Hypothesizing on photon mode of travel in double slit or similar experimental setups

[eaglelake]

perhaps there is a "dimension" in addition to time-space, through which quantum mechanics operates? the "probability wave function" operates in that dimension.

when we try to measure a photon's position, the wave function collapses, the photon moves back into the time-space dimension

Your word “perhaps” says it all. We are forced to speculate about what is “really happening” because Quantum Mechanics tells us nothing about how the photon gets through the apparatus.

A quantum experiment consists of the entire apparatus, including the photon and the measuring device, as well as the experimental result. Everything is set up in space-time.

Photon detection is a real event that we do observe. But, we have no evidence for any other dimension that might help us understand “what is really happening” to the photon before it is detected. Any discussion of photon behavior prior to detection is pure speculation.

We do know that the wave function is defined in a Hilbert space. But as far as we know, it is not a part of the experiment; no one has ever observed the wave function “moving through” the apparatus. Nor has anyone observed its collapse when the photon is detected.

Please forgive me for being so harsh, but it does seem futile to suggest explanations that have no verifiable evidence to support them. But, you are not alone. There are lots of other bright people expending much time, effort, and brainpower in such endeavors.

Best wishes.