that the wavefunctions of the photons decoheres in space according to how long the particle pair took to decay (which is exponential), and that the probability of simultaneous detection depends on the exponential of the product of the lifetime of positronium and the detection time interval.