Do photons affect one another

This question can have many answers. For one, I would be enlightened to understand whether two photons can truly create an electron-positron pair, as well I would like to know if a photon is able to change other photon's directional path.

I've read on wikipedia about matter creation and that it is possible to convert two bosons into two fermions, yet I haven't found a single experiment that says this has been done. I as well cannot find anything online that says whether a photon can influence another photon's path.

Finally, I want to just say that my brother has put this idea in my head that photons simply pass through one another without any effect whatsoever, so if you can ingrain a more true to reality understanding of photons affecting one another, that would be phenomenal.

Answer

Photons are elementary particles and their interactions are dictated by quantum mechanics.

In quantum mechanics the strength of the interactions comes from the coupling constant that characterizes the the strength of the force between the interacting particles. To see if a particle interacts with another particle we write down Feynman diagrams (page down on the link). When one calculates the probability of an interaction, one calculates the square of a Feynman diagram , and in the calculation every vertex of the diagram has a coupling constant.

In the case of photon photon interactions there are many vertices which enter :

A Feynman diagram (box diagram) for photon–photon scattering, one photon scatters from the transient vacuum charge fluctuations of the other

The square of the final calculation of this will be proportional to the tiny electromagnetic coupling raised to the 8th power, as it is multiplicative. Thus the probability of a photon to interact with another photon is to all intents and purposes zero for light and the low energies in our environment (other factors contribute to the crossection and can raise the probability).

Thus there is a very very small probability of a photon influencing another photon's path, unmeasurable at normal energies of photons . When gamma ray energies are reached, order of MeV, extra diagrams open, of pair creation, and this is a different story, because the number of electromagnetic vertices is halved thus the probability is much higher, and also the probability grows with energy . There are proposals for gamma gamma colliders.

Photons do get in step with each other, i.e. they create a coherent electromagnetic wave, and there is a collective wave function which can show interference effects, but it is a superposition, an addition of wavefunctions, not an interaction. The complex conjugate squared of the collective wavefunction is the measurable quantity.

As for your other questions,

Two bosons to two fermions: it is possible as far as quantum number conservations go, except that the bosons we can control in the laboratory are unstable and cannot be used in scattering experiments which are the only ones we can control. We depend on the fact that the standard model is validated and argue from the theoretical properties it gives to particles. These reactions are important in a cosmological model where there exists a soup of energy and particles at the very early times, after 10^-32 seconds.