Quantum Interaction Probabilities Versus State Probabilities

 In (1), it is argued that the Schrodinger cat paradox arises due to a superposition state being considered “physical” instead of an “an expectation over possible future outcomes”

. This is consistent with ideas linked to a quantum directional or interaction probability versus a state probability which we have discussed in various notes (2). In particular, classically there exist states, like heads up for a coin, a certain number of a die, an incident, reflected or refracted state for a photon, etc. We have suggested in (2) that exp(ipx) is a directional or interaction probability in that this probability is linked to the probability to have a p in a two-body scattering experiment and is involved in conservation of momentum. A state probability should not depend on x as the state is determined by p (and mo). 

  For example, an incident, reflected or refracted photon probability does not depend on x, rather it is specifically given by AA/c, BB/c or CC/c2, where c is the speed of light in n1=1 (index of refraction), c2= c/n2 and AA,BB,CC are the fluxes of the incident, reflected and refracted photons. Thus, exp(ipx) is linked to the state through p, but through x it is linked to position. This means that for a given p there is uncertainty in x quantified by the wavelength hbar/p. This means there is position uncertainty with respect to an impulse hit making this an interaction probability and a directional one because p and -p have different effects for a conservation of momentum equation. 

  As argued in (2), interactions are based on exp(ipx) because they involve impulse hits and so even though classical state probabilities exist, the physical problem is solved through considerations of exp(ipx)s. In particular, sums or OR situations of exp(ipx)s arise due to uncertainty in x. It is the directional/interaction probability exp(ipx) which predicts the x uncertainty and also appears in so-called superposition equations which represent different possible outcomes which may all exist in a tiny dx during the interaction. One should not think in terms of a state vector, but rather possible interaction probabilities exp(ipx). These are OR or sums of possible probabilities which interact in x and not a mixture of states. In other words, one does not have a dead cat mixed with a living one or an incident photon mixed with a reflected one. Rather, one adds directional/interaction probabilities for different states because one is uncertain which state exists in dx. This leads to math conditions on the exp(ipx)s as discussed in (2) which then ultimately govern the classical probabilities for one to have a particular state or another. The point we make is that exp(ipx) is not a state probability, but an interaction one which is consistent with the ideas of (1).