Then you would have a black room. If the light source itself were visible, then you would see a hall-of-mirrors effect where there's a grid of repeating light sources that shrink away into infinity, and everything else would be black. If the room were all portals you would see the same thing.
[edit: I should add the caveat here that I'm assuming the reflective surfaces are perfectly specular. A perfect reflector could also be diffuse, in which case I'd say the room ought to be fully lit and ought to perpetually accumulate. If the surfaces are specular (mirror) then you'd be dealing with reflections that shrink away at an inverse square rate. I'm not sure if that fall-off will reach some effective asymptote-like threshold or if the emitters will just get too small to contribute any meaningful energy. It's possible that every view vector (pixel coordinate in the camera) would end up corresponding to one of the infinite reflections, in which case the entire view should be lit to some degree. It's good to remind oneself that RT/PT is not physically modeling the camera itself; it's a passive element that does not absorb energy even though it should be in these thought-experiments. I was curious to see how Cycles or Octane would represent this infinite reflection example, but once you get into thousands of bounces it doesn't behave very well. They may also being contending with precision/epsilon-related problems when asking them to scale that high.]
In terms of path-tracing and the rendering equation, I don't think there's any concept of photons being in-flight, but rather it's just a model of how light energy intersects materials and where it gets transmitted and reflected. That's where the energy conservation occurs. My point of contention is that twitter post saying that portals somehow break the PBR premise, when I really don't think portals are any different to mirrors in the context of path-tracing.
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