When we see the sky along a direction, we see blue color. But there’s nothing in the atmosphere except for air molecules and dust, why do we perceive blue color?

A common explanation is Rayleigh Scattering, which explains how lights with various wavelengths are scattered by air molecules and end up with a mix of lights, that are perceived as blue color by human.

However, this explanation becomes confusing if we take the definition of light in Quantum Electrodynamics. In Quantum Electrodynamics, light is defined as photons, instead of wavelengths. All photons are the same (i.e. travel in the same speed in medias, and are absorbed and scattered in the same way by matters). Given that a photon can be scattered by an air molecule to any direction, a team of photons can be scattered by an air molecule to any directions too, but most photons are scattered to similar directions (no scientific explanation on this phenomenon), we should see a gray sky with gradients caused by different amounts of photons arriving to our eyes at different view directions.

I think that to make blue sky explainable with quantum electrodynamics, we need to question the definition that all photons are the same (unless I got it wrong?). Maybe there are different photons? They travel in different speed in medias, and follow different probabilities of deflected direction when scattered by an air molecule? Then, when different kinds of photons arrive our eyes, we perceive blue color as a magic interaction of our visual system and these photons?