- This thread is for the discussion of issues specific to the thermal interpretation of the double slit experiment.
I prefer to discuss in the double-slit experiment light in place of electrons since it makes the underlying principle more clear. Consider the quantum system consisting of the screen and an external (classical) electromagnetic field. This a very good approximation to many experiments, in particular to those where the light is coherent. The standard analysis of the response of the electrons in the screen to the field (see, e.g., Chapter 9 in the quantum optics book by Mandel and Wolf) gives - according to the standard interpretation - a Poisson process for the electron emission, at a rate proportional to the intensity of the incident field. This is consistent with what is observed when doing the experiment with with coherent light. A local measurement of the parameters of the Poisson process therefore provides a measurement of the intensity of the field.Take an electron in the double-slit experiment: A single electron's measured position on the screen is usually not found to be at the place given by the position expectation value. It's of course pretty probable to land in the main maximum of the distribution, which in this case is the expectation value, but it's also found somewhere else. Thus in this case, which is the paradigmatic example for the probabilistic interpretation of QT, solving the infamous "wave-particle dualism self-contradiction" of the "old quantum theory": There's nothing that precisely determines at which position the electron will hit the screen. All that can be known are the probabilities where it hits the screen, and what's found is that it hits the screen anywhere, but in a single measurement it's not found to have hit the screen on the average position given by the quantum state!
There is nothing probabilistic or discrete about the field; it is just a term in the Hamiltonian of the system. Thus, according to the standard interpretation, the probabilistic response is in this case solely due to the measurement apparatus - the screen, the only quantum system figuring in the analysis. At very low intensity, the electron emission pattern appears event by event, and the interference pattern emerges only gradually. Effectively, the screen begins to stutter like a motor when fed with gas at an insufficient rate. But nobody ever suggested that the stuttering of a motor is due to discrete eigenvalues of the gas. Therefore there is no reason to assume that the stuttering of the screen is due to discrete eigenvalues of the intensity - which in the analysis given is not even an operator but just a coefficient in the Hamiltonian!
In the thermal interpretation, one assumes a similar stuttering effect at low intensity of a quantum field (whether the photon field or the electron field or a silver field or a water field), illustrated by the quantum bucket introduced in post #272 and post #6 of a companion thread.