Reply to: Comment on “Bohmian prediction about a two double-slit experiment and its disagreement with SQM”

In a recent paper, Struyve et al. [Struyve W, De Baere W, De Neve J and De Weirdt S 2003 J. Phys. A 36 1525] attempted to show that the thought experiment proposed in [Golshani M and Akhavan O 2001 J. Phys. A 34 5259] cannot distinguish between standard and Bohmian quantum mechanics. Here, we want to show that, in spite of their objection, our conclusion still holds out. PACS number(s): 03.65.Bz Recently, a thought experiment was proposed in [1] to show that the standard quantum mechanics (SQM) can present incompatible predictions as compared with Bohmian quantum mechanics (BQM) at the individual level of particles. But, this proposal was diligently criticized by Struyve et al. [2] by resorting to the quantum equilibrium hypothesis (QEH). It seems useful, before any discussion on the raised objection, to outline the proposed experiment. Consider an original type of EPR source [3] which emits a pair of identical non-relativistic particles labelled by 1 and 2 with vanishing total momentum. The source is placed at the origin of the x − y coordinate system which is taken to be the geometrical center of two identical double-slit screen in parallel to the y-axis. The slits are labelled by A and B as well as A and B on the right and left screens, respectively. They have the coordinates (±d,±Y ) with the half-width of each slit being σ0. For simplicity, let us suppose that there is just one pair of particles in the system at any moment. Thus, the general wave function of the system describing the two entangled particles emerging from the slits can be written as ψ(x1, y1;x2, y2; t) = N [ψA(x1, y1, t)ψB′ (x2, y2, t)± ψA(x2, y2, t)ψB′ (x1, y1, t) +ψB(x1, y1, t)ψA′ (x2, y2, t)± ψB(x2, y2, t)ψA′ (x1, y1, t)] (1) where N is a renormalization constant and the upper (lower) sign refers to bosonic (fermionic) property of the two-particle system. Furthermore, it is assumed that the slits produce Gaussian wave functions in the form ψA,B(x, y, t) = (2πσ 2 t ) exp[−(±y − Y − h̄kyt/m) /4σ0σt] ×exp[i(kx(x− d− h̄kxt/2m) + ky(±y − Y − h̄kyt/2m)] (2) where the index A(B) is related to the upper (lower) sign, and σt = σ0(1 + ih̄t 2mσ 0 ). (3) Notice that, the form of ψA′,B′ is the same as ψA,B with the parameter d being replaced by −d in Eq. (2). A joint detection of the two particles is simultaneously done on two screens placed at ±(D+ d), E-mail: [email protected] E-mail: [email protected]