It may not be possible to meaningfully answer this question in this case.
If we're talking about something like fluorescence, there's a fairy clear point where one photon disappears and another appears.
In a linear process like this, photons are not really absorbed by the material. In fact, the quantum behavior of photons is not relevant to the process, so you can just treat it purely as a wave phenomenon.
In cases like this, I would generally say that it is the "same" photon, but again, not really appropriate to think in terms of photons when there is nothing about the process that depends on quantization.
In my opinion, this question is impossible to properly answer in the framework of Maxwell's equations / field representation, since it cannot be defined in those terms.
If I were to answer this question in terms of photons as small amounts of field oscillations, I would argue that these are "new" photons, due to the fact that the "old" ones induced oscillations in the dipole moment of the material, which then in turn radiated energy out as the "new" photons.
But you can just as easily think of it as the material "suggesting" a better direction to the field propagating through it, and thus reorienting it. This is just very difficult to imagine and describe, at least for me.
It’s both and neither since photons are particles and waves and focusing on one or the other to build intuition can be useful in some cases and not other.
How light actually behaves is probably beyond the ability of human cognition (since so much happens in a billionth of a second)
> How light actually behaves is probably beyond the ability of human cognition (since so much happens in a billionth of a second)
This is not remotely true. The behavior of light is very well understood and relatively simple to model compared to other, less linear physical processes.
We have some great models but what actually happens doesn't quite fit into any one model. For example all photons are constantly redshifted as they travel through space because space is expanding. That’s not really relevant on human timescales but it is an effect that takes place between your monitor and your eyes.
When you really dig into this stuff your realise stuff like the density of air is really an abstraction that doesn't quite fit what is actually going on.
If we're talking about something like fluorescence, there's a fairy clear point where one photon disappears and another appears.
In a linear process like this, photons are not really absorbed by the material. In fact, the quantum behavior of photons is not relevant to the process, so you can just treat it purely as a wave phenomenon.
In cases like this, I would generally say that it is the "same" photon, but again, not really appropriate to think in terms of photons when there is nothing about the process that depends on quantization.