Legion, what are the photons doing in laymens terms.
In layperson's terms, photons don't exist. Photons, after all, are discrete units (i.e., particles) of "light", and neither quantum mechanics, QFT, or particle physics allow for actually discrete units of photons, electrons, quarks, etc. Also, there is a very famous question about the state of quantum systems prior to measurement, e.g., A. Danan, D. Farfurnik, S. Bar-Ad, and L. Vaidman (2013). Asking photons where they have been.
Phys. Rev. Lett. 111, 240402.
The standard (even outside of the Copenhagen interpretation of QM) response to this question is that it is meaningless.
Do we think it is bleeping al over the board, traveling in theses spaces.
We think it doesn't have defined properties or existence until we force it to by interacting with "light".
What is the nature of the wave function
It's a mathematical entity that is used to predict the outcomes of experiments in QM that is not, in general, either useful or even possible to use in quantum physics more generally.
what is it making a photon do
A photon is the result of measurement and the wave function (or some other mathematical device/function/field/entity).
bleep in and out of existence
Who says it exists (and in what sense)?
Most I figure is its using whatever tricks spacetime allows it.
If we make quantum mechanics compatible with spacetime (as we have), then wavefunctions cease to work and are obsolete.
As we approach the speed of light special relativity remains true and doesn't become incompatible just because you actually hit the speed of light and your poor maths break
Special relativity is designed, from the ground up, to deal with the speed of light. Quantum physics is not. It is quantum physics that breaks down at speeds near or equal to that of light, not special relativity.