Imagine a photon hits an object, then bounces off and travels in the other direction, all while retaining it’s wavelength.
If the object is slightly accelerated in the direction of the incident photon’s travel, then it seems like conservation of energy is violated, because the photon lost no energy and the object gained kinetic energy.
If the object is not accelerated, it seems like conservation of momentum is violated, because the net velocity of the entire system (the object and the photon) has changed; the object doesn’t move but the photon changed direction.
Is it even possible for a photon to change directions without changing wavelength? If so, why is this paradox invalid?