Originally Posted by wogoga
You don't need to reason from analogy. If there is a force between photons, we would be able to measure it. Many, many experiments have searched for this "force" at optical wavelengths, and all have shown that photon-photon interactions are incredibly small. The force was finally observed in a special case (inelastic gamma ray interactions) and it agreed with all theoretical predictions.
Thanks for the hypothesis, Wogoga! Unfortunately it has been falsified by these experiments.