The probability amplitude equation of quantum entanglement : the Australian connection

50(1) | JAN–FEB 2013 In a recent paper [1], originally written to explain the origin of experimental configurations to determine the quantum entanglement of photons traveling in opposite directions, the issue of the corresponding probability amplitude surfaced. As it turns out, Australian physicists J C Ward and R H Dalitz played key roles in this field, roles that are largely unrecognised, or unknown, by the physics community. Here, a succinct description of these crucial contributions is provided. The initial discussion on the use of quantum theory to describe the polarisation correlation of quanta propagating in opposite directions was given by Wheeler in 1946 [2]: “According to the pair theory, if one of these photons is polarized in one plane, then the photon that goes off in the opposite direction with equal momentum is linearly polarized in the perpendicular plane.” This is the essence of entanglement. The pair theory that Wheeler refers to is the Dirac theory of electron-positron pairs [3]. Ward in 1949 [4] mentions Wheeler’s contribution and then continues to explain that Wheeler did attempt to calculate this effect but “through the neglect of interference terms he derived an incorrect, and in fact, far too small value for the angular correlations of the scattered quanta” [4]. Ward’s thesis [4] includes the physics used to derive the quantum formula for correlated polarisations published by Pryce and Ward in 1947 [5] which was also independently published by Snyder et al. [6] in 1948. Ward’s approach begins by listing the polarisation alternatives related to x and y polarisation axes related to two counter propagating photons: 〉 〉 〉 〉 y y x y y x x x , | , , | , , | , , | [4]. Here, the first coordinate refers to photon 1 and the second coordinate to photon 2. Eventually, Ward [4] arrives at the probability amplitude for entangled polarisations ( ) 〉 〉− = 〉 x y y x , | , | |ψ . Using the identity given by Dirac ( ) = y x y x , | | | [7] , once normalised, this expression can be restated as