Quantum Two Slit Interference and Determinism Versus Probability in Interactions
Francesco R. Ruggeri
In classical physics, interactions appear to be of the form of cause and effect, as in Newton’s second law is: F = dp/dt. The force F governs the interaction and dp/dt is the effect. In quantum mechanics, there is a probability for an impulse hit interaction by a particle given by exp(ipx) within a wavelength region of size hbar/p. As a result, instead of an interaction occurring within dx->0, the particle itself dictates an interaction region of the size hbar/p. Consequently, in a 2-slit interaction, the slits should be about a wavelength hbar/p apart. In classical physics, an interaction occurs within the interaction region (dx->0), but in the 2-slit case the interaction region includes the space from the first slit to the second, so to ask: What is happening as the particle interacts within this region? means that a particle can pass through one slit and inteact with the other, or it can interact with the slit through which it passes. The interaction region is the smallest region in which the interaction occurs (as if it were a black box). The particle physically passes through one slit or the other, but interacts either way with both slits probabilisitcally because otherwise the interaction region would only be one slit or the other contradicting the probabilistic range hbar/p of interaction. As a result, a two-slit calculation is really a calculation of an interaction within an hbar/p region including both slits. This interaction is probabilistic due to the exp(ipx) interaction hit nature of the particle and so it is the particle which dictates the interaction to a large degree. The fact that the particle must pass through one slit or the other, together with a probabilistic interaction over the hbar/p region means that two key notions are at work, one being the physical location of the particle (passing through one slit or the other) which governs how the probabilistic interaction (due to the particle) operates. In particular, one draws two parallel rays, one from the center of each slit towards a fixed point on a screen far away. The interaction is based on the exp(ipx) probabilistic interaction of the particle and the separation of the two slits because the particle interacts with both as it passes through only one. In other words, reality is not simply based on what one can measure during an interaction. The fact that one does measure through which slit the particle passes does not mean that the positions of the slits cannot stil helpl lead to determinate statements such as zero particles arrive at certain x points on the screen. The slit separation is part of the physical reality of the problem. (Note: there is also diffraction from the two edges of each slit, i.e. diffraction, which follows the same ideas and so one has a combination of diffraction from each slit together with interference.) As a result, we suggest that one consider the entire region from one slit to the other as a quantum interaction region similar to the dx->0 used in Newtonian mechanics. Quantum mechanics then provides a probabilistic, not deterministic, descripition of possible interactions and their probability weights, unlike the cause (force) and effect (deterministic change in p of the particle) of Newtonian mechanics. The exp(ipx), hbar/p gradation form of probability, allows for probabilities to add or subtract at different x points. The walls of the 2-slit apparatus are linked with probabilistic momentum angle changing, with each angle having the same probability (uniform distribution), but otherwise much of the interaction is dictated by the particle, unlike in Netwonian mechanics. For a V(x) = Sum over i Vk exp(ikx), both exp(ipx) and exp(ikx) are one a similar footing.
•Aug 4, 2026•0 citations