I will talk about the effective field theory space describing low energy light by light scattering (LbyL). Modern dispersive techniques lead to a simple two sided bound on the ratio of the leading Wilson coefficients. The Standard Model (SM) resides deep inside this theory space. The question then arises what is so special about the SM and what is the signature of new physics. To address this, we will consider Bell correlations in LbyL scattering at low energies. I will argue that the known SM contributions lead to a fine-tuning problem, different from the strong CP problem. Incorporating a light axion/axion-like particle (ALP) removes this problem. We constrain the axion-coupling--axion-mass parameter space inside which the axion may be found in near-future experiments searching for low mass axions.