But as to whether or not reality violates the Laws of Thought, I don't know. I'd like your input on the quantum eraser experiment.
First, I'll say that such experiments have always fascinated the crap out of me. Literally ever since I was a child, such things have just blown my mind. Indeed, it was exactly that sort of experiment that made me think that I wanted to be a physicist all through high school. It wasn't until I well into college that I figured out that it was actually philosophy that I was really interested in and that I had therefore basically wasted (or I thought so at the time) a lot of time and energy studying the sciences.
As for what the experimental results mean, I don't know. But what I do know is that your statement that "photons are both particles and waves" is false. They are either a particle, a wave, or something else, but that are not both a particle and a wave.
Further, the fact that we cannot observe the contradiction doesn't remove the fact that the theory states and indeed is dependent upon the truth of the contradiction.
Now, as for the rest of what you said, the first of the two sentences quoted above is the killer. What is science if not the dispassionate pursuit of the truth concerning whatever it is that one is studying, whether it be physics, geology, astronomy, meteorology dog grooming, ditch digging, or whatever?
Regardless of how you answer that question the fact is that if you are willing to accept the possibility that reality can be in violation of the laws of reason, you remove from yourself the ability to know anything at all. The laws of reason are the very foundation of all knowledge of any kind, including scientific knowledge. Science cannot even be done without using reason. It is therefore irrational in the extreme to use science, which is predicated on reason, to argue against the veracity of reason, which is precisely what you just did.
Further, we can know that reality is independent of our perception of it. Imagine for a moment that everything is merely a figment of your own imagination. How would you explain you ability to imagine into existence a book written in a language you don't know which can be read by whole populations of people? How could you explain your ability to go to a school, spend years studying in or to gain the ability to go back and read the very same book that a year or more before you were completely unable to read? And, when you read the book, you find that it is full of concepts and ideas that you never thought of before but that you can look around you and see have been understood and implemented by thousands of others for decades or centuries?
All the astounding complexity and regularity around you and your own epistemological perspective insists that you don't really know for sure that any of it corresponds with reality.
If reality doesn't have to be rational, how do you know that anything is real? How do you know that your perceptions are real? How do even know that you are real?
Do you know that you are real?
Resting in Him,
Clete
