Can photons pass through each other? The below passage has been extracted form the book "Feyman's lectures on Physics. Vol I"  

"...We have heard that idea so long that we accept it, and it is almost impossible for us to realize that very intelligent men have proposed contrary theories--that something comes out of the eye and feels for the object, for example. Some other important observations are that, as light goes from one place to another, it goes in straight lines, if there is nothing in the way, and that the rays do not seem to interfere with one another. That is, light is crisscrossing in all directions in the room, but the light that is passing cross our line of vision does not affect the light that comes to us from the object. This was once a most powerful argument aganist the corpuscular theory; it was used by Huygens. If light were like a lot of arrows shooting along, how could other arrows go through them so easily? Such philosophical arguments are not of much weight. One could always say that light is made up of arrows which go through each other!.."  

Does the above passage mean photons can pass through each other?  
 A: In the elementary particle framework, when an elementary particle meets another elementary particle, it is called scattering.
Passing through would mean that the two  particles  continue on their way, momentum and energy unchanged. 
Not passing through is called interaction.
This is the elementary particle table that is part of the standard model  :


The Standard Model of elementary particles, with the three generations of matter, gauge bosons in the fourth column, and the Higgs boson in the fifth.

Elementary particles are in the quantum mechanical frame.
With the standard model we can compute particle/particle scattering crossections, i.e. the probability that two particles meeting will interact and change momentaa, energies and even masses.
The question then becomes: what is the probability that in photon photon scattering an interaction  will occur and the two photons will affect each other? The answer is in the calculation of the crossection using the appropriate Feynman diagram that describes the photon photon scattering:

There are four vertices, each gets a (1/137)^1/2 from the coupling constant so that already is a factor of about 10^-4 multiplying the wavefunction. As the scattering crossection  is proportional to the square we get 10^-8, a very small number. Thus we can say that for all intents and purposes photons scatter on each other without interacting. 
This is especially true of optical and lower frequencies because for those energies ( E=h*nu)  the possible particles in the loop are very much off mass shell depressing the crossection even more. It is only with high energy photons, called gammas , that we can measure a photon photon interaction.
A: The idea of a photon as a "particle" in the sense of our everyday use of the word, that is, as a small round hard thing, is useful for many purposes.   But it is only a model, and like all models it resembles the true object in many ways, but does a poor job representing other aspects.   A model airplane has no engine, and possibly no moving parts at all.  It looks a lot like an airplane, but in many respects does not behave like one.  If you depend on the model to be a real airplane, you will eventually get into trouble.
A photon is an object that is not a particle.  It's not a wave, either.  It's an entirely different object that has no analogue in the world of everyday experience.  But we do find it useful to model it sometimes as a particle and sometimes as a wave.  It looks a lot like a particle, but in many respects doest not behave like one.  If you depend on the photon to be a real particle, you will eventually get into trouble.   And you have just gotten into trouble.
In a sense the answer is "yes", photons pass through each other.  But this picture is highly dissonant with our mental picture of what a particle is.  It's best to take a different attitude:  I don't have a good model for a quantum of electromagnetic radiation, but I have just learned another property a good model should have.
A: Einstein's introduce the concept of photon to describe the photoelectric effect and proposed that it has energy = hν and has mass approximately zero but has a momentum. So it being an amount of energy it obviously can pass through each other. In case of interference phenomena we may say that there is a redistribution of photon energy. Interference phenomena can be batter understood by wave property of light. So there is a duality in the concept of E.M. wave.    
