In the standard scientific experiment of wave-particle duality, photons of light build up a pattern of light and dark bands as if wave-like interference was occurring as the photon passes through the two slits.
1) The double-slit experiment is not a "standard scientific experiment of wave-particle duality" nor does it require photons. Wave-particle duality is, for the most part, an unfortunate relic that remains due to the overwhelming influence on standard textbook quantum mechanics as well as an older generation of physicists that Bohr had. Few have adopted his actual philosophy underlying the notion (complementarity), and even his and Heisenberg's (disparate) views underlying the Copenhagen interpretation and the supposed impossibility of a quantum world beyond a classical description have long been questioned and often rejected.
2) The photon doesn't pass through the slits. It actually isn't necessary in the description of the entire process apart from the registration of an excitation (mode) of the quantized electromagnetic energy by the detector. Actually, as it is only the relative phases of the (electric/electromagnetic) field operators via linear superposition that is relevant phenomenologically to the experiment, the whole notion of photons is unnecessary except as a linguistic aid to a blurry understanding.
3) This experiment has been simulated famously using the Bohmian formulation, which does involve definite trajectories rather than the lip-service to Bohrian duality. It has also been successfully explained in terms of the GRW approach. Even in standard quantum mechanics, the only actual component of the theory relevant to the interference pattern that comes into play here in an odd way is the fact that the probabilities for detection at various locations is obtained successfully by summing the probabilities derived from the amplitudes (this is actually where the interference term comes from).
This is supernatural science at its finest.
Why? It is entirely predictable. Generally, when people refer to the supernatural, they have trouble when it comes to empirical support because almost by definition that which is supernatural cannot be derived from repeated, replicable, and variously implemented experiments that are explained by (or at least understood in terms of) well-worn and tested physical theories.
As it suggests that something extra to what can be perceived is causing the interference.
Fields in general can't be perceived. This is true of classical fields.
In the 1970s technology became sophisticated enough that detectors were used to determine which slit the photon passed through.
This is not true. It was always possible to determine which slit the photon or electron or whatever passed through. The problem was that knowledge of the path destroys the interference effect.
This phenomenon led to the development of the many-worlds theory
This was developed about 20 years earlier in the 50s by a PhD student of Wheeler's who disliked the of the added structure of thee collapse postulate (or any such discontinuous "jump") imposed on the unitary evolution of quantum systems.