A simple case: the sun illuminating a large white room through a small window. The light creeps all over the room, not just at the direct illuminated spot, as you'd expect If you were to do a simple camera-trace.
The issue at hand is: we don't experience it, but light behaves in a thermodynamic (dynamic) equilibrium way. You don't see the transients, because the equilibrium takes nanoseconds to converge, but when you turn on a light all your room is exchanging photons until it settles at a rate where everywhere is receiving as much as it's irradiating plus what's wasted as heat, and the total heat is equal to the energy coming through the light sources. Finding those values is solving the so called light transport equation -- and this clearly requires probing geometrical information from all over the place.
In the sunlit room case, all that light is a) heating the room and b) going outside. Now let me try to build a physical model based on your intuition: this equilibrium dynamic depends on the rate of absorption/reflection of each surface. If you have experience with EE, the room is essentially a resonator, where walls are reflecting some and absorbing some until it's absorbing as much as there is light coming in. The less absorbing the walls are, the greater the Q factor of the resonator is: the light is going to bounce a lot and build intensity before it gets absorbed. This is why dark walled rooms are so dramatically, well, darker than white rooms -- the Q factor is not bounded. If your walls were perfect mirrors the intensity would build up with time to +inf.
The issue at hand is: we don't experience it, but light behaves in a thermodynamic (dynamic) equilibrium way. You don't see the transients, because the equilibrium takes nanoseconds to converge, but when you turn on a light all your room is exchanging photons until it settles at a rate where everywhere is receiving as much as it's irradiating plus what's wasted as heat, and the total heat is equal to the energy coming through the light sources. Finding those values is solving the so called light transport equation -- and this clearly requires probing geometrical information from all over the place.
In the sunlit room case, all that light is a) heating the room and b) going outside. Now let me try to build a physical model based on your intuition: this equilibrium dynamic depends on the rate of absorption/reflection of each surface. If you have experience with EE, the room is essentially a resonator, where walls are reflecting some and absorbing some until it's absorbing as much as there is light coming in. The less absorbing the walls are, the greater the Q factor of the resonator is: the light is going to bounce a lot and build intensity before it gets absorbed. This is why dark walled rooms are so dramatically, well, darker than white rooms -- the Q factor is not bounded. If your walls were perfect mirrors the intensity would build up with time to +inf.